Contents
Preface 1
Organizing Committee 3
Scientific Committee 5
ISDE Advisory Committee 7
Welcome from the ISDE President 9
ISDE Board of Directors 11
Schedule 13
Monday, July 21 (One-Hour Talks) . . . . . . . . . . . . . . . . . . . . . . 15
Monday, July 21 (Contributed Talks) . . . . . . . . . . . . . . . . . . . . . 17
Tuesday, July 22 (One-Hour Talks) . . . . . . . . . . . . . . . . . . . . . . 19
Tuesday, July 22 (Contributed Talks) . . . . . . . . . . . . . . . . . . . . . 21
Thursday, July 24 (One-Hour Talks) . . . . . . . . . . . . . . . . . . . . . . 23
Thursday, July 24 (Contributed Talks) . . . . . . . . . . . . . . . . . . . . 25
Friday, July 25 (One-Hour Talks) . . . . . . . . . . . . . . . . . . . . . . . 27
Friday, July 25 (Contributed Talks) . . . . . . . . . . . . . . . . . . . . . . 29
One-Hour Speakers 31
Abstracts of One-Hour Talks 35
Agarwal, Ravi (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Akın-Bohner, Elvan (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Alseda, Lluıs (Spain) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
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Dosly, Ondrej (Czech Republic) . . . . . . . . . . . . . . . . . . . . . . . . 39
Gesztesy, Fritz (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Gyori, Istvan (Hungary) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Hilger, Stefan (Germany) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Kloeden, Peter (Germany) . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Kocak, Huseyin (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Ladas, Gerasimos (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Mawhin, Jean (Belgium) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Peterson, Allan (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Smith, Hal (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Vanderbauwhede, Andre (Belgium) . . . . . . . . . . . . . . . . . . . . . 49
Yorke, James A. (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Zafer, Agacık (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Zeidan, Vera (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Abstracts of Contributed Talks 53
Abderraman, Jesus (Spain) . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Adıvar, Murat (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Afshar Kermani, Mozhdeh (Iran) . . . . . . . . . . . . . . . . . . . . . . . 56
Aghazadeh, Nasser (Iran) . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Albayrak, Incı (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Aldea Mendes, Diana (Portugal) . . . . . . . . . . . . . . . . . . . . . . . 59
Al-Sharawi, Ziyad (Oman) . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Alzabut, Jehad (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Appleby, John (Ireland) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Aseeri, Samar (Saudi Arabia) . . . . . . . . . . . . . . . . . . . . . . . . . 63
Atasever, Nurıye (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Atay, Fatıhcan M. (Germany) . . . . . . . . . . . . . . . . . . . . . . . . . 65
Atıcı, Ferhan (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Awerbuch Friedlander, Tamara (USA) . . . . . . . . . . . . . . . . . . . . 67
Batıt, Ozlem (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Bernhardt, Chris (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
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Bodine, Sigrun (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Bolat, Yasar (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Cakmak, Devrım (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Camouzis, Elias (Greece) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Canovas, Jose S. (Spain) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Cetın, Erbıl (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Cıbıkdıken, Alı Osman (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . 76
Costa, Sara (Spain) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Cushing, J. M. (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Dannan, Fozi (Syria) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Dosla, Zuzana (Czech Republic) . . . . . . . . . . . . . . . . . . . . . . . . 80
Duman, Ahmet (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Erbe, Lynn (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Erol, Meltem (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Esty, Norah (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Fernandes, Sara (Portugal) . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Gomes, Orlando (Portugal) . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Gumus, Ozlem Ak (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Guseinov, Gusein (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Guvenılır, A. Feza (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Guzowska, Małgorzata (Poland) . . . . . . . . . . . . . . . . . . . . . . . 90
Hashemiparast, Moghtada (Iran) . . . . . . . . . . . . . . . . . . . . . . . 91
Heim, Julius (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Hilscher, Roman (Czech Republic) . . . . . . . . . . . . . . . . . . . . . . 93
Jimenez Lopez, Vıctor (Spain) . . . . . . . . . . . . . . . . . . . . . . . . . 94
Kalabusic, Senada (Bosnia and Herzegovina) . . . . . . . . . . . . . . . . 95
Karpuz, Basak (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Keller, Christian (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Kent, Candace (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Kharkov, Vitaliy (Ukraine) . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Kipnis, Mikhail (Russia) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Kostrov, Yevgeniy (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
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Kulik, Tomasia (Australia) . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Laitochova, Jitka (Czech Republic) . . . . . . . . . . . . . . . . . . . . . . 103
Lawrence, Bonita (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Luıs, Rafael (Portugal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Matthews, Thomas (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
McCarthy, Michael (Ireland) . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Mendes, Vivaldo (Portugal) . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Mert, Razıye (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Mesgarani, Hamid (Iran) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Michor, Johanna (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Migda, Małgorzata (Poland) . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Morales, Leopoldo (Spain) . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Oban, Volkan (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Oberste-Vorth, Ralph (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Oliveira, Henrique (Portugal) . . . . . . . . . . . . . . . . . . . . . . . . . 116
Ozturk, Rukıye (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Papaschinopoulos, Garyfalos (Greece) . . . . . . . . . . . . . . . . . . . . 118
Park, Choonkil (South Korea) . . . . . . . . . . . . . . . . . . . . . . . . . 119
Pinelas, Sandra (Portugal) . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Pituk, Mihaly (Hungary) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Pop, Nicolae (Romania) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
Popescu, Emil (Romania) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Popescu, Nedelia Antonia (Romania) . . . . . . . . . . . . . . . . . . . . . 124
Pospısil, Zdenek (Czech Republic) . . . . . . . . . . . . . . . . . . . . . . 125
Potzsche, Christian (Germany) . . . . . . . . . . . . . . . . . . . . . . . . 126
Predescu, Mihaela (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Rabbani, Mohsen (Iran) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
Rachidi, Mustapha (France) . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Radin, Michael (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Rasmussen, Martin (Germany) . . . . . . . . . . . . . . . . . . . . . . . . 131
Rehak, Pavel (Czech Republic) . . . . . . . . . . . . . . . . . . . . . . . . 132
Reinfelds, Andrejs (Latvia) . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
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Rodkina, Alexandra (Jamaica) . . . . . . . . . . . . . . . . . . . . . . . . . 134
Romero i Sanchez, David (Spain) . . . . . . . . . . . . . . . . . . . . . . . 135
Saker, Samir (Saudi Arabia) . . . . . . . . . . . . . . . . . . . . . . . . . . 136
Sanchez-Moreno, Pablo (Spain) . . . . . . . . . . . . . . . . . . . . . . . . 137
Schinas, Christos (Greece) . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
Schmeidel, Ewa (Poland) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Sekercı, Nurcan (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Shahrezaee, Mohsen (Iran) . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Siddikov, Bakhodirzhon (USA) . . . . . . . . . . . . . . . . . . . . . . . . 142
Simon, Moritz (Germany) . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Sırma, Alı (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
Stefanidou, Gesthimani (Greece) . . . . . . . . . . . . . . . . . . . . . . . 145
Stehlik, Petr (Czech Republic) . . . . . . . . . . . . . . . . . . . . . . . . . 146
Teschl, Gerald (Austria) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Tıryakı, Aydın (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
Tlemcani, Mouhaydine (Portugal) . . . . . . . . . . . . . . . . . . . . . . 149
Topal, Fatma Serap (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . 150
Yantır, Ahmet (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Yıldırım, Ahmet (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
Zaidi, Atiya (Australia) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Zakeri, Ali (Iran) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
Zemanek, Petr (Czech Republic) . . . . . . . . . . . . . . . . . . . . . . . 155
Other Participants 157
Abdeljawad, Thabet (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . 158
Adıyaman, Meltem (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . 158
Akman, Murat (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
Altunkaynak, Meltem (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . 159
Aydın, Kemal (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Bas, Mujgan (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Bohner, Martin (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
Bozok, Ilknur (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
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Budakcı, Gulter (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
Can, Canan (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Caylak, Duygu (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Celebi, Okay (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Celık, Cem (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
Celık Kızılkan, Gulnur (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . 162
Cınar, Cengız (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
Das, Sebahat Ebru (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Denız, Aslı (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Dong, Zhaoyang (Spain) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Duman, Melda (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
Elaydi, Saber (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
Getimane, Mario (Mozambique) . . . . . . . . . . . . . . . . . . . . . . . 164
Gumus, Ibrahım Halıl (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . 165
Hatıpoglu, Veysel Fuat (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . 165
Intepe, Gokce (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Jantarakhajorn, Khajee (Thailand) . . . . . . . . . . . . . . . . . . . . . . . 166
Kara, Rukıye (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
Kayar, Zeynep (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
Kaymakcalan, Bıllur (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . 167
Kıyak Ucar, Yelız (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
Kongnuan, Supachara (Thailand) . . . . . . . . . . . . . . . . . . . . . . . 167
Kosareva, Natalia (Russia) . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Kulik, Yakov (Australia) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Kutay, Vıldan (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Leonhardt, Andreas (Germany) . . . . . . . . . . . . . . . . . . . . . . . . 169
Lesaja, Goran (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Marsh, Robert L. (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Mısır, Adıl (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
Nurkanovic, Mehmed (Bosnia and Herzegovina) . . . . . . . . . . . . . . 170
Nurkanovic, Zehra (Bosnia and Herzegovina) . . . . . . . . . . . . . . . . 170
Ocalan, Ozkan (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
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Okumus, Israfıl (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
Ozkan, Umut Mutlu (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . 171
Ozpınar, Fıgen (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Ozturk, Sermın (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Ozugurlu, Ersın (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Reankittiwat, Paramee (Thailand) . . . . . . . . . . . . . . . . . . . . . . . 173
Ruffing, Andreas (Germany) . . . . . . . . . . . . . . . . . . . . . . . . . . 173
Savun, Ipek (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
Selmanogulları, Tugcen (Turkey) . . . . . . . . . . . . . . . . . . . . . . . 174
Seneetantikul, Soporn (Thailand) . . . . . . . . . . . . . . . . . . . . . . . 174
Seyhan, Gızem (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
Sımsek, Dagıstan (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
Sizer, Walter (USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
Suhrer, Andreas (Germany) . . . . . . . . . . . . . . . . . . . . . . . . . . 175
Taskara, Necatı (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
Thongjub, Nawalax (Thailand) . . . . . . . . . . . . . . . . . . . . . . . . 176
Tollu, D. Turgut (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
Ucar, Denız (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
Unal, Mehmet (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
Vesarachasart, Sirichan (Thailand) . . . . . . . . . . . . . . . . . . . . . . 177
Vu, Dominik (Austria) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
Yalazlar, Gulcın (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
Yalcınkaya, Ibrahım (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . 178
Yıgıder, Muhammed (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . 179
Yıldız, Mustafa Kemal (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . 179
Yılmaz, Ozlem (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Yoruk, Fulya (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
Local Organization Assistants 181
Aydın, M. Aslı (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
Bayat, Kemal (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
Dagyar, Nazlı Ceren (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . 182
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Emul, Yakup (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Erkal, Durdane (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Karahan, Gokce (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Karakelle, Musa (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
Ozdemır, Huseyın (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . 184
Ozen, Bahadır (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
Conference Proceedings 185
Social Program 187
Maps 189
Istanbul 197
Useful Information 205
Index and E-mail Addresses 209
x
Preface
Dear Colleague:
It is our great pride and pleasure to offer ourwarmest greetings to you, the participants of the “14thInternational Conference on Difference Equations andApplications (ICDEA2008)” at the Besiktas campus ofBahcesehir University in Istanbul, Turkey. This confer-ence is sponsored by TUBITAK (Scientific and Tech-nical Research Council of Turkey), Bahcesehir Univer-sity, Dentur Avrasya, Duran Sandwiches, Pırıl Pırıl,and the Turkish Ministry of Culture and Tourism.
The purpose of the conference is to bring together both experts and novicesin the theory and applications of difference equations and discrete dynamicalsystems. The main theme of the meeting is dynamic equations on time scales.The previous ICDEA conferences were held in Lisbon (2007), Kyoto (2006), Mu-nich (2005), Los Angeles (2004), Brno (2003), Changsha (2002), Augsburg (2001),Temuco (2000), Poznan (1998), Taipei (1997), Veszprem (1995), and San Antonio(1994).
In addition to attending the conference’s exciting sessions, we encourageeach of the participants to take advantage of our historic city of Istanbul, whichis the cradle of many civilizations, to share beauty and scientific knowledge. Lastbut not least we want to extend our best wishes to all of the conference partici-pants and to its Scientific and Organizing Committee members.
Sincerely,
Dr. Mehmet UnalChair of Organizing CommitteeBahcesehir UniversityTR-34538 Bahcesehir/Istanbul, Turkey
Conference web site: http://icdea.bahcesehir.edu.tr
1
2
Organizing Committee
Mehmet Unal (Chair)Bahcesehir University
Istanbul, Turkey
Martin Bohner (Co-Chair)Missouri S&T
Rolla, Missouri, USA
Okay CelebiYeditepe University
Istanbul, Turkey
Gerasimos LadasUniversity of Rhode Island
Kingston, Rhode Island, USA
Aydın TıryakıGazi UniversityAnkara, Turkey
Agacık ZaferMiddle East Technical University
Ankara, Turkey
3
4
Scientific Committee
Martin Bohner (Chair)Missouri S&T
Rolla, Missouri, USA
Zuzana Dosla (Co-Chair)Masaryk University
Brno, Czech Republic
Saber ElaydiTrinity University
San Antonio, Texas, USA
Metin GursesBilkent University
Ankara, Turkey
Gusein GuseinovAtılım UniversityAnkara, Turkey
Bıllur KaymakcalanGeorgia Southern University
Statesboro, Georgia, USA
Peter KloedenJohann Wolfgang Goethe University
Frankfurt am Main, Germany
5
Werner KratzUniversity of Ulm
Ulm, Germany
Donald LutzSan Diego State UniversitySan Diego, California, USA
Jean MawhinUniversite Catholique de Louvain
Louvain-la-Neuve, Belgium
Donal O’ReganNational University of Ireland
Galway, Ireland
Allan PetersonUniversity of Nebraska–Lincoln
Lincoln, Nebraska, USA
Alexander SharkovskyNational Academy of Sciences
Kiev, Ukraine
Gerald TeschlUniversity of Vienna
Vienna, Austria
6
ISDE Advisory Committee
Kazuo Nishimura (Chair)Kyoto University
Kyoto, Japan
Andreas Ruffing (Co-Chair)Technical University Munich
Munich, Germany
Henrique OliveiraInstituto Superior Tecnico Lisbon
Lisbon, Portugal
Robert J. SackerUniversity of Southern California
Los Angeles, California, USA
7
8
Welcome from the ISDE President
Dear Colleagues and ISDE Members:
It is an honor to welcome you to the annual meet-ing of the International Society of Difference Equa-tions in Istanbul, Turkey. The Fourteenth InternationalConference on Difference Equations and ApplicationsICDEA2008 is held on the campus of Bahcesehir Uni-versity, July 21–25, 2008.
I welcome you to this historical meeting, wherewest meets east; you may be able to cross on foot from Asia to Europe and viceversa. Not only we have an excellent scientific program, but we have a splendidsocial program; don’t forget your camera.
The ISDE Board of Directors meets on Tuesday, July 22th, 2008, 5:45 pm in theauditorium BFSAY. The general assembly of the society meets on Thursday, July24th, 2008, 5:45 pm in the auditorium BFSAY. The main event is the presentationof the prize for the best paper published in the Journal of the Society (JDEA) in2007. The prize carries the amount of £500 granted by Taylor & Francis.
Finally, I would like to thank, on behalf of all of you, Dr. Mehmet Unal of theUniversity of Bahcesehir for his relentless efforts to make ICDEA2008 a reality. Iam grateful to all members of the organizing, scientific, and advisory committeesfor their hard work and efforts to make this conference the best it can be.
Sincerely,
Dr. Saber ElaydiPresident of ISDETrinity University
San Antonio, Texas, USA
9
10
ISDE Board of Directors
Saber Elaydi (President)Trinity University
San Antonio, Texas, USA
George Sell (Vice President)University of Minnesota
Minneapolis, Minnesota, USA
Martin BohnerMissouri S&T
Rolla, Missouri, USA
J. M. CushingUniversity of ArizonaTucson, Arizona, USA
Istvan GyoriUniversity of Pannonia
Veszprem, Hungary
11
Gerasimos LadasUniversity of Rhode Island
Kingston, Rhode Island, USA
Allan PetersonUniversity of Nebraska–Lincoln
Lincoln, Nebraska, USA
Andreas RuffingTechnical University Munich
Munich, Germany
Robert J. SackerUniversity of Southern California
Los Angeles, California, USA
12
Schedule
13
Time July 20 July 21 July 22 July 23 July 24 July 25
Sunday Monday Tuesday Wednesday Thursday Friday
8:00–9:00 Registration Istanbul
9:00–9:45 Opening Tour
9:45–10:40 Plenary Talk Plenary Talk Plenary Talk Plenary Talk
1 3 Istanbul 5 710:45–11:00 Refreshment Break Tour Refreshment Break
11:00–11:55 Plenary Talk Plenary Talk Plenary Talk Plenary Talk
2 4 Istanbul 6 812:00–13:00 Lunch Tour Lunch
13:00–13:55 Main Talks Main Talks Main Talks Plenary Talk
1–3 4–6 Istanbul 7–8 914:00–14:25 Registration Talks Talks Tour Talks Talks
1–4 29–32 57–60 81–8414:30–14:55 Talks Talks Istanbul Talks Talks
5–8 33–36 Tour 61–64 85–8815:00–15:25 Talks Talks Talks Talks
9–12 37–40 Istanbul 65–68 89–9215:25–16:15 Registration Refreshment Break Tour Refreshment Break
16:15–16:40 Talks Talks Talks Talks
13–16 41–44 Istanbul 69–72 93–9616:45–17:10 Talks Talks Tour Talks Talks
17–20 45–48 73–76 97–10017:15–17:40 Registration Talks Talks Istanbul Talks Closing
21–24 49–52 Tour 77–8017:45–18:10 Talks Talks ISDE
25–28 53–56 Yacht Meeting
Evening Welcome Sightseeing Sightseeing Tour Farewell Sightseeing
Party free time free time Dinner free time
14
Monday, July 21 (One-Hour Talks)
Time BFSAY A101 A205
8:00–9:00 Registration
9:00–9:45 Opening
Chair M. Bohner
9:45–10:40
AllanPeterson
(USA)page 47
10:45–11:00 Refreshment Break
11:00–11:55
RaviAgarwal
(USA)page 36
12:00–13:00 Lunch Break
Chair G. Ladas R. Hilscher B. Kaymakcalan
13:00–13:55
IstvanGyori
(Hungary)page 41
VeraZeidan(USA)
page 52
StefanHilger
(Germany)page 42
15
? Agarwal, Ravi: Discrete Lidstone boundary value problems
? Gyori, Istvan: Asymptotic representation of solutions of difference equations and limitformulas
? Hilger, Stefan: Difference equations appearing in ladder theory
? Peterson, Allan: An overview of dynamic equations on time scales
? Zeidan, Vera: Variational problems over time scales
16
Monday, July 21 (Contributed Talks)
Time A101 A205 A206 A207
Chair V. Zeidan C. Kent J. Appleby N. Aghazadeh
14:00–14:25
RomanHilscher
(Czech Republic)page 93
TamaraAwerbuch Friedlander
(USA)page 67
OrlandoGomes
(Portugal)page 86
NicolaePop
(Romania)page 122
14:30–14:55
LynnErbe
(USA)page 82
MihaelaPredescu
(USA)page 127
VivaldoMendes
(Portugal)page 108
VolkanOban
(Turkey)page 114
15:00–15:25
NorahEsty
(USA)page 84
GaryfalosPapaschinopoulos
(Greece)page 118
SenadaKalabusic
(Bosnia/Herz.)page 95
BakhodirzhonSiddikov
(USA)page 142
15:25–16:15 Refreshment Break
Chair S. Bodine E. Camouzis L. Alseda N. Popescu
16:15–16:40
RalphOberste-Vorth
(USA)page 115
ChristosSchinas(Greece)page 138
DianaAldea Mendes
(Portugal)page 59
IncıAlbayrak(Turkey)page 58
16:45–17:10
AhmetYantır
(Turkey)page 151
VıctorJimenez Lopez
(Spain)page 94
ChrisBernhardt
(USA)page 69
MohsenShahrezaee
(Iran)page 141
17:15–17:40
PetrStehlik
(Czech Republic)page 146
SandraPinelas
(Portugal)page 120
Jose S.Canovas(Spain)page 74
MoghtadaHashemiparast
(Iran)page 91
17:45–18:10
MuratAdıvar
(Turkey)page 55
NurıyeAtasever(Turkey)page 64
SaraCosta
(Spain)page 77
NasserAghazadeh
(Iran)page 57
17
? Adıvar, Murat: Periodicity in nonlinear systems of dynamic equations? Aghazadeh, Nasser: Using B-spline scaling functions for solving integro-differential equa-
tions? Albayrak, Incı: A trace formula for an abstract Sturm–Liouville operator? Aldea Mendes, Diana: Periodic and eventually periodic orbits for skew-product maps? Atasever, Nurıye: On a class of rational difference equations? Awerbuch Friedlander, Tamara: Constructing difference equations models for public health
policy? Bernhardt, Chris: A Sharkovsky theorem for maps on trees? Canovas, Jose S.: A characterization of k-cycles? Costa, Sara: Study of attractors for two-dimensional skew-products whose basis is a Den-
joy counterexample? Erbe, Lynn: Comparison and oscillation theorems for linear and half-linear dynamic equa-
tions on time scales? Esty, Norah: Convergence of hyperspaces under the Fell topology, especially of time scales? Gomes, Orlando: Optimal monetary policy with partially rational agents? Hashemiparast, Moghtada: Solving systems of nonlinear equations by using difference
equations? Hilscher, Roman: Riccati equations for linear Hamiltonian systems? Jimenez Lopez, Vıctor: On the global stability of xn+1 = p+qxn
1+xn−1
? Kalabusic, Senada: Period-two trichotomies of a difference equation of order higher thantwo
? Mendes, Vivaldo: Learning to play Nash in deterministic uncoupled dynamics? Oban, Volkan: Numerical solutions of nonlinear differential-difference equations by the
variational iteration method? Oberste-Vorth, Ralph: Solution spaces of dynamic equations over time scales space? Papaschinopoulos, Garyfalos: Boundedness, attractivity, stability of a rational difference
equation with two periodic coefficients? Pinelas, Sandra: Bounded solutions of a rational difference equation? Pop, Nicolae: Generalized Jacobians for solving nondifferentiable equations arising from
contact problems? Predescu, Mihaela: A nonlinear system of difference equations? Schinas, Christos: Boundedness, periodicity, attractivity of the difference equation xn+1 =An +
(xn−1xn
)p
? Shahrezaee, Mohsen: Heat solutions by using Fibonacci tane function? Siddikov, Bakhodirzhon: Applications of finite difference methods in the field of magnetic
refrigeration? Stehlik, Petr: Basic properties of partial dynamic operators? Yantır, Ahmet: Positive solutions of a second-order m-point BVP on time scales
18
Tuesday, July 22 (One-Hour Talks)
Time BFSAY A101 A205
Chair Z. Dosla
9:45–10:40
HuseyinKocak(USA)
page 44
10:45–11:00 Refreshment Break
11:00–11:55
AndreVanderbauwhede
(Belgium)page 49
12:00–13:00 Lunch Break
Chair C. Potzsche A. Peterson G. Teschl
13:00–13:55
LluısAlseda(Spain)page 38
ElvanAkın-Bohner
(USA)page 37
FritzGesztesy
(USA)page 40
19
? Alseda, Lluıs: A lower bound for the maximum topological entropy of 4k + 2-cycles
? Akın-Bohner, Elvan: Quasilinear dynamic equations
? Gesztesy, Fritz: Borg–Marchenko-type uniqueness results for CMV operators and elementsof Weyl–Titchmarsh theory
? Kocak, Huseyin: Rigorous computations in chaotic dynamical systems
? Vanderbauwhede, Andre: Stability of bifurcating periodic orbits of reversible maps
20
Tuesday, July 22 (Contributed Talks)
Time A101 A205 A206 A207
Chair F. Atıcı S. Pinelas M. Rasmussen V. Mendes
14:00–14:25
ThomasMatthews
(USA)page 106
EliasCamouzis(Greece)page 73
SaraFernandes(Portugal)
page 85
JohnAppleby(Ireland)page 62
14:30–14:55
JuliusHeim(USA)
page 92
YevgeniyKostrov(USA)
page 101
LeopoldoMorales(Spain)
page 113
AlexandraRodkina(Jamaica)page 134
15:00–15:25
BonitaLawrence
(USA)page 104
MustaphaRachidi(France)page 129
HenriqueOliveira
(Portugal)page 116
MichaelMcCarthy(Ireland)page 107
15:25–16:15 Refreshment Break
Chair L. Erbe M. Predescu H. Oliveira A. Rodkina
16:15–16:40
TomasiaKulik
(Australia)page 102
MichaelRadin(USA)
page 130
ChristianPotzsche
(Germany)page 126
JitkaLaitochova
(Czech Republic)page 103
16:45–17:10
ChristianKeller(USA)
page 97
CandaceKent
(USA)page 98
AndrejsReinfelds(Latvia)page 133
JesusAbderraman
(Spain)page 54
17:15–17:40
AtiyaZaidi
(Australia)page 153
GesthimaniStefanidou
(Greece)page 145
MartinRasmussen(Germany)page 131
Alı OsmanCıbıkdıken
(Turkey)page 76
17:45–18:10
FerhanAtıcı
(USA)page 66
NurcanSekercı(Turkey)page 140
MouhaydineTlemcani(Portugal)page 149
AhmetDuman(Turkey)page 81
21
? Abderraman, Jesus: General solution of linear homogeneous difference equations withvariable coefficients
? Appleby, John: Growth, long memory and heavy tails in difference equation models ofinefficient financial markets
? Atıcı, Ferhan: Initial value problems in discrete fractional calculus? Camouzis, Elias: On the global character of solutions of a rational system of difference
equations? Cıbıkdıken, Alı Osman: Effect of floating point on computation of monodromy matrix? Duman, Ahmet: Sensitivity of Schur stable linear systems with periodic coefficients? Fernandes, Sara: Systoles and topological entropy in discrete dynamical systems? Heim, Julius: The dynamic multiplier-accelerator model in economics? Keller, Christian: Dynamic equations with piecewise continuous argument? Kent, Candace: A cardiac loop reentry model with thresholds? Kostrov, Yevgeniy: Existence of unbounded solutions in rational equations? Kulik, Tomasia: Solution to integral equations on time scales: Existence, uniqueness and
successive approximations? Laitochova, Jitka: Linear kth order functional and difference equations in the space of
strictly monotonic functions? Lawrence, Bonita: The Marshall differential analyzer: Dynamic equations in motion!? Matthews, Thomas: Ostrowski inequalities on time scales? McCarthy, Michael: Numerical detection of explosions and asymptotic behaviour of delay-
differential equations? Morales, Leopoldo: An example of a strongly invariant, pinched core strip? Oliveira, Henrique: Bifurcations for nonautonomous interval maps? Potzsche, Christian: Nonautonomous continuation and bifurcation, revisited!? Rachidi, Mustapha: On some rational difference equations via linear recurrence equations
properties? Radin, Michael: Multiple periodic solutions of a second-order nonautonomous rational
difference equation? Rasmussen, Martin: Morse spectrum for linear nonautonomous difference equations? Reinfelds, Andrejs: Decoupling and simplifying of discrete dynamical systems in the neigh-
bourhood of invariant manifold? Rodkina, Alexandra: On oscillation of solutions of stochastically perturbed difference equa-
tions? Sekercı, Nurcan: On the behaviour of the difference equationx(n+ 1) = max1/x(n),min1, A/x(n)
? Stefanidou, Gesthimani: On a system of max-difference equations? Tlemcani, Mouhaydine: Analysis of a nonlinear discrete dynamical system, signal coding
and reconstruction? Zaidi, Atiya: A result on successive approximation of solutions to dynamic equations on
time scales
22
Thursday, July 24 (One-Hour Talks)
Time BFSAY A101
Chair J. Cushing
9:45–10:40
James A.Yorke(USA)
page 50
10:45–11:00 Refreshment Break
11:00–11:55
HalSmith(USA)
page 48
12:00–13:00 Lunch Break
Chair F. Gesztesy B. Lawrence
13:00–13:55
JeanMawhin(Belgium)page 46
AgacıkZafer
(Turkey)page 51
23
? Mawhin, Jean: Boundary value problems for nonlinear difference equations with discretesingular φ-Laplacian
? Smith, Hal: Some persistence results for discrete-time dynamical systems and applications
? Yorke, James A.: Period doubling cascades in one-parameter families of maps in high di-mensions
? Zafer, Agacık: Interval criteria for second-order super-half-linear functional dynamic equa-tions
24
Thursday, July 24 (Contributed Talks)
Time A101 A205 A206 A207
Chair N. Esty S. Hilger T. Awerbuch Friedlander A. Tıryakı
14:00–14:25
DevrımCakmak(Turkey)page 72
ZuzanaDosla
(Czech Republic)page 80
MoritzSimon
(Germany)page 143
MikhailKipnis(Russia)page 100
14:30–14:55
PavelRehak
(Czech Republic)page 132
VitaliyKharkov(Ukraine)page 99
MałgorzataGuzowska
(Poland)page 90
Ozlem AkGumus(Turkey)page 87
15:00–15:25
RazıyeMert
(Turkey)page 109
GuseinGuseinov(Turkey)page 88
RafaelLuıs
(Portugal)page 105
ChoonkilPark
(South Korea)page 119
15:25–16:15 Refreshment Break
Chair M. Adıvar J. Michor A. Reinfelds G. Guseinov
16:15–16:40
BasakKarpuz(Turkey)page 96
MihalyPituk
(Hungary)page 121
ZiyadAl-Sharawi
(Oman)page 60
JehadAlzabut(Turkey)page 61
16:45–17:10
ErbılCetın
(Turkey)page 75
GeraldTeschl
(Austria)page 147
J. M.Cushing
(USA)page 78
AydınTıryakı(Turkey)page 148
17:15–17:40
ZdenekPospısil
(Czech Republic)page 125
RukıyeOzturk
(Turkey)page 117
FoziDannan(Syria)page 79
SigrunBodine(USA)
page 70
17:45–18:10 ISDE General Meeting (BFSAY)
25
? Al-Sharawi, Ziyad: The effect of harvesting strategies on the discrete Beverton–Holt model
? Alzabut, Jehad: Asymptotic behavior of linear impulsive delay difference equations
? Bodine, Sigrun: Exponentially asymptotically constant systems of difference equationswith applications
? Cakmak, Devrım: On the equivalence of Rolle’s and generalized mean value theorems ontime scales
? Cetın, Erbıl: Higher-order boundary value problems on time scales
? Cushing, J. M.: Difference equations arising in dynamic models of biological evolution
? Dannan, Fozi: A new proof for the Levin–May criterion of asymptotic stability
? Dosla, Zuzana: On nonoscillation of Emden–Fowler difference equations
? Gumus, Ozlem Ak: Stability boundary for asymptotic stability of scalar equations
? Guseinov, Gusein: Spectral analysis of a non-selfadjoint second-order difference operator
? Guzowska, Małgorzata: Discrete Haavelmo growth cycle model
? Karpuz, Basak: Iterated oscillation criteria for delay dynamic equations of first order
? Kharkov, Vitaliy: Asymptotic behavior of one class solutions of the second-order Emden–Fowler difference equation
? Kipnis, Mikhail: Stability via Convexity
? Luıs, Rafael: Nonautonomous periodic systems with Allee effect
? Mert, Razıye: Time scale extensions of a theorem of Wintner on systems with asymptoticequilibrium
? Ozturk, Rukıye: On the spectrum of normal difference operators of first order
? Park, Choonkil: Classification and stability of functional equations
? Pituk, Mihaly: Nonoscillatory solutions of a second-order difference equation of Poincaretype
? Pospısil, Zdenek: Dynamic replicator equation and its transformation
? Rehak, Pavel: Power type comparison theorems for half-linear dynamic equations
? Simon, Moritz: Spectral theory of birth-and-death processes
? Teschl, Gerald: Relative oscillation theory for Jacobi operators
? Tıryakı, Aydın: Reducibility and stability results for linear systems of difference equations
26
Friday, July 25 (One-Hour Talks)
Time BFSAY
Chair O. Celebi
9:45–10:40
OndrejDosly
(Czech Republic)page 39
10:45–11:00 Refreshment Break
11:00–11:55
PeterKloeden
(Germany)page 43
12:00–13:00 Lunch Break
13:00–13:55
GerasimosLadas(USA)
page 45
27
? Dosly, Ondrej: Symplectic difference systems
? Kloeden, Peter: Spatial discretisation of dynamical systems
? Ladas, Gerasimos: Open problems and conjectures in difference equations
28
Friday, July 25 (Contributed Talks)
Time A101 A205 A206 A207
Chair A. Zafer M. Pituk B. Siddikov J. Laitochova
14:00–14:25
OzlemBatıt
(Turkey)page 68
MałgorzataMigda
(Poland)page 112
Nedelia AntoniaPopescu
(Romania)page 124
JohannaMichor(USA)
page 111
14:30–14:55
PetrZemanek
(Czech Republic)page 155
EwaSchmeidel
(Poland)page 139
DavidRomero i Sanchez
(Spain)page 135
PabloSanchez-Moreno
(Spain)page 137
15:00–15:25
Fatma SerapTopal
(Turkey)page 150
YasarBolat
(Turkey)page 71
AlıSırma
(Turkey)page 144
SamarAseeri
(Saudi Arabia)page 63
15:25–16:15 Refreshment Break
Chair F. Topal O. Ocalan A. Sırma S. Aseeri
16:15–16:40
MozhdehAfshar Kermani
(Iran)page 56
A. FezaGuvenılır(Turkey)page 89
AhmetYıldırım(Turkey)page 152
MeltemErol
(Turkey)page 83
16:45–17:10
Fatıhcan M.Atay
(Germany)page 65
MohsenRabbani
(Iran)page 128
AliZakeri(Iran)
page 154
HamidMesgarani
(Iran)page 110
17:15–17:40 Closing (BFSAY)
29
? Afshar Kermani, Mozhdeh: A new method for solving fuzzy partial differential equations
? Aseeri, Samar: Asymptotic formulas for Laplace integrals
? Atay, Fatıhcan M.: Stability of coupled difference equations with delays
? Batıt, Ozlem: Fredholm integral equations on time scales
? Bolat, Yasar: Necessary and sufficient conditions for oscillation of certain higher orderpartial difference equations
? Erol, Meltem: The structure of the spectrum for normal operators
? Guvenılır, A. Feza: Interval oscillation of second-order difference equations with oscilla-tory potentials
? Mesgarani, Hamid: A new approach for solving Fredholm integro-difference equations
? Michor, Johanna: Algebro-geometric solutions of the Ablowitz–Ladik hierarchy
? Migda, Małgorzata: Oscillatory and asymptotic properties of solutions of nonlinear neutral-type difference equations
? Popescu, Nedelia Antonia: Finite size scaling technique and applications
? Rabbani, Mohsen: Galerkin method for solving nonlinear Fredholm–Hammerstein integralequations with multiwavelet basis
? Romero i Sanchez, David: Invariant objects through wavelets
? Sanchez-Moreno, Pablo: Discrete densities and Fisher information
? Schmeidel, Ewa: Oscillation of nonlinear three-dimensional difference systems
? Sırma, Alı: Numerical solution of nonlocal boundary value problems for the Schrodingerequation
? Topal, Fatma Serap: Multiple positive solutions for a system of higher-order boundaryvalue problems on time scales
? Yıldırım, Ahmet: Numerical solutions of nonlinear differential-difference equations by thehomotopy perturbation method
? Zakeri, Ali: Application of the WKB estimation method for determining heat flux on theboundary
? Zemanek, Petr: Trigonometric and hyperbolic systems on time scales
30
One-Hour Speakers
Ravi AgarwalFlorida Institute of Technology
Melbourne, Florida, USA
Elvan Akın-BohnerMissouri S&T
Rolla, Missouri, USA
Lluıs AlsedaUniversitat Autonoma de Barcelona
Cerdanyola del Valles, Spain
Ondrej DoslyMasaryk University
Brno, Czech Republic
Fritz GesztesyUniversity of Missouri
Columbia, Missouri, USA
Istvan GyoriUniversity of Pannonia
Veszprem, Hungary
31
Stefan HilgerCatholic University of Eichstatt
Eichstatt, Germany
Peter KloedenJohann Wolfgang Goethe University
Frankfurt am Main, Germany
Huseyin KocakUniversity of MiamiMiami, Florida, USA
Gerasimos LadasUniversity of Rhode Island
Kingston, Rhode Island, USA
Jean MawhinUniversite Catholique de Louvain
Louvain-la-Neuve, Belgium
Allan PetersonUniversity of Nebraska–Lincoln
Lincoln, Nebraska, USA
32
Hal SmithArizona State University
Tempe, Arizona, USA
Andre VanderbauwhedeGhent UniversityGhent, Belgium
James A. YorkeUniversity of Maryland
College Park, Maryland, USA
Agacık ZaferMiddle East Technical University
Ankara, Turkey
Vera ZeidanMichigan State University
East Lansing, Michigan, USA
33
34
Abstracts of One-Hour Talks
35
Discrete Lidstone boundary value problems
RAVI AGARWAL
Florida Institute of Technology
Department of Mathematics
Melbourne, Florida, USA
http://cos.fit.edu/math/faculty/agarwal
We shall provide sufficient conditions for the existence of single and multiple positive solu-tions of higher order smooth as well as singular difference equations involving Lidstone bound-ary conditions. As an application, we shall investigate the existence of radial solutions of certainpartial difference equations. To show how easily our results can be applied in practice we shallillustrate many examples.
36
Quasilinear dynamic equations
ELVAN AKIN-BOHNER
Missouri University of Science and Technology
Department of Mathematics and Statistics
Rolla, Missouri, USA
http://web.mst.edu/˜akine
We consider a quasilinear dynamic equation reducing to a half-linear equation, Emden–Fowler equation or a Sturm–Liouville equation on a time scale, which is a nonempty closed subsetof the real numbers. Any nontrivial solution of a quasilinear equation is eventually monotone. Inother words, it can be either positive decreasing (negative increasing) or positive increasing (neg-ative decreasing). We shall provide certain integral conditions to classify solutions and investigatetheir asymptotic behaviors.
AMS Subject Classification: 39A10.Keywords: Time scales, quasilinear, half-linear equation.
37
A lower bound for the maximum
topological entropy of 4k + 2-cycles
LLUIS ALSEDA
Universitat Autonoma de Barcelona
Departament de Matematiques
Cerdanyola del Valles, Spain
http://www.mat.uab.cat/˜alseda
For continuous interval maps we formulate a conjecture on the shape of the cycles of maxi-mum topological entropy of period 4k + 2. We also present numerical support for the conjecture.This numerical support is of two different kinds. For periods 6, 10, 14 and 18 we are able tocompute the maximum entropy cycles by using nontrivial, ad hoc numerical procedures and theknown results of Jungreis (1991). In fact, the conjecture we formulate is based on these results.
For periods n = 22, 26 and 30 we compute the maximum entropy cycle of a restricted sub-family of cycles denoted by C∗n. The obtained results agree with the conjectured ones. The con-jecture that we can restrict our attention to C∗n is motivated theoretically. On the other hand, it isworth noticing that the complexity of examining all cycles in C∗22, C∗26 and C∗30 is much less thanthe complexity of computing the entropy of each cycle of period 18 in order to determine the oneswith maximal entropy, therefore making it a feasible problem.
AMS Subject Classification: 37B40, 37E15, 37M99.Keywords: Combinatorial dynamics, interval map.This is joint work with David Juher and Deborah King.
38
Symplectic difference systems
ONDREJ DOSLY
Masaryk University
Department of Mathematics and Statistics
Brno, Czech Republic
http://www.muni.cz/people/Ondrej.Dosly
Symplectic diference systems are first order systems with the property that their fundamen-tal matrix is symplectic whenever it is symplectic at one point. From this point of view, they canbe regarded as a discrete counterpart of linear Hamiltonian differential systems.
Symplectic systems cover a large variety of difference equations and systems, among themthe second order Sturm–Liouville difference equation whose oscillation theory is deeply devel-oped. We will present recent results of the oscillation and spectral theory of symplectic systems.In particular, it will be shown that the classical Sturmian separation and comparison theory canbe extended to symplectic systems.
The presented results have been achieved in the joint research with Martin Bohner (Univ.Rolla, Missouri, USA) an Werner Kratz (Univ. Ulm, Germany).
AMS Subject Classification: 39A10.Keywords: Sturmian theory, focal point, Picone’s identity.
39
Borg–Marchenko-type uniqueness results for CMV
operators and elements of Weyl–Titchmarsh theory
FRITZ GESZTESY
University of Missouri
Department of Mathematics
Columbia, Missouri, USA
http://www.math.missouri.edu/˜fritz
We review local and global versions of Borg–Marchenko-type uniqueness theorems for half-lattice and full-lattice CMV operators (CMV for Cantero, Moral, and Velazquez) with matrix-valued Verblunsky coefficients. While our half-lattice results are formulated in terms of matrix-valued Weyl–Titchmarsh functions, our full-lattice results involve the diagonal and main off-diagonal Green’s matrices.
We also hint at the basics of Weyl–Titchmarsh theory for CMV operators with matrix-valuedVerblunsky coefficients as this is of independent interest and an essential ingredient in provingthe corresponding Borg–Marchenko-type uniqueness theorems.
This is based on joint work with Steve Clark and Maxim Zinchenko.
AMS Subject Classification: Primary 34E05, 34B20, 34L40; Secondary 34A55.Keywords: CMV operators, (inverse) spectral theory.
40
Asymptotic representation of solutions of
difference equations and limit formulas
ISTVAN GYORI
University of Pannonia
Department of Mathematics and Computing
Veszprem, Hungary
http://www.szt.vein.hu/˜gyori
In this lecture we investigate the growth/decay rate of solutions of linear and quasilineardifference equations. The results can be applied to a particular kind of weight sequences whichcan be either exponential or slowly decaying. Examples are given to illustrate the sharpness ofthe results.
AMS Subject Classification: 39A12.Keywords: Limit formulas, difference equations.
41
Difference equations appearing in ladder theory
STEFAN HILGER
Catholic University of Eichstatt
Mathematisch-Geographische Fakultat
Eichstatt, Germany
http://www.ku-eichstaett.de/Fakultaeten/MGF/
→Didaktiken/dphys/Mitarbeiter.de
A ladder consists of a sequence of vector spaces (Vn) and linear operators (A+n ), (A−n ), de-
pending on n, acting between these vector spaces in ascending and descending direction. Thejob in ladder theory is to find SIE-subladders, on which the intrinsic endomorphisms A−nA+
n andA+
nA−n act as scalars αn. A fundamental ladder theorem will provide conditions on the (gener-
alized) commutators or anticommutators assuring the existence of SIE-subladders. Elementarydifference operators will enter into those conditions. The second part contains examples of lad-ders from classical quantum mechanics or orthogonal polynomials. In a final part we point outhow to generalize the notion of a ladder to higher dimensional settings with corresponding bidi-rectional operators.
AMS Subject Classification: 81S05, 39A10, 42C05, 46L65, 34L40.Keywords: Ladder theory, canonical commutator relations.
42
Spatial discretisation of dynamical systems
PETER KLOEDEN
Johann Wolfgang Goethe University
Department of Mathematics
Frankfurt am Main, Germany
http://www.math.uni-frankfurt.de/˜numerik/kloeden
We consider the effects of spatial discretisation on the dynamical behavior of discrete timedynamical systems which are generated by difference equations. This is important, for examplewhen we simulate such systems on computers which have only finite number fields. What is theffect of round-off? A simple example is the chaotic behavior of the tent mapping on the unitinterval, which collapses when the mapping is restricted to a the subset of N -dyadic numbers.We will show that invariant measures are more robust to approximation. We consider a Lebesguemeasure preserving mapping on torus and its approximation by a permutation of a uniform gridon the torus. Then, more generally, we show how Markov chains can be used to obtain approxi-mations to the invariant measures of discrete time dynamical systems.
Keywords: Discretisation, invariant measures, Markov chains.
43
Rigorous computations in chaotic dynamical systems
HUSEYIN KOCAK
University of Miami
Department of Mathematics / Department of Computer Science
Miami, Florida, USA
http://www.math.miami.edu/˜hk
Numerical simulations are indespensible in the investigation of specific dynamical systems.Unfortunately, since chaotic dynamical systems amplify small errors at an exponential rate, theresults of most simulations are unreliable. In this talk, we will descibe the medhod of shadowingfor extracting mathematically rigorous results from numerical computations. In particular, wewill present a computer-assisted procedure for proving the existence of transversal homoclinicand heteroclinic orbits. The talk will be illustrated with computer simulations.
44
Open problems and conjectures
in difference equations
GERASIMOS LADAS
University of Rhode Island
Department of Mathematics
Kingston, Rhode Island, USA
http://www.math.uri.edu/˜gladas
We present some open problems and conjectures about some interesting types of differenceequations. We are primarily interested in the boundedness nature of solutions, the periodic char-acter of the equation, the global stability behavior of the equilibrium points, and with convergenceto periodic solutions including periodic trichotomies.
45
Boundary value problems for nonlinear difference
equations with discrete singular φ-Laplacian
JEAN MAWHIN
Universite Catholique de Louvain
Department of Mathematics
Louvain-la-Neuve, Belgium
We study the existence and multiplicity of solutions for boundary value problems of the type
∇[φ(∆xk)] + fk(xk,4xk) = 0 (2 ≤ k ≤ n− 1), l(x,4x) = 0,
where φ : (−a, a) → R denotes an increasing homeomorphism such that φ(0) = 0 and 0 <
a < ∞, l(x,4x) = 0 denotes the Dirichlet, periodic or Neumann boundary conditions and fk
(2 ≤ k ≤ n − 1) are continuous functions. Our main tool is Brouwer degree together with fixedpoint reformulations of the above problems.
AMS Subject Classification: 39A12, 55M25.Keywords: Nonlinear difference equations, φ-Laplacian.This is joint work with Cristian Bereanu.
46
An overview of dynamic equations on time scales
ALLAN PETERSON
University of Nebraska–Lincoln
Department of Mathematics
Lincoln, Nebraska, USA
http://www.math.unl.edu/˜apeterson1
The talk will be an overview of dynamic equations on time scales. We will discuss the im-portance of this emerging area of mathematics and discuss some important results in this area.Some introductory results will also be presented.
AMS Subject Classification: 39.Keywords: Time scales, dynamic equations.
47
Some persistence results for discrete-time
dynamical systems and applications
HAL SMITH
Arizona State University
Department of Mathematics
Tempe, Arizona, USA
http://math.la.asu.edu/˜halsmith
The theory of persistence focuses on identifying sufficient conditions for certain subsets ofthe state space to be repellers for the considered dynamics. In an ecological setting, these subsetsare often extinction states for one or more populations while in an epidemiological setting theymay be disease-free states. We survey some recent results in this area and apply them to modelsin population biology and epidemiology.
Keywords: Persistence theory.
48
Stability of bifurcating periodic
orbits of reversible maps
ANDRE VANDERBAUWHEDE
Ghent University
Department of Mathematics
Ghent, Belgium
http://cage.ugent.be/˜avdb
The Lyapunov–Schmidt method for the bifurcation of periodic orbits of local diffeomor-phisms results in a reduced problem with an additional cyclic symmetry. We show how themethod can be refined such that it also gives information on the stability of the bifurcating pe-riodic orbits. We apply this approach (via a Poincare map) to the problem of subharmonic bi-furcations in continuous reversible systems, discussing both the generic case and a particulardegenerate case. A numerical study of a model example for this degenerate situation revealssome nongeneric stability behaviour in the presence of certain first integrals. We describe theresults of a detailed analysis for this conservative case, including the transition scenario to thenonconservative case.
This is joint work with Francisco Javier Munoz-Almaraz (Valencia), and Jorge Galan andEmilio Freire (Sevilla).
49
Period doubling cascades in one-parameter
families of maps in high dimensions
JAMES A. YORKE
University of Maryland
Department of Mathematics
College Park, Maryland, USA
http://yorke.umd.edu
Evelyn Sander and I show infinite period-doubling cascades exist for high-dimensional sys-tems.
50
Interval criteria for second-order super-half-linear
functional dynamic equations
AGACIK ZAFER
Middle East Technical University
Department of Mathematics
Ankara, Turkey
http://www.metu.edu.tr/˜zafer
Interval oscillation criteria are established for second-order forced super half-linear dynamicequations on time scales containing both delay and advance arguments, where the potentialsare allowed to change sign. Examples are given to illustrate the relevance of the results. Thetheory can be applied to second-order dynamic equations regardless of the choice of delta ornabla derivatives.
AMS Subject Classification: 34K11, 34C10, 39A11, 39A13.Keywords: Time scales, oscillation, functional, half-linear.This is joint work with Douglas R. Anderson.
51
Variational problems over time scales
VERA ZEIDAN
Michigan State University
Department of Mathematics
East Lansing, Michigan, USA
http://www.math.msu.edu/˜zeidan
This talk focuses on the study of variational problems over time scale which encompassesboth nonlinear optimal control and calculus of variations problems. The main goal is centeredon the question of deriving necessary and sufficient optimality criteria of first and second order.The special feature resides in the fact that these conditions are formulated in terms of a certain“Hamiltonian” corresponding to the nonlinear problem. The second order conditions are ob-tained in terms of the accessory problem. However, Reid roundabout theorems, that are recentlyobtained with R. Hilscher, allow these conditions to be equivalently phrased in terms of conjoinedbasis and Riccati equations corresponding to the accessory problem.
52
Abstracts of Contributed Talks
53
General solution of linear homogeneous difference
equations with variable coefficients
JESUS ABDERRAMAN
Universidad Politecnica de Madrid, Campus Montegancedo
Department of Applied Mathematics, Faculty of Computer Science
Madrid, Spain
http://www.dma.fi.upm.es/jesus
A constructive theory for the general solution of kth-order difference equation
x(k)(n+ 1) =k−1∑i=0
pi+1(n)x(k)(n− i)
is given as in a forthcoming paper of the author. As complement of the analytical theory [GeorgeD. Birkhoff, General theory of linear difference equations, Transactions of the American Mathe-matical Society, volume 12, number 2, pages 243–284, 1911], this constructive approach permitsus an explicit and nonrecurrent representation of the general solution, for any initial conditions,x−1, x0, . . . , xk−2, and any sequences of complex numbers, pi+1(j)n−1
j=k−2, i = 0, . . . , k − 1. Ifk = 1, then the solution is straightforward. For k > 1, a simple change of variable produces anequivalent kth-order linear difference equation that permits us to solve x(k)(n), n ≥ k − 1, byinduction on n. Since the representation for the general case is too long, the solution for k = 2 isprovided here as an illustration:
x(2)(n) =n−1∏i=0
p1(i)(c0Φ(2,0)
n (α2(1), . . . , α2(n− 1)) + c−1α2(0)Φ(2,1)n−1 (α2(2), . . . , α2(n− 1))
),
where c−1, c0 are arbitrary numbers, n ≥ 1, j = 0, 1, α2(k) = p2(k)p1(k−1)p1(k) , α2(0) = p2(0)
p1(0). Φ(2,j)
n−j (~α)are:
Φ(2,j)n−j (~α) =
bn−j2 c∑
l=0
n−1∑k1=2l−1+j
α2(k1)
k1−2∑k2=2(l−1)−1+j
α2(k2)
· · ·kl−1−2∑
kl=1+j
α2(kl)
.
When l = 0, the sum is 1 by convention.
AMS Subject Classification: 39A05.Keywords: Linear difference equations.
54
Periodicity in nonlinear
systems of dynamic equations
MURAT ADIVAR
Izmir University of Economics
Izmir, Turkey
http://homes.ieu.edu.tr/˜madivar
By means of Schaefer’s fixed point theorem, we show the existence of periodic solutions ofa nonlinear system of Volterra-type integro-dynamic equations. Furthermore, we provide severalapplications to scalar equations, where we develop a time scale analogue of Lyapunov’s directmethod and prove an analogue of Sobolev’s inequality on time scales to arrive at a priori boundon all periodic solutions.
AMS Subject Classification: 39A10.Keywords: Time Scale, dynamic equation, fixed point theorems.This is joint work with Youssef Raffoul.
55
A new method for solving
fuzzy partial differential equations
MOZHDEH AFSHAR KERMANI
Islamic Azad University North Tehran Branch
Department of Mathematics
Tehran, Iran
In this talk a new method for solving “fuzzy partial differential equations” (FPDE) is consid-ered. This numerical method based on the definition of derivative that considered by Y. Chalco-Cano, H. Roman-Flores. We present a difference method to solve FPDEs such as the fuzzy hyper-bolic equation and fuzzy parabolic equation, then see if stability of this method exist, and condi-tions for stability are given. Examples are presented showing the Hausdorff distance between theexact solution and approximate solution is small.
Keywords: Fuzzy partial differential equation, difference method.
56
Using B-spline scaling functions
for solving integro-differential equations
NASSER AGHAZADEH
Azarbaijan University of Tarbiat Moallem
Department of Mathematics
Tabriz, Iran
http://www.azaruniv.edu/˜aghazadeh
In this talk, quadratic semiorthogonal B-spline scaling functions together with their dualfunctions are developed to approximate the solutions of linear second-order Fredholm integro-differential equations. The quadratic B-spline scaling functions, their properties and the opera-tional matrices of derivative for B-spline scaling functions are presented and are utilized to reducethe solution of Fredholm integro-differential to the solution of algebraic equations. The methodis computationally attractive, some numerical examples are presented to support our work.
AMS Subject Classification: 45B05, 45A05, 65D07, 42C05.Keywords: Quadratic spline, Fredholm integro-differential equation.
57
A trace formula for an
abstract Sturm–Liouville operator
INCI ALBAYRAK
Yıldız Technical University
Mathematical Engineering Department
Istanbul, Turkey
http://www.mtm.yildiz.edu.tr/cvler/ialbayrak
In this talk we investigate and obtain a regularized trace formula for the operator in theHilbert space L2([0, 1],H) generated by the expression
−y′′(x) +Q(x)y(x)
with the boundary conditions
y(0) = 0, y′(1) +Ay(1) = 0,
where H is a separable Hilbert space, for x ∈ [0, 1], Q(x) is a self-adjoint nuclear operator definedin H , and A is a real number.
This is joint work with Kevser Koklu and Azad Bayramov
58
Periodic and eventually periodic orbits
for skew-product maps
DIANA ALDEA MENDES
IBS-ISCTE Business School, ISCTE
Department of Quantitative Methods
Lisbon, Portugal
http://iscte.pt/˜deam
In this talk we consider triangular (or skew-product) maps of the real plane that admit peri-odic and eventually periodic critical orbits. A corresponding Markov partition will be constructedfor these maps. We also show that there exist an invariant probability measures, namely the Parrymeasure. In order to obtain these, we apply some tensor products between the invariants associ-ated with the one-dimensional components of the triangular map. An immediate consequence isthe computation of the topological and metric entropy for these maps.
AMS Subject Classification: Primary 37B10, 37B40, 37E30; Secondary 15A69.Keywords: Skew product, periodic orbits, Markov partition.
59
The effect of harvesting strategies on
the discrete Beverton–Holt model
ZIYAD AL-SHARAWI
Sultan Qaboos University
Department of Mathematics and Statistics
Al-Khod, Muscat, Oman
We discuss the effect of constant, periodic and conditional harvesting strategies on the dis-crete Beverton–Holt model. We find that for large initial populations, constant harvesting givesthe maximum sustainable yield. Periodic harvesting has a short term advantage when the initialpopulation is small, and conditional harvest has the advantage of lowering the risk of extinction.Also, we discuss the periodic character in each case, and show that periodic harvesting drivespopulation cycles to be multiples (period wise) of the harvesting period.
AMS Subject Classification: 39A11, 92D25, 92B99.Keywords: Beverton–Holt model, optimal harvesting.This is joint work with Mohamed Rhouma.
60
Asymptotic behavior of linear
impulsive delay difference equations
JEHAD ALZABUT
Cankaya University
Department of Mathematics and Computer Science
Ankara, Turkey
http://math.cankaya.edu.tr/˜jehad
In this talk, it is shown that if a linear impulsive delay difference equation satisfies Perron’scondition, then its trivial solution is asymptotically stable.
AMS Subject Classification: 39A13, 34K45.Keywords: Impulse, delay, adjoint, Perron, stability.This is joint work with Thabet Abdeljawad.
61
Growth, long memory and heavy tails in difference
equation models of inefficient financial markets
JOHN APPLEBY
Dublin City University
School of Mathematical Sciences
Dublin, Ireland
http://webpages.dcu.ie/˜applebyj
In this talk we explore the asymptotic behaviour of a stochastic difference equation modelof a financial market in which traders use the past behaviour of prices to guide their investmentdecisions.
For a class of affine and maximum type functional difference equations we find an exactexponential rate of growth, just as is seen in classical efficient market models. We also show thatthese models possess the property of “long memory” in that the autocovariance function of thereturns decays so slowly that it is nonintegrable. Furthermore, the asset returns are seen to exhibit“heavy tails”, in that the distribution function of the returns decay polynomially.
All the results will be shown to be dynamically consistent with corresponding continuous-time functional differential equation models. The work is joint with Huizhong Wu and CatherineSwords and is supported by the SFI RFP Grant 05/MAT/0018 “Stochastic Functional DifferentialEquations with Long Memory”.
Keywords: Stochastic difference equation, long memory.This is joint work with Catherine Swords and Huizhong Wu.
62
Asymptotic formulas for Laplace integrals
SAMAR ASEERI
Umm Al-Qura University
Department of Mathematics
Makkah, Saudi Arabia
Solutions of boundary value problems of mathematical physics often involve infinite inte-grals containing a term consisting of a trigonometrical or Bessel function, with the aid of Laplaceintegral transform, as an integral equation of the first kind, the solution of the integral equation isobtained. In this talk, many applications on this manner are discussed and solved.
AMS Subject Classification: 65R10.Keywords: Laplace transforms, boundary value problems.
63
On a class of rational difference equations
NURIYE ATASEVER
Selcuk University
Department of Mathematics, Education Faculty
Konya, Turkey
atasever [email protected]
In this talk we study the behaviour of the positive solutions of the nonlinear difference equa-tion
xn+1 = ((xn−k)/(1 + xn−1xn−3 . . . xn−(k−2))), n = 0, 1, 2, . . . ,
where k > 2 is an odd integer.
AMS Subject Classification: 39A10.Keywords: Difference equation, positive solutions.This is joint work with Cengiz Cinar, Dagıstan Simsek, and Ibrahim Yalcınkaya.
64
Stability of coupled difference equations with delays
FATIHCAN M. ATAY
Max Planck Institute
Mathematics in the Sciences
Leipzig, Germany
http://personal-homepages.mis.mpg.de/fatay
Networks of diffusively-coupled scalar maps are considered with weighted connections whichmay include a time delay. The stability of equilibria is studied with respect to the delays and con-nection structure. It is shown that the largest eigenvalue of the graph Laplacian determines theeffect of the connection topology on stability. The stability region in the parameter plane shrinkswith increasing values of the largest eigenvalue, or of the time delay of the same parity. In partic-ular, all bipartite graphs have an identical stability region, regardless of the delay or graph size,which is also the smallest stability region among those of all graphs. Furthermore, for certainparameter ranges, unstable (and possibly chaotic) maps can be stabilized via diffusive couplingwith an odd time delay, provided that the network does not have a nontrivial and connected bi-partite component. On the other hand, stabilization is not possible for even values of the delay orfor bipartite networks.
Reference: F. M. Atay and O. Karabacak. Stability of coupled map networks with delays.SIAM Journal on Applied Dynamical Systems, 5:508–527, 2006.
AMS Subject Classification: 39A11, 37E05, 94C15.Keywords: Network, delay, stability, synchronization, chaos, Laplacian.
65
Initial value problems in discrete fractional calculus
FERHAN ATICI
Western Kentucky University
Department of Mathematics
Bowling Green, Kentucky, USA
http://www.wku.edu/˜ferhan.atici
This paper is devoted to the study of discrete fractional calculus; the particular goal is todefine and solve well-defined discrete fractional difference equations. For this purpose we firstcarefully develop the commutativity properties of the fractional sum and the fractional differenceoperators. Then a ν-th (0 < ν ≤ 1) order fractional difference equation is defined. A nonlinearproblem with an initial condition is solved and the corresponding linear problem with constantcoefficients is solved as an example. Further, the half-order linear problem with constant coef-ficients is solved with a method of undetermined coefficients and with a transform method.
AMS Subject Classification: 39A12, 34A25, 26A33.Keywords: Discrete fractional calculus.This is joint work with Paul Eloe.
66
Constructing difference equations models
for public health policy
TAMARA AWERBUCH FRIEDLANDER
Harvard School of Public Health
Department of Global Health and Population
Boston, Massachusetts, USA
http://www.hsph.harvard.edu/research/
→tamara-awerbuchfriedlander
Difference equations modeling exploits the natural connection between events occurring atdiscrete intervals and the inherent discrete nature of difference equations. We will show exam-ples used for understanding complex interactions among ecological components that lead to thespread of diseases transmitted by vectors such as ticks and mosquitoes. The emergence of Lymedisease and its early stages was represented and analyzed as a linear system; the system repre-senting later stages of the tick population growth rendered a delay equation with two parameterswhich are real numbers representing biological characteristics of the tick life-cycle. The mathe-matical analysis enables us to detect parameter regions of local and global stability, boundednessand oscillatory behavior of solutions. Another example is the construction of nonlinear systemsdescribing community intervention in mosquito control through management of their habitats.One system consists of two equations; representing a more complex intervention resulted in asystem of three difference equations. The work has been carried out by a collaboration of aninterdisciplinary team of mathematicians, biologists, ecologist, sociologists.
Keywords: System, difference equations, infectious diseases.
67
Fredholm integral equations on time scales
OZLEM BATIT
Ege University
Department of Mathematics
Izmir, Turkey
http://sci.ege.edu.tr/˜math/index.php?
→option=com content&task=view&id=55
In this talk, we study linear and nonlinear Fredholm integral equations on time scales. Firstseparable kernels and then symmetric kernels are considered for the linear case. For the nonlinearcase, we use the monotone iterative technique to obtain approximations to a unique solution andgive some applications.
AMS Subject Classification: 45B05.Keywords: Time scales, Fredholm integral equations.
68
A Sharkovsky theorem for maps on trees
CHRIS BERNHARDT
Fairfield University
Department of Mathematics and Computer Science
Fairfield, Connecticut, USA
http://cs.fairfield.edu/˜bernhardt
The proof of Sharkovsky’s theorem is combinatorial in nature. This means that instead ofviewing it as a theorem about maps of the interval one can view it as a theorem about maps ontrees that permute the vertices in the special case when the tree is topologically an interval. Thisway of viewing Sharkovsky’s theorem leads to the natural question of whether there is such atheorem for trees in general.
In this talk we give a Sharkovsky-type ordering for trees in general. We also show the con-verse — that given any n there is a tree and a map that has exactly the periods given by thetheorem.
69
Exponentially asymptotically constant systems
of difference equations with applications
SIGRUN BODINE
University of Puget Sound
Department of Mathematics and Computer Science
Tacoma, Washington, USA
We consider the asymptotic behavior of solutions of systems of linear difference equationsof the form
y(n+ 1) = [A+R(n)] y(n) , n ≥ n0,
where A is a constant, invertible matrix and R(n) is an exponentially small perturbation, i.e.,|R(n)| ≤ Kεn for some 0 < ε < 1. While classical results yield, for n sufficiently large, theexistence of a fundamental matrix of the form
Y (n) = [I + o(1)]An as n→∞,
we want to find more precise estimates of the error term o(1). In particular, we are interested inits dependence on ε and the eigenvalues of A.
We also present an application to nonlinear autonomous dynamical systems with hyperbolicequilibria.
Our results were motivated by a recent paper by R. Agarwal and M. Pituk who studied scalarlinear difference equations with exponentially small perturbations.
AMS Subject Classification: 39A11.Keywords: Exponentially small perturbations, asymptotics.This is joint work with D. A. Lutz.
70
Necessary and sufficient conditions for oscillation
of certain higher order partial difference equations
YASAR BOLAT
Afyon Kocatepe University
Department of Mathematics
Afyonkarahisar, Turkey
http://www2.aku.edu.tr/˜yasarbolat
In this talk, some necessary and sufficient conditions for the oscillation of a certain higherorder partial difference equation are obtained.
AMS Subject Classification: 39A11, 34K11, 34C10.Keywords: Partial difference equation, oscillation, oscillatory.This is joint work with Omer Akın.
71
On the equivalence of Rolle’s and generalized
mean value theorems on time scales
DEVRIM CAKMAK
Gazi University
Department of Mathematics Education
Ankara, Turkey
http://websitem.gazi.edu.tr/dcakmak
In this talk, by using elementary time scale calculus, we recall the equivalence between well-known Rolle’s and Generalized Mean Value Theorems on time scales.
AMS Subject Classification: 26A24, 39A12.Keywords: Rolle’s theorem, mean value theorem, time scales.
72
On the global character of solutions of a
rational system of difference equations
ELIAS CAMOUZIS
American College of Greece
Department of Mathematics and Natural Sciences
Athens, Greece
In this talk we study the global character of solutions of a rational system of difference equa-tions. In particular, we examine the boundedness of solutions, the stability of the equilibriumpoints, and the periodic character of solutions.
AMS Subject Classification: 39A10.Keywords: Rational system, boundedness, stability, periodicity.
73
A characterization of k-cycles
JOSE S. CANOVAS
Technical University of Cartagena
Department of Applied Mathematics and Statistics
Cartagena, Spain
http://filemon.upct.es/˜jose
We study global periodicity for the difference equation of order l given by
xn+l = f(xn+l−1, xn+l−2, . . . , xn),
where f : (0,∞)l → (0,∞) is a continuous map, l ∈ Z+. Our main results are the following. Weprove that if any solution of the equation is periodic, then there is a minimal k ∈ N such that theperiod of any solution divides k (and therefore f is called a k-cycle). In addition, if l = 2, then forany k > 2 there are, up to conjugacy, only a k-cycle. Finally, if l > 2 and f gives a (l + 1)-cycle,then f is conjugated to:
• xn+l = 1xn·xn+1·...·xn+l−1
, if l is even.
• The previous equation or xn+l =
(l+1)/2Qj=1
xn+2j−2
(l−1)/2Qj=1
xn+2j−1
, if l is odd.
AMS Subject Classification: 39A05.Keywords: Cycles, conjugacy.This is joint work with Antonio Linero and Gabriel Soler.
74
Higher-order boundary value problems on time scales
ERBIL CETIN
Ege University
Department of Mathematics
Izmir, Turkey
http://sci.ege.edu.tr/˜math/index.php?
→option=co m content&task=view&id=63
In this talk, we give the existence of positive solutions of the Lidstone boundary value prob-lem (LBVP) (−1)ny4
2n
(t) = f(t, yσ(t)), t ∈ [0, 1],
y42i
(0) = y42i
(σ(1)) = 0, 0 ≤ i ≤ n− 1,
where n ≥ 1 and f : [0, σ(1)]× R → R is continuous.
Firstly, by using the Schauder fixed point theorem in a cone, we obtain the existence of solu-tions to a Lidstone boundary value problem (LBVP). Secondly, an existence result for this problemis also given by the monotone method. Finally, by using the Krasnosel’skii fixed point theorem, itis proved that the LBVP has a positive solution.
AMS Subject Classification: 39A10.Keywords: Positive solutions, upper and lower solutions.This is joint work with Fatma Serap Topal.
75
Effect of floating point on computation
of monodromy matrix
ALI OSMAN CIBIKDIKEN
Selcuk University
Department of Computer Technology and Programming
Konya, Turkey
asp.selcuk.edu.tr/asp/personel/
→web/goster.asp?sicil=5377
LetA(n) be a matrix of dimensionN×N with period T and consider the difference equationsystem
x(n+ 1) = A(n)x(n), n ∈ Z. (1)
With X(T ) being the monodromy matrix of the system (1), it is well known that
ω1(A, T ) =
∣∣∣∣∣∣∣∣∣∣∞∑
k=0
(X∗(T ))k(X(T ))k
∣∣∣∣∣∣∣∣∣∣ <∞ (2)
implies Schur stability of the system (1) [Kemal Aydın, A. Ya. Bulgakov, Gennadii Demidenko,Numerical characteristics of asymptotic stability of solutions of linear difference equations withperiodic coefficients, Siberian Mathematical Journal, volume 41, number 6, pages 1005–1014,2000]. By the spectral criterion, each eigenvalue of the monodromy matrix X(T ) belongs to theunit disk [Saber Elaydi, An introduction to difference equations, third edition, undergraduatetexts in mathematics, Springer, New York, 2005]. Schur stability of the system (1) depends on themonodromy matrix X(T ) in both cases. Therefore, Schur stability of the system (1) and quality ofSchur stability are related to the results of computation errors on computation of the monodromymatrix X(T ). In this study, the effect of floating point on computation of the monodromy matrixX(T ) is investigated. The bound is obtained for ||X(T )− Y (T )|| in which the matrix Y (T ) is thecomputed value of the monodromy matrix.
AMS Subject Classification: 39A11, 65G50.Keywords: Schur stability, monodromy matrix, roundoff error.This is joint work with Kemal Aydın.
76
Study of attractors for two-dimensional
skew-products whose basis
is a Denjoy counterexample
SARA COSTA
Universitat Autonoma de Barcelona
Departament de Matematiques
Bellaterra (Cerdanyola del Valles), Spain
Since Keller studied, in 1996, the existence of strange nonchaotic attractors in a particularkind of two-dimensional quasiperiodically forced skew-products defined on M+ := S1 × [0,∞),several extensions of his results have been published. All these extensions have in common thatthe system are defined on M+, and the component on the basis is always an irrational rotation.We extend the Keller and Haro results to similar systems defined on S1 × R, in this case we canhave two attractors given by the graph of a map defined on S1 or only one given by the graph of atwo-valued correspondence. If we exchange the irrational rotation by a Denjoy counterexample,the results are quite similar with the difference that the map, or correspondence, whose graphgives the attractor is defined on P ⊂ S1, where P is the support of the unique invariant measureof the Denjoy counterexample.
This is joint work with Lluıs Alseda.
77
Difference equations arising in dynamic
models of biological evolution
J. M. CUSHING
University of Arizona
Department of Mathematics
Tucson, Arizona, USA
http://math.arizona.edu/˜cushing
I will describe some nonlinear difference equation models that arise in modeling the evolu-tion of biological populations. The state variables are mean phenotypic traits of species as well asthe usual population densities, and consequently the models involve systems of (or higher order)nonlinear difference equations. The models typically have several equilibria and a fundamentalquestion concerns which are stable. I will give some stability results and some open problemsand conjectures.
AMS Subject Classification: 37N25, 92D25.Keywords: Difference equations, models of evolution.
78
A new proof for the Levin–May
criterion of asymptotic stability
FOZI DANNAN
Arab International University
Department of Mathematics
Damascus, Syria
Levin and May obtaind an easy necessary and sufficient condition for the asymptotic stabil-ity of the difference equation x(n+ 1)− x(n) + qx(n− k) = 0. In this talk we give a new proof forthis condition.
AMS Subject Classification: 39A11.Keywords: Levin–May, asymptotic stability, difference equation.
79
On nonoscillation of
Emden–Fowler difference equations
ZUZANA DOSLA
Masaryk University
Department of Mathematics and Statistics
Brno, Czech Republic
http://www.math.muni.cz/˜dosla
Asymptotic properties of nonoscillatory solutions of the Emden–Fowler equation
∆(an|∆xn|αsgn ∆xn) + bn|xn+1|β sgn xn+1 = 0, α 6= β, (1)
are investigated using the half-linearization technique.
Some interesting discrepancies concerning oscillation and nonoscillation of (1) and its con-tinuous counterpart will be given.
This is joint work with Mariella Cecchi and Mauro Marini.
80
Sensitivity of Schur stable linear systems
with periodic coefficients
AHMET DUMAN
Afyon Kocatepe University
Department of Mathematics
Afyonkarahisar, Turkey
http://www.akademi.aku.edu.tr/
→frmCvler.aspx?SicilNo=KA0992
Let A(n) be an N ×N -matrix with period T and consider the difference equation system
x(n+ 1) = A(n)x(n), n ∈ Z. (1)
With X(T ) being the monodromy matrix of (1), it is well known that
w1(A, T ) =
∣∣∣∣∣∣∣∣∣∣∞∑
k=0
(X∗(T ))k (X(T ))k
∣∣∣∣∣∣∣∣∣∣ <∞
implies Schur stability of the system (1) [Kemal Aydın, A. Ya. Bulgakov, Gennadii Demidenko,Numerical characteristics of asymptotic stability of solutions of linear difference equations withperiodic coefficients, Siberian Mathematical Journal, volume 41, number 6, pages 1005–1014,2000]. Let B(n) be a matrix of dimension N × N with period T . There are some results givenon the Schur stability of the perturbated system
y(n+ 1) = [A(n) +B(n)]y(n), n ∈ Z, (2)
whereB(n) is the perturbation matrix [Kemal Aydın, Haydar Bulgak, Gennadii Demidenko, Con-tinuity of numeric characteristics for asymptotic stability of solutions to linear difference equa-tions with periodic coefficients, Selcuk Journal of Applied Mathematics, volume 2, number 2,pages 5–10, 2001]. Note: Haydar Bulgak is the same person as A. Ya. Bulgakov.
In this talk, we give new results for Schur stability of the system (2) and compare thesenew results with the existing ones in the literature. The results are supported with numericalapplications too.
AMS Subject Classification: 39A11.Keywords: Schur stability, monodromy matrix, sensitivity.This is joint work with Kemal Aydın.
81
Comparison and oscillation theorems for linear and
half-linear dynamic equations on time scales
LYNN ERBE
University of Nebraska–Lincoln
Department of Mathematics
Lincoln, Nebraska, USA
http://www.math.unl.edu/˜lerbe2
We obtain some new oscillation and comparison results for the second-order linear (or half-linear) dynamic equation of the form (r(x∆)α)∆(t)+p(t)xα(σ(t)) = 0. We are primarily interestedin the case when the coefficient p(t) changes sign for arbitrarily large values of t. The resultsimprove and extend some earlier criteria, in both the continuous and discrete cases, as well as formore general time scales.
AMS Subject Classification: 34K11, 39A10.Keywords: Comparison theorems, oscillation, half-linear.This is joint work with Jia Baoguo and Allan Peterson.
82
The structure of the spectrum for normal operators
MELTEM EROL
Karadeniz Technical University
Department of Mathematics
Trabzon, Turkey
We have investigated the structure of the spectrum for normal operators on a Hilbert spacewith a new method and asymptotic behavior of its eigenvalues. The obtained results in thiswork can be applied to a normal extension of minimal operators generated by a linear differentialoperator expression in a Hilbert space of vector functions in finite intervals.
AMS Subject Classification: 47A10.Keywords: Normal operators, spectrum.This is joint work with Zameddin Ismailov.
83
Convergence of hyperspaces under the Fell topology,
especially of time scales
NORAH ESTY
Stonehill College
Department of Mathematics
Boston, Massachusetts, USA
In this talk we will examine various topologies on hyperspaces, and in particular those whichare most useful in the context of time scales. After demonstrating that the Fell topology is the mostappropriate, we will state (and time permitting, prove) several theorems about convergence inhyperspaces of locally compact metric spaces under the Fell topology. Finally we will state/proveanalogous theorems for the particular case of time scales, where the hyperspace in questions isCL(R).
AMS Subject Classification: 54B20.Keywords: Hyperspaces, time scales, Fell topology.This is joint work with Stefan Hilger.
84
Systoles and topological entropy
in discrete dynamical systems
SARA FERNANDES
Universidade de Evora / CIMA-UE
Research Centre in Mathematics and Application
Evora, Portugal
http://evunix.uevora.pt/˜saf
The fruitful relationship between the geometry and the graph theory has been explored byseveral authors in the sense of bringing important results for the discrete dynamical systems seenas Markov chains in graphs. In this work we will explore the relationship between the topologicalentropy and systoles in the context of maps on the interval.
AMS Subject Classification: 37A35, 37B10.Keywords: Dynamical systems, topological entropy, systole.This is joint work with Clara Gracio and Carlos Ramos.
85
Optimal monetary policy with
partially rational agents
ORLANDO GOMES
Instituto Politecnico de Lisboa, UNIDE/ISCTE
Escola Superior de Comunicacao Social
Lisbon, Portugal
We explore the dynamic behavior of a New Keynesian monetary policy problem with expec-tations formed, partially, under adaptive learning. We consider two alternative cases: on the firstsetting, the private economy has the ability to predict rationally real economic conditions (theoutput gap) but it needs to learn about the future values of the nominal variable (the inflationrate); on the second setup, private agents are fully aware of future inflation rates, however theylack the ability to predict instantly the correct values of the output gap (learning is attached to thisvariable). In both cases, we find a simple condition indicating the required learning quality thatis needed to guarantee local stability. To achieve convergence to the steady state, the economydoes not need to attain full learning efficiency; it just has to secure a minimum learning quality inorder to attain the desired long run result.
Keywords: Optimal monetary policy, adaptive learning.This is joint work with Vivaldo M. Mendes and Diana A. Mendes.
86
Stability boundary for asymptotic stability
of scalar equations
OZLEM AK GUMUS
Selcuk University
Department of Mathematics, Faculty of Science and Literature
Konya, Turkey
http://asp.selcuk.edu.tr/asp/personel/web/
→goster.asp?sicil=6644
We consider the scalar equation of the form
x(n+ 2k) + px(n+ k) + qx(n) = 0
and obtain stability regions in the plane by using the Schur–Cohn criterion. In the case of p = 1 orp = −1, the obtained stability region is restricted to a narrow area by the found values of q whenk is a positive even integer.
Keywords: Stability, discrete-time system, stability criteria.This is joint work with Necati Taskara.
87
Spectral analysis of a non-selfadjoint
second-order difference operator
GUSEIN GUSEINOV
Atılım University
Department of Mathematics
Ankara, Turkey
http://www.atilim.edu.tr/˜guseinov
Non-Hermitian (non-selfadjoint) Hamiltonians and complex extension of quantum mechan-ics have recently received a lot of attention [C. M. Bender, Making sense of non-Hermitian Hamil-tonians, Rep. Progr. Phys. 70(2007), 947–1018]. In this study, we develop spectral analysis of thediscrete problem
−∆2yn−1 + qnyn = λρnyn, n ∈ . . . ,−3,−2,−1 ∪ 2, 3, 4, . . ., (1)
y−1 = y1, ∆y−1 = e2iδ∆y1, (2)
in the Hilbert space l2, where (yn), n ∈ Z = 0,±1,±2,±3, . . ., is a desired solution, ∆ denotesthe forward difference operator defined by ∆yn = yn+1−yn (so that ∆2yn−1 = yn−1−2yn +yn+1),qn ≥ 0, λ is a spectral parameter, and
ρn =
e2iδ, n ≤ −1,e−2iδ, n ≥ 0,
(3)
for a δ ∈ [0, π/2). The main distinguishing features of problem (1), (2) are that it involves acomplex coefficient ρn of the form (3) and that transition conditions (impulse conditions) of theform (2) are presented which also involve a complex coefficient. Such a problem is not self adjointwith respect to the usual inner product of space l2 and it arises as a discrete version of somequantum systems on a complex contour.
AMS Subject Classification: 39A70.Keywords: Difference operator, spectrum, completely continuous operator.This is joint work with Ebru Ergun.
88
Interval oscillation of second-order difference
equations with oscillatory potentials
A. FEZA GUVENILIR
Ankara University
Department of Mathematics
Ankara, Turkey
Interval oscillation criteria are established for second-order difference equations of the form
∆(k(n)∆x(n)) + p(n)x(g(n)) + q(n)|x(g(n))|α−1x(g(n)) = e(n),
where n ≥ n0, n0 ∈ N = 0, 1, . . ., α > 1; k(n), p(n), q(n), g(n), and e(n) are sequencesof positive real numbers, k(n) > 0 is nondecreasing, g(n) is nondecreasing with g(n) → ∞ asn→∞, ∆ is the forward difference operator defined as usual by ∆x(n) = x(n+ 1)− x(n).
AMS Subject Classification: 34K11, 34C15.Keywords: Interval oscillation, second order, delay argument.
89
Discrete Haavelmo growth cycle model
MAŁGORZATA GUZOWSKA
University of Szczecin
Department of Econometrics and Statistics
Szczecin, Poland
A discretization method attributed to Kahan is used to approximate the Haavelmo growthcycle model. The local dynamics of this discrete-time Haavelmo growth cycle model are analyzed.
Keywords: Kahan’s method, discrete time, Haavelmo model.
90
Solving systems of nonlinear equations
by using difference equations
MOGHTADA HASHEMIPARAST
K. N. T. University of Technology
Department of Mathematics and Statistics
Tehran, Iran
http://www.math.kntu.ac.ir/hashemiparast.htm
There are many numerical methods in obtaining the solution of integral equations, system ofintegral equations or integro-differential equations which reduce to a system of nonlinear equa-tions. These problems are often ill posed, and are difficult to be solved. In this talk, by usinga moment characteristic function, these systems are transferred to a set of difference equations.The solution is obtained, by referring to the applied characteristic function. Finally, numericalexamples are given.
Keywords: Characteristic function, difference equation.
91
The dynamic multiplier-accelerator
model in economics
JULIUS HEIM
Missouri University of Science and Technology
Department of Mathematics and Statistics
Rolla, Missouri, USA
http://math.mst.edu
In this work we derive a linear second-order dynamic equation which describes multiplier-accelerator models in economics on time scales. After we provide the general form of the dy-namic equation, which considers both taxes and foreign trade, i.e., imports and exports, we givefour special cases of this general multiplier-accelerator model: (1) Samuelson’s basic multiplier-accelerator model. (2) We extend this model with the assumption that taxes are raised by the gov-ernment and that these taxes are immediately reinvested by the government. (3) We give Hicks’extension of the basic multiplier-accelerator model as an example and (4) extend this model byallowing foreign trade in the next step. For each of these models we present the dynamic equationin both expanded and self-adjoint form and give examples for particular time scales. Finally wepresent a criterion under which each solution of the dynamic equation oscillates.
AMS Subject Classification: 91B62, 34C10, 39A10, 39A11, 39A12, 39A13.Keywords: Time scales, multiplier-accelerator, dynamic equation, self adjoint, economics.This is joint work with Martin Bohner.
92
Riccati equations for linear Hamiltonian systems
ROMAN HILSCHER
Masaryk University
Department of Mathematics and Statistics
Brno, Czech Republic
http://www.math.muni.cz/˜hilscher
In this talk we will discuss Riccati matrix differential and difference equations for (possiblyabnormal) linear Hamiltonian and symplectic systems. The abormality is reflected in the (possi-ble) noninvertibility of the corresponding principal solution. We show that even in this case onecan characterize the nonnegativity and positivity of the associated quadratic functional via certainimplicit Riccati equations. These results are derived through the general time scales theory andextend the known classical continuous time results e.g., by Reid and Coppel and recent discretetime results e.g., by Bohner, Dosly, Kratz, and Ruzickova.
AMS Subject Classification: 34C10, 39A12.Keywords: Time scale, Riccati equation, generalized inverse.This is joint work with Vera Zeidan.
93
On the global stability of xn+1 = p+qxn1+xn−1
V ICTOR JIMENEZ LOPEZ
Universidad de Murcia
Departamento de Matematicas
Murcia, Spain
http://www.um.es/docencia/vjimenez
For a long time it has been conjectured that the unique positive equilibrium of the equationfrom the title attracts all its positive solutions. The conjecture is known to be true in the casesq < 1 (Kulenovic and Ladas, 2001) and p ≤ q (Kocic and Ladas, 1993). Under the assumptionsq ≥ 1 and q < p it has been proved in progressively more general settings by Kocic, Ladas andRodrigues (1993), Ou Tang and Luo (2000) and Nussbaum (2007). A paper by Li, Zhang and Su(2005) purportedly provides a full proof of the conjecture but in fact has a rather basic mistake.
In this work we use a modified version of the so-called dominance condition, a tool recentlyintroduced by H. El-Morshedy and the author (“Global attractors for difference equations dom-inated by one-dimensional maps”, J. Difference Equ. Appl. 14 (2008), 391–410) to give a unifiedproof on the conjecture in the cases listed above and improve Nussbaum’s bounds.
AMS Subject Classification: 39A11, 37C70.Keywords: Global attractor, rational difference equation.
94
Period-two trichotomies of a difference equation
of order higher than two
SENADA KALABUSIC
University of Sarajevo
Department of Mathematics, Faculty of Science
Sarajevo, Bosnia and Herzegovina
http://www.pmf.unsa.ba
We investigate the period-two trichotomies of solution of the equation
xn+1 = f(xn, xn−1, xn−2), n = 0, 1 . . . ,
where the function f satisfies certain monotonicity conditions. We give fairly general conditionsfor period-two trichotomies to occur and illustrate the results with numerous examples.
AMS Subject Classification: 39A10, 39A11.Keywords: Attractivity, period two solution, unbounded.This is joint work with Dz. Burgic and M. R. S. Kulenovic.
95
Iterated oscillation criteria for delay
dynamic equations of first order
BASAK KARPUZ
Afyon Kocatepe University
Department Mathematics
Afyonkarahisar, Turkey
http://www.akademi.aku.edu.tr/
→frmCvler.aspx?SicilNo=KA1798
We obtain new sufficient conditions for the oscillation of all solutions of first-order delaydynamic equations on arbitrary time scales, hence combining and extending results for corre-sponding differential and difference equations.
AMS Subject Classification: 39A10, 34C10.Keywords: Oscillation, first-order delay dynamic equations.This is joint work with Martin Bohner and Ozkan Ocalan.
96
Dynamic equations with
piecewise continuous argument
CHRISTIAN KELLER
Missouri University of Science and Technology
Department of Mathematics and Statistics
Rolla, Missouri, USA
We extend the theory of differential equations with piecewise continuous argument to gen-eral time scales. Systems with alternating retarded and advanced argument will be investigatedand conditions for globally asymptotic stability of those systems will be stated. Furthermore westudy the oscillatory behaviour for several dynamic equations with piecewise continuous argu-ment.
AMS Subject Classification: 34K11, 39A10, 39A11, 39A12, 39A13.Keywords: Dynamic equation, time scale, piecewise continuous, retarded, advanced, delay.This is joint work with Martin Bohner.
97
A cardiac loop reentry model with thresholds
CANDACE KENT
Virginia Commonwealth University
Department of Mathematics and Applied Mathematics
Richmond, Virginia, USA
http://www.math.vcu.edu/faculty/kent.html
We investigate the two-dimensional, multiple threshold map, or bimodal system,
F (x , y) =
G(x , y) , if (x , y) ∈ TH(x , y) , if (x , y) /∈ T ,
where G : R2+ → R2
+ and H : R2+ → R2
+ are continuous and T is the intersection of five thresholdregions. Sufficient conditions are placed on G and H that guarantee that either every orbit underF that begins in T leaves T and never returns or there exist orbits under F that begin in T andpass between T and its complement infinitely often. Our bimodal system is intended to serve asa simple discrete model of the dynamics of a circulating pulse of depolarization in a ring of twocardiac cells within the context of cardiac arrhythmias or irregular heartbeat.
This is joint work with Hassan Sedaghat.
98
Asymptotic behavior of one class solutions of the
second-order Emden–Fowler difference equation
VITALIY KHARKOV
I. I. Mechnikov Odessa National University
Department of Mathematics
Odessa, Ukraine
kharkov v [email protected]
In this talk we investigate and obtain necessary and sufficient conditions for existence ofone nontrivial class solutions of the second-order Emden–Fowler difference equation. Moreover,asymptotic representations of solutions from this class are established.
AMS Subject Classification: 34D05.Keywords: Asymptotics, Emden–Fowler equation.
99
Stability via Convexity
MIKHAIL KIPNIS
Chelyabinsk State Pedagogical University
Department of Mathematics
Chelyabinsk, Russia
Stability analysis of the Volterra difference equations
xn +n∑
m=1
amxn−m = 0, n = 1, 2 . . . (1)
is presented, with assumption that the series∑∞
m=1 am is convergent, and inequalities am ≥ 0and ∆2am = am − 2am+1 + am+2 ≥ 0 hold for all m ∈ N. For example, let am = β/ms for real βand s > 1. The criterion for asymptotic stability of equation (1) is given by
− 1ζ(s)
= − 1∑∞m=1
1ms
< β <1∑∞
m=1(−1)m+1 1ms
=1
(1− 21−s) ζ(s),
where ζ(s) is Riemann’s zeta function. Results obtained for the difference equations of the k-thorder were compared with the Enestrom–Kakeya stability conditions.
AMS Subject Classification: 39A11, 34K20.Keywords: Volterra equations, stability, convexity.This is joint work with Vitaliy Gilyazev.
100
Existence of unbounded solutions
in rational equations
YEVGENIY KOSTROV
University of Rhode Island
Department of Mathematics
Kingston, Rhode Island, USA
We exhibit a range of parameters and a set of initial conditions where the rational differenceequation
xn+1 =
α+2k∑i=0
βixn−i
A+k∑
j=0
B2jxn−2j
has unbounded solutions.
AMS Subject Classification: 39A10, 39A11.Keywords: Existence of unbounded solutions, rational difference equation.This is joint work with E. Camouzis, E. A. Grove, and G. Ladas.
101
Solution to integral equations on time scales:
Existence, uniqueness and successive approximations
TOMASIA KULIK
University of New South Wales
School of Mathematics and Statistics
Sydney, Australia
http://web.maths.unsw.edu.au/˜tomasia
I will present my research on applying Banach’s and Granas’s fixed point theory to establishtheorems with sufficient conditions for existence, uniqueness of solutions to integral equations ontime scales, as well as methods of successive approximation to find the solution to any desiredaccuracy.
In particular, I will discuss integral equations on time scales over unbounded intervals andapplications of the results to examining and finding solutions of dynamic or integro-differentialequations on time scales and the additional conditions requited for existence and uniqueness inthese problems.
I will discuss applications of dynamic equations on time scales, to modeling various dynam-ical systems with complex dynamics, which varies continuously part of the time and discretelypart of the time.
This is joint work with Christopher C Tisdell.
102
Linear kth order functional and difference equations
in the space of strictly monotonic functions
JITKA LAITOCHOVA
Palacky University
Department of Mathematics, Faculty of Education
Olomouc, Czech Republic
Abel functional equations are associated to a linear homogeneous functional equation withconstant coefficients. The work uses the space S of continuous strictly monotonic functions Φ :(−∞,∞) → (a, b) equipped with a multiplication f g = fX−1g, the symbol X being a pre-selected canonical function in S. Because of the space S, classical terms like composite function,iterates of a function, Abel functional equation and linear homogeneous functional equation, mustbe re-defined.
We consider the functional equation
akf Φk(x) + · · ·+ a0f Φ0(x) = 0,
which is solved using roots of the characteristic equation and a continuous solution of the Abelfunctional equation
α Φ(x) = X(x+ 1) α(x).
The classical theory of linear homogeneous functional and difference equations is obtained as aspecialization of the theory in space S. All functional equation results apply to difference equa-tions.
AMS Subject Classification: 39B05, 39B12.Keywords: Difference equation, functional equation.
103
The Marshall differential analyzer:
Dynamic equations in motion!
BONITA LAWRENCE
Marshall University
Department of Mathematics
Huntington, West Virginia, USA
http://www.science.marshall.edu/lawrence
The Marshall University differential analyzer team has completed the construction of a fourintegrator, primarily mechanical differential analyzer. Machines of this type, first built in the late1920s and the early 1930s, were designed to solve differential equations and plot the solutions.Our machine, known to the team as “Art”, is modeled after the first differential analyzer built inEngland and named for its builder, Dr. Arthur Porter. It is built almost exclusively from Meccanoor (Meccano type) components and was constructed by a team of undergraduate and graduatestudents from Marshall University. This talk will begin with a discussion of the constructionof the machine and its fundamental components. The machine offers a fantastic physical andvisual interpretation of a differential equation. How this visualization is achieved through thefundamental mechanics and the programming of the machine will then be addressed. Examplesof machine setups will be presented.
AMS Subject Classification: 34.Keywords: Dynamic equations, differential analyzer.
104
Nonautonomous periodic systems with Allee effect
RAFAEL LUIS
Center for Mathematical Analysis and Dynamical Systems
Department of Mathematics
Lisbon, Portugal
http://members.netmadeira.com/rafaelluis
We introduce a new class of maps, called unimodal Allee maps (UAM). These maps arise inthe study of population dynamics in which the system has three fixed points, a stable fixed pointzero, an unstable positive fixed point (Allee point) and a stable positive fixed point (carryingcapacity). We analyse the properties of the Allee points and the carrying capacity and establishtheir stability, for nonautonomous periodic systems formed by unimodal Allee maps.
Keywords: Allee effect, Allee point, carrying capacity, UAM.This is joint work with Saber Elaydi and Henrique Oliveira.
105
Ostrowski inequalities on time scales
THOMAS MATTHEWS
Missouri University of Science and Technology
Department of Mathematics and Statistics
Rolla, Missouri, USA
The presentation contains proofs of Ostrowski inequalities (regular and weighted cases) ontime scales and thus unifies and extends corresponding continuous and discrete versions fromthe literature. An application to the quantum calculus case will also be provided.
This is joint work with Martin Bohner.
106
Numerical detection of explosions and asymptotic
behaviour of delay-differential equations
MICHAEL MCCARTHY
Dublin City University
School of Mathematical Sciences
Dublin, Ireland
http://student.dcu.ie/˜mccarm29/index.html
In this talk we study scalar delay-differential equations whose solutions explode in finitetime. Our goal is to devise a discretisation of the equation such that: (i) the discrete equation “ex-plodes”; (ii) the rate at which the explosion occurs is preserved by discretising; (iii) the explosiontime can be approximated arbitrarily well by making a sufficiently large computational effort.
We show that these goals are all achieved by making an adaptive time-discretisation wherethe length of the step size tends to zero as the explosion time is approached. The same adap-tive method also reproduces the asymptotic behaviour of rapidly growing solutions of a similarclass of nonexploding equations: Therefore, the method does not induce spurious explosions notpresent in continuous time.
The work is joint with John Appleby and is supported by the IRCSET Embark Initiativeunder the project “Explosions in stochastic dynamical systems applied to finance”.
Keywords: Delay differential equation, explosions.This is joint work with John Appleby.
107
Learning to play Nash in
deterministic uncoupled dynamics
VIVALDO MENDES
ISCTE
Department of Economics
Lisbon, Portugal
In a boundedly rational game, where players cannot be as super-rational as in Kalai andLeher (1993), are there simple adaptive heuristics or rules that can be used in order to secure con-vergence to Nash equilibria? Young (2008) argues that if an adaptive learning rule obeys threeconditions – (i) it is uncoupled, (ii) each player’s choice of action depends solely on the frequencydistribution of past play, and (iii) each player’s choice of action, conditional on the state, is deter-ministic – no such rule leads the players’ behavior to converge to Nash equilibra. In this paperwe present a counterexample, showing that there are in fact simple adaptive rules that secureconvergence in a fully deterministic and uncoupled game. We used the Cournot model with non-linear costs and incomplete information for this purpose and also illustrate that the convergenceto Nash equilibria can be achieved with or without any coordination of the players actions.
AMS Subject Classification: 91A25, 91A26, 91A50.Keywords: Uncoupled dynamics, Nash equilibrium, convergence.This is joint work with Orlando Gomes and Diana Mendes.
108
Time scale extensions of a theorem of Wintner
on systems with asymptotic equilibrium
RAZIYE MERT
Middle East Technical University
Department of Mathematics
Ankara, Turkey
http://www.metu.edu.tr/˜raziye
We consider quasilinear dynamic systems of the form
x∆ = A(t)x+ f(t, x), t ∈ [a,∞)T,
where T is a time scale, and extend theorems obtained for differential equations by Trench [SIAMJ. Math. Anal.] to dynamic equations on time scales; thus provide extensions of a theorem ofWintner on systems with asymptotic equilibrium to time scales. In particular, we give sufficientconditions for the asymptotic equilibrium of the above system in the sense that there is a solutionsatisfying
limt→∞
x(t) = c
for any given constant vector c. Our results are new for difference and q-difference equations eventhough their analogues for differential equations have been known for some time.
Keywords: Asymptotic equilibrium, dynamic system, time scales.This is joint work with Agacık Zafer.
109
A new approach for solving Fredholm
integro-difference equations
HAMID MESGARANI
Shahid Rajaee University
Department of Mathematics
Tehran, Iran
The Taylor expansion approach to solve higher-order linear difference equations has beengiven by Sezer. In this paper, we modify and develop for solving the Fredholm integro-differenceequation. Also, examples that illustrate the pertinent features of the method are presented andthe results are discussed.
Keywords: Integro-difference, Fredholm, Taylor expansion.This is joint work with M. Shahrezaee.
110
Algebro-geometric solutions of the
Ablowitz–Ladik hierarchy
JOHANNA MICHOR
New York University
Courant Insitute of Mathematical Sciences
New York, New York, USA
http://www.mat.univie.ac.at/˜jmichor
Algebro-geometric solutions of soliton equations are a class of solutions which can be con-structed explicitly using tools from algebraic geometry. We present a derivation of all algebro-geometric finite-band solutions of the Ablowitz–Ladik equation, which is a complexified versionof the discrete nonlinear Schrodinger equation.
In addition, we survey a recursive construction of the associated Ablowitz–Ladik hierarchy,a completely integrable sequence of systems of nonlinear evolution equations on the lattice Z.This is done by means of a zero-curvature and Lax approach.
AMS Subject Classification: 37K10, 37K15, 35Q55.Keywords: Discrete NLS, algebro-geometric solution, Lax pair.This is joint work with Fritz Gesztesy, Helge Holden, and Gerald Teschl.
111
Oscillatory and asymptotic properties of solutions
of nonlinear neutral-type difference equations
MAŁGORZATA MIGDA
Poznan University of Technology
Institute of Mathematics
Poznan, Poland
http://www.math.put.poznan.pl/˜mmigda
We consider higher-order neutral difference equations of the form
∆m(xn + pnxn−τ ) = f(n, xn, xσ(n)) + hn,
where m ≥ 2, (pn), (hn) are sequences of real numbers, τ is a nonnegative integer, (σ(n)) is aninteger sequence with σ(n) ≤ n and lim
n→∞σ(n) = ∞, f : N× R× R → R.
The study of asymptotic behavior of solutions of nonlinear equations of this type often re-quires that the sequence (pn) satisfies pn > 0 or pn < 0. We examine the case when (pn) is anoscillatory sequence.
AMS Subject Classification: 39A10, 39A11.This is joint work with Janusz Migda.
112
An example of a strongly invariant, pinched core strip
LEOPOLDO MORALES
Universitat Autonoma de Barcelona
Departament de Matematiques
Barcelona, Spain
In [Roberta Fabbri, Tobias Jager, Russel Johnson, Gerhard Keller, A Sharkovskii-type the-orem for minimally forced interval maps, Topological Methods in Nonlinear Analysis, volume26, number 1, pages 163–188, 2005], the authors define the concept of Pinched core strip. So far ithas not been given an example of such an object that is strongly invariant under a quasi-periodictriangular function and it is not a curve. In this talk we will describe how to construct such anexample.
This is joint work with Lluıs Alseda and Francesc Manosas.
113
Numerical solutions of nonlinear
differential-difference equations by the
variational iteration method
VOLKAN OBAN
Ege University
Department of Mathematics
Izmir, Turkey
We extend He’s variational iteration method to find approximate solutions for nonlineardifferential-difference equations such as Volterra’s equation. A simple but typical example is ap-plied to illustrate the validity and great potential of the generalized variational iteration methodin solving nonlinear differential-difference equations. The results reveal that the method is veryeffective and simple. We find the extended method for nonlinear differential-difference equationsis of good accuracy.
Keywords: He’s variational iteration method, differential-difference, Volterra equation.This is joint work with Ahmet Yıldırım.
114
Solution spaces of dynamic equations
over time scales space
RALPH OBERSTE-VORTH
Marshall University
Department of Mathematics
Huntington, West Virginia, USA
http://www.marshall.edu/math/contact.asp
We prove a recent conjecture characterizing the Fell topology on the space of time scales. Wepursue basic questions of how a changes in time scale may affect the solutions of a given dynamicequation. Insight into these questions are of interest both for applications as well as in theory.
AMS Subject Classification: 37.Keywords: Time scales, dynamic equation, Fell topology.
115
Bifurcations for nonautonomous interval maps
HENRIQUE OLIVEIRA
Instituto Superior Tecnico Lisbon
Department of Mathematics
Lisbon, Portugal
http://www.math.ist.utl.pt/˜holiv
In this work we investigate attracting periodic orbits for nonautonomous discrete dynamicalsystems with two maps using a new approach. We study some types of bifurcation in these sys-tems. We show that the pitchfork bifurcation plays an important role in the creation of attractingorbits in families of alternating systems with negative Schwarzian derivative and it is central inthe geometry of the bifurcation diagrams.
AMS Subject Classification: Primary: 37E05; Secondary: 37E99.Keywords: Nonautonomous system, bifurcation.This is joint work with Emma D’Aniello.
116
On the spectrum of normal
difference operators of first order
RUKIYE OZTURK
Karadeniz Technical University
Department of Mathematics
Trabzon, Turkey
In this talk the normality and spectrum of some first order difference operators in the Hilbertspace of sequences l2(N) are investigated. For example, a result has been established in the fol-lowing form.
Let S and A be respectively a right shift and a linear self-adjoint operator in the space l2(N)and (ImS)l2(N) ⊂ D(A). Then
1. The operator L = 1 − S + A, L : D(A) ⊂ l2(N) → l2(N) is normal in l2(N) if and only ifA = f(ImS) (here f is a function from σ(ImS) to R).
2. If L = 1 − S + A, L : D(A) ⊂ l2(N) → l2(N) is a normal operator and A − S = h(ImS),h : σ(ImS) → C, h ∈ C(σ(ImS)), then the spectrum of the operator L is the form σ(L) =(1 + h)([−1, 1]).
AMS Subject Classification: 47A10.Keywords: Space of sequences, difference operators.This is joint work with Zameddin Ismailov.
117
Boundedness, attractivity, stability of a rational
difference equation with two periodic coefficients
GARYFALOS PAPASCHINOPOULOS
Democritus University of Thrace
Department of Environmental Engineering
Xanthi, Greece
We study the boundedness, the attractivity and the stability of the positive solutions of therational difference equation
xn+1 =pnxn−2 + xn−3
qn + xn−3, n = 0, 1, . . . ,
where pn, qn, n = 0, 1, . . . are positive sequences of period 2.
AMS Subject Classification: 39A10.Keywords: Difference equation, boundedness, stability.This is joint work with G. Stefanidou and C. J. Schinas.
118
Classification and stability of functional equations
CHOONKIL PARK
Hanyang University
Department of Mathematics
Seoul, South Korea
In this talk, we classify and prove the generalized Hyers–Ulam stability of linear, quadratic,cubic, quartic and quintic functional equations in complex Banach spaces.
AMS Subject Classification: 39B72.Keywords: Fixed point, functional equations, stability.This is joint work with Young Hak Kwon.
119
Bounded solutions of a rational difference equation
SANDRA PINELAS
Azores University
Mathematical Department
Ponta Delgada, Portugal
http://www.uac.pt/˜spinelas
This talk studies the existence of bounded solutions of the rational difference equation
xn+1 =βnxn + xn−1
xn−2, n = 1, 2, . . .
with initial conditions x−2, x−1, x0 ∈ R+ and 0 < βn < 1.
120
Nonoscillatory solutions of a second-order
difference equation of Poincare type
MIHALY PITUK
University of Pannonia
Department of Mathematics and Computing
Veszprem, Hungary
http://www.szt.vein.hu/˜pitukm
Poincare’s classical theorem about the convergence of the ratios of successive values of thesolutions of linear homogeneous difference equations applies if the characteristic values of thelimiting equation are simple and have different moduli. In this talk we show that for the nonoscil-latory solutions the conclusion of Poincare’s theorem is also true in the case when the limitingequation has a double positive characteristic value.
This is joint work with Rigoberto Medina.
121
Generalized Jacobians for solving nondifferentiable
equations arising from contact problems
NICOLAE POP
North University of Baia Mare
Department of Mathematics and Computer Science
Baia Mare, Romania
http://www.ubm.ro
The aim of this talk is to give an algorithm for solving nondifferentiable equations usinggeneralized Jacobians with applications in contact problems. In contact problems, the functionalwhich describes the influence of the friction is nondifferentiable. For solving the discretized con-tact problem, the Newton method for linearization is employed, where generalized Jacobiansmust be used. The generalized Jacobians and the generalized gradient coincide. This method canbe used to apply the conjugate gradient method for solving of the equation that contains a non-differentiable nonlinear operator which is reduced to the successive solution of auxiliary linearequations. This linear operator (equations) can be regarded as a special kind of preconditioner.See also Axelson, O., Chronopoulos, A. T., On nonlinear generalized conjugate gradient methods,Numer. Math., 69 (1994), No. 1, pp. 1–15 and Clarke, F. H., Optimization and nonsmooth analysis,Wiley and Sons, 1983.
AMS Subject Classification: 35J85, 74G15.Keywords: Generalized Jacobian, contact problems.
122
Integro-difference equation associated
to a reaction-diffusion equation
EMIL POPESCU
Technical University of Bucharest
Civil Engineering
Bucharest, Romania
Using a product formula and the discretization of the time for a reaction-diffusion equa-tion, we present a sequential splitting schema which gives corresponding discrete time integro-difference equation.
This is joint work with Nedelia Antonia Popescu.
123
Finite size scaling technique and applications
NEDELIA ANTONIA POPESCU
Romanian Academy of Sciences
Astronomical Institute
Bucharest, Romania
The finite size scaling technique is applied on the Ulysses/VHM data in order to study thescaling of the magnetic field magnitude (B) and energy density (B2) fluctuations of the interplan-etary magnetic field.
The basic considered quantity is the change in the normalizedB,B(t)/〈B〉, at different scales(time lags) τn = 2n (days), n = 0, 1, 2, . . . as follows:
dBn = dBn(ti, τn) = [B(ti + τn)−B(ti)] /〈B〉,
where ti is the time (day); < B > is the average of B over 1 year at a specific distance; B(ti) is thedaily average of B.
This is joint work with Emil Popescu.
124
Dynamic replicator equation and its transformation
ZDENEK POSPISIL
Masaryk University
Department of Mathematics and Statistics
Brno, Czech Republic
http://www.math.muni.cz/˜pospisil
The replicator equation is a vector ordinary differential equation with a cubic nonlinearity. Itprovides a description of game dynamics as well as evolutionary models for population genetics.The contribution introduces a dynamic replicator equation for Sn valued function x(t) =
(xi(t)
):
x∆i (t) = xi(t)
(n∑
k=1
aikxσi (t)− x(t)TAxσ(t)
), i = 1, 2, . . . , n;
here A = (aij) is an n × n real matrix and Sn is the n-dimensional probability simplex. Basicqualitative properties of the solution will be shown. The main result is that under some assump-tions, there exists a time scale such that the replicator equation is equivalent to the Lotka–Volterradynamic equation
y∆j (τ) = yj(τ)
(rj +
n−1∑k=1
bjkyσk (τ)
), j = 1, 2, . . . , n− 1
for y(τ) =(yj(τ)
)from positive (n− 1)-dimensional orthant.
AMS Subject Classification: 34A34, 39A12, 92B05.Keywords: Dynamic nonlinear equation, transformation.
125
Nonautonomous continuation
and bifurcation, revisited!
CHRISTIAN POTZSCHE
Munich University of Technology
Center for Mathematical Sciences
Munich, Germany
http://www-m12.ma.tum.de/poetzsche
We investigate local continuation and bifurcation properties for nonautonomous differenceequations. Due to their arbitrary time dependence, equilibria or periodic solutions typically donot exist and are replaced by bounded globally defined solutions.
Following this leitmotiv, hyperbolicity properties are formulated via the Sacker–Sell spec-trum and exponential dichotomies yield a robust framework for local continuation arguments us-ing the (surjective) implicit function theorem. Dichotomies in variation also provide a Fredholmtheory. Thus, we employ a Lyapunov–Schmidt-reduction to deduce nonautonomous versions ofthe classical fold, transcritical and pitchfork bifurcation patterns.
Finally, Sacker–Sell spectral intervals crossing the stability boundary give rise to a new 2-stepbifurcation pattern not present in the autonomous situation.
Keywords: Nonautonomous bifurcation, Sacker–Sell spectrum.
126
A nonlinear system of difference equations
MIHAELA PREDESCU
Bentley College
Department of Mathematical Sciences
Waltham, Massachusetts, USA
http://web.bentley.edu/empl/p/mpredescu
We investigate the global stability character and the behavior of solutions of the nonlinearsystem of difference equations
Mn+1 = aMn + bHn(1− e−Mn)
Hn+1 = cHn
1+pAn+ 1
1+qAn
An+1 = rAn +Mn,
n = 0, 1, . . . .
The initial conditions are nonnegative, the parameters are positive and a, c, r ∈ (0, 1).
AMS Subject Classification: 39A11.This is joint work with T. Awerbuch, E. Camouzis, E. A. Grove, G. Ladas, and R. Levins.
127
Galerkin method for solving nonlinear
Fredholm–Hammerstein integral equations
with multiwavelet basis
MOHSEN RABBANI
Islamic Azad University, Sari Branch
Department of Mathematics
Sari, Iran
In this talk, we solve nonlinear Fredholm–Hammerstein integral equations by using multi-wavelets constructed from Legendre polynomials. For reducing the operations in comparing withsimilar works, we used some modifications in approximation coefficients calculating scheme. Thenumerical examples for the method are of good accuracy.
Keywords: Multiwavelet, Fredholm–Hammerstein, nonlinear.
128
On some rational difference equations via
linear recurrence equations properties
MUSTAPHA RACHIDI
LEGT - F. Arago. Academie de Reims
Mathematics Section
Reims, France
The purpose of this talk is to examine the local stability of the following class of rationaldifference equations
xn+1 =∑k−1
i=0 aixn−i−1∑k−1i=0 bixn−i−1
, (1)
where ai ≥ 0, bi ≥ 0 (i = 0, 1, . . . , k) and the initial conditions x−k, x−k+1, . . . , x0 are arbitraryreal numbers. The approach used here is based on the properties of the linear recurrence partassociated to equation (1). More precisely, we consider some properties on the convergence oflinear recursive sequences, which permits us to obtain some new results on the local stability ofequation (1). In addition, for a particular case of equation (1), a straightforward computationleads to the extension of some recent results concerning the global attractivity and boundednessof this equation.
Keywords: Difference equations, stability, recursiveness.This is joint work with Rajae Ben Taher and Mohamed El Fetnassi.
129
Multiple periodic solutions of a second-order
nonautonomous rational difference equation
MICHAEL RADIN
Rochester Institute of Technology
School of Mathematical Sciences
Rochester, New York, USA
http://www.rit.edu/cos/math/Directory/
→Standard/marsma.html
We will investigate the existence of multiple periodic solutions of a second order nonau-tonomous rational difference equation. We will discover the necessary and sufficient conditionsfor existence of multiple periodic solutions, the pattern of the periodic solutions and convergenceto zero and to multiple periodic solutions.
AMS Subject Classification: 39A.Keywords: Convergence, periodic solutions, boundedness.This is joint work with Nicholas Batista.
130
Morse spectrum for linear
nonautonomous difference equations
MARTIN RASMUSSEN
University of Augsburg
Department of Mathematics
Augsburg, Germany
http://www.math.uni-augsburg.de/˜rasmusse
In this talk, the concept of a Morse spectrum is introduced for nonautonomous linear dif-ference equations. In contrast to other spectral notions such as the Sacker-Sell spectrum (whichyields a linear decomposition), the Morse spectrum is based on a linear decomposition, the finestMorse decomposition. The existence of such a Morse decomposition is reviewed, and basic prop-erties of the Morse spectrum are discussed. The content of this talk is based on joint work withFritz Colonius (University of Augsburg) and Peter Kloeden (University of Frankfurt).
This is joint work with Fritz Colonius and Peter Kloeden.
131
Power type comparison theorems for
half-linear dynamic equations
PAVEL REHAK
Academy of Sciences of the Czech Republic
Institute of Mathematics
Brno, Czech Republic
http://www.math.muni.cz/˜rehak
We establish conditions which guarantee that oscillatory properties of a half-linear dynamicequation are preserved when the power in the nonlinearities is changed. We discuss the discrep-ancies between the results on different time scales. The results are original also in the differentialand difference equations cases.
132
Decoupling and simplifying of discrete dynamical
systems in the neighbourhood of invariant manifold
ANDREJS REINFELDS
University of Latvia
Institute of Mathematics and Computer Science
Riga, Latvia
http://home.lanet.lv/˜reinf
In a Banach space X×E, the discrete dynamical systemx(t+ 1) = g(x(t)) +G(x(t), p(t)),
p(t+ 1) = A(x(t))p(t) + Φ(x(t), p(t))(1)
is considered. Sufficient conditions under which there is an Lipschitzian invariant manifoldu : X → E are obtained. Using this result we find sufficient conditions of conjugacy of (1) andx(t+ 1) = g(x(t)) +G(x(t), u(x(t)),
p(t+ 1) = A(x(t))p(t).
Relevant results concerning partial decoupling and simplifying of the semidynamical systems aregiven also.
AMS Subject Classification: 39A, 37D30, 34C31.Keywords: Conjugacy, dynamical systems, invariant manifold.
133
On oscillation of solutions of stochastically
perturbed difference equations
ALEXANDRA RODKINA
University of the West Indies
Department of Mathematics and Computer Science
Kingston, Jamaica
http://www.mona.uwi.edu/dmcs/staff/
→arodkina/alya.htm
We discuss the path-wise oscillatory behavior of the scalar nonlinear stochastic differenceequation
X(n+ 1) = X(n)− f(X(n)) + g(n,X(n))ξ(n+ 1), n = 0, 1, . . . ,
with nonrandom initial value X0 ∈ R. Here (ξ(n))n≥0 is a sequence of independent randomvariables with zero mean and unit variance. The functions f : R → R and g : N × R → Rare presumed to be continuous. We consider state-independent perturbation, when g does notdepend on the second variable, as well as the state-dependent perturbation.
AMS Subject Classification: 37H10, 39A11, 60H10, 34F05, 65C20.Keywords: Stochastic difference equations, oscillation.
134
Invariant objects through wavelets
DAVID ROMERO I SANCHEZ
Universitat Autonoma de Barcelona
Departament de Matematiques
Bellaterra (Cerdanyola del Valles), Spain
http://www.gsd.uab.cat/personal/dromero
A standard approach used in the literature to compute and work with invariant objects ofsystems exhibiting periodic or quasi-periodic behaviour is to use finite Fourier approximations,namely
F(ξ) = a0 +N∑
n=1
(an cos(nξ) + bn sin(nξ)) .
Finite wavelet expansions could be used instead,
F(ξ) =N∑
j=0
Nj∑n=0
cj,nψj,n(ξ),
where ψj,n(ξ) is obtained by translation and dilation of a mother wavelet ψ(x).
Since wavelets can capture different frequencies at different regions of the space, this ap-proach is expected to be more efficient than the Fourier one. The aim of this talk is to comparethe (computional) efficiency of both approaches. For that, we will briefly introduce the necessarytools for wavelet basis and multiresolution analysis.
This is joint work with Lluıs Alseda and Josep M. Mondelo.
135
Compatibility of local and global stability conditions
for some discrete population models
SAMIR SAKER
King Saud University
Department of Mathematics
Riyadh, Saudi Arabia
In this talk, we consider a model that has been proposed to study the growth of bobwhitequail populations of Northern Wisconsin and prove that the local stability implies the globalstability. We will prove the results by using a suitable Lyapunov function and for illustrationwe apply the results on the Hassell and Smith models. We will show that for different values ofthe parameters, the population will exhibit some time varying dynamics. For parameters closeto stable region, this will be a simple two-cycle and if the system is moved in a direction awayfrom stability, by increasing the parameters then the dynamics become more complex and thesystem undergoes a series of bifurcations which leading to increasingly longer periodic cycles andfinally deterministic chaos. Some illustrative examples and graphs are included to demonstratethe validity and applicability of the results.
AMS Subject Classification: 39A10, 92D25.Keywords: Local, global stability, population dynamics.
136
Discrete densities and Fisher information
PABLO SANCHEZ-MORENO
University of Granada
Institute Carlos I for Theor. and Comput. Physics
Granada, Spain
http://www.ugr.es/˜pablos
Analytic information theory of discrete distributions was initiated in 1998 by C. Knessel,P. Jacquet and S. Szpankowski who addressed the precise evaluation of the Renyi and Shannonentropies of the Poisson, Pascal (or negative binomial) and binomial distributions. They wereable to derive various asymptotic approximations and, at times, lower and upper bounds forthese quantities. Here we extend these investigations in a twofold way. First, we consider amuch larger class of distributions, involving discrete hypergeometric-type polynomials which areorthogonal with respect to the weight function of Poisson, Pascal, binomial and hypergeometrictypes; that is the polynomials of Charlier, Meixner, Kravchuck and Hahn. Second we compute, attimes explicitly, the Fisher informations of the four families of these Rakhmanov distributions.
AMS Subject Classification: 62B10, 30G25.Keywords: Fisher information, discrete densities.This is joint work with J. S. Dehesa, R. J. Yanez.
137
Boundedness, periodicity, attractivity of the
difference equation xn+1 = An +(
xn−1xn
)p
CHRISTOS SCHINAS
Democritus University of Thrace
Department of Electrical and Computer Engineering
Xanthi, Greece
http://utopia.duth.gr/˜cschinas
This talk studies the boundedness, the persistence, the periodicity and the stability of thepositive solutions of the nonautonomous difference equation
xn+1 = An +(xn−1
xn
)p
, n = 0, 1, . . . ,
where An is a positive bounded sequence, p ∈ (0, 1) ∪ (1,∞) and x−1, x0 ∈ (0,∞).
AMS Subject Classification: 39A10.Keywords: Boundedness, persistence, periodicity, stability.This is joint work with G. Papaschinopoulos and G. Stefanidou.
138
Oscillation of nonlinear
three-dimensional difference systems
EWA SCHMEIDEL
Poznan University of Technology
Institute of Mathematics
Poznan, Poland
http://www.put.poznan.pl/˜schmeide
Oscillatory properties of solutions are investigated usually for two-dimensional differencesystems only, but we have not seen too many oscillatory results for three-dimensional systemsof the general form. This observation motivated us to consider nonlinear three-dimensional dif-ference systems and to investigate its oscillatory or almost oscillatory behavior. Moreover, it isan interesting problem to extend oscillation criteria for third-order nonlinear difference equationsto the case of nonlinear three-dimensional difference systems since such systems include, in par-ticular, third-order nonlinear difference equations as a special case. We shall provide sufficientconditions under which the considered system is oscillatory or almost oscillatory.
AMS Subject Classification: 39A10, 39A11.Keywords: Nonlinear difference system, oscillation.
139
On the behaviour of the difference equation
x(n + 1) = max1/x(n), min1, A/x(n)
NURCAN SEKERCI
Selcuk University
Department of Mathematics
Konya, Turkey
We study the behavior of the solution of the difference equation
x(n+ 1) = max1/x(n),min1, A/x(n),
where A is a real number and the initial condition x(0) is a nonzero real number. In the cases ofA > 0 and A < 0 we determine the behaviour of the equation with A, x0.
AMS Subject Classification: 39A10, 39A11.Keywords: Difference equation, periodicity, behaviour.This is joint work with Necati Taskara and D. Turgut Tollu.
140
Heat solutions by using Fibonacci tane function
MOHSEN SHAHREZAEE
Imam Hossein University
Department of Mathematics
Tehran, Iran
In this talk we introduce and use symmetrical Fibonacci tane for solving heat equation. Weknow the symmetrical Fibonacci tane is constructed according to the symmetrical Fibonacci sineand cosine in the model of
SFS(x) =αx − α−x
√5
CFS(x) =αx + α−x
√5
and tFS will be defined by
tFS(x) =αx − α−x
αx + α−x.
As one of its applications an algorithm is devised to obtain exact traveling heat solutions forthe differential-difference equations by means of the property of function tane. In fact, we havedevised a straightforward algorithm to compute traveling heat solutions without using explicitintegration.
141
Applications of finite difference methods
in the field of magnetic refrigeration
BAKHODIRZHON SIDDIKOV
Ferris State University
Department of Mathematics
Big Rapids, Michigan, USA
http://www.ferris.edu/htmls/colleges/
→artsands/faculty desc.cfm?FSID=174
Magnetic refrigeration is rapidly developing and becoming competitive with conventionalgas compression technology, primarily because the most inefficient component of the refrigerator– the compressor – is eliminated. In this talk, we will discuss a time-dependent one-dimensionalmodel of the active magnetic regenerator which was developed as a highly nonlinear systemof partial differential equations. One of the difficulties in the numerical simulations of the activemagnetic regenerator is determination of the heat capacity of the magnetic material (gadolinium),C = C(T,H), which depends on the temperature of the material, T = T (x, t), as well as on themagnetic induction, H = H(t), where x is a spatial coordinate and t is a chronological coordi-nate. I will present an approximation surface for C = C(T,H), which was obtained by using theleast-squares surface fitting technique and experimental measurements at 460 data points. Wedeveloped the numerical scheme for the computer simulations of the active magnetic regeneratorby using a finite-difference method. We will analyze the performance of the numerical schemefor stability and convergence.
AMS Subject Classification: 47N.Keywords: Finite difference method, magnetic refrigeration.
142
Spectral theory of birth-and-death processes
MORITZ SIMON
Munich University of Technology
Department of Mathematics
Munich, Germany
http://ibb.gsf.de/person.php?name=Moritz+Simon
This talk gives an outline of the author’s PhD thesis about birth–and–death processes withkilling [Moritz Simon, Spectral Theory of Birth-and-Death Processes, PhD thesis (TUM), Sierke Ver-lag, Gottingen, 2008]. Such stationary Markov processes admit a representation of their transitionprobabilities via orthogonal polynomials (OP) with respective spectral measure. The recursionof the OP depends purely on the birth, death and killing rates in the population process. Linearrates for instance admit an explicit computation of the OP and their spectral measure, which inturn allow to determine the stochastic dynamics of the process. Problems come in as soon as therates are sufficiently complicated: explicit methods are no more tractable then! Anyway, the useof regular perturbation theory for corresponding Jacobi operators enables one to determine thespectrum in qualitative and approximate respects, at least under a certain domination of killing.
143
Numerical solution of nonlocal boundary value
problems for the Schrodinger equation
ALI SIRMA
Bahcesehir University
Department of Mathematics and Computer Sciences
Istanbul, Turkey
In this talk the numerical solution of the multipoint nonlocal boundary value problemiut −
m∑r=1
(ar(x)uxr)xr
+ σuf(t, x), 0 < t < T, x ∈ Ω,
u(0, x) =p∑
j=1
αju(λj , x) + ϕ(x), x ∈ Ω,
u(t, x) = 0, ∂u(t,x)∂−→n = 0, x ∈ S, 0 ≤ t ≤ T,
for the Schrodinger equation is considered. Here, ar(x) (x ∈ Ω), ϕ(x) (x ∈ Ω), f(t, x) (t ∈ [0, T ],x ∈ Ω) are smooth functions and σ > 0 is a constant. Ω is the unit cube in the m-dimensionalEuclidean space Rm (0 < xk < 1, 1 ≤ k ≤ m) with boundary S and Ω = Ω ∪ S, −→n denotes thenormal vector to boundary S.
AMS Subject Classification: 65N14.Keywords: Schrodinger equation, stability.This is joint work with Allaberen Ashyralyev.
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On a system of max-difference equations
GESTHIMANI STEFANIDOU
Democritus University of Thrace
Department of Electrical and Computer Engineering
Xanthi, Greece
In this talk we study the periodic nature of the positive solutions of the system of differenceequations
yn = maxA1
zn−1,B1
zn−3,C1
zn−5
, zn = max
A2
yn−1,B2
yn−3,C2
yn−5
, n ≥ 0,
whereAi, Bi, Ci, i ∈ 1, 2, are positive real constants and the initial values yi, zi, i ∈ −5,−4, . . . ,−1are positive numbers. In addition, we give conditions so that the solutions of this system are un-bounded.
AMS Subject Classification: 39A10.Keywords: Difference equations, periodicity, unboundedness.This is joint work with G. Papaschinopoulos and C. J. Schinas.
145
Basic properties of partial dynamic operators
PETR STEHLIK
University of West Bohemia
Department of Mathematics
Pilsen, Czech Republic
http://www.kma.zcu.cz/stehlik
Motivated by the importance of maximum principles in the theory of partial differentialequations and in numerical analysis, we establish simple maximum principles for basic partialdynamic operators on multidimensional time scales. As in the case of ordinary dynamic oper-ators we reveal a set of results and counterexamples which illustrate the distinct behaviour inthe continuous and discrete cases. Finally, we provide some immediate consequences and proveuniqueness results to problems involving partial dynamic operators.
This is joint work with Bevan Thompson.
146
Relative oscillation theory for Jacobi operators
GERALD TESCHL
University of Vienna
Faculty of Mathematics
Vienna, Austria
http://www.mat.univie.ac.at/˜gerald
Classical oscillation theory establishes the connection between the number of eigenvaluesand sign flips of certain solutions of a Jacobi operator respectively matrix. We add a new wrinkleto this theory by showing how the number of sign flips of Wronski (resp. Casorati) determinantsof solutions can be connected to differences of numbers of eigenvalues.
AMS Subject Classification: 39A10, 39A12.Keywords: Oscillation theory, Jacobi operators.
147
Reducibility and stability results for
linear systems of difference equations
AYDIN T IRYAKI
Gazi University
Department of Mathematics
Ankara, Turkey
http://websitem.gazi.edu.tr/tiryaki
In this talk, we first give a theorem on the reducibility of a linear system of difference equa-tions of the form x(n+1) = A(n)x(n). Next, by means of Floquet theory, we obtain some stabilityresults. Moreover, some examples are given to illustrate the importance of the results.
AMS Subject Classification: 39A05, 39A11.Keywords: Reducibility, periodic matrix, Floquet exponents.This is joint work with Adil Mısır.
148
Analysis of a nonlinear discrete dynamical system,
signal coding and reconstruction
MOUHAYDINE TLEMCANI
Universidade de Evora
Centro de Geofısica de Evora (CGE)
Evora, Portugal
In this talk, we present a study of different iterated maps in which we are looking for in-variants that link their dynamics. Various approaches of conductivity of dynamical systems areanalyzed looking for real physical examples. The notion of conductance of a discrete nonlineardynamical system is linked to a physical time dependent example. The time series issued froma physical system behaviour are processed from a new point of view in order to extract hiddeninformation.
AMS Subject Classification: 37B10, 37A35.Keywords: Dynamical systems, conductance, time series.This is joint work with Sara Fernandes.
149
Multiple positive solutions for a system of
higher-order boundary value problems on time scales
FATMA SERAP TOPAL
Ege University
Department of Mathematics
Izmir, Turkey
http://sci.ege.edu.tr/˜math/index.php?
→option=com content&task=view&id=48
In this talk, by applying fixed point theorems in cones and under suitable conditions, wepresent the existence of single and multiple solutions for the following system of higher-orderboundary value problems:
(−1)ny42n
1 (t) = f1(t, yσ1 (t), yσ
2 (t)), t ∈ [0, 1],
(−1)my42m
2 (t) = f2(t, yσ1 (t), yσ
2 (t)), t ∈ [0, 1],
y42i
1 (0) = y42i
1 (σ(1)) = 0, 0 ≤ i ≤ n− 1,
y42j
2 (0) = y42j
2 (σ(1)) = 0, 0 ≤ j ≤ m− 1.
AMS Subject Classification: 39A10, 34B15, 34A40.Keywords: Positive solutions, cone, fixed point theorems.This is joint work with Erbil Cetin.
150
Positive solutions of a second-order
m-point BVP on time scales
AHMET YANTIR
Atılım University
Department of Mathematics
Ankara, Turkey
http://www.atilim.edu.tr/˜ayantir
In this study, we are concerned with proving the existence of multiple positive solutions of ageneral second-order nonlinear m-point boundary value problem
u∆∇(t) + a(t)u∆(t) + b(t)u(t) + λh(t)f(t, u) = 0, t ∈ [0, 1],
u(ρ(0)) = 0, u(σ(1)) =m−2∑i=1
αiu(ηi)
on time scales. The proofs are based on fixed point theorems in a Banach space. We present anexample to illustrate how our results work.
AMS Subject Classification: 39A10, 34B18, 34B40, 45G10.Keywords: Multi-point BVPs, positive solutions, time scales.This is joint work with Fatma Serap Topal.
151
Numerical solutions of nonlinear
differential-difference equations
by the homotopy perturbation method
AHMET YILDIRIM
Ege University
Department of Mathematics
Izmir, Turkey
http://sci.ege.edu.tr/˜math/index.php?
→option=com content&task=view&id=58
A new scheme, deduced from He’s homotopy perturbation method, is presented for solvingdifferential-difference equations. A simple but typical example is applied to illustrate the valid-ity and great potential of the generalized homotopy perturbation method in solving differential-difference equations. The results reveal that the method is very effective and simple.
Keywords: He’s homotopy perturbation method, differential-difference, Volterra equation.This is joint work with Gulcin Yalazlar.
152
A result on successive approximation of solutions to
dynamic equations on time scales
ATIYA ZAIDI
University of New South Wales
School of Mathematics and Statistics
Sydney, Australia
http://www.maths.unsw.edu.au/˜atiya
We establish a Picard–Lindelof theorem for first order initial value problems on time scales,where a time scale is a nonempty closed subset of reals. The theorem involves sufficient condi-tions under which a problem will have a unique solution. At the heart of the approach is themethod of successive approximations. The investigation relies on ideas from classical analysisrather than functional analysis.
The results guarantee that the “error” estimate between the actual and the approximate so-lution goes to zero as the number of iterations are increased indefinitely.
An example regarding the application of the above method to a nonlinear dynamic equationon time scales is also presented. Several open questions will be posed that concern successive ap-proximations in the time scale setting. This talk will be suitable particularly for graduate students.
Keywords: Time scales, successive approximations, dynamic equation.This is joint work with Christopher Tisdell.
153
Application of the WKB estimation method for
determining heat flux on the boundary
ALI ZAKERI
K. N. Toosi University
Department of Mathematics
Tehran, Iran
This talk considers a linear one-dimensional inverse heat conduction problem with noncon-stant thermal diffusivity. It has been associated with the estimation of an unknown boundaryheat flux. For this purpose, by using temperature measurements taken below the boundary sur-face and using a semi-implicit finite difference method, the problem will be converted to a systemof ordinary differential equations of second order depending on a small parameters with initialconditions. Then WKB estimation method gives asymptotic solutions for this system. The solu-tions that are produced in this algorithm make the process ill-posed. Then by choosing suitablevalues of small parameters, this algorithm is modified. Finally, a numerical experiment will bepresented.
AMS Subject Classification: 35R30.Keywords: Inverse problem, implicit finite difference method.
154
Trigonometric and hyperbolic systems on time scales
PETR ZEMANEK
Masaryk University
Department of Mathematics and Statistics
Brno, Czech Republic
http://www.math.muni.cz/˜xzemane2
In this talk we discuss trigonometric and hyperbolic systems on time scales. These systemsgeneralize and unify their corresponding continuous-time and discrete-time analogues, namelythe systems known in the literature as trigonometric and hyperbolic linear Hamiltonian systemsand discrete symplectic systems. We provide time scale matrix definitions of the usual trigono-metric and hyperbolic functions and show that many identities known from the basic calculusextend to this general setting, including the time scale differentiation of these functions.
AMS Subject Classification: 39A12.Keywords: Time scale, Hamiltonian system, trigonometric system.This is joint work with Roman Hilscher.
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156
Other Participants
157
THABET ABDELJAWAD
Cankaya University
Department of Mathematics
Ankara, Turkey
http://math.cankaya.edu.tr/˜thabet
MELTEM ADIYAMAN
Dokuz Eylul University
Department of Mathematics
Izmir, Turkey
MURAT AKMAN
Middle East Technical University
Department of Mathematics
Ankara, Turkey
158
MELTEM ALTUNKAYNAK
Dokuz Eylul University
Department of Mathematics
Ankara, Turkey
KEMAL AYDIN
Selcuk University
Department of Mathematics
Konya, Turkey
MUJGAN BAS
Afyon Kocatepe University
Department of Mathematics
Afyonkarahisar, Turkey
159
MARTIN BOHNER
Missouri University of Science and Technology
Department of Mathematics and Statistics
Rolla, Missouri, USA
http://web.mst.edu/˜bohner
ILKNUR BOZOK
Atılım University
Department of Mathematics
Ankara, Turkey
kuzu [email protected]
GULTER BUDAKCI
Dokuz Eylul University
Department of Mathematics
Izmir, Turkey
160
CANAN CAN
Atılım University
Department of Mathematics
Ankara, Turkey
canan can [email protected]
DUYGU CAYLAK
Dokuz Eylul University
Department of Mathematics
Izmir, Turkey
duygu [email protected]
OKAY CELEBI
Yeditepe University
Department of Mathematics
Istanbul, Turkey
http://www.math.metu.edu.tr/˜celebi
161
CEM CELIK
Dokuz Eylul University
Department of Mathematics
Izmir, Turkey
GULNUR CELIK KIZILKAN
Selcuk University
Department of Mathematics
Konya, Turkey
http://asp.selcuk.edu.tr/asp/personel/
→web/goster.asp?sicil=6228
CENGIZ CINAR
Selcuk University
Department of Mathematics, Education Faculty
Konya, Turkey
162
SEBAHAT EBRU DAS
Yıldız Technical University
Department of Mathematics
Istanbul, Turkey
ASLI DENIZ
Izmir Institute of Technology
Department of Mathematics
Izmir, Turkey
ZHAOYANG DONG
Universitat Autonoma de Barcelona
Departament de Matematiques
Barcelona, Spain
163
MELDA DUMAN
Dokuz Eylul University
Department of Mathematics
Izmir, Turkey
SABER ELAYDI
Trinity University
Department of Mathematics
San Antonio, Texas, USA
http://www.trinity.edu/selaydi
MARIO GETIMANE
Instituto Superior de Transportes e Communicacoes
Department of Mathematics
Maputo, Mozambique
164
IBRAHIM HALIL GUMUS
Selcuk University
Department of Mathematics
Konya, Turkey
VEYSEL FUAT HATIPOGLU
Mugla University
Department of Mathematics
Mugla, Turkey
GOKCE INTEPE
Dokuz Eylul University
Department of Mathematics
Izmir, Turkey
165
KHAJEE JANTARAKHAJORN
Thammasat University
Department of Mathematics and Statistics
Phatumthani, Thailand
http://math.sci.tu.ac.th/people 001.html
RUKIYE KARA
Mimar Sinan University
Department of Mathematics
Istanbul, Turkey
ZEYNEP KAYAR
Middle East Technical University
Department of Mathematics
Ankara, Turkey
166
B ILLUR KAYMAKCALAN
Georgia Southern University
Department of Mathematical Sciences
Statesboro, Georgia, USA
http://math.georgiasouthern.edu/˜billur
YELIZ KIYAK UCAR
Afyon Kocatepe University
Department of Mathematics
Afyonkarahisar, Turkey
SUPACHARA KONGNUAN
Thammasat University
Department of Mathematics and Statistics
Phatumthani, Thailand
http://math.sci.tu.ac.th/people 017.html
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NATALIA KOSAREVA
Moscow Institute of Electronics and Mathematics
Cybernetics Department
Moscow, Russia
YAKOV KULIK
University of New South Wales
School of Physics
Sydney, Australia
V ILDAN KUTAY
Ankara University
Department of Mathematics
Ankara, Turkey
vildan [email protected]
168
ANDREAS LEONHARDT
Technical University Munich
Department of Mathematics
Munich, Germany
GORAN LESAJA
Georgia Southern University
Department of Mathematical Sciences
Statesboro, Georgia, USA
ROBERT L. MARSH
East Georgia College
Mathematics / Science Division
Statesboro, Georgia, USA
http://personal.georgiasouthern.edu/˜rmarsh
169
ADIL MISIR
Gazi University
Department of Mathematics
Ankara, Turkey
MEHMED NURKANOVIC
University of Tuzla
Department of Mathematics
Tuzla, Bosnia and Herzegovina
http://www.pmf.untz.ba
ZEHRA NURKANOVIC
University of Tuzla
Department of Mathematics
Tuzla, Bosnia and Herzegovina
http://www.pmf.untz.ba
170
OZKAN OCALAN
Afyon Kocatepe University
Department of Mathematics
Afyonkarahisar, Turkey
http://www2.aku.edu.tr/˜ozkan
ISRAFIL OKUMUS
Erzincan University
Department of Mathematics
Erzincan, Turkey
UMUT MUTLU OZKAN
Afyon Kocatepe University
Department of Mathematics
Afyonkarahisar, Turkey
umut [email protected]
171
F IGEN OZPINAR
Afyon Kocatepe University
Department of Mathematics
Afyonkarahisar, Turkey
SERMIN OZTURK
Afyon Kocatepe University
Department of Mathematics
Afyonkarahisar, Turkey
ERSIN OZUGURLU
Bahcesehir University
Department of Mathematics
Istanbul, Turkey
172
PARAMEE REANKITTIWAT
Thammasat University
Department of Mathematics and Statistics
Phatumthani, Thailand
http://math.sci.tu.ac.th/people 010.html
ANDREAS RUFFING
Technical University Munich
Department of Mathematics
Munich, Germany
http://www-m6.ma.tum.de/˜ruffing
IPEK SAVUN
Dokuz Eylul University
Department of Mathematics
Izmir, Turkey
ipek [email protected]
173
TUGCEN SELMANOGULLARI
Mimar Sinan University
Department of Mathematics
Istanbul, Turkey
SOPORN SENEETANTIKUL
Thammasat University
Department of Mathematics and Statistics
Phatumthani, Thailand
http://math.sci.tu.ac.th/people 018.html
G IZEM SEYHAN
Ankara University
Department of Mathematics
Ankara, Turkey
174
DAGISTAN S IMSEK
Selcuk University
Department of Mathematics, Education Faculty
Konya, Turkey
http://asp.selcuk.edu.tr/asp/personel/
→web/goster.asp?sicil=5960
WALTER SIZER
Minnesota State University
Department of Mathematics
Moorhead, Minnesota, USA
http://www.mnstate.edu/sizer
ANDREAS SUHRER
Technical University Munich
Department of Mathematics
Munich, Germany
175
NECATI TASKARA
Selcuk University
Department of Mathematics, Education Faculty
Konya, Turkey
NAWALAX THONGJUB
Thammasat University
Department of Mathematics and Statistics
Phatumthani, Thailand
http://math.sci.tu.ac.th/people 006.html
D. TURGUT TOLLU
Selcuk University
Department of Mathematics, Education Faculty
Konya, Turkey
hasan [email protected]
176
DENIZ UCAR
Usak University
Department of Mathematics
Usak, Turkey
MEHMET UNAL
Bahcesehir University
Department of Software Engineering
Istanbul, Turkey
http://web.bahcesehir.edu.tr/munal
SIRICHAN VESARACHASART
Thammasat University
Department of Mathematics and Statistics
Phatumthani, Thailand
http://math.sci.tu.ac.th/people 020.html
177
DOMINIK VU
Vienna University of Technology
Institute of Analysis and Scientific Computing
Vienna, Austria
GULCIN YALAZLAR
Ege University
Department of Mathematics
Izmir, Turkey
sugulu [email protected]
IBRAHIM YALCINKAYA
Selcuk University
Department of Mathematics, Education Faculty
Konya, Turkey
http://asp.selcuk.edu.tr/asp/personel/
→web/goster.asp?sicil=5925
178
MUHAMMED Y IGIDER
Erzincan University
Department of Mathematics
Erzincan, Turkey
m.yigider [email protected]
MUSTAFA KEMAL YILDIZ
Afyon Kocatepe University
Department of Mathematics
Afyonkarahisar, Turkey
OZLEM YILMAZ
Ege University
Department of Mathematics
Izmir, Turkey
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Local Organization Assistants
181
M. ASLI AYDIN
Bahcesehir University
Faculty of Arts and Sciences
Istanbul, Turkey
KEMAL BAYAT
Bahcesehir University
Faculty of Engineering
Istanbul, Turkey
NAZLI CEREN DAGYAR
Bahcesehir University
Faculty of Arts and Sciences
Istanbul, Turkey
182
YAKUP EMUL
Bahcesehir University
Faculty of Arts and Sciences
Istanbul, Turkey
DURDANE ERKAL
Bahcesehir University
Faculty of Arts and Sciences
Istanbul, Turkey
GOKCE KARAHAN
Bahcesehir University
Faculty of Arts and Sciences
Istanbul, Turkey
183
MUSA KARAKELLE
Bahcesehir University
Faculty of Engineering
Istanbul, Turkey
HUSEYIN OZDEMIR
Bahcesehir University
Faculty of Engineering
Istanbul, Turkey
BAHADIR OZEN
Bahcesehir University
Faculty of Engineering
Istanbul, Turkey
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Conference Proceedings
The conference publishes refereed proceedings of accepted papers. The Proceedings are pub-lished by Ugur – Bahcesehir University Publishing Company (ISBN 978-975-6437-80-3). Contrib-utors receive the proceedings free of charge. The deadline to receive submissions prepared usingthe style file available from the conference website is October 31, 2008. The maximum page limitfor contributed talk papers is 8 printed pages. Please send the manuscript to the e-mail of theconference [email protected] or directly to any of the following editors.
Martin BohnerMissouri S&T
Rolla, Missouri, USA
Zuzana DoslaMasaryk University
Brno, Czech Republic
Gerasimos LadasUniversity of Rhode Island
Kingston, Rhode Island, USA
Mehmet UnalBahcesehir University
Istanbul, Turkey
Agacık ZaferMiddle East Technical University
Ankara, Turkey
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Social Program
Sunday, July 20, 2008, 6 pm:
Bahcesehir University invites you to join the Welcome Party at the roof of the Besiktas buildingoverlooking the Bosporus. This event is included in the registration fee.
Monday, July 21, 2008, 6:15 pm:
Sightseeing, free time. Suggestions (on participants’ expenses): Visit to Dolmabahce Palace, Or-takoy, Taksim, Cicek Pasajı, and dinner in the Galata Tower.
Tuesday, July 22, 2008, 6:15 pm:
Sightseeing, free time (on participants’ expenses).
Wednesday, July 23, 2008, 9 am:
Istanbul tour (Topkapı Palace – Ayasofya Mosque – Archeology Museum). The Bosporus yachttour (on private yacht) including dinner starts at 7 pm and will take about 5 hours. The entire daytrip including all admission tickets and including the yacht tour is covered by the registration fee.
Thursday, July 24, 2008, 8 pm:
Bahcesehir University invites you to join the Farewell Dinner at the roof of the Besiktas buildingoverlooking the Bosporus. This event is included in the registration fee.
Friday, July 25, 2008, 6:15 pm:
More sightseeing, free time (on participants’ expenses).
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Maps
ICDEA08 Staff meets you at the exit gate of Ataturk International Airport Terminal from 7:00 to23:30 on July 18–20, 2008 to help your transfer.
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The conference site is on the Besiktas Campus of Bahcesehir University, on the European shoresof the Bosporus, a short walk from the ferry landing of the Besiktas (Europe) – Uskudar (Asia)connection (Besiktas Vapur Iskelesi).
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The address of the Taslık Hotel is Suleyman Seba Caddesi No:75.
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The address of the Yurdum Guest House (female) is Tavukcu Fethi Sokak No:29.
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The address of the Yurdum Guest House (male) is Tas Basamak Sokak No:20.
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About Istanbul
“There, God and human, nature and art are together, they have created such aperfect place that it is valuable to see.” Lamartine’s famous poetic line revealshis love for Istanbul, describing the embracing of two continents, with one armreaching out to Asia and the other to Europe.
Istanbul, once known as the capital of capital cities, has many unique fea-tures. It is the only city in the world to straddle two continents, and the only oneto have been a capital during two consecutive empires – Christian and Islamic.Once capital of the Ottoman Empire, Istanbul still remains the commercial, his-torical and cultural pulse of Turkey, and its beauty lies in its ability to embraceits contradictions. Ancient and modern, religious and secular, Asia and Europe,mystical and earthly all co-exist here.
Its variety is one of Istanbul’s greatest at-tractions: The ancient mosques, palaces, mu-seums and bazaars reflect its diverse history.The thriving shopping area of Taksim buzzeswith life and entertainment. And the serenebeauty of the Bosporus, Princes Islands andparks bring a touch of peace to the otherwisechaotic metropolis.Districts: Adalar, Avcilar, Bagcilar, Bahcelievler,Bakirkoy, Besiktas, Bayrampasa, Beykoz, Beyoglu, Eminonu, Eyup, Fatih, Gazi-osmanpasa, Kadıkoy, Kagithane, Kartal, Kucukcekmece, Pendik, Sarıyer, Sisli,Umraniye, Uskudar, Zeytinburnu, Buyukcekmece, Catalca, Silivri, Sile, Esenler,Gungoren, Maltepe, Sultanbeyli, Tuzla.
Golden Horn: This horn-shaped estuary di-vides European Istanbul. One of the best natu-ral harbours in the world, it was once the cen-tre for the Byzantine and Ottoman navies andcommercial shipping interests. Today, attrac-tive parks and promenades line the shores, apicturesque scene especially as the sun goesdown over the water. At Fener and Balat,neighbourhoods midway up the Golden Horn,
there are entire streets filled with old wooden houses, churches, and synagoguesdating from Byzantine and Ottoman times. The Orthodox Patriarchy resides at
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Fener and a little further up the Golden Horn at Eyup, are some wonderful ex-amples of Ottoman architecture. Muslim pilgrims from all over the world visitEyup Camii and Tomb of Eyup, the Prophet Mohammed’s standard bearer, andit is one of the holiest places in Islam. The area is still a popular burial place,and the hills above the mosque are dotted with modern gravestones interspersedwith ornate Ottoman stones. The Pierre Loti Cafe, atop the hill overlooking theshrine and the Golden Horn, is a wonderful place to enjoy the tranquility of theview.
Beyoglu and Taksim: Beyoglu is an interesting example of a district with European-influenced architecture, from a century before. Europe’s second oldest subway,Tunel was built by the French in 1875, must be also one of the shortest offeringa one-stop ride to start of Taksim. Near to Tunel is the Galata district, whoseGalata Tower became a famous symbols of Istanbul, and the top of which offersa tremendous 180 degree view of the city.
From the Tunel area to Taksim square isone of the city’s focal points for shopping, en-tertainment and urban promenading: IstiklalCadesi is a fine example of the contrasts andcompositions of Istanbul; fashion shops, book-shops, cinemas, markets, restaurants and evenhand-carts selling trinkets and simit (sesamebread snack) ensure that the street is packed throughout the day until late intothe night. The old tramcars re-entered into service, which shuttle up and downthis fascinating street, and otherwise the street is entirely pedestrianised. Thereare old embassy buildings, Galatasaray High School, the colourful ambience ofBalık Pazarı (Fish Bazaar) and restaurants in Cicek Pasajı (Flower Passage). Alsoon this street is the oldest church in the area, St. Mary’s Draperis dating back to1789, and the Franciscan Church of St. Antoine, demolished and then rebuilt in1913.
The street ends at Taksim Square, a huge open plaza, the hub of modern Is-tanbul and always crowded, crowned with an imposing monument celebratingAtaturk and the War of Independence. The main terminal of the new subway isunder the square, adjacent is a noisy bus terminal, and at the north end is theAtaturk Cultural Centre, one of the venues of the Istanbul Theatre Festival. Sev-eral five-star hotels are dotted around this area, like the Hyatt, Intercontinentaland Hilton (the oldest of its kind in the city). North of the square is the IstanbulMilitary Museum.
Taksim and Beyoglu have for centuries been the centre of nightlife, and nowthere are many lively bars and clubs off Istiklal Cadesi, including some of theonly gay venues in the city. Beyoglu is also the centre of the more bohemian artsscene.
Sultanahmet: Many places of tourist interest are concentrated in Sultanahmet,heart of the Imperial Centre of the Ottoman Empire. The most important placesin this area, all of which are described in detail in the Places of Interest section,
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are Topkapı Palace, Aya Sofia, Sultan Ahmet Camii (the Blue Mosque), the Hip-podrome, Kapalı Carsı (Covered Market), Yerebatan Sarnıcı and the Museum ofIslamic Art.
In addition to this wonderful selection ofhistorical and architectural sites, Sultanahmetalso has a large concentration of carpet andsouvenir shops, hotels and guesthouses, cafes,bars and restaurants, and travel agents.Ortakoy: Ortakoy was a resort for the Ot-toman rulers because of its attractive locationon the Bosporus, and is still a popular spot forresidents and visitors. The village is within a
triangle of a mosque, church and synagogue, and is near Cıragan Palace, KabatasHigh School, Feriye, Princess Hotel.
The name Ortakoy reflects the university students and teachers who wouldgather to drink tea and discuss life, when it was just a small fishing village. Thesedays, however, that scene has developed into a suburb with an increasing amountof expensive restaurants, bars, shops and a huge market. The fishing, however,lives on and the area is popular with local anglers, and there is now a huge wa-terfront tea-house which is crammed at weekends and holidays.Sarıyer: The first sight of Sarıyer is where the Bosporus connects with the BlackSea, after the bend in the river after Tarabya. Around this area, old summerhouses, embassies and fish restaurants line the river, and a narrow road whichseparates it from Buyukdere, continues along to the beaches of Kilyos.
Sariyer and Rumeli Kavagı are the final wharfs along the European side vis-ited by the Bosporus boat trips. Both these districts, famous for their fish restau-rants along with Anadolu Kavagı, get very crowded at weekends and holidayswith Istanbul residents escaping the city.
After these points, the Bosporus is lined with tree-covered cliffs and littlehabitation. The Sadberk Hanım Museum, just before Sarıyer, is an interestingplace to visit; a collection of archaeological and ethnographic items, housed intwo wooden houses. A few kilometres away is the huge Belgrade Forest, once ahaunting ground of the Ottomans, and now a popular weekend retreat into thelargest forest area in the city.Uskudar: Relatively unknown to tourists, thesuburb of Uskudar, on the Asian side of theBosporus, is one of the most attractive suburbs.Religiously conservative in its background, ithas a tranquil atmosphere and some fine ex-amples of imperial and domestic architecture.The Iskele, or Mihrimah Camii is opposite themain ferry pier, on a high platform with a hugecovered porch in front, often occupied by olderlocal men watching life around them. Opposite this is Yeni Valide Camii, built in
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1710, and the Valide Sultan’s green tomb rather like a giant birdcage. The CiniliMosque takes its name from the beautiful tiles which decorate the interior, andwas built in 1640.
Apart from places of religious interest, Uskudar is also well known as a shop-ping area, with old market streets selling traditional local produce, and a goodfleamarket with second hand furniture. There are plenty of good restaurants andcafes with great views of the Bosporus and the rest of the city, along the quayside.In the direction of Haydarpasa is the lhe Karaca Ahmet Cemetery, the largestMuslim graveyard in Istanbul. The front of the Camlıca hills lie at the ridge ofarea and also offer great panoramic views of the islands and river.Kadıkoy: Further south along the Bosporus towards the Sea of Marmara, Kadıkoyhas developed into a lively area with up-market shopping, eating and entertain-ment making it popular especially with wealthy locals. Once prominent in thehistory of Christianity, the 5th century hosted important consul meetings here,but there are few reminders of that age. It is one of the improved districts ofIstanbul over the last century, and fashionable area to promenade along the wa-terfront in the evenings, especially around the marinas and yacht clubs.
Bagdat Caddesi is one of the most trendy and label-conscious fashion shop-ping streets, and for more down-to-earth goods, the Gen Azım Gunduz Caddesiis the best place for clothes, and the bit pazarı on Ozelellik Sokak is good forbrowsing through junk. In the district of Moda is the Benadam art gallery, as wellas many foreign cuisine restaurants and cafes.Haydarpasa: To the north of Kadıkoy is Haydarpasa, and the train station builtin 1908 with Prussain-style architecture which was the first stop along the Bagh-dad railway. Now it is the main station going to eastbound destinations bothwithin Turkey, and internationally. There are tombs and monuments dedicatedto the English and French soldiers who lost their lives during the Crimean War(1854–56), near the military hospital. The north-west wing of the 19th CenturySelimiye Barracks once housed the hospital, used by Florence Nightingale to carefor soldiers, and remains to honour her memory.Polonezkoy: Polonezkoy, although still within the city, is 25 km away from thecentre and not easy to reach by public transport. Translated as village of thePoles, the village has a fascinating history: It was established in 1848 by PrinceCzartorisky, leader of the Polish nationals who was granted exile in the OttomanEmpire to escape oppression in the Balkans. During his exile, he succeeded inestablishing a community of Balkans, which still survives, on the plot of landsold to him by a local monastery.
Since the 1970s the village has become a popular place with local Istanbu-lites, who buy their pig meat there (pig being forbidden under Islamic law andtherefore difficult to get elsewhere). All the Poles have since left the village, andthe place is inhabited now by wealthy city people, living in the few remainingCentral European style wooden houses with pretty balconies.
What attracts most visitors to Polonezkoy is its vast green expanse, whichwas designated Istanbul’s first national park, and the walks though forests with
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streams and wooden bridges. Because of its popularity, it gets crowded at week-ends and the hotels are usually full.
Kilyos: Kilyos is the nearest beach resort to the city, on the Black Sea coast on theEuropean side of the Bosporus. Once a Greek fishing village, it has quickly beendeveloped as a holiday-home development, and gets very crowded in summer.Because of its ease to get there, 25 km and plenty of public transport, it is good fora day trip, and is a popular weekend getaway with plenty of hotels, and a coupleof campsites.
Sile: A pleasant, small holiday town, Sile lies 50 km from Uskudar on the BlackSea coast and some people even live here and commute into Istanbul. The whitesandy beaches are easily accessible from the main highway, lying on the west,as well as a series of small beaches at the east end. The town itself if perchedon a clifftop over looking the bay tiny island. There is an interesting French-built black-and-white striped lighthouse, and 14th century Genoese castle on thenearby island. Apart from its popular beaches, the town is also famous for itscraft; Sile bezi, a white muslin fabric a little like cheesecloth, which the localwomen embroider and sell their products on the street, as well as all over Turkey.
The town has plenty of accommodation available, hotels, guest houses andpansiyons, although can get very crowded at weekends and holidays as it is verypopular with people from Istanbul for a getaway, especially in the summer. Thereare small restaurants and bars in the town.
Prince’s Islands: Also known as Istanbul Islands, there are eight within one hourfrom the city, in the Marmara Sea. Boats ply the islands from Sirkeci, Kabatasand Bostancı, with more services during the summer. These islands, on whichmonasteries were established during the Byzantine period, were a popular sum-mer retreat for palace officials. It is still a popular escape from the city, withwealthier owning summer houses.
The largest and most popular is Buyukada(the Great Island). Large wooden man-sions still remain from the 19th century whenwealthy Greek and Armenian bankers builtthem as holiday villas. The island has alwaysbeen a place predominantly inhabited by mi-norities, hence Islam has never had a strongpresence here. Buyukada has long had a his-tory of people coming here in exile or retreat;its most famous guest being Leon Trotsky, who stayed for four years writing ‘TheHistory of the Russian Revolution’. The monastery of St. George also played hostto the granddaughter of Empress Irene, and the royal princess Zoe, in 1012. Theisland consists of two hills, both surmounted by monasteries, with a valley be-tween. Motor vehicles are banned, so getting around the island can be done bygraceful horse and carriage, leaving from the main square off Isa Celebi Sokak.Bicycles can also be hired. The southern hill, Yule Tepe, is the quieter of the twoand also home of St. George’s Monastery. It consists of a series of chapels on three
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levels, the site of which is a building dating back to the 12th century. In Byzan-tine times it was used as an asylum, with iron rings on the church floors used torestrain patients. On the northern hill is the monastery Isa Tepe, a 19th centuryhouse. The entire island is lively and colourful, with many restaurants, hotels,tea houses and shops. There are huge well-kept houses, trim gardens, and pinegroves, as well as plenty of beach and picnic areas.
Smaller and less of a tourist infrastructure is Burgazada. The famous Turkishnovelist, Sait Faik Abasiyanik lived here, and his house has been turned into amuseum dedicated to his work, and retains a remarkable tranquil and hallowedatmosphere.
Heybeliada, ‘Island of the Saddlebag’, be-cause of its shape, is loved for its naturalbeauty and beaches. It also has a highlyprestigious and fashionable watersports clubin the northwest of the island. One of itsbest-known landmarks is the Greek OrthodoxSchool of Theology, with an important collec-tion of Byzantine manuscripts. The school sitsloftily on the northern hill, but permission is
needed to enter, from the Greek Orthodox Patriarchate in Fener. The Deniz HarpOkulu, the Naval High School, is on the east side of the waterfront near the jetty,which was originally the Naval War Academy set up in 1852, then a high schoolsince 1985. Walking and cycling are popular here, plus isolated beaches as wellas the public Yoruk Beach, set in a magnificent bay. There are plenty of goodlocal restaurants and tea houses, especially along Ayyıldız Caddesi, and the at-mosphere is one of a close community.
Environment: Wide beaches of Kilyos at European side of Black Sea at 25th kmoutside Istanbul, are attracting Istanbul residents during summer months. Bel-grade Forest, inside from Black Sea, at European Side is the widest forest aroundIstanbul. Istanbul residents, at weekends, come here for family picnic with bra-zier at its shadows. 7 old water tank and some natural resources in the regioncompose a different atmosphere. Moglova Aqueduct, which is constructed byMimar Sinan during 16th century among Ottoman aqueducts, is the greatest one.800 m long Sultan Suleyman Aqueduct, which is passing over Golf Club, and alsoa piece of art of Mimar Sinan is one of the longest aqueducts within Turkey.
Polonezkoy, which is 25 km away from Istanbul, is founded at Asia coastduring 19th century by Polish immigrants. Polonezkoy, for walking in villageatmosphere, travels by horse, and tasting traditional Polish meals served by rel-atives of initial settlers, is the resort point of Istanbul residents. Beaches, restau-rants and hotels of Sile at Black Sea coast and 70 km away from Uskudar, areturning this place into one of the most cute holiday places of Istanbul. Regionwhich is popular in connection with tourism, is the place where famous Sile clothis produced.
Bayramoglu - Darica Bird Paradise and Botanic Park is a unique resort place
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38 km away from Istanbul. This gargantuan park with its trekking roads, restau-rants is full of bird species and plants, coming from various parts of the world.
Sweet Eskihisar fisherman borough, towhose marina can be anchored by yachtsmenafter daily voyages in Marmara Sea is at southeast of Istanbul. Turkey’s 19th century famouspainter, Osman Hamdi Bey’s house in boroughis turned into a museum. Hannibal’s tomb be-tween Eskihisar and Gebze is one of the sitesaround a Byzantium castle.
There are lots of Istanbul residents’ sum-mer houses in popular holiday place 65 km away from Istanbul, Silivri. This is ahuge holiday place with magnificent restaurants, sports and health centers. Con-ference center is also attracting businessmen, who are escaping rapid tempo ofurban life for “cultural tourism” and business - holiday mixed activities. Sched-uled sea bus service is connecting Istanbul to Silivri.
Islands within Marmara Sea, which is adorned with nine islands, was thebanishing place of the Byzantium princes. Today they are now wealthy Istanbulresidents’ escaping places for cool winds during summer months and 19th cen-tury smart houses. The biggest one of the islands is Buyukada. You can have amarvelous phaeton travel between pine trees or have a swim within one of thenumerous bays around islands!
Other popular islands are Kınali, Sedef, Burgaz and Heybeliada. Regularferry voyages are connecting islands to both Europe and Asia coasts. There is arapid sea bus service from Kabatas during summers.
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Useful Information
Airport
Istanbul has two airports, the major Ataturk International Airport on the Euro-pean shore of the Sea of Marmara and Sabiha Gokcen Airport on the east sideof the Bosporus. Most long-haul international flights to Turkey land at AtaturkInternational Airport (IST) 23 km (14 miles) west of the city center at Yesilkoy.ICDEA08 Staff will meet you at the exit gate of Ataturk International AirportTerminal and help your transfer. The modern International Terminal (Dis Hat-lar Terminali) is spacious and efficient, with all the expected services includingATMs (cash machines) from which you can obtain New Turkish Liras, currencyexchange offices, restaurants, cafes, shops, Emanet (Baggage Check, Left Lug-gage). An underground passage (15-minute walk) connects the International Ter-minal with the older Domestic Terminal (Ic Hatlar Terminali) and also the Istan-bul Metro, called the Hafif Metro (”Light rail system”) on airport terminal signs.You can board a Metro train right from the airport and ride to Zeytinburnu, whereyou can transfer to the Zeytinburnu-Besiktas tram for the ride to SultanahmetSquare, Sirkeci Station, the Eminonu ferry and Sea Bus docks, the Galata Bridge,Karakoy and its ferry docks, and the Kabatas ferry docks and Funikuler to Tak-sim Square. A faster way to Taksim Square is by express city bus 96T, stoppingat Yenikapi, Aksaray and Taksim. A taxi from the airport to Sultanahmet costsabout US$18 to $25; to Taksim Square, about US$21 to $26; add 50% if you travelbetween 24:00 (midnight) and 06:00 am. The trip takes between 35 and 75 min-utes, depending on traffic. Havas airport buses, long the mainstay of airport-citytransfers, are being phased out. Traditionally, they departed the Arrivals level ofboth the International and Domestic terminals. The trip to Taksim takes between45 and 65 minutes, depending upon traffic.
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Passport and visa
Most of the travelers to Turkey require a visa. For most of them visas can beobtained at the port of entry in Turkey or from the Turkish Consulate Generalor Turkish Diplomatic Missions of their home countries. Sticker type visas areissued at the port of entry and allow staying in Turkey for up to 90 days. It isadvisable to have a minimum of six months validity on your passport from thedate of your entry into Turkey.
Banking and currency
The currency of Turkey is New Turkish Lira (YTL) as of 1 January 2005. 1YTLequals to 100 New Kurus (YKR) Banknotes come in 1YTL, 5YTL, 10YTL, 20YTL,50YTL & 100YTL and coins come in 1, 5YKR, 10YKR, 25YKR and 50YKR and1YTL. Currency exchange facilities are available in all banks, hotels and airports.24 hour cash machines providing banking services by different banks are locatedat suitable points throughout the 3 terminals of Antalya Airport. US dollars andEuros are also widely accepted. Credit cards are accepted at most restaurants andshops, the most widely used being MasterCard & Visa. Please kindly note thatAmerican Express, Diners Club and JCB Cards are not commonly accepted.
Business hours
Banks are generally open from 09:30–16:00 hours Monday–Friday. General officehours are 09:00–17:00 Monday–Friday. Post offices operate within these hours,however stamps are often available from hotels.
Electricity
Turkey operates on 220 volts, 50 Hz, with round-prong European-style plugs thatfit into recessed wall sockets/points. Check your appliances before leaving hometo see what you’ll need to plug in when you travel in Turkey. Many appliancessuch as laptop computers and digital cameras with their own power adapterscan be plugged into either 120-volt or 220-volt sockets/points and will adapt to
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the voltage automatically. But you will need a plug adaptor that can fit into therecessed wall socket/point. Read the technical stuff on your power adapter tosee “INPUT: A.C. 100-240V”. If it reads that way, it can operate on either 120 or220 voltage. If it says something like “INPUT: 100-125V”, then it can’t run onTurkey’s 220 volts and you’ll need to bring a voltage converter.
Shopping
Shops are usually open between 8:30–19:00 and usually closed on Sunday. Turkey,as a result of its geographical location, is a treasure-house of hand-made products.These range from carpets and kilims, to gold and silver jewelry, ceramics, leatherand suede clothing, ornaments fashioned from alabaster, onyx, copper, and meer-schaum. When purchasing carpets, jewellery or leather products, it is advisableto consult your guide or do your shopping at a reputable store rather than in thestreet from vendors.
Tax refund
All goods and services in Turkey are applicable to 18% Value Added Tax. Youcan receive a tax refund for the goods you purchased in Turkey. Refunds willbe made to travelers who do not reside in Turkey. All goods are included inthe refunds with the exclusion of services rendered and the minimum amount ofpurchase that qualifies for refund is 5YTL. Retailers that qualify for tax refundsmust be “AUTHORIZED FOR REFUND”. These retailers must display a permitreceived from their respective tax office. The retailer will make four copies ofthe receipt for your refund, three of which will be received by the purchaser.If photocopies of the receipt are received the retailer must sign and stamp thecopies to validate them. If you prefer the refund to be made by check, a Tax-freeShopping Check for the amount to be refunded to the customer must be givenalong with the receipt. For the purchaser to benefit from this exemption he mustleave the country within three months with the goods purchased showing themto Turkish customs officials along with the appropriate receipts and or check.There are four ways to receive your refund:
1. If the retailer gives you a check, it can he cashed at a bank in the customsarea at the airport.
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2. If customer sends a copy of the receipt to the retailer showing that the goodshave left the country within one month, the retailer will send a bank transferto the purchaser’s bank or credit card within ten days upon receiving thereceipt.
3. If the certified receipt and check are brought back to the retailer on a sub-sequent visit thin one-month of the date of customs certification, the refundcan be made directly to the purchaser.
4. The refund may be made by the organization of those companies that areauthorized to make tax refunds.
Geography
The summer months in Istanbul are generally hot and quite humid. The winterscan be cold and wet, although not as extreme as other areas of the country. Thesea temperature is creep up to 30 degrees in June, July and August, with verylittle rain. Spring and autumn are popular times to visit because of the comfort-able climate, good for lots of walking and sightseeing, with highs between 15–25degrees C, in April, May, September and October. By the winter, the dry cold airmass from the Black Sea and cold damp front from the Balkans brings a chillyseason with daytime highs of between 10–15 degrees C, and nights much colder.Although rarely falling to freezing point, there is the occasional light snow in thecity.
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Index and E-mail Addresses
209
A
Abdeljawad, Thabet (Turkey), [email protected]
158Abderraman, Jesus (Spain), [email protected]
21, 22, 54Adıvar, Murat (Turkey), [email protected]
17, 18, 25, 55Adıyaman, Meltem (Turkey), [email protected]
158Afshar Kermani, Mozhdeh (Iran), mog [email protected]
29, 30, 56Agarwal, Ravi (USA), [email protected]
15, 16, 31, 36Aghazadeh, Nasser (Iran), [email protected]
17, 18, 57Akın-Bohner, Elvan (USA), [email protected]
19, 20, 31, 37Akman, Murat (Turkey), [email protected]
158Albayrak, Incı (Turkey), [email protected]
17, 18, 58Aldea Mendes, Diana (Portugal), [email protected]
17, 18, 59Alseda, Lluıs (Spain), [email protected]
17, 19, 20, 31, 38Al-Sharawi, Ziyad (Oman), [email protected]
25, 26, 60Altunkaynak, Meltem (Turkey), [email protected]
159Alzabut, Jehad (Turkey), [email protected]
25, 26, 61Appleby, John (Ireland), [email protected]
17, 21, 22, 62Aseeri, Samar (Saudi Arabia), [email protected]
29, 30, 63Atasever, Nurıye (Turkey), atasever [email protected]
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17, 18, 64Atay, Fatıhcan M. (Germany), [email protected]
29, 30, 65Atıcı, Ferhan (USA), [email protected]
21, 22, 66Awerbuch Friedlander, Tamara (USA), [email protected]
17, 18, 25, 67Aydın, Kemal (Turkey), [email protected]
159Aydın, M. Aslı (Turkey), [email protected]
182
B
Bas, Mujgan (Turkey), [email protected]
159Batıt, Ozlem (Turkey), [email protected]
29, 30, 68Bayat, Kemal (Turkey), [email protected]
182Bernhardt, Chris (USA), [email protected]
17, 18, 69Bodine, Sigrun (USA), [email protected]
17, 25, 26, 70Bohner, Martin (USA), [email protected]
3, 5, 11, 15, 160, 185Bolat, Yasar (Turkey), [email protected]
29, 30, 71Bozok, Ilknur (Turkey), kuzu [email protected]
160Budakcı, Gulter (Turkey), [email protected]
160
C
Cakmak, Devrım (Turkey), [email protected]
25, 26, 72Camouzis, Elias (Greece), [email protected]
17, 21, 22, 73
211
Can, Canan (Turkey), canan can [email protected]
161Canovas, Jose S. (Spain), [email protected]
17, 18, 74Caylak, Duygu (Turkey), duygu [email protected]
161Celebi, Okay (Turkey), [email protected]
3, 27, 161Celık, Cem (Turkey), [email protected]
162Celık Kızılkan, Gulnur (Turkey), [email protected]
162Cetın, Erbıl (Turkey), [email protected]
25, 26, 75Cıbıkdıken, Alı Osman (Turkey), [email protected]
21, 22, 76Cınar, Cengız (Turkey), [email protected]
162Costa, Sara (Spain), [email protected]
17, 18, 77Cushing, J. M. (USA), [email protected]
11, 23, 25, 26, 78
D
Dagyar, Nazlı Ceren (Turkey), [email protected]
182Dannan, Fozi (Syria), [email protected]
25, 26, 79Das, Sebahat Ebru (Turkey), [email protected]
163Denız, Aslı (Turkey), [email protected]
163Dong, Zhaoyang (Spain), [email protected]
163Dosla, Zuzana (Czech Republic), [email protected]
5, 19, 25, 26, 80, 185
212
Dosly, Ondrej (Czech Republic), [email protected]
27, 28, 31, 39Duman, Ahmet (Turkey), [email protected]
21, 22, 81Duman, Melda (Turkey), [email protected]
164
E
Elaydi, Saber (USA), [email protected]
5, 9, 11, 164Emul, Yakup (Turkey), [email protected]
183Erbe, Lynn (USA), [email protected]
17, 18, 21, 82Erkal, Durdane (Turkey), [email protected]
183Erol, Meltem (Turkey), [email protected]
29, 30, 83Esty, Norah (USA), [email protected]
17, 18, 25, 84
F
Fernandes, Sara (Portugal), [email protected]
21, 22, 85
G
Gesztesy, Fritz (USA), [email protected]
19, 20, 23, 31, 40Getimane, Mario (Mozambique), [email protected]
164Gomes, Orlando (Portugal), [email protected]
17, 18, 86Gumus, Ibrahım Halıl (Turkey), [email protected]
165Gumus, Ozlem Ak (Turkey), [email protected]
25, 26, 87
213
Gurses, Metin (Turkey), [email protected]
5Guseinov, Gusein (Turkey), [email protected]
5, 25, 26, 88Guvenılır, A. Feza (Turkey), [email protected]
29, 30, 89Guzowska, Małgorzata (Poland), [email protected]
25, 26, 90Gyori, Istvan (Hungary), [email protected]
11, 15, 16, 31, 41
H
Hashemiparast, Moghtada (Iran), [email protected]
17, 18, 91Hatıpoglu, Veysel Fuat (Turkey), [email protected]
165Heim, Julius (USA), [email protected]
21, 22, 92Hilger, Stefan (Germany), [email protected]
15, 16, 25, 32, 42Hilscher, Roman (Czech Republic), [email protected]
15, 17, 18, 93
I
Intepe, Gokce (Turkey), [email protected]
165
J
Jantarakhajorn, Khajee (Thailand), [email protected]
166Jimenez Lopez, Vıctor (Spain), [email protected]
17, 18, 94
K
Kalabusic, Senada (Bosnia/Herz.), [email protected]
17, 18, 95
214
Karahan, Gokce (Turkey), [email protected]
183
Karakelle, Musa (Turkey), [email protected]
184
Kara, Rukıye (Turkey), [email protected]
166
Karpuz, Basak (Turkey), [email protected]
25, 26, 96
Kayar, Zeynep (Turkey), [email protected]
166
Kaymakcalan, Bıllur (USA), [email protected]
5, 15, 167
Keller, Christian (USA), [email protected]
21, 22, 97
Kent, Candace (USA), [email protected]
17, 21, 22, 98
Kharkov, Vitaliy (Ukraine), kharkov v [email protected]
25, 26, 99
Kipnis, Mikhail (Russia), [email protected]
25, 26, 100
Kıyak Ucar, Yelız (Turkey), [email protected]
167
Kloeden, Peter (Germany), [email protected]
5, 27, 28, 32, 43
Kocak, Huseyin (USA), [email protected]
19, 20, 32, 44
Kongnuan, Supachara (Thailand), [email protected]
167
Kosareva, Natalia (Russia), [email protected]
168
Kostrov, Yevgeniy (USA), [email protected]
21, 22, 101
Kratz, Werner (Germany), [email protected]
6
Kulik, Tomasia (Australia), [email protected]
21, 22, 102
215
Kulik, Yakov (Australia), [email protected]
168Kutay, Vıldan (Turkey), vildan [email protected]
168
L
Ladas, Gerasimos (USA), [email protected]
3, 12, 15, 27, 28, 32, 45, 185Laitochova, Jitka (Czech Republic), [email protected]
21, 22, 29, 103Lawrence, Bonita (USA), [email protected]
21–23, 104Leonhardt, Andreas (Germany), [email protected]
169Lesaja, Goran (USA), [email protected]
169Luıs, Rafael (Portugal), [email protected]
25, 26, 105Lutz, Donald (USA), [email protected]
6
M
Marsh, Robert L. (USA), [email protected]
169Matthews, Thomas (USA), [email protected]
21, 22, 106Mawhin, Jean (Belgium), [email protected]
6, 23, 24, 32, 46McCarthy, Michael (Ireland), [email protected]
21, 22, 107Mendes, Vivaldo (Portugal), [email protected]
17, 18, 21, 108Mert, Razıye (Turkey), [email protected]
25, 26, 109Mesgarani, Hamid (Iran), [email protected]
29, 30, 110
216
Michor, Johanna (USA), [email protected]
25, 29, 30, 111Migda, Małgorzata (Poland), [email protected]
29, 30, 112Mısır, Adıl (Turkey), [email protected]
170Morales, Leopoldo (Spain), [email protected]
21, 22, 113
N
Nishimura, Kazuo (Japan), [email protected]
7Nurkanovic, Mehmed (Bosnia/Herz.), [email protected]
170Nurkanovic, Zehra (Bosnia/Herz.), [email protected]
170
O
Oban, Volkan (Turkey), [email protected]
17, 18, 114Oberste-Vorth, Ralph (USA), [email protected]
17, 18, 115Ocalan, Ozkan (Turkey), [email protected]
29, 171Okumus, Israfıl (Turkey), [email protected]
171Oliveira, Henrique (Portugal), [email protected]
7, 21, 22, 116O’Regan, Donal (Ireland), [email protected]
6Ozdemır, Huseyın (Turkey), [email protected]
184Ozen, Bahadır (Turkey), [email protected]
184Ozkan, Umut Mutlu (Turkey), umut [email protected]
171
217
Ozpınar, Fıgen (Turkey), [email protected]
172Ozturk, Rukıye (Turkey), [email protected]
25, 26, 117Ozturk, Sermın (Turkey), [email protected]
172Ozugurlu, Ersın (Turkey), [email protected]
172
P
Papaschinopoulos, Garyfalos (Greece), [email protected]
17, 18, 118Park, Choonkil (South Korea), [email protected]
25, 26, 119Peterson, Allan (USA), [email protected]
6, 12, 15, 16, 19, 32, 47Pinelas, Sandra (Portugal), [email protected]
17, 18, 21, 120Pituk, Mihaly (Hungary), [email protected]
25, 26, 29, 121Popescu, Emil (Romania), [email protected]
123Popescu, Nedelia Antonia (Romania), [email protected]
17, 29, 30, 124Pop, Nicolae (Romania), [email protected]
17, 18, 122Pospısil, Zdenek (Czech Republic), [email protected]
25, 26, 125Potzsche, Christian (Germany), [email protected]
19, 21, 22, 126Predescu, Mihaela (USA), [email protected]
17, 18, 21, 127
R
Rabbani, Mohsen (Iran), [email protected]
29, 30, 128
218
Rachidi, Mustapha (France), [email protected]
21, 22, 129Radin, Michael (USA), [email protected]
21, 22, 130Rasmussen, Martin (Germany), [email protected]
21, 22, 131Reankittiwat, Paramee (Thailand), [email protected]
173Rehak, Pavel (Czech Republic), [email protected]
25, 26, 132Reinfelds, Andrejs (Latvia), [email protected]
21, 22, 25, 133Rodkina, Alexandra (Jamaica), [email protected]
21, 22, 134Romero i Sanchez, David (Spain), [email protected]
29, 30, 135Ruffing, Andreas (Germany), [email protected]
7, 12, 173
S
Sacker, Robert J. (USA), [email protected]
7, 12Saker, Samir (Saudi Arabia), [email protected]
136Sanchez-Moreno, Pablo (Spain), [email protected]
29, 30, 137Savun, Ipek (Turkey), ipek [email protected]
173Schinas, Christos (Greece), [email protected]
17, 18, 138Schmeidel, Ewa (Poland), [email protected]
29, 30, 139Sekercı, Nurcan (Turkey), [email protected]
21, 22, 140Sell, George (USA), [email protected]
11
219
Selmanogulları, Tugcen (Turkey), [email protected]
174Seneetantikul, Soporn (Thailand), [email protected]
174Seyhan, Gızem (Turkey), [email protected]
174Shahrezaee, Mohsen (Iran), [email protected]
17, 18, 141Sharkovsky, Alexander (Ukraine), [email protected]
6Siddikov, Bakhodirzhon (USA), [email protected]
17, 18, 29, 142Simon, Moritz (Germany), [email protected]
25, 26, 143Sımsek, Dagıstan (Turkey), [email protected]
175Sırma, Alı (Turkey), [email protected]
29, 30, 144Sizer, Walter (USA), [email protected]
175Smith, Hal (USA), [email protected]
23, 24, 33, 48Stefanidou, Gesthimani (Greece), [email protected]
21, 22, 145Stehlik, Petr (Czech Republic), [email protected]
17, 18, 146Suhrer, Andreas (Germany), [email protected]
175
T
Taskara, Necatı (Turkey), [email protected]
176Teschl, Gerald (Austria), [email protected]
6, 19, 25, 26, 147Thongjub, Nawalax (Thailand), [email protected]
176
220
Tıryakı, Aydın (Turkey), [email protected]
3, 25, 26, 148Tlemcani, Mouhaydine (Portugal), [email protected]
21, 22, 149Tollu, D. Turgut (Turkey), hasan [email protected]
176Topal, Fatma Serap (Turkey), [email protected]
29, 30, 150
U
Ucar, Denız (Turkey), [email protected]
177Unal, Mehmet (Turkey), [email protected]
1, 3, 177, 185
V
Vanderbauwhede, Andre (Belgium), [email protected]
19, 20, 33, 49Vesarachasart, Sirichan (Thailand), [email protected]
177Vu, Dominik (Austria), [email protected]
178
Y
Yalazlar, Gulcın (Turkey), sugulu [email protected]
178Yalcınkaya, Ibrahım (Turkey), [email protected]
178Yantır, Ahmet (Turkey), [email protected]
17, 18, 151Yıgıder, Muhammed (Turkey), m.yigider [email protected]
179Yıldırım, Ahmet (Turkey), [email protected]
29, 30, 152Yıldız, Mustafa Kemal (Turkey), [email protected]
179
221
Yılmaz, Ozlem (Turkey), [email protected]
179Yorke, James A. (USA), [email protected]
23, 24, 33, 50Yoruk, Fulya (Turkey), fulya [email protected]
180
Z
Zafer, Agacık (Turkey), [email protected]
3, 23, 24, 29, 33, 51, 185Zaidi, Atiya (Australia), [email protected]
21, 22, 153Zakeri, Ali (Iran), [email protected]
29, 30, 154Zeidan, Vera (USA), [email protected]
15–17, 33, 52Zemanek, Petr (Czech Republic), [email protected]
29, 30, 155
222