18
1 COMPARSION OF COMPRESSION STRENGTH OF CONVENTIONAL CONCRETE WITH SELF-CURING CONCRETE BY USING POLYETHYLENE GLYCOL Anish C 1 , Thendral S 2 Assistant Professor 1,2 ,Department of Civil Engineering 1,2 BIST, BIHER, Bharath University [email protected] . ABSTRACT A self-curing concrete is given to retain water from air to accomplish better hydration of bond in solid which takes care of the issue of brought down bond hydration in light of disgraceful curing, and in this manner unsuitable properties of cement. The present examination includes the utilization of self-curing specialist viz., polyethylene glycol (PEG) of sub-atomic weights (PEG 400) for measurements extending between 1% 2% and 3% by weight of concrete added to blending water.Near investigations were completed for water retentively, compressive quality following 28 days for ordinary cured and self-cured cement. The properties of self-cured cement are at any rate tantamount to and at some point superior to those of cement with customary curing. INTRODUCTION CURING Curing of concrete is maintaining satisfactory moisture content in concrete during its early stages in order to develop the desired properties. However, good curing is not always practical in many cases[1-7]. Several investigators explored the possibility of accomplishing self- curing concrete. Therefore, the need to develop self-curing agents attracted several researchers. SELF CURING The concept of self-curing agents is to reduce the water evaporation from concrete, and hence increase the water retention capacity of the concrete compared to conventional concrete . It was found that water soluble polymers can be used as self-curing agents in concrete. Concrete incorporating self-curing agents will represent a new trend in the concrete construction in the new millennium[8-14]. Curing of concrete plays a major role in developing the concrete microstructure and pore structure, and hence improves its durability and performance. The concept of self-curing agents is to reduce the water evaporation from concrete, and hence increase the water retention capacity of the concrete compared to conventional concrete. The use of self-curing admixtures is very important from the point of view that water resources are getting valuable every day (i.e., each 1cu.m of concrete requires about 3cu.m of water for construction most of which is for curing). International Journal of Pure and Applied Mathematics Volume 119 No. 12 2018, 8421-8438 ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu Special Issue ijpam.eu 8421

COMPARSION OF COMPRESSION ST RENGTH OF … · 1 COMPARSION OF COMPRESSION ST RENGTH OF CONVENTIONAL CONCRETE WITH SELF -CURING CONCRETE BY USING POLYETHYLENE GLYCOL Anish C 1, Thendral

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1

COMPARSION OF COMPRESSION STRENGTH OF CONVENTIONAL CONCRETE

WITH SELF-CURING CONCRETE BY USING POLYETHYLENE GLYCOL

Anish C1, Thendral S

2

Assistant Professor1,2

,Department of Civil Engineering 1,2

BIST, BIHER, Bharath University

[email protected] .

ABSTRACT

A self-curing concrete is given to retain water from air to accomplish better hydration of bond in

solid which takes care of the issue of brought down bond hydration in light of disgraceful curing,

and in this manner unsuitable properties of cement. The present examination includes the

utilization of self-curing specialist viz., polyethylene glycol (PEG) of sub-atomic weights (PEG

400) for measurements extending between 1% 2% and 3% by weight of concrete added to

blending water.Near investigations were completed for water retentively, compressive quality

following 28 days for ordinary cured and self-cured cement. The properties of self-cured cement

are at any rate tantamount to and at some point superior to those of cement with customary

curing.

INTRODUCTION

CURING

Curing of concrete is maintaining satisfactory moisture content in concrete during its

early stages in order to develop the desired properties. However, good curing is not always

practical in many cases[1-7]. Several investigators explored the possibility of accomplishing self-

curing concrete. Therefore, the need to develop self-curing agents attracted several researchers.

SELF CURING

The concept of self-curing agents is to reduce the water evaporation from concrete, and

hence increase the water retention capacity of the concrete compared to conventional concrete. It

was found that water soluble polymers can be used as self-curing agents in concrete. Concrete

incorporating self-curing agents will represent a new trend in the concrete construction in the

new millennium[8-14].

Curing of concrete plays a major role in developing the concrete microstructure and pore

structure, and hence improves its durability and performance. The concept of self-curing agents

is to reduce the water evaporation from concrete, and hence increase the water retention capacity

of the concrete compared to conventional concrete. The use of self-curing admixtures is very

important from the point of view that water resources are getting valuable every day (i.e., each

1cu.m of concrete requires about 3cu.m of water for construction most of which is for curing).

International Journal of Pure and Applied MathematicsVolume 119 No. 12 2018, 8421-8438ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

8421

2

Excessive evaporation of water (internal or external) from fresh concrete should be

avoided; otherwise, the degree of cement hydration would get lowered and thereby concrete may

develop unsatisfactory properties. Curing operations should ensure that adequate amount of

water is available for cement hydration to occur[15-19].

This investigation discusses different aspects of achieving optimum cure of concrete

without the need for applying external curing methods. The effect of curing, particularly new

techniques such as "self-curing", on the properties of high performance concrete is of primary

importance to the modern concrete industry.

MECHANISM OF SELF CURING

The mechanism of self-curing can be explained as follows:

Continuous evaporation of moisture takes place from an exposed surface due to the

difference in chemical potentials (free energy) between the vapor and liquid phases.

The polymers added in the mix mainly form hydrogen bonds with water molecules and

reduce the chemical potential of the molecules which in turn reduces the vapor pressure

which reduces the rate of evaporation from the surface.

OBJECTIVES

In this study the compressive strength of concrete containing self-curing agent is

investigated and compared with conventional curing. Concrete strength with the age of concrete

was carried out in order to evaluate the compressive strength for different dosages of self-curing

agent and for different conditions[20-26].

The objective of the paper is to study the effect of polyethylene glycol (PEG 400) on

strength characteristics of Self-curing concrete. The objective is to study the mechanical

characteristic of concrete i.e., compressive strength by varying the percentage of PEG from 1%

to 3% by weight of cement for both M20 grade of concrete[27-35]. The objective is study the

mechanical characteristics of concrete such as compressive strength, by varying the percentage

of PEG from 1% to 3% by weight of cement for M20 grades of concrete.

International Journal of Pure and Applied Mathematics Special Issue

8422

3

METHODOLOGY

Fig 1: Flow chart of the method followed

COLLECTION OF

REQUIRED MATERIALS

TESTING OF

PROPERTIES OF

MATERIALS

MIX DESIGN OF

CONCRETE

CASTING OF CUBES

1. CONVENTIONAL CONCERTE

2. SELF CURING CONCRETE (PEG-400)

11111%, 2%, 3%

REGULAR MONITORING OF

COMPRESSIVE STRENGTH

FOR 7, 14, 28 DAYS

COMPARING THE COMPRESSIVE

STRENGTH OF S.C.C.WITH

CONVENTINAL CONCRTE

STRENGTH

International Journal of Pure and Applied Mathematics Special Issue

8423

4

POLYETHYLENE GLYCOL (PEG)

Polyethylene glycol is a condensation polymers of ethylene oxide and water with the general

formula H (OCH2CH2) nOH, where n is the average number of repeating ox ethylene groups

typically from 4 to about 180. The low molecular weight members from n=2 to n=4 are

diethylene glycol, triethylene glycol and tetraethylene glycol respectively, which are produced as

pure compounds. The low molecular weight compounds up to 700 are colourless, odourless

viscous liquids with a freezing point from 10 C (diethylene glycols), while polymerized

compounds with higher molecular weight than 1,000 are wax like solids with melting point up to

67 C for n 180. The abbreviation (PEG) is termed in combination with a numeric suffix which

indicates the average molecular weights. One common feature of PEG appears to be water-

soluble. The specification of PEG400.It is soluble also in many organic solvents including

aromatic hydrocarbons (not aliphatic). They are used to make emulsifying agents and

detergents, and as plasticizers, humectants, and water-soluble textile lubricants. The wide range

of chain lengths provides identical physical and chemical properties for the proper application

selections directly or indirectly in the field of;

Alkyd and polyester resin preparation to enhance water dispensability and water-based

coatings.

Ant dusting agent in agricultural formulations

Brightening effect and adhesion enhance in electroplating and electroplating process.

Cleaners, detergents and soaps with low volatility and low toxicity solvent properties.

Coupling agent, humectants, solvent and lubricant in cosmetics and personal care bases.

Dimensional stabilizer in wood working operations

Dye carrier in paints and inks

Heat transfer fluid formulation and defoamer formulations.

Low volatile, water soluble and noncorrosive lubricant without staining residue in food and

package process.

Paper coating for ant sticking, colour stabilizing, good gloss.

Plasticizer to increase lubricity and to impart a humectants property in ceramic mass,

adhesives and binders.

Softener and antistatic agent for textiles

Soldering fluxes with good spreading property.

Polyethylene glycol is non-toxic, odourless, neutral, lubricating, non-volatile and no irritating

and is used in a variety of pharmaceuticals and in medications as a solvent, dispensing agent,

ointment and suppository bases[36-41], vehicle, and tablet excipient. Chemical structure of PEG

shown below.

International Journal of Pure and Applied Mathematics Special Issue

8424

5

Polyethylene glycol is produced by the interaction of ethylene oxide with water, ethylene

glycol or ethylene glycol oligomers.

Test data for design

Concrete compressive strength required in the field @ 28 days= 20N/𝑚𝑚2

Maximum size of aggregate = 20mm

Degree of Workability = 0.90 (C.F)

Degree of quality control = Good

Type of Exposure = Mild

Specific Gravity of cement = 3.15

Specific gravity of coarse aggregate = 2.81

Specific gravity of fine aggregate = 2.59

Water absorption

Coarse aggregate = 0.50%

Fine aggregate = 1.00%

Free moisture

Coarse aggregate = Nil

Fine aggregate = 2%

Design Calculation

a) for conventional concrete

M20 = 1:1.5:3:0.5

Volume = 1+1.5+3 = 5.5

Selection of Coarse aggregate

20mm aggregate is taken as per the analysis from IS 10262

Total volume ingredients for using = 1.57

Selection for Fine aggregate

Air content for 20mm aggregate = 2% by volume of concrete

Selection of w/c ratio

W/c is taken from IS 10262 = 0.5

International Journal of Pure and Applied Mathematics Special Issue

8425

6

Max. W/c ratio As per IS 456-2000 = 0.6

Calculation

Volume of broken stone required = (3/5.5) x 1.57 = 0.856 𝑚3

Volume of sand required = (1.5/5.5) x 1.57 = 0.471 𝑚3

Volume of cement = (1/5.5) x 1.57 = 0.285 𝑚3

=0.285 x 1440 = 441Kg

For 1 𝑚3 of M20 (1:1.5:3)

Broken stone = 0.856 𝑚3

Sand = 0.472 𝑚3

Cement = 8.22 Kg

Table 1: MIX RATIO OF CONVENTIONAL CONCRETE M20

SL.N

O

NO OF

CUBES

(7DAY

S)

NO

OF

CUBE

S

(14

DAYS

)

NO

OF

CUBE

S (28

DAYS

)

TOTA

L NO

CUBE

S

CEMEN

T

OPC(Kg

s)

FINE

AGGREGA

TE

(Kgs)

COARSE

AGGREGA

TE

(Kgs)

WATE

R

(Lts)

1 3 3 3 9 17.65 29.6 37.6 6.3

2 3 3 3 9 17.65 29.6 37.6 6.3

3 3 3 3 9 17.65 29.6 37.6 6.3

b) for self-curing concrete

M20 = 1:1.5:3:0.5

Volume = 1+1.5+3 = 5.5

Selection of Coarse aggregate

20mm aggregate is taken as per the analysis from IS 10262

Total volume ingredients for using = 1.57

International Journal of Pure and Applied Mathematics Special Issue

8426

7

Selection for Fine aggregate

Air content for 20mm aggregate = 2% by volume of concrete

Selection of w/c ratio

W/c is taken from IS 10262 = 0.5, Max. W/c ratio As per IS 456-2000 = 0.6

Calculation

Volume of broken stone required = (3/5.5) x 1.57 = 0.856 𝑚3

Volume of sand required = (1.5/5.5) x 1.57 = 0.471 𝑚3

Volume of cement = (1/5.5) x 1.57 = 0.285 𝑚3

=0.285 x 1440 = 441Kg

For 1 𝒎𝟑 of M20 (1:1.5:3)

Broken stone = 0.856 𝑚3

Sand = 0.472 𝑚3

Cement = 8.22 Kg

Self-curing agent

Table 2: PEG-Mix ratios for different PEG-400 (1%, 2%, and 3%)

For 3 cubes of self-curing concrete

SL.N

O

PEG

WITH

DIFFER

ENT

RATIO

S

NO

OF

CUB

ES

(7DA

YS)

NO

OF

CUB

ES

(14

DA

YS)

NO

OF

CUB

ES

(28

DA

YS)

TOT

AL

NO

CUB

ES

CEM

ENT

OPC(

Kgs)

FINE

AGGRE

GATE

(Kgs)

COARSE

AGGRE

GATE

(Kgs)

WAT

ER

(Lts)

PEG-

400

(mgs)

1 PEG-

1%

3 3 3 9 17.65 29.6 37.6 6.3 365

2 PEG-

2%

3 3 3 9 17.65 29.6 37.6 6.3 740

3 PEG-

3%

3 3 3 9 17.65 29.6 37.6 6.3 1100

International Journal of Pure and Applied Mathematics Special Issue

8427

8

Volume of PEG-1% = 40.6mgs (as per the volume of cement)

Volume of PEG-2% = 83.4mgs (as per the volume of cement)

Volume of PEG-3% = 124.5mgs (as per the volume of cement)

TEST RESULT FOR PEG (400)-1%

Table 3: Comparison of compressive strength for S.C.C and conventional concrete PEG-1%

COMPRESSIVE STRENGTH (N/mm2)

7 DAY STRENGTH 14 DAY STRENGTH 28 DAY STRENGTH

1 2 3 AVG 1 2 3 AVG 1 2 3 AVG

SELF

CURING 14.5 15

14.

5 14.6 21

21.

5

20.

5 21.5

30.

5

3

1 31 30.83

CONVENTIO

NAL CURING 15.85

16.

5 16 16.15

22.1

5

21.

5

22.

5 22.04

27.

5

2

8

28.1

5 27.88

LOADS ACTED

FOR PEG-1% 450 KN 435 KN

Compressive

stress N/mm²

1% Self curing30.83 N/mm2

Conventional concrete27.88 N/mm2

0

10

20

30

40

7 14 28

Com

pre

ssiv

e st

rength

(N/m

m²)

Days

PEG-1%

self curing concrete

conventional concrete

International Journal of Pure and Applied Mathematics Special Issue

8428

9

Graph 1: Gain strength in concrete in PEG-1%

Fig 2: Observation of crack in self-curing concrete PEG -1%

As per the following are the observations on compressive strength of concrete for 1% of PEG

It can be observed that conventional curing is reflecting change in strength over

period of 28 days i.e.) but losing strength after 28 days compared to self-curing

concrete[42-45].

Self-curing samples are showing loss of strength till day 14 but thereafter it is gaining

strength at the same rate when compared to conventional concrete.

If 28 day strength is compared, then self-curing is good to conventional curing in case

of 1% PEG-400 i.e.) there is increase in 11.8% of compression strength.

COMPRESSIVE STRENGTH (N/mm2)

7 DAY STRENGTH 14 DAY STRENGTH 28 DAY STRENGTH

1 2 3 AVG 1 2 3 AVG 1 2 3 AVG

SELF

CURING(wit

h chemical) 15.23 14.8 14.07 15.07 23.45 23 23.85 23.45 25.5 25.5 24.85 25.28

CONVENTI

ONAL

CURING 15.85 16.5 16 16.15 22.15 21.5 22.5 22.04 27.5 28 28.15 27.8

Loads acting

on 2%

610 kN

500Kn

International Journal of Pure and Applied Mathematics Special Issue

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10

TEST RESULT FOR PEG – 2%

Table 4: Description of compressive strength for S.C.C and C.C PEG-2%

Graph 2: Gain strength in concrete in PEG-2%

As per following are the observations on compressive strength of concrete for 2% of PEG.

Self-curing is showing steady gain of strength for 7 to 14 days but the strength gain

after 28 days is not significant[46-50].

Conventional curing is showing some decrease in strength at 7 to14 days but gaining

strength from thereafter. Gain of strength is not significant compared to 7 day

strength.

Thus there is a decrease in compressive strength of self-curing concrete when the

percentage of PEG is added to it.

0

10

20

30

7 14 28

Com

pre

ssiv

e

stre

ngth

(N

/mm

²)

Days

PEG-2%

self curing concrete

conventional concrete

Compressive

stress N/mm²

for 2%

Self Curing25.28(N/mm2) Compressive Concrete27.8N/mm

2

COMPRESSIVE STRENGTH N/mm²

7 DAY STRENGTH 14 DAY STRENGTH 28 DAY STRENGTH

1 2 3 AVG 1 2 3 AVG 1 2 3 AVG

International Journal of Pure and Applied Mathematics Special Issue

8430

11

TEST RESULTS FOR PEG-3%

Table 5: Description of compressive strength for S.C.C and conventional concrete PEG-3%

GRAPH FOR PEG-3%

Graph 3: Gain strength in PEG-3%

0

5

10

15

20

25

30

7 14 28Com

pre

ssiv

e st

rength

(N/m

m²)

Days

PEG-3%

self curing concrete

conventional concrete

SELF

CURING(with

chemical) 13.5 13.5 12.5 13.16 20.5 20.83 21 20.17 24.5 24.5 23.5 24.16

CONVENTIONAL

CURING 15.85 16.5 16 16.15 22.15 21.5 22.5 22.05 27.5 28 28.15 27.85

Loads acting on

3% 520KN 500 KN

Compressive

stress N/mm² for

3% Self Curing23.33 N/mm² Conventional Curing 22.25N/mm²

International Journal of Pure and Applied Mathematics Special Issue

8431

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Fig 3: Observation of crack in self curing concrete PEG-3%

As per following are the observations on compressive strength of concrete for 3% of PEG

3% PEG, instead of gaining strength it is losing strength at 7 to 14 days.

And also there is a decrease in compressive strength when compared to other

percentage of PEG-1%, 2%.

Conventional curing shows rapid gain of strength from 14 day to 28 day, but from 7

day to 14 day it is losing strength when compared with self-curing concrete of PEG-

3%.

Thus, in this proportion the compressive strength of self-curing concrete gets reduced.

ANALYSIS OF TEST RESULTS

COMPASION OF PEG- 1%, 2%, 3%

The compressive strength was found to increase in self curing concrete comparing to

conventional concrete.

The result of compressive strength for different dosage of PEG-400 is represented in

the below table 10.

Thus, with these values the opium gain strength in PEG-400 is obtained by plotting

the graph[7-16].

This optimum dosage in PEG-400 is compared with the conventional concrete and

the increase in strength is determined.

Table 6: Comparison of grain strength in different ratio of PEG-400

No. Of days PEG 1% PEG 2% PEG 3%

7 days 14.8 14 13.16

14 days 16.6 16.6 18

28 days 25.16 27.16 23.33

International Journal of Pure and Applied Mathematics Special Issue

8432

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Graph 4: Comparison strength of gain strength in PEG-400

The graph represented in the above fig 16, gives the variation in the compression

strength depending upon the mix ratio i.e. with respect to the addition of admixture

PEG-400.

In this analysis, the addition of admixture i.e. PEG 1% to the concrete, gives the gain

strength in concrete comparing to the conventional concrete.

Where in addition to the admixture i.e. PEG 2% to the concrete, there will be increase

in of strength in the concrete comparing to the conventional concrete[32-38].

Further addition of admixture i.e. PEG 3% to the concrete, there will be loss in

compression strength comparing to PEG 1% and 2%.

Thus, from the above discussions it is concluded that the admixture added to the

concrete i.e. PEG 2% gives the optimum increase in the compression strength than

the other dosage of PEG 1%, 3% comparing with the conventional concert.

CONCLUSION

After the investigation of the consequence of the trial program the accompanying conclusions

were arrived. Concrete containing Ordinary Portland Cement with bring down sub-atomic weight

PEG 1% measurements (by weight of bond) has most extreme weight pick up contrasted with the

2% and 3%. Concrete containing Ordinary Portland cement with bring down sub-atomic weight

PEG 2 % measurements (by weight of bond) has least weight reduction contrasted with the 1%

and customary cement. Concrete containing Ordinary Portland cement with bring down sub-

atomic weight PEG 3% dose (by weight of bond) has least weight reduction contrasted with the

1% and 2% and traditional cement. In this examination, it is unmistakably seen that solid

containing Ordinary Portland Cement with bring down atomic weight PEG-1% (by weight of

bond) gives better outcomes when contrasted with the customary cement. As level of PEG-400

droop is expanded for M20 review concrete. Quality of self-curing concrete is keeping pace with

20

22

24

26

28

PEG 1% PEG 2% PEG 3%

Com

pre

ssiv

e

stre

ngth

(N

/mm

²)

Different dosage of PEG

GRAIN STRENGTH

28 days …

International Journal of Pure and Applied Mathematics Special Issue

8433

14

traditional cement. Self-curing concrete is the response to numerous issues confronted because of

absence of appropriate curing.

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33. Sartiha, B., Chockalingam, M.P., Photocatalytic

decolourisationoftextileindustrywastewaterby TiO2, International Journal of Pure and

Applied Mathematics, V-116, I-18 Special Issue, PP-221-224, 2017

34. Sartiha, B., Chockalingam, M.P., Study on photocatalytic degradation of Crystal

Violet dye using a semiconductor, International Journal of Pure and Applied

Mathematics, V-116, I-18 Special Issue, PP-209-212, 2017

35. Shanthi, E., Nalini, C., Rama, A., The effect of highly-available epistemologies on

hardware and architecture, International Journal of Pharmacy and Technology, V-8, I-

3, PP-17082-17086, 2016

36. Shanthi, E., Nalini, C., Rama, A., Drith: Autonomous,random communication,

International Journal of Pharmacy and Technology, V-8, I-3, PP-17002-17006, 2016

37. Shanthi, E., Nalini, C., Rama, A., A case for replication, International Journal of

Pharmacy and Technology, V-8, I-3, PP-17234-17238, 2016

38. Shanthi, E., Nalini, C., Rama, A., Elve: A methodology for the emulation of robots,

International Journal of Pharmacy and Technology, V-8, I-3, PP-17182-17187, 2016

39. Shanthi, E., Nalini, C., Rama, A., Autonomous epistemologies for 802.11 mesh

networks, International Journal of Pharmacy and Technology, V-8, I-3, PP-17087-

17093, 2016

40. Sharavanan, R., Golden Renjith, R.J., Design and analysis of fuel flow in bend pipes,

International Journal of Pure and Applied Mathematics, V-116, I-15 Special Issue,

PP-59-64, 2017

41. Sharavanan, R., Jose Ananth Vino, V., Emission analysis of C.I engine run by

diesel,sunflower oil,2 ethyl hexyl nitrate blends, International Journal of Pure and

Applied Mathematics, V-116, I-14 Special Issue, PP-403-408, 2017

42. Sharavanan, R., Sabarish, R., Design of built-in hydraulic jack for light motor

vehicles, International Journal of Pure and Applied Mathematics, V-116, I-17 Special

Issue, PP-457-460, 2017

43. Sharavanan, R., Sabarish, R., Design and fabrication of aqua silencer using charcoal

and lime stone, International Journal of Pure and Applied Mathematics, V-116, I-14

Special Issue, PP-513-516, 2017

44. Sharmila, G., Thooyamani, K.P., Kausalya, R., A schoolwork on customer

relationship management with special reference to domain 2 host, International

Journal of Pure and Applied Mathematics, V-116, I-20 Special Issue, PP-199-203,

2017

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45. Sharmila, S., Jeyanthi Rebecca, L., Anbuselvi, S., Kowsalya, E., Kripanand, N.R.,

Tanty, D.S., Choudhary, P., SwathyPriya, L., GC-MS analysis of biofuel extracted

from marine algae, Der Pharmacia Lettre, V-8, I-3, PP-204-214, 2016

46. Sidharth Raj, R.S., Sangeetha, M., Data embedding method using adaptive pixel pair

matching method, International Journal of Pure and Applied Mathematics, V-116, I-

15 Special Issue, PP-417-421, 2017

47. Sidharth Raj, R.S., Sangeetha, M., Android based industrial fault monitoring,

International Journal of Pure and Applied Mathematics, V-116, I-15 Special Issue,

PP-423-427, 2017

48. Sidharth Raj, R.S., Sangeetha, M., Mobile robot system control through an brain

computer interface, International Journal of Pure and Applied Mathematics, V-116, I-

15 Special Issue, PP-413-415, 2017

49. Sivaraman, K., Sundarraj, B., Decisive lesion detection in digital fundus image,

International Journal of Pure and Applied Mathematics, V-116, I-10 Special Issue,

PP-161-164, 2017

50. Sridhar, J., Sriram, M., Cloud privacy preserving for dynamic groups, International

Journal of Pure and Applied Mathematics, V-116, I-8 Special Issue, PP-117-120,

2017

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