# NCMTA 2015-National Conference on Mathematical Techniques and its Applications

"NCMTA 2015 Conference Papers "

**Graceful Labeling of Arbitrary Supersubdivision of Grid graph and Cyclic snake****[Full-Text ]**

A. Elumalai, A. Anand EphremnathAim of this paper is to prove the graph obtained by arbitrary supersubdivision of grid graph Ps × Pt is graceful and the arbitrary supersubdivision of k-block generalized cyclic snake with string-1 is graceful. Also we define a k- block generalized cyclic snake in the increasing length and we prove that such graph is graceful.

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**Cryptographic Techniques for High Security Enabled Near Field Communication****[Full-Text ]**

Ashwin S, Priyatam ChThis paper presents the design and implementation of Near-Field Communication (NFC) architecture and implementation with high security support enabled by AES algorithm. NFC standards include exchange of data within a close proximity range and data transmission protocols. Due to the recent developments and applications of Near Field Communication technology, security has to be provided with reduction in complexity. For achieving this, an AES algorithm of 128-bit based Near Field Communication Cryptographic Tag architecture controlled by an 8 bit microcontroller has been designed in our work. Recent applications of RFID tags are controlled and monitored by finite state machines embedded in its hardware. But with the support of additional functionality like security, their design complexity drastically increases. Cryptographic techniques monitored by microcontroller leads to the reduction of this design complexity, because the hardware requirement for AES algorithm is very less compared to other Asymmetric cryptography techniques. This Cryptographic technique has been successfully synthesized, simulated and implemented using Xilinx ISE DS 13.2.2.using VHDL source code.

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**Fuzzy Hungarian Method for Solving Intuitionistic Fuzzy Assignment Problems****[Full-Text ]**

K. Prabakaran and K. GanesanIn this paper we propose a new approach for an intuitionistic fuzzy optimal solution of assignment problems whose decision parameters are triangular intuitionistic fuzzy numbers. We develop a fuzzy version of Hungarian algorithm for the solution of intuitionistic fuzzy assignment problems involving triangular intuitionistic fuzzy numbers without converting them to classical assignment problems. The proposed method is easy to understand and to apply for finding solution of intuitionistic fuzzy assignment problems occurring in real life situations. To illustrate the proposed method numerical examples are provided and the obtained results are discussed.

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**Parameter Estimation of Antibody Control of EIAV in SCID to Stimulate the Immune System****[Full-Text ]**

Geethamalini S, Balamuralitharan S, Sundarammal KesavanIn this paper, we introduce viral dynamic modeling of antibody protection from Equine Infectious Anemia Virus (EIAV) infection in Severe Combined Immunodeficiency (SCID) horses may lead to insights into the FFT (Fast Fourier Transform) simulation of control of infection by antibody vaccination. Circumstances are determined under which wild-type infection is eradicated with the antibody vaccine. Also a three-strain competition model is considered in which a second mutant strain may coexist with the first mutant strain. The conditions that permit viral escape by the mutant strains are determined. This work provides insights into the development of vaccines that stimulate the immune system to control infection effectively.

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**Effect of AC electric field on thermal convective instability in a dielectric fluid saturated porous medium****[Full-Text ]**

Deepa K Nair, Potluri Geetha Vani and I. S. ShivakumaraThe effect of vertical AC electric field on the onset of convection in a horizontal layer of a dielectric fluid saturated Brinkman porous medium heated from below is investigated. The lower and upper boundaries of the fluid are considered to be rigid and isothermal. As observed in the classical dielectric fluid layer, oscillatory convection is found to occur provided the Prandtl number is less than unity. Therefore it is not a preferred mode of instability because the Prandtl number is greater than unity for dielectric fluids for poorly conducting liquids, so only the steady onset is considered for all the three types of boundary conditions. The eigenvalue problem is solved numerically using the Galerkin method. The effects of Darcy number, the ratio of viscosities, are analyzed on the stability of the system. The necessary conditions for the oscillatory instability to occur are independent of AC electric Rayleigh number. The effect of increasing AC electric Rayleigh number is to enhance the heat transfer and to hasten the onset of convection. The rigid boundaries offer more stabilizing effect on the system than free-free and rigid-free boundaries. Thus the foregoing study throws light on the control of electrohydrodynamic instability by a proper choice of velocity boundary conditions and AC electric field.

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**Structure of gem-graphs****[Full-Text ]**

H.P. Patil and V. RajaThe purpose of this paper is to introduce the gem-graphs, which are the natural extensions of trees and higher-dimensional trees (such as k-trees and k- trees) and determine their basic properties. We obtain a characterization of gem-graphs over paths of length at least 4 or cycles of length at least 5, and also determine their connectivity, centrality, planarity and Hamiltonian -property.

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**Optimal solution of Fuzzy Transportation Problem Using Hexagonal Fuzzy Numbers****[Full-Text ]**

A.Thamaraiselvi and R.SanthiIn this paper we introduce a fuzzy transportation problem with hexagonal fuzzy numbers. In which the transportation parameters like demand, supply and transportation cost are hexagonal fuzzy numbers. Vogel’s approximation method is used to obtain a fuzzy basic feasible solution and the optimal solution is obtained by fuzzy zero point method. These procedures are illustrated with numerical example. The minimum hexagonal fuzzy total transportation cost with maximum membership value is shown graphically and compared.

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**A Study of Rough Set Approximations for a Complementary Graph****[Full-Text ]**

S.Dhanalakshmi, N.Parvathi and R. ArulprakasamThe objective of the paper is to compute the definable sub graph of a complement graph based on the approximations of rough set using neighborhood relation. By applying the concepts of accuracy measures of approximations of subgraph H of a complementary graph , the calculation of exactness and roughness of subgraph a complementary graph are to be made. Furthermore properties of approximations are discussed and concluded.

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**THE DEFECT-CORRECTION METHOD APPLIED TO SINGULARLY PERTURBED ELLIPTIC PROBLEMS****[Full-Text ]**

J. JayakumarIn this paper the defect–correction method has been applied to solve some singularly perturbed elliptic boundary value problems of convection-diffusion type. From the available literature from an earlier work, it was proved that the use of standard defect–correction technique allows one to improve the order of convergence of stable low order finite difference schemes. However, it is difficult to prove the uniform convergence for one dimensional problem and we do not know at present any theoretical result proving uniform convergence for general two dimensional elliptic problems. By an another approach proposed, it was found that a simplified analysis is used for one dimensional problems of convection-diffusion type which gives almost second order uniform convergence of the method. In this work we show numerically that it is poss-ible to extend this parameter-uniform method and the simplified analysis to the case of a two dimensional elliptic boundary value problems.

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**Securing cloud data by Identity Based Proxy Re-encryption****[Full-Text ]**

Mrs. S.Jayashree, Dr. R.S. Sankara SubramanianIn a Proxy Re-encryption without seeing the underlying plaintext semi trusted proxy (Cloud Service Provider) converts a cipher text for User A (data owner) into a cipher text for User B (data Storage). In this paper the Identity based proxy re-encryption is used to provide data security while transiting the data from proxy –cloud service provider (CSP) to data storage also for secret key generation respectively. This system is secure and safe based on standard hardness assumption of Bilinear and DiffieHellman computation.

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**Special Function Solutions of a Class of Certain Non-autonomous Nonlinear Ordinary Differential Equations****[Full-Text ]**

K.M.Tamizhmani, K.Krishnakumar, A. AnnamalaiWe apply a direct linearization technique to a class of certain nonlinear n o n - a u t o n omo u s second-order ordinary differential equations with cubic nonlinearities and obtained special function solutions of them.

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**A New Tactic for Finding Irrelevant Constraints in Linear Programming Problems****[Full-Text ]**

DR.P.SUMATHI DR.P.BALACHANDER MRS.A.KARPAGAM MR.P.PUGAZHENTHIRedundancy in mathematical programming is a common occurrence, generally brought about by the lack of complete knowledge about the system of constraints and the desire on the part of the problem formulator not to omit essential elements of the formulation. .Something is redundant if it can be omitted without consequences for the system concerned. This paper presents a new method for selecting a constraint in linear programming problems to identify the irrelevant constraints. The computational results are presented and analyzed for small scale problems in this paper.

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**Some Results on Fixed Points of Asymptotically Regular Mappings****[Full-Text ]**

B.Baskaran, C.RajeshIn this paper we extend some results of fixed points for asymptotically regular mappings on a complete 2-metric space. We generalize some fixed point theorem of ‘Slobodan C. Nesic’ in the context of 2-metric space

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**GENERALIZED KNOT SYMMETRIC ALGEBRAS IN Z*****[Full-Text ]**

R.Selvarani and 2M.KamarajIn this paper we define Generalized knot Symmetric Algebras in Z* and also define a new multiplication and prove associativity.

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**ASSIGNMENT PROBLEM WITH GENERALIZED INTERVAL ARITHMETIC****[Full-Text ]**

G. Ramesh and K. GanesanLinear assignment problems are very well known linear programming problems of assignment problem. In a ground reality the entries of the cost matrix are not always crisp. In many application this parameters are uncertain and this uncertain parameters are represented by interval. In this contribution we propose a new computational procedure to solve assignment problem with generalized interval arithmetic interval Hungarian method.

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**Pseudo Edge Geodetic Number and Perfect Edge Geodetic Graph****[Full-Text ]**

D. StalinAn edge geodetic set of G is a set S V (G) such that every edge of G is contained in a geodesic joining some pair of vertices in S. The edge geodetic number g_1 (G) of G is the minimum order of its edge geodetic sets and any edge geodetic set of order g_1 (G) is an edge geodetic basis of G or a g_1- set of G. A set of vertices S’ in G is called Pseudo edge geodetic set if the set of vertices which are not belongs to any edge geodetic basis of G and. The Maximum cardinality of a Pseudo edge geodetic set of G is its Pseudo edge geodetic number and is denoted by g_1^' .A Pseudo edge geodetic set of size g_1^' (G) is said to be a g_1^' set. Pseudo edge geodetic number of certain classes of graphs is determined. Also if g_1^' (G) =0 then G is called Perfect edge geodetic graph.

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**Dependability Analysis of Heterogeneous Distributed Systems****[Full-Text ]**

G VijayalakshmiDistributed computing is an enabling technology for many current and future application areas and is increasingly pervasive. Distributed systems consisting of interconnected sets of dissimilar hardware or software systems are commonly referred to as heterogeneous distributed systems. As a consequence of large scale, heterogeneity is often inevitable in distributed systems. Furthermore, often heterogeneity is preferred by many users because heterogeneous distributed systems provide the flexibility to their users of different computer platforms for different applications. A Markov model of the Heterogeneous distributed system (HDS) with a circular consecutive configuration is developed and the availability and reliability measures are obtained.

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**A Super Edge Anti-Magic Total Labeling of the Cycle Cn with P3 Chords****[Full-Text ]**

L.Girija, A.ElumalairIn this paper, we have proved super edge anti-magic total labeling of cycles with P3 chords.

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**Edge Domination Number of Jump Graph****[Full-Text ]**

M.Karthikeyan, A.ElumalaiA Set is dominating set of jump graph, if every edge not in D is adjacent to a edge in D. The domination number of the jump graph is the minimum cardinality of dominating set of jump graph J(G).We also study the graph theoretic properties of γ^' [J(G)] and its exact values for some standard graphs. The relation between γ^' [J(G)] with other parameter are also investigated.

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**SEMILINEAR DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER WITH NONLOCAL CONDITIONS****[Full-Text ]**

M.Punitha, Dr.A.SanthaThe aim of this paper is to prove the existence and uniqueness of mild solutions for a semilinear differential equation of fractional order with nonlocal conditions in a Banach space. We also give an application for integro-partial differential equations of fractional order.

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**A Novel Method To Construct Deterministic Finite Automata From AGiven Regular Grammar****[Full-Text ]**

K.Senthil Kumar, D.MalathiMembership checking is an important task in language formalism. In regular Language ,Deterministic Finite Automata plays membership checking in a convenient way. Regular language is normally represented by regular expression from which people are finding Deterministic Finite Automata through Non Deterministic Finite Automata. In this paper we have proposed a second degree polynomial algorithm to find the Deterministic Finite Automata for a given Regular grammar.This paper describes a novel method which finds Deterministic Finite Automata directly from a given regular grammar without going through NFA .We extend the idea of GOTO and CLOSURE functions in LR parsing model to Regular grammars and use the same to find the states of the required Deterministic Finite Automata. Also we have proposed a new algorithm which minimizes the number of states of the obtained Deterministic Finite Automata.

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**On Difference Orlicz Space Xn****[Full-Text ]**

B. Baskaran and S. ThalapathirajThis paper is devoted to a study of the general properties of in respect of the difference sequence space

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**Analytic representation of Transition probability matrix for Exponential Queues with Hyper-exponential service times****[Full-Text ]**

Lavanya Gowrishankar, Vidhyacharan Bhaskar and Sundarammal KesavanIn this paper we obtain the probability function and moment generating function of an open queuing network node with restriction imposed on their combined distribution. The model is the same as in [1]. The arrival rate of the jobs is taken to be exponential in nature and hence their mixed distribution follows hyper exponential distrib In this paper we obtain the probability function and moment generating function of an open queuing network node with restriction imposed on their combined distribution. The model is the same as in [1]. The arrival rate of the jobs is taken to be exponential in nature and hence their mixed distribution follows hyper exponential distribution. The expression for the transition matrix has been analytically derived.

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**Second Order Necessary conditions in Non-linear Programming ****[Full-Text ]**

K.JeyalakshmiIn this paper, we consider conditions which are necessary for a directionally differentiable function to have an unconstrained local minimum at a point x0 ⋴ X where X is a normed linear space. The necessary conditions are expressed in terms of first order directional derivatives of non-linear analysis and certain second order directional derivatives.

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**Fuzzy Completely Weakly e -irresolute Functions****[Full-Text ]**

A. Vadivel and M. PalanisamyIn this paper, we introduce a new class of functions called fuzzy completely -irresolute functions between fuzzy topological spaces and also in this paper, fuzzy -open sets and fuzzy -closed sets are used to define and investigate a new class of functions called fuzzy completely weakly -irresolute. Relationships between the new class and other classes of functionsare established.

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**Common Fixed Point Theorem Satisfying an Integral Type Contractive Condition in Fuzzy Metric Space****[Full-Text ]**

Dr.C.Sreedhar, Dr.Devanad Ram, S.SreelathaUsing a contractive condition of integral type , we have proved a fixed point theorem in fuzzy metric space with the concept of weakly compatible mappings

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**Study on Multi Server Markov Modulated queue with finite capacity****[Full-Text ]**

R.Sakthi andV.VidyaMarkov modulated queuing models are those in which the primary arrival and service mechanism are influenced by change of phase in secondary Markov process. In this paper we study Markov Modulated Poisson Process with multi server queue with finite capacity and we provide the exact computable matrix expression of the rate matrix that can be used to obtain the performance measures.

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**An Evolutionary Algorithm Applied for Optimisation of Single Objective (makespan minimisation) Job Shop Scheduling Problems.****[Full-Text ]**

K.C. Udaiyakumar, Dr. M.Chandrasekaran.Job shop scheduling problem is well known common production problems which consists of ‘n’-Jobs and ‘m’-Machine. Many researchers applied varied approaches with existing heuristics for small size problems with near optimal solutions. This paper presents the criterion of minimisation of makespan for the different size Job Shop Scheduling problems. The proposed computational method of selective breeding Algorithm is used for finding optimal makespan values of different size problems. This algorithm is tested with 10 bench mark problems. The result shows that the proposed algorithm is a most efficient and effective algorithm which produced better result than other algorithm compared in literature. Hence the proposed algorithm is a good tool for problem solving technique for such kind of scheduling problems.

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**Numerical solutions for network simulation model of free convective flow past a vertical plate****[Full-Text ]**

Bapuji Pullepu, Sambath P, Selva rani M, Kannan R M, Immanuel YThe numerical study of laminar free convective flow past a viscous incompressible fluid past a vertical plate with heat and mass transfer is considered. The governing boundary layer equations of continuity, Momentum, Energy and concentration are transformed into non-dimensional form by using the non-dimensional quantities and are solved by using Network Simulation Method. The velocity, temperature, and concentration profiles have been studied for various parameters such as Schmidt number Sc, Prandtl number Pr, buoyancy ratio parameter Nare discussed and analyzed graphically.

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**Evaluating Blocking Probability In Series Queue with Multi Server Stations****[Full-Text ]**

G.ArulFreedaVinodhini, V. VidhyaSeriesqueueswith blocking are widely used in mathematical modeling of computer and telecommunication system, emergency health care units. Although there are various publications on series queues with blocking, all models deal with single server in each station. In this paper we presented a two station tandem queue model with 2 servers in first station and c servers in second station and obtained the stationary blocking probabilities.

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**“INVENTORY PLANNING OPTIMIZATION” THE CHALLENGES WITH SEGMENTING AND EXTRAPOLATING DEMAND****[Full-Text ]**

Dr.Y.Lokeswara Choudary & Dr .Neelisetty BalajiInventory Planning requires in-depth knowledge of DEMAND which is influenced by several internal and external factors. Several of these factors include seasonalities, trends, historical data, randomness, etc. Complexities in planning increase if there is variability in supply of raw materials and internal resources. There are several forecasting methods and models available and can be selectively applied. To increase the efficiency of the forecast it is important products/items are appropriately classified. There are a lot of ways inventory is classified in the industry. The focus in this paper is on how products classification can be optimized so that any forecasting model and/or methods may be applied.

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**“Internet Banking Services usage in Indian banks: Security Issues” - A Meta Analysis****[Full-Text ]**

Mr.M.Ezhumalai & Dr.C.VatchalaTechnology banking is order of the day. The usage of technology is in the initial stage in rural areas. Some of the services like ATMs and Credit cards are widely used in both rural and urban areas. The issues in the usage of Internet Banking Services of banking are multiple due to lack of awareness, availability and access of the technology by the customers. In this scenario, it is necessary to have a Meta analysis on various dimensions of the study. The study results exhibit that, there is a highly significant difference between the mean scores of the level of awareness of technology enabled services, Problems in Using Technology Enabled Services, reasons for not using the Internet Banking Services in banking, and Factors influencing the usage of level of Internet Banking Services among the sample is significant at 1% level of significance.

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**JOB SATISFACTION OF NURSES AND ITS IMPACT ON SERVICE QUALITY: EMPIRICAL EVIDENCE FROM CHENNAI CITY USING FRIEDMANTEST****[Full-Text ]**

Prasanna Ganesan & Dr.S.S.RauJob satisfaction represents a combination of positive or negative feelings that workers have towards their work. Meanwhile, when a worker employed in a business organization, brings with it the needs, desires and experiences which determinates expectations that he has dismissed. Job satisfaction represents the extent to which expectations are and match the real awards. Job satisfaction is closely linked to that individual's behaviour in the work place (Davis et al.,1985). Herzberg’s Two Factor Theory is probably the most often cited point of view. In fact the main idea is that employees in their work environment are under the influence of factors that cause job satisfaction and factors that cause job dissatisfaction. Therefore all factors that have derived from a large empirical research and divided in factors that cause job satisfaction (motivators) and factors that cause job dissatisfaction (hygiene factors).

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**Role of Socio Economic Variables in the Polarization of Luxury Value of Branded Products: A Study among the Selected Shoppers in Chennai****[Full-Text ]**

S.Savitha & Dr.K.SathyanarayanLuxury branding is a whole new ball-game altogether, which is unique and different from other industries, both from the perspective of the marketer as well as the luxury consumer. The luxury consumers always look for newer ways to satisfy his continuously changing needs. Gone are the days when people make buying decisions on store purchase, but now luxury market has revolutionize to the control over shopping which made shopping experience effortless, “swipe the card and bag the box”. Though luxury brands have often been associated with the level of core competences of creativity, exclusivity, craftsmanship, precision, high quality, innovation and premium pricing; there is a enormous paradigm shift for not only luxury consumers but also for the luxury brand. This sector targets products and services at consumers on the top-end of the wealth spectrum. However, no marketer can afford treating its consumers as a loosely bunched segment. The primary objective of the study is to study the Role of Socio Economic Variables in the Polarization of Luxury Value of Branded Products in Chennai city. The study reveals that, statistically there is a highly significant difference between marital status with respect to factors of luxury brand among the shoppers in the sample. Based on the mean value, it is noted that, the high level of functional, individual, social and luxury value is perceived by the married shoppers when compared to unmarried in the sample.

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**To analyze the problems of Transgender in India/Study Using New Triangular Combined Block Fuzzy Cognitive Maps (TrCBFCM)****[Full-Text ]**

A. Saraswathi, A. Praveen PrakashTransgender is an Umbrella term for persons whose gender identity and gender expressions or behavior do not conform to that typically associated with the sex to which they were assigned at birth. Gender Identity refers to a person’s internal sense of being male, female or something else. Gender expression refers to the way a person communicates gender identity to others through behavior, clothing, hair styles, voice or body characteristics etc. FCM we analyze the causes and effects of the relationships among the concepts to model the behavior of any system. But this new model gives the causes and effect of the relationships among the concepts to model behavior with ranking of any system. In this paper, we analyze the Transgender problem using Combined Block Triangular Fuzzy Cognitive Maps. Based on our studies we can give the conclusion and suggestions based on our study.

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**Graceful Labeling for Graph Pn ʘ K2 ****[Full-Text ]**

S. Vidyanandini, N.ParvathiA graceful labeling of a graph G with q edges is an injective assignment of labels from {0,1,2......,q} to the vertices of G so that when each edge is assigned to the absolute value of the difference of the vertex labels it connects, the resulting edge labels are distinct. In this paper, we show that all graphs Pn ʘ K2 for n=1,2,3,...,5 admits graceful labeling. Also, we show that all graphs K3 ʘ K3 admits graceful labeling. Finally, we pose a question that whether graphs admit graceful labeling for n>3.

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**Chemical Reaction Effects on Radiative MHD Oscillatory Flow in a Porous Channel with Mass Transfer and Heat absorption****[Full-Text ]**

R. Vijayalakshmi, A. Govindarajan, J.Sasi kumar, E.P.SivaAn attempt has been made to study the chemical reaction effects on radiative MHD oscillatory flow in a porous channel with mass transfer and heat absorption in a symmetric channel. On the basis of certain assumptions, the momentum, energy, concentration equations are obtained. The governing equations of MHD oscillatory flow were non-dimensionalised, simplified and solved. The closed analytical form solutions for velocity, temperature and concentration were obtained. The numerical computations were presented graphically to show the salient features of the physical parameters Peclet number, Grashof number, Reynolds number, Hartmann number, porous medium shape factor. The skin friction, Nusselt number and Sherwood number were also presented graphically and analyzed qualitatively.

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**Production Inventory Model with Deteriorating Items and Price****[Full-Text ]**

C.K.SivashankariAn Economic Production Quantity (EPQ) model is an inventory control model that determines the amount of product to be produced on a single facility so as to meet a deterministic demand over an infinite planning horizon. In all inventory models a general assumption is that products generated have indefinitely long lives. In general, almost all items deteriorate over time. Often the rate of deterioration is low and there is little need to consider the deterioration in the determination of economic lot size. Nevertheless, there are many products in the real world that are subject to a significant rate of deterioration and age-independent on-going deterioration. In this paper, a dynamic inventory model which is considered with deteriorating production in which each of the production, the demand and the deterioration rates, as well as all cost parameters are assumed to be general functions of time is considered. The objective is to minimize the total net inventory cost. The optimal production cycle time and economic production quantity are derived. The relevant model is built, solved. Necessary and sufficient conditions for a unique and global optimal solution are derived. An illustrative example is provided and numerically verified. The validation of result, this model was coded in Microsoft Visual Basic 6.0

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**SOME RESULTS ON FIXED POINT THEORY IN CONE METRIC SPACES****[Full-Text ]**

Senthil .S , Indo American College, CheyyarWe prove two fixed point theorems for mappings satisfying integral type contractive condition. These results extend the work of B.E.Rhoades [7] and Hardy and Rogers [8] to cone metric spaces.

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**B-Chromatic Number Of Line Graph Of Wheel Graph****[Full-Text ]**

Dr. N. Parvathi, R. NagarathinamA proper k-colouring of a graph G = (V (G), E (G)) is a mapping f: V (G) N such that every two adjacent vertices receive different colours. The chromatic number of a graph G is denoted by χ(G), is the minimum number for which G has a proper k-colouring. The set of vertices with a specific colour is called a colour class. A b-colouring of a graph G is a variant of proper k-colouring such that every colour class has a vertex which is adjacent to at least one vertex in every other colour classes and such a vertex is called a colour dominating vertex. The b-chromatic number (G) is the largest integer k such that G admits a b-colouring with k colours. Here we investigated the b-chromatic number of Line graph of wheel graph.

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**VERTEX DEGREE OF CARTESIAN PRODUCT OF INTUITIONISTIC FUZZY GRAPH****[Full-Text ]**

T.Pathinathan, J.Jesintha RoslineA new intuitionistic fuzzy graph can be generated by the use of the cartesian product of two intuitionistic fuzzy graphs. Degree of vertices in an intuitionistic fuzzy graph gives a complicated picture when we consider the cartesian product for intuitionistic fuzzy graphs with large number of vertices. We propose a methodology to find the degree of vertices for the cartesian product of intuitionistic fuzzy graph from the degree of vertices of two intuitionistic fuzzy graphs under certain conditions. This methodology simplifies the process and the outcome of the newly generated intuitionistic fuzzy graphs. These concepts are analyzed through suitable illustrations.

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**Solving Fuzzy Nonlinear Equation using Harmonic Mean Method****[Full-Text ]**

L.S. Senthilkumar and K. GanesanIn this paper, a new algorithm is proposed to solve fuzzy nonlinear equations without converting it to crisp equivalent problem and obtained a fuzzy solution using Harmonic mean method .Instead of bisecting the interval, we divide the interval using Harmonic mean to find the approximate root. A numerical example is provided to illustrate the method proposed in this paper.

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**MHD Peristaltic Flow of a Couple Stress Fluids Permeated with Suspended Particles****[Full-Text ]**

Siva.E.P, Govindarajan.A, Balamuralidharan.SThe MHD peristaltic flow of a couple stress fluid permeated with suspended particles through a two dimensional flexible channel under long wave length and low Reynolds approximation is studied. A analytical method of solution is obtained in terms of wall slope parameter and closed form of expressions has been derived for axial velocity and transverse velocity in fluid phase and particle phase. The expression for velocity profile and pressure gradient and the volumetric flow rate in the wave frame is obtained. The graphical results obtained for velocity profile and pressure gradient. It is observe that velocity profile decreases with increase in Hartmann number M and couple stress parameter S. The pressure gradient has an opposite behavior compared with velocity profile for Hartmann number M.

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**Peristaltic Motion of a Couple Stress Fluid of Three Dimensional Analysis with Parameter Estimation****[Full-Text ]**

B.Vijayakumar, Sundarammal Kesavan, S.BalamuralitharanThe peristaltic motion of a couple stress fluid of three dimensional analysis with parameter estimation through a two dimensional flexible channel under long wave length approximation and low Reynolds number is studied. A perturbation method of solution is obtained in terms of wall slope parameter and closed form of expressions has been derived for axial velocity and transverse velocity in fluid phase. The graphical results have been presented to discuss the physical behavior of various physical parameters on axial velocity and transverse velocities. It is observed that axial velocity decreases with increase in couple stress parameter and increases as geometric parameter increases wheras transverse increases with increase in cou-ple stress parameter and decreases as geometric parameter decreases.

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**On Some Prime Graphs****[Full-Text ]**

Dr. S. MEENA, P. KAVITHAA graph with vertices is said to admit prime labeling if its vertices can be labeled with distinct positive integers not exceeding such that the label of each pair of adjacent vertices are relatively prime. A graph G which admits prime labeling is called a prime graph. And a graph G is said to be a strongly prime graph if for any vertex of G there exists a prime labeling satisfying . In this paper we investigate prime labeling for some graphs related to H- graph, ladder graph, comb graph and also we prove that comb graph is a strongly prime graph.

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**An Optimal Solution of Fuzzy Transportation Problem****[Full-Text ]**

T. Leelavathy and K. GanesanIn this paper, we present a methodology for solving Fuzzy Transportation Problem (FTP) when all the cost coefficients are fuzzy numbers and all demands and supplies are crisp numbers. To obtain Initial Fuzzy Basic Feasible Solution (IFBFS) we use fuzzy version of Vogel’s Approximation Method (FVAM) and then by using fuzzy version of Modified Distribution Method (FMODI), we obtain the fuzzy optimal solution for fuzzy transportation problem without converting to a classical transportation problem. Finally the feasibility of the proposed study is discussed with a numerical example.

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**Velocity and frictional effects of porous elliptical plates lubricated with couple stress fluid considering the effects of slip velocity****[Full-Text ]**

E.Sujatha, Sundarammal kesavan, S.BalamuralidharanThe analysis of the squeeze film between porous elliptic plates is extended to include the effect of velocity slip at the fluid and the porous material interface. On the basis of Stokes micro continuum theory of couple stress fluid, a modified Reynolds equation is derived governing the fluid velocity and pressure. The present study is to analyse the effect of velocity and friction, considering slip velocity.

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**A study on Some Difference sequence spaces and their Matrix transformations over Non –Archimedean fields****[Full-Text ]**

J. Uma, V. SrinivasanIn this paper we define some difference sequence spaces over non-Archimedean fields and the matrix transformations of these sequence spaces, where the sequences, series and infinite matrices have entries in a complete non-trivially valued non-Archimedean field K as in [7].

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**Free Convective MHD Oscillatory flow Past Parallel Plates in a Porous Medium with Heat Source and Chemical Reaction****[Full-Text ]**

J.Sasikumar, A.GovindarajanThe effect of magnetic field on unsteady free convection oscillatory flow through infinite vertical parallel flat plates in a porous medium with heat source and chemical reaction, when free strem velocity, temperature and concentration oscillate in time about a non zero constant mean has been investigated. A cosed form analytical method is employed to solve the momentum and energy and concentration equations. Effects of various non dimensional parameters on velocity, temperature and concentration profiles have been analysed in detail and results shown in graphs.

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**A fourth order Runge-Kutta Method for the Numerical Solution of first order Fuzzy Differential Equations****[Full-Text ]**

S. Sindu Devi and K.GanesanWe propose fuzzy version of Runge – Kutta method of order four, for the solution of first order linear fuzzy differential equations without converting them to crisp form. The accuracy and efficiency of the proposed method is illustrated by solving a fuzzy initial value problem with trapezoidal fuzzy number.

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**Implementation of Fuzzy Random Variable in Imprecise Modelling of Contaminant Migration through a Soil Layer****[Full-Text ]**

D. DattaFuzzy random variables possess several interpretations. Historically, they were proposed either as a tool for handling linguistic label information in statistics or to represent uncertainty about classical random variables. Accordingly, there are two different approaches to the definition of the variance of a fuzzy random variable. In the first one, the variance of the fuzzy random variable is defined as a crisp number that makes it easier to handle in further processing. In the second case, the variance is defined as a fuzzy interval, offering a gradual description of our incomplete knowledge about the variance of an underlying, imprecisely observed, classical random variable. In this work, we first discuss another view of fuzzy random variables that comes down to a set of random variables induced by a fuzzy relation describing an ill-known conditional probability. This view leads to yet another definition of the variance of a fuzzy random variable, in the context of the theory of imprecise probabilities. The new variance is a real interval, which achieves a compromise between both previous definitions in terms of representation simplicity. Our main objective is to demonstrate, with the help of simple examples, the practical significance of these definitions of variance induced by various existing views of fuzzy random variables. Finally, fuzzy random variable concept is implemented in modeling of contaminant migration through a soil layer. The transport of contaminant through a saturated soil layer is modeled by advection, dispersion, sorption and first order degradation. The parameters of the contaminant migration model such as seepage velocity, porosity of soil, dispersion coefficient and distribution coefficient are taken into consideration as fuzzy random variable due to their dual nature of fuzziness and randomness.

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**SENSORY DATA FUSION IN ROBOTICS THROUGH FUZZY AND INTERVAL MATHEMATICS****[Full-Text ]**

Debanik RoyTraditionally, the domain of model-intensive data fusion of sensory systems depend largely on two vital aspects, namely, ‘sensor type’ and ‘sensor layout’. Although a sound definition or problem identification about the sensor classification leads to a fruitful fused data at the end using deterministic calculations all through, the exercise turns futile when fuzziness exits in the sensor-data itself. Thus, in this article, we will focus on the paradigms of novel models for sensory data fusion using the concept of Interval Mathematics, exclusively for re-christening the time-varying data-clusters. This very concept of imbibing the alteration of data through re-representation in “interval” bounds gives enough flexibility in understanding the true phenomena of sensor fusion in real-time.

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