Table of contents

Ramapuram Campus

Dr. Shakeela Sathish,

Head of the Department

Department of Mathematics

SRM Institute of Science and Technology is the number one private institution in the country, which has set standards in experimental education and knowledge creation across various fields. It has inspired students with an international standards of education, world class infrastructure and industry ready curriculum. A continuous emphasis on modern teaching methods, global links for research, student exchange and knowledge sharing and industry- institute interactions have consistently placed SRM, well ahead in every field. SRM Institute of Science and Technology has been categorized as grade 'A' by Ministry of Human Resource Development (MHRD), Government of India. SRM is accredited by NAAC with 'A++' grade in the year 2018. SRM Institute of Science and Technology Ramapuram established in 2004, is located at the heart of the city. This charming enclave provides the facilities and infrastructre, necessary for Dental, Health Sciences, Engineering and Technology and Science and Humanities.

We are pleased to inform you that, Department of Mathematics is organisising a National conference on "Progress in Mathematics towards Industrial Applications", which is aiming to promote interaction between academy and industry, leading to innovation in both fields and providing unique opportunity to discuss the latest ideas, problems and methodologies, and contributing to the advancement of science and technology. It also encourages industrial sectors to propose challenging problems where Mathematicians can provide insights and fresh perspectives.

The purpose of this conference is to bring together leading academic scientists, experts from industry and young researchers and provide a platform in which significant advances in Mathematics are presented & widespread discussions are held, to promote the use of innovative Mathematics in industry. This conference will provide a unique opportunity to exchange ideas, problems and methodologies, bridging the gap between Mathematics and industry and contributing to the advancement of science and technology to benefit the society. The conference will have keynote addresses by renowned experts and Research paper presentations.

Dr. Shakeela Sathish,

Convener

PMTIA– 2019

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

In this article we admit Bi- Conditional for Duplicate graph of Quadrilateral Snake EDG(QS_m)m ≥ 2, Double Quadrilateral SnakeGraphs EDG(DQS_m)m ≥ 2, and Triangular ladder graph. EDG(TQL_m)m ≥ 2.

In this article, the dynamical behaviour of a discrete fractional order Lorenz-Chen-Lu like chaotic system is investigated. A discretization process is used to obtain a discrete version. The system has three constants, three fixed points and generates typical chaotic attractors. Numerical verifications are presented for the analysis of dynamical system. The chaotic attractors, bifurcation diagrams and phase portraits are provided for distinctive values of parameters. The sensitivity to initial conditions of the parameter values for the fixed points is also discussed.

In this article, we investigate the existence and uniqueness of solutions for boundary value problem (BVP) of fractional order difference equations (FODE) of the form

${\Delta }^{\upsilon }w(s)=-f(s+\upsilon -1,w(s+\upsilon -1))$,

$w(\upsilon -2)=\psi (w),w(\upsilon +k)=\phi (w)$,

where s ∈ [0, k]_N0, f : [υ − 2, υ − 1, ..., υ + k]_Nυ−2 × R [0, + ∞] is a continuous function ψ, φ : C ([υ − 2, υ + k]_Nυ−2) → R are given functions and $1\lt \upsilon \le 2$. Existence and uniqueness of solutions are established by the Brouwer fixed point theorem and contraction mapping principle.

Let G_m be a undirected graph. Having a Molecule, atoms indicate by vertices and bonds indicate by edges. The main aim of this paper explains Extended Medium Domination on Linear Benzenoid Chain like Benzene, Naphthalene, Anthracene and their generalisation will be proved.

The aim of this paper is to prove that the extended duplicate graph of arrow graph and splitting graph of path admits difference cordial labeling and strongly multiplicative labelling.

In this paper, we have investigate the extended duplicate graph of triangular snake graph is 3-total edge sum cordial labeling and Integer edge cordial labeling.

In this paper, we determine chromatic index, acyclic chromatic and star chromatic number for the human chain and circular human chain graphs.

In this paper, some new class of sets R*_I-S(X), R*_I-P(X) and R*_I-α(X) which are the collection of all 'R*_I-semi –open', 'R*_I -pre-open' and 'R*_I-α-open set's are introduced and we analysed how the sets are related with them and examine the relationship the other similar collection of weak open sets in ideal and general topological spaces. Also we obtained an equivalent wayof representing continuous function interms of funcions which are defined using weak open sets in R*-topological spaces.

In this paper, we present an extended case of Two Dimensional Legendre & Chebyshev wavelet to solve a system of PDE's and a Comparative Study of these two wavelets. In this article, we construct an operational matrix from two Dimensional Chebyshev and Legendre wavelets which is then used to convert PDE into some algebraic equations and hence we solve by the method of collocation. A new operational matrix was derived and it is utilized to convert PDE with BVP to a set of algebraic equations. Some examples are given to evaluate the effectiveness of the newly found approximation technique and compared with the existing result

In this paper a discussion of OTSMO Labeling (One Third Sum Modulo 3, introduced by the Researcher) on Generalized Petersen graphs GP(n, 2) is done.

The object of the present paper is to assess speculation of the Hyers-Ulam stability theorem for the complex additive functional equation on abelian groups and stability results have been gotten by a fixed point technique. This technique demonstrates that the stability is identified with some fixed point of an appropriate operator.

This paper presents a method to analyze the traffic flow pattern at a crowded junction in Chennai, one of the metropolitan cities in India, using waiting time in the signal in different time intervals with the help of Fuzzy Cognitive Map and Induced Fuzzy Cognitive Map.

Ngurahet. al. [2010] noted super magic coverings of fans and ladders. Ahmad et. al. [2011] enumerated super edge-magic labeling for the union of non-isomorphic graphs. Lopez et.al. [2012] suggested perfect super edge-magic graphs of path and cycle. Gao and Fan [2013] analyzed super edge-magic labelings of multi-star St(a1,..., an), Ali et. al. [2013] magic Labelings of type (a, b, c) of families of wheels.In this article, edge bimagiclabelings for bipartite complete graph, double bipartite complete graph, bistar merging with a path, one point union of finite copies of cycle having four vertices, and closed double wheel are found.

Various graph labeling that generalize the idea of a magic square have been discussed. In particular, a magic labeling on a graph with v vertices and e edges will be defined as a one to one map taking the vertices and edges onto integers 1, 2,..., v+e with the property that the sum of the label on an edge and the labels of its end points is constant, independent of the choice of edge.

Start your abstract hereIn this paper we consider Magenetohydrodynamic viscous oscillatory flow of incompressible linearly density stratified fluid in a long vertical rectangular channel with injection through y – axis and suction through the plate parallel to y - axis. In the undisturbed state the density distribution is assumed to be linearly distributed. Closed form solutions are obtained using similarity transformation. The effects on axial and transverse velocity profiles due to various parameters involved in the problem are illustrated in the figures. The graphical representations of the investigation show that the stratification effects are more on transverse velocity profiles than that of axial velocity. For constant density and zero electromagnetic induction the result reduces to that of viscous oscillatory flow between parallel plates

Financial instability estimates the changes of the cost of a monetary instrument. It is a proportion of properties of the Stock prices stability. Fractal investigations are used to assess the money related instability. Forecasting of stock prices acts as an important challenge based on the Random Walk theory. This paper deals with comparison of two years 2013 -2014 and 2017(Jun to Nov) of stock prices. Explain the instability by the method of Box-Counting technique to find the Fractal dimensions of the Geometric Brownian Motion based on the Random Walk defective value. This creates the possibility that Fractal measurement is related with the monetary unpredictability. Its an essential instrument for both money related investigators and Financial specialists.

Our intention of this paper is to initiate the new notions on I_ˇ -closed set and s-closed sets. Some properties and relationships to other known closed sets are analyzed. Further we define and discuss I_ˇ-continuous and s -continuous functions and their basic properties.

Thenotionofsoftsetsisintroducedasageneralmathematicaltool for dealing with uncertainty. In this work, we consider the concepts of soft closed set, soft dense setwere introducedinthesoftideal topologicalspace(SS(X)_E, τ, J). Also, westudiedthe operations on this new soft s-closed and soft s-dense sets.

Using ideals defined, on a set many new sets and topologies were defined by many authors. We define a new set (τ_I- mini open set) in ideal space with the use of an ideal and later we proved the collection of that new sets has the properties of generating a new topology which we named as introduce a new topology called τ_I- topology which is containing the actual topology τ.

The present paper describes no job block criteria using NEH technique in a Flow Shop Scheduling Model for five machines. In flow shop, constraints demand that the jobs passing the machine are same. The probabilities are associated with their respective processing times, in which the optimization criteria is the utilization of 5 machines. For a group of jobs in 5 machines, with no job block and No-wait time is considered in the paper. Our agenda is to reduce the total completion time and the shortest job sequence path using NEH algorithm. Sample numerical illustrations are provided to understand the NEH algorithm easily.

In this paper, we discuss Trapezoidal intuitionistic fuzzy assignment quandary(TrIFAP). In classical assignment quandary, Cost always remains same. But, here we develop an method to solve Trapezoidal intuitionistic fuzzy assignment quandary where cost is not deterministic numbers but infelicitous ones. Here, the costs(profits) matrix have all the elements they are TrIFN and others have been immensely colossal demonstration against the classical method. Then its trapezoidal membership and non-membership functions are defined. In general compare the findings from different methods attested the same picture. Numerical examples show that an intuitionistic fuzzy ranking method is very efficacious and utilizable method for handling a TrIFAP.

Solving Multiple Attribute Group Decision Making (MAGDM) problems has become one of the most important research in the recent trends. The information or data is in the form of Intuitionistic Triangular Fuzzy Number (ITrFN). The weights are derived from the numerical solutions of partial differential equations of Laplace's equation and poisson`s equation. The weights obtained from the methods are applied in decision making problems. The Intuitionistic Triangular Fuzzy Ordered Weighted Averaging (ITrFOWA) operator and the Intuitionistic Triangular Fuzzy Hybrid Aggregation (ITrFHA) operator are used to combine the decision matrix. Distance function is used as a tool for ranking the best alternatives. Numerical illustration is proposed to show the effectiveness of the method.

In this paper, we present an algorithm to find triangular fuzzy star graph K_{1, n} atmost 1241 edges. We show that it admits triangular fuzzy labeling. Also we prove that it satisfies triangular fuzzy graceful labeling.

In this paper we propose a new idea for the readers on the use of fuzzy in a real-life application in the triangular rule for solving the analytical solution of the second-order linear fuzzy differential equation (LFDE) under Hukuhara differentiability, especially increasing length of support. The case study is provided to show the advantages in the future.

This work discusses the effect of heat transfer and viscous dissipation on unsteady MHD (Magneto Hydro Dynamic or Hydromagnetic) oscillatory dusty fluid flow through a vertical porous channel. The governing equations for both fluid and particle phase are solved separately to get the exact solution for velocity and temperature profiles. The effect of various dimensionless parameters are displayed graphically and discussed qualitatively.

In the current world, day-by-day, huge amount of data being generated at a rate far higher than by which it can be examined by human comprehension alone, in this case, data mining became an important task for extracting useful information from large amount of data. Especially in these cases, the standard techniques of datamining plays in a better way such as Evolutionary approaches performs more efficient as well as more accurate. The objective of this paper is to compare Fuzzy based Evolutionary Algorithm with other machine learning classifiers to improve the classification of medical dataset of heart disease.

A Mean Square Cordial Labeling (MSCL) of a Graph G(V, E) with p vertices and q edges is a bijection from V to {0, 1} such that each edge uv is assigned the label $(\lceil (f{(u)}^{2}+f{(v)}^{2})/2\rceil )$ where ⌈x⌉ (ceil( x)) is the least integer greater than or equal to x with the condition that the number of vertices labeled with 0 and the number of vertices labeled with 1 differ by at most 1 and the number of edges labeled with 0 and the number of edges labeled 0 and the number of edges labeled with 1 differ by at most 1. In this paper it is analyzed that some star related graphs like Bistar graph B(k, k), Subdivision of a star graph S(S_k), Coconut tree CT(k, k), Merge graph C_k*S_k,, Graph P_mΘ K_{1, n} and Banana tree BT(k, k) admits mean square cordial labeling.

Artificial Neural Network has become a popular tool in developing systems that encircles human proficiency. The importance of exact detection is exceptionally important for proper treatment and preserve of disease. Clinical cytology has improved tremendously in disease diagnosis. In this paper, two Artificial Neural Network (ANN) methods, Multilayer Perceptron (MLP) and Radial Basis Function (RBF) network are compared. The RBF network predicts comparatively better accuracy in compared to MLP methods. Also it was detected that the RBF method requires a lesser amount of time for the development of the model, this is because there is no repetition to reach the favourable parameters in the model.

Graph theoretical analysis plays a vital role in various fields. In Graph theory, Graph labeling is the major area of application. Graph labeling is the assignment of labels to the vertices and edges of a graph pertaining to certain conditions. Graph theory finds its applications in Coding theory, Radar, Astronomy, Circuit designs, Communication networks, X-ray crystallography, Data base management and a major role in medical field like Brain network, Forensics and Cephalometric analysis. Here we would like to enhance the graph theory applications in the field of Psychology. This paper gives an overview of graph techniques applied in Sociometry using Sociogram. Sociometry is a quantitative method for measuring social relationships and Sociogram is a tool to find Sociometry of a social space. In this article, an analysis in a classroom climate with of a group of 50 college students was done after they were subjected to answer a series of questions probing for affiliations with other classmates. A graphical representation (sociogram) of the social links of each student was constructed by plotting the structure of interpersonal relations in the group. This graphical representation depicts the social relations, channels of influence, attraction towards others, hatred, isolation and lines of communication of the group.

Breast cancer is one of the major causes of death among women. Small clusters of micro calcifications appearing as collection of white spots on mammograms show an early warning of breast cancer. Image segmentation is an important element of Digital Image processing that subdivides the image into discrete regions/objects, each identified by the property of homogeneity of pixels. X-ray mammography is used as diagnostic tool for diagnosis of breast cancer. Edge detection of micro calcification clusters in mammogram images is the main issue of early detection of breast cancer. Fractals are of rough or fragmented geometric shape that can be subdivided in parts, each of which is a reduced similar of the whole. Fractal dimension and Hurst exponent are used to locate the micro calcifications in the mammogram. The concept of fractal is associated with geometrical objects satisfying criteria such as self-similarity and fractal dimensionality. Present method of edge detection is superior compared to conventional Sobel method, in which detection of edges of the regions or objects in an image takes place by the Fudge factor. The paper presents the application of fractals for early detection of breast cancer.

This paper reviews modern genetic algorithm based approaches for solving job shop scheduling problems. This paper elaborates the types of crossover methods such as Partially Mapped crossover (PMX), Order One Crossover (OX), etc involved in Genetic Algorithm (GA) that are used for Job Shop Scheduling problems. Job Shop Scheduling represents one of the hardest combinatorial optimization problems where number of possible schedules drastically increases with the number of operations and machines. Normal crossover operators will often lead to inadmissible solution . Many specialized combining order or adjacency information from the two parents. The crossover method operators builds an offspring by choosing a subsequence of elements from one parent and preserving the order and position of as many elements as possible from the other parent. A subsequence of elements is selected by choosing two random cut points, which serve as boundaries for the swapping operations. There are few distinct mutation operators widely used for JSS problems such as swap, inversion, insertion (shift) and displacement mutation. Here some modern genetic algorithm-based approaches from the literature are also discussed as well.

In this paper two units system engenders two different products for sale. The two products are engendered piecemeal in pairs. The sale time commences when k dyads are engendered or when the two units system fails whichever occurs first. Postulating the engenderment and sale time of products have general distribution and the failure and rehabilitate rates of the two units are constants, the double Laplace Stieltjes transform of the joint distribution function of the time to sale and sale time are obtained. Their prospect of engenderment time E (T), sales time E(R) is derived by varying the number of engenderment k. To illustrate the application of Numerical results are distribution by giving different values for λ1 λ2 μ.

In this chapter an application of cubic transition matrix in agricultural planning is provided. This chapter is concluded with a decision theory on product fuzzy soft matrices.

In this paper, we define g-compatible ideal with respect to g-open sets and characterize g-local functions in codense ideal topological spaces. Also, we establish some properties of g-local functions with the compatibility of I with τ with respect to g-open sets and the relative topology

In this paper, the author introduces a new subclasses of analytic functions with respect to (j, k)-symmetric points and investigate various inclusion properties for these classes.Integral representation for functions in these classes and some interesting applications.

The classes V_k(α), R_k(α), V_k1(α) and R_k1(α) of analytic function, We establish a relation between the functions of bounded boundary and bounded radius rotations.

In this paper, we investigate the total neighbourhood prime labelling of Lily graphs, Umbrella graph, Friendship graph F_n, Generalised friendship graph $F{r}_{n}{}^{(4)},\bar{F}{r}_{n}{}^{(3)}$ and $\bar{F}{r}_{n}{}^{(4)}$.

The crisp transportation problem is one of the special case of linear programming problems. It is explained with the hypothesis that the cost parameters are indicated inaccurate way. But in the present world, the transportation parameters may be uncertain due to many uncontrolled factors; this gives rise to fuzzy environment. Here, we proposed a method for the solution of fully fuzzy multi objective transportation problems involving triangular fuzzy numbers. We solve the fully fuzzy multi objective transportation problems without converting it into crisp form. A numerical example is discussed to demonstrate the theory formulated in this article.

A sequencing problem is to select the order in which the vital tasks are to be done to minimize the total elapsed time taken for all the tasks. Generally, in job sequencing problems, the processing times are precisely valued. But in reality, it is observed that the processing times during the performance of the job are indefinite. For that reason, the conception of fuzzy job sequencing problem make available for use an effective outline which is useful for real-life situations with fuzzy processing times. Here, we suggest a new technique for solution of fuzzy sequencing problems involving triangular fuzzy numbers (TFN) without transforming them into equivalent crisp sequencing problem.

In this paper, we propose a method of solving the fully fuzzy linear fractional programming problems, Express all the parameters and variables are triangular fuzzy numbers. Convert all the triangular fuzzy numbers in their parametric form, we convert the fractional programming problem in to a single objective linear programming problem in parametric form. We put new fuzzy arithmetic and fuzzy ranking, we obtain the optimal solution the given fully fuzzy linear fractional programming problem without converting to its equivalent crisp linear programming problem. A numerical example is provided to illustrate the efficiency of the proposed method.

This paper aims to obtain a minimum fuzzy assignment cost for a fuzzy assignment problem by using fuzzy branch and bound technique. Without transforming the fuzzy assignment problem into a corresponding crisp assignment problem a solution procedure to assign different resources to different activities is proposed to attain the fuzzy optimal cost. In this paper for comparing fuzzy numbers a ranking function in terms of parametric form is used. To showcase the proposed method an example is discussed and a comparison is made with a existing method.

This paper focuses on obtaining a solution to generalized trapezoidal fuzzy least cost route problem using fuzzy dynamic programming approach. Using the fuzzy forward and backward recursive equations the fuzzy optimal solution is developed by without converting them into an equivalent crisp problem. Using appropriateranking and arithmetic operation in terms of parametric form the minimized fuzzy cost is attained. To explain the procedure an example is illustrated.

In this paper, we suggest an interval Transportation problem where the source and destination parameters are chosen as interval numbers. The main objective of the problem is to minimize the total transportation cost and total delivery time. Algorithm is proposed (VAM and MODI) to determine initial allocation to the basic cells and the corresponding interval transportation cost. The optimal solution is obtained without converting the problem to its classical version. Numerical example is obtained which will be easy to understand the solution and procedure of the proposed method.

In this article, we intend to determine the total duration of completion of the project for fuzzy networking problem with the activity duration represented as trapezoidal fuzzy number using Critical Path technique. A new fuzzy arithmetic operation, ranking method and a precise step by step plan is designed to obtain the total fuzzy duration, utilizing the available resources. Finally the proposed study is discussed with a numerical example.

In this paper, we suggested a new approach to obtained an optimal sequence "for fuzzy sequencing problem with trapezoidal fuzzy number." Using new fuzzy arithmetic operation and ranking method, an improved algorithm is proposed to obtain the fuzzy total elapsed time for processing all the jobs without converting problem into classical form. The approach is efficiently illustrated with a numerical example.

In this paper, we focus on the solution procedure for fully interval assignment problem (FIAP), Hungarian method is considered into account. In consideration method the given FIAP is decayed into Interval Assignment Problem, solving it with existing method and by using its optimal solutions, an optimal interval assignment solution to the given FIAP is obtained. Although the assignment problem can be solved as an ordinary transportation problem or as Linear programming problem, its unique structure can be exploited, resulting in special purpose algorithm, is called Hungarian method. A numerical example is provided to illustrate the solution procedure developed in this paper.

The main purpose of this paper is to study the existence of a fixed point in fuzzy automata normed linear space. In particular, fixed point for a self map on compact fuzzy automata normed linear space has been established.

We propose a simple method for solving multi objective travelling salesman problem whose decision parameters are expressed as triangular fuzzy number. We apply arithmetic operation and ranking for the parametric form of triangular fuzzy number. The proposed gives preference solution to the decision maker without change to classical travelling salesman problem. A numerical example is provided to show the efficiency of the propose method.

In this paper we propose a novel approach for the solution of fuzzy multi objective assignment problem whose parameters are expressed as triangular fuzzy numbers. We apply arithmetic operations and ranking in the parametric form of triangular fuzzy numbers to solve fuzzy multi objective assignment problem without converting to classical form. The proposed method gives flexibility to the decision maker to his/her preferred fuzzy optimal solution. A numerical example is also given based on this novel method.