Articles in Press Volume 8, Issue 3 (2020)

Authors : M.Arunkumar, E. Sathya and C. Pooja
Title : Single Variable Generalized Additive - Quadratic and Generalized Cubic- Quartic Functional Equations in Various Banach Spaces
Volume, Issue, Year : 8(3)(2020)
Pages : 1−42

Abstract: In this paper, we introduce and examine the generalized Ulam - Hyers stability of single variable generalized additive-quadratic and generalized cubic-quartic functional equations in various Banach spaces with the help of two different methods.

Keywords: Functional equation, Generalized Hyers-Ulam stability, Banach space, (Beta;p) Banach space, Intuitionistic Fuzzy Banach space.

Authors : R. Savithiri and A. Manonmani
Title : A Bitopological $(1,2)^*$ - $\mathop{\alpha }\limits^{\bullet } $ - Homeomorphisms
Volume, Issue, Year : 8(3)(2020)
Pages : 43−49

Abstract: In this paper, a new concept of homeomorphisms, say $(1,2)^*$ - $\mathop{\alpha }\limits^{\bullet } $ homeomorphisms, $(1,2)^*$ - $\mathop{\alpha }\limits^{\bullet } c$ - homeomorphisms, $(1,2)^*$ - $\alpha gg$-homeomorphisms and $(1,2)^*$ - $\alpha ggc$ - homeomorphisms are introduced and analyzed in bitopological spaces. Also $(1,2)^*$ - $\mathop{\alpha }\limits^{\bullet } $ - $T_{1/2}$ - space and $(1,2)^*$ - $T_{\mathop{\alpha }\limits^{\bullet } }$ - space are introduced and studied.

Keywords: $(1,2)^*$ - $\mathop{\alpha }\limits^{\bullet } $ - homeomorphisms, $(1,2)^*$ - $\mathop{\alpha }\limits^{\bullet } $c - homeomorphisms, $(1,2)^*$ - $\alpha gg$ - homeomorphisms, $(1,2)^*$ - $\alpha ggc$ - homeomorphisms, $(1,2)^*$ - $\mathop{\alpha }\limits^{\bullet } $ - $T_{1/2}$ - space, $(1,2)^*$ - $T_{\mathop{\alpha }\limits^{\bullet } }$ - space.

Authors : M. P. Aparna and R. Akhila
Title : Principal Topology on a Rees Matrix Semigroup using Green's Left Quasiorder
Volume, Issue, Year : 8(3)(2020)
Pages : 51−57

Abstract: This paper introduces a principal topology on a Rees matrix semigroup using Green's left quasiorder. Since principal topologies are in one-one correspondance with quasiorder relations on a set, the relations are commonly used for constructing such topologies. The basis for the topology is the collection of minimal open neighbourhoods corresponding to each element in a given set. When semigroups are considered with Green's left quasiorder, minimal open neighbourhoods are the principal left ideals. Hence, the collection of principal left ideals will turn out to be a basis for the principal topology on a semigroup. As long as a Rees matrix semigroup is considered, it is observed that these ideals exhibit certain interesting properties. This paper analyses these ideals in the context of a Rees matrix semigroup. The properties thus observed actually determine the number of elements in the so formed principal topology. Further, the topology hence obtained is an example for a finite topology on an infinite set, provided the order of the Rees matrices is finite.

Keywords: Green's left quasiorder, Principal topology, Rees matrix semigroup.

Authors : S. S. Mahde, S. I. Khalaf, Y. N. Shawawreh, B. Shanmukha, A. M. Nour
Title : Laplacian Minimum Hub Energy of a Graph
Volume, Issue, Year : 8(3)(2020)
Pages : 59−69

Abstract: In this paper, we introduce Laplacian minimum hub energy $LE_H(G)$ of a graph $G$, and compute Laplacian minimum hub energies of some standard graphs, also for a number of well-known families of graphs. Upper and lower bounds for $LE_H(G)$ are established.

Keywords: Minimum hub set, Laplacian minimum hub matrix, Laplacian minimum hub eigenvalue, Laplacian minimum hub energy of a graph.

Authors : Soham Konar
Title : Delaunay Triangulations
Volume, Issue, Year : 8(3)(2020)
Pages : 71−76

Abstract: We examine a methodology to construct 3D maps. We assume the height above sea level is known only at a finite number of points. Mathematically, this problem is equivalent to reconstructing the graph of a function of two variables when the values of the function are only known at a finite number of points. This leads to a discussion of Delaunay triangulations and the algorithm to compute them. We illustrate the concept discussed with examples.

Keywords: Computational Geometry, Delaunay Triangulations, Algorithms.

Authors : S. A. Bhanotar
Title : Fibonacci and Lucas Numbers-Continued Fraction Expansion
Volume, Issue, Year : 8(3)(2020)
Pages : 77−84

Abstract: In modern science, there are lots of applications of Fibonacci and Lucas numbers have been used in number theory, computer science, applied mathematics and biology. In this paper, I have discussed Fibonacci number, Lucas number, the golden ratio, and their relations to them. I study numerous new properties of these sequences and focused to the generalized the formula for the Fibonacci number, Lucas number and some important identity; some observation of sunflower the head is carried out with the angular momentum velocity and represented continued fraction expansion of such number based on the golden ratio.

Keywords: Fibonacci number, Lucas number, Golden Ratio, Continued fraction expansion.

Authors : Arun Kumar Rao and Himanshu Pandey
Title : Estimation of Shape Parameter of Exponentiated Pareto Distribution Via Bayesian Approach
Volume, Issue, Year : 8(3)(2020)
Pages : 85−91

Abstract: In this paper, the exponentiated Pareto distribution is considered for Bayesian analysis. The expressions for Bayes estimators of the parameter have been derived under squared error, precautionary, entropy, K-loss, and Al-Bayyati's loss functions by using quasi and gamma priors.

Keywords: Bayesian method, exponentiated Pareto distribution, quasi and gamma priors, squared error, precautionary, entropy, K-loss, and Al-Bayyati's loss functions.

Authors : Nikky Kumari
Title : Intuitive Approach for Nonlinear Transportation Problem
Volume, Issue, Year : 8(3)(2020)
Pages : 93−98

Abstract: An intuitive approach has been developed for finding an optimal solution of nonlinear transportation problem. Method is presented in the form of an algorithm and illustrated through a numerical example. Approach is simple, easy to understand and apply.

Keywords: Nonlinear transportation problem, intuitive approach, active cell, allocation, optimal solution.

Authors : Jeffrey Wang
Title : Oscillation of Bridge: Mathematical Modeling of the Amplitude Under Different Situations
Volume, Issue, Year : 8(3)(2020)
Pages : 99−104

Abstract: We consider a function that shows the position of a bridge. This function includes the effect of the force applied by the soldier marching on it. We analyze the function and obtain how the impulse effect the position of the bridge in different cases, such as the resonance case-when the soldier applies a force with the same frequency as the frequency of the bridge oscillations-and the non-resonance case-when the soldier applies a force with a different frequency from the frequency of the bridge oscillations.

Keywords: Bridge, Oscillation, Modeling.

Authors : S. Arul Ravi
Title : Best Proximity Point Theorem for $\Phi$-Weak Contractions
Volume, Issue, Year : 8(3)(2020)
Pages : 105−110

Abstract: Fixed point theory for generalized $\phi$-weak contractions have been extended for Best proximity point using $p$-property.

Keywords: Best Proximity point, $p$-property, generalized $\phi$-weak contraction, complete metric spaces, lower semi-continuous.

Authors : P. Jaish and A. Joseph Kennedy
Title : The Rook Class Partition Algebras
Volume, Issue, Year : 8(3)(2020)
Pages : 111−123

Abstract: The Class partition algebras $P_{k}(n,m)$ have been studied independently in \cite{JK} by Kennedy and also studied in \cite{ME} by Martin and Elgamal. We introduce the rook version of class partition algebras $P_{k}(n,m)$, which is subalgebra of the algebra $P_{k}(n)\otimes P_{k}(m)$ tensor product partition algebra. We also find corresponding schur--weyl dualities.

Keywords: Wreath product , Symmetric group, Partition algebra, Centralizer algebra.

Authors : Chiraag Kambalimath
Title : Algorithmic Modeling of a Genome Sequence
Volume, Issue, Year : 8(3)(2020)
Pages : 125−139

Abstract: We describe how genomes are assembled and read. This involves the implementation of graph theory and the development of algorithms. The algorithms are written in Python.

Keywords: Genome Reconstruction, Algorithms, Bioinformatics.

Authors : V. Durai Murugan, R. Seethalakshmi and P. Namasivayam
Title : The Lattice Structure of the Subgroups of Order 42 and 48 in the Subgroup Lattices of $2 \times 2$ Matrices Over $Z_{7}$
Volume, Issue, Year : 8(3)(2020)
Pages : 141−146

Abstract: Let $\mathcal{G}= \left\{\left( \begin{array}{cc} a & b \\ c & d \end{array} \right): a,b,c,d \in Z_{p}, ad-bc \neq 0\right\}$. Then $\mathcal{G}$ is a group under matrix multiplication modulo p. Let $G = \left\{\left( \begin{array}{cc} a & b \\ c & d \end{array} \right)\in \mathcal{G} : ad-bc = 1\right\}$. Then G is a subgroup of $\mathcal{G}$. We have, $o(\mathcal{G}) = p(p^{2}-1)(p-1)$ and $o(G) = p(p^{2}-1)$. Let $L(G)$ denotes the lattice of subgroups of G, where G is the group of $2\times 2$ matrices over $Z_p$ having determinant value 1 under matrix multiplication modulo p, where p is a prime number. In this paper, we give the structure of the subgroups of order 42 and 48 of $L (G)$ in the case when $p=7$.

Keywords: Matrix group, subgroups, Lagrange's theorem, Lattice, Atom.

Authors : Ammar Alsinai, Anwar Alwardi and N. D. Soner
Title : An Atlas of Different Distances Sets Polynomials of Graphs of Order at most Six
Volume, Issue, Year : 8(3)(2020)
Pages : 147−161

Abstract: The different distances sets polynomial of a graph $G$ of order $p$ is defined as $D_{d}(G,x)=\sum\limits_{i=1}^pd_{d}(G,i)x^i$, where $d_{d}(G,i)$ is the number of different distances sets polynomials of $G$ of size $i$, \cite{Alsinai}. We call the roots of different distances sets polynomial of a graph the different distances roots of that graph. In this article, we compute different distances sets polynomial of all graphs of order less than or equal six and their roots and present them in tables.

Keywords: Different distances sets, different distances sets polynomials.

Authors : S. R. Jog, S. L. Patil and J. R. Gurjar
Title : Degree Sum Exponent Distance Index of a Graph
Volume, Issue, Year : 8(3)(2020)
Pages : 163−175

Abstract: In this paper, we determine degree sum exponent distance $\chi_{dist}(G)$ for some standard graphs and some graphs arising from complete graph, by taking it as a particular case of general sum-connectivity index.

Keywords: Degree, Distance, Degree sum distance exponent index.

Authors : Mohand M. Abdelrahim and Abdelilah K. Hassan
Title : The Use of Adomian Decomposition Method for Solving Nonlinear Wave-Like Equation With Variable Coefficients
Volume, Issue, Year : 8(3)(2020)
Pages : 177−186

Abstract: The Adomian Decomposition Method (ADM) has been widely applied in solving partial differential equations which represent various phenomena in engineering and physics. In this paper, nonlinear wave-like equations with variable coefficients are solved using Sawi Adomian De-composition Method (SADM). Sawi decomposition method is a combined form of Sawi transform method and the Adomian decomposition method. The nonlinear term can easily be handled with the help of Adomian polynomials which is considered to be a significant advantage of this technique over the other methods. We shall show that SADM is able to solve this type of equations effectively and accurately.

Keywords: Sawi transform, Sawi A domian decomposition, Wave-like equation.

Authors : P. R. K. Kishore and M. H. Melesse
Title : Fuzzy Ideals and Fuzzy Congruences of a Generalised Lattice
Volume, Issue, Year : 8(3)(2020)
Pages : 187−191

Abstract: This paper deals with the correspondence between fuzzy ideals, fuzzy filters and fuzzy congruences in a generalised lattice. Proved that lattice of fuzzy ideals (fuzzy filters) of a generalised lattice is isomorphic to the lattice of fuzzy ideals of a corresponding lattice. Finally observed that the lattice of fuzzy ideals of a type of generalised lattice is isomorphic to the lattice of fuzzy congruences of that.

Keywords: Poset, Lattice, Fuzzy lattice, Fuzzy ideal, Fuzzy congruence.

Authors : S. K. Tiwari and M. Gauratra
Title : Study of Problem of Some Fixed Point Result For Kannan and Chhatterjea Contraction on Generalized Complex Valued Metric Spaces
Volume, Issue, Year : 8(3)(2020)
Pages : 193−200

Abstract: In this paper, we study and established some fixed point theorem for general Kannan and Chhattrjea type contraction in generalized complex valued metric spaces. The results extend and improve the common fixed point result of Elkouch \& Marhrani \cite{elkmar}, which is introduced by Issara et al. \cite{issdee}.

Keywords: Fixed point, Common fixed point, General Kannan contraction, General Chhatterjea contraction, Generalized complex valued metric spaces.

Authors : Xinran Zheng
Title : Linear Regression With Only One Feature and Applications
Volume, Issue, Year : 8(3)(2020)
Pages : 201−206

Abstract: We review how to obtain, by elementary means, the equations that determine the slope and $y$-intercept of the line that best fits a certain given data. We illustrate the use of these equations with an example.

Keywords: Linear Regression, Elementary Means, Data Science.