## Issue 2Volume 7 (2019)

 Authors : Saidat Fehintola Olaniran Title : Laplace Approximation to the Posterior of Bayesian Weibull Model with Time-Varying Effect Volume, Issue, Year : 7(2)(2019) Pages : 1−6

Abstract: In this paper, the estimation of the parameter of the Bayesian Weibull model with time-varying effect is considered. The Laplace approximation was developed and compared to the maximum likelihood approach achieved via the Newton-Raphson procedure. The efficiency of the two methods was analyzed using Monte-Carlo samples drawn from the time-varying Weibull model.

Keywords: Bayesian Weibull model, Newton-Raphson procedure, time-varying Weibull model.

 Authors : Ch. Srinivasa Rao, K. Satya Murthy, S. S. A. Sastri and K. Sujatha Title : Some Fixed Point Theorems in Dislocated Quasi b-metric Spaces Volume, Issue, Year : 7(2)(2019) Pages : 7−12

Abstract: In this paper we have given a fixed point theorem in dislocated quasi b-metric spaces which is generalization of dislocated quasi metric, partial b-metric spaces and the Banach contraction principle.

Keywords: Metric Space, Dislocated Quasi b- Metric Space, Contraction, Fixed Point.

 Authors : P. O. Mogotu, N. B. Okelo and Omolo Ongati Title : On Compactness of Similarity Orbits of Norm-Attainable Operators Volume, Issue, Year : 7(2)(2019) Pages : 13−21

Abstract: The notion of compactness plays an important role in analysis. It has been extensively discussed on both metric and topological spaces. Various properties of compactness have been proved under the underlying spaces. However, if we consider these sets to be from similarity orbits of norm-attainable operators, little has been done to investigate their compactness. In this paper, we introduce the concept of compactness of similarity orbits of norm-attainable operators in aspect of invariant topological spaces and investigate their properties.

Keywords: Similarity orbits; invariant subsets; compactness and Topological space.

 Authors : S. Kabbadj Title : Entropic Approximation Volume, Issue, Year : 7(2)(2019) Pages : 23−38

Abstract: In this article, we study the theoretical aspect of the entropic approximations of a convex function on $R^{p}$, we put in evidence it properties of regulirization and approximation of those approximates, we find the most of the approximal properties of Moreau-Yosida.

Keywords: Convex minimization, Approximation of Moreau-Yosida, Bregman's function, Legendre's function, Entropic approximation.

 Authors : J. Suresh Kumar Title : Graph Algorithms and Abstraction for Number Theoretic Concepts Volume, Issue, Year : 7(2)(2019) Pages : 39−41

Abstract: In this paper, we discuss graph theoretic representation of the number theoretic concepts such as relatively prime numbers, Greatest Common Divisor (GCD), Geometric mean (GM) and Fibonacci numbers using graph labeling. We also propose a new generalization of Geometric mean.

Keywords: Graph, Greatest Common Divisor, Geometric mean.

 Authors : S. Vijayabarathi Title : Positive Pre $A^*$-algebra Function in terms of DNF Volume, Issue, Year : 7(2)(2019) Pages : 43−47

Abstract: In this paper, positive Pre $A^*$-algebra function is defined and to support this two theorems have been proved.

Keywords: Positive Pre $A^*$-algebra function, prime implicants, absorption,monotone function.

 Authors : R. Deepa, T. Surendiran, D. Michael Raj and S. Suresh Title : Some Properties of Spectral Theorem Over Hilbert Space Volume, Issue, Year : 7(2)(2019) Pages : 49−50

Abstract: The aim of this paper is to study some properties over spectral theorem of finite dimensional Hilbert space H.

Keywords: Eigen values, Eigen spaces, Closed sub-spaces, Normal operator.

 Authors : Abul Kalam Mondal Title : Some Global Properties of Almost Pseudo Ricci Symmetric Manifolds Satisfying Codazzi Type of Ricci Tensor Volume, Issue, Year : 7(2)(2019) Pages : 51−57

Abstract: The object of the present paper is to study some global properties of almost pseudo Ricci symmetric manifold satisfying Codazzi type of Ricci tensor. Among others, it is proved that if a compact, orientable $A(PRS)_n$ satisfying Codazzi type of Ricci tensor without boundary admits a non-isometric conformal transformation, then the $A(PRS)_n$ is isometric to a sphere. Also we obtain a sufficient condition for a compact, orientable $A(PRS)_n$ satisfying Codazzi type of Ricci tensor without boundary to be conformal to a sphere in $E_{n+1}$.

Keywords: Almost pseudo Ricci symmetric manifold, compact, orientable manifold of this without boundary.

 Authors : T. K. Mathew Varkey and A. M. Shyla Title : Some Properties of Intuitionistic Fuzzy Soft Graph Volume, Issue, Year : 7(2)(2019) Pages : 59−73

Abstract: We present a novel framework for handling intuitionistic fuzzy soft information by combining the theory of intuitionistic fuzzy soft sets with graphs. We presented the notions of Intuitionistic Fuzzy Soft graph, Strong intuitionistic fuzzy soft graph, Complete intutionistic fuzzy soft graph in our previous paper. In this article, we introduce some new concepts of intuitionistic fuzzy soft graph, explain notion of ifs-complement of an intuitionistic fuzzy soft graph and ifs-$\phi$-complement of an intuitionistic fuzzy soft graph with example. Finally, we investigate the properties of ifs-complement and ifs-$\phi$-complement of an intuitionistic fuzzy soft graph.

Keywords: Intuitionistic Fuzzy Soft Graph, ifs-Complement of an Intuitionistic Fuzzy Soft Graph, ifs-$\phi$-Complement of an Intuitionistic Fuzzy Soft Graph.

 Authors : L. Njagi, B. M. Nzimbi and S. K. Moindi Title : On Pseudo-inverses and Duality of Frames in Hilbert Spaces Volume, Issue, Year : 7(2)(2019) Pages : 75−88

Abstract: In this paper, we show how to find dual frames using the notion of singular value decomposition and pseudo-inverses of an operator in a Hilbert space. We will also show how properties of dual frames are linked to the spectral properties of the dual frame operator and the Grammian.

Keywords: Frame, dual frame, tight frame, canonical tight frame, Parseval, frame operator, analysis operator, Grammian.

 Authors : V. S. Dhakar and Smita Sharma Title : Basic Analogue of Fractional Derivative and Some Special Functions Volume, Issue, Year : 7(2)(2019) Pages : 89−96

Abstract: The main objects of this paper is devoted to the basic analogues of fractional differentiation of classical functions and a theorem on term by term basic analogues of fractional differentiation has been derived, which is an extension of the result given by Yadav and Purohit (2004) [11]. Several special cases are also mentioned.

Keywords: The basic q-analogue, q-integral and differentia operator, Bessel-Maitland function, multiindex Mittag-Leffler function and F-function.

 Authors : T. A. Akugre and K. Nantomah Title : On Some Properties of the Real Matrix-Variate Gamma Function Volume, Issue, Year : 7(2)(2019) Pages : 97−103

Abstract: In this paper, we prove that the real matrix-variate gamma function is logarithmically convex and as a consequence, we derive some inequalities involving the function. Also, we introduce the real matrix-variate digamma function and as applications, we derive some inequalities for certain ratios of the real matrix-variate gamma function. The methods of proofs are analytical in nature.

Keywords: Real matrix-variate gamma function, real matrix-variate digamma function, logarithmically convex, inequality.

 Authors : Ankita Sharma and Rajan Arora Title : Analytical and Numerical Analysis of Newell--Whitehead--Segel equations by HAM Volume, Issue, Year : 7(2)(2019) Pages : 105−113

Abstract: In this paper, we employ Homotopy Analysis Method (HAM) to Newell--Whitehead--Segel equation which is used in different fields of sciences like bio-engineering, chemical engineering, biology, mechanical engineering and ecology etc. Approximate series solutions have been obtained and the results are compared with the closed form solutions of the equation which shows that this technique gives high accurate results. HAM is a reliable technique, easy to use and is widely applicable to a large class of non-linear differential equations.

 Authors : S. Kabbadj Title : Inexact Version of the Entropic Proximal Point Algorithm Volume, Issue, Year : 7(2)(2019) Pages : 115−124

Abstract: In this paper, we study an inexact version of the entropic proximal point algorithm defined by $$x^{k} \in \varepsilon_{k} - Argmin \lbrace f(.) + \lambda_{k}^{-1} D_{h} ( ., x^{k-1} ) \rbrace.$$ This study recovers the most of the algotithms of the proximal point.

Keywords: Convex optimization, Bregman's function, Entropic approximation.

 Authors : Jai Prakash Patel and Neelam Pandey Title : Fractional Calculus and Certain Integral Transform of Extended $\tau$-Hypergeometric Function Volume, Issue, Year : 7(2)(2019) Pages : 125−136

Abstract: In this paper, authors establish the some new integral and derivative formulas of generalized $\tau$-hypergeometric functions $_3\Gamma_2 ^{\tau} (z)$ defined by (R. K. Gupta [3,4]). Furthermore by applying some integral transforms as Beta-transform, Verma transform, Whittaker transform, Laplace transform and $P_\alpha$-transform on the resulting formulas.

Keywords: Extended $\tau$-Hypergeometric Function,Incomplete Pochhammer symbols, Incomplete Gamma function, Fractional derivative and integral operators, integral transform.

 Authors : Hailemariam Abebe Tekile Title : Gradient Descent Method for Perron Eigenvalue Minimization of Incomplete Pairwise Comparison Matrices Volume, Issue, Year : 7(2)(2019) Pages : 137−148

Abstract: Pairwise comparison matrices are often employed as a basic tool in multi-criteria decision-making. Incomplete matrix appears when some elements are missing. The paper aims to implement Gradient descent method for minimization of Perron eigenvalue problem that arises from incomplete pairwise comparison matrices. Numerical example is given at the end.

Keywords: Perron eigenvalue, Incomplete pairwise comparison matrix, Gradient descent method, Convex programming.

 Authors : G. Chandra Shekara Title : Chebyshev Spectral Collocation Solution of Non-Linear Time Dependent Partial Differential Equation With Time Derivative Boundary Conditions Volume, Issue, Year : 7(2)(2019) Pages : 149−156

Abstract: The present paper demonstrate the implementation of time derivative boundary conditions in the Chebyshev differentiation matrices. The non-linear time dependent partial differential equations with time derivative boundary conditions(mixed boundary conditions) is considered and the spectral collocation algorithm is developed and solutions are presented. Quasi-linearization technique is used to convert the non-linear partial differential equation into linear form by using Taylor series approximation about the initial guess. Lagrange interpolating polynomials are used as basis of the solution at the Gauss-Labatto grid points. Also the time derivative boundary conditions are incorporated within the Chebyshev differentiation matrices. MATLAB software is used to implement this algorithm and numerical results are depicted graphically. The case study problem is solved using this approach and the solution found by the this method is more accurate compared to the finite difference method with uniform grid points.

Keywords: Spectral-Collocation, Quasi-Linearization, Gauss-Labatto points, Lagrange polynomials, Cheb function, Cauchy-Boundaries.

 Authors : R. Karthikeyan and R. Dinesh Kumar Title : MHD Oscillatory Rotation Flow With Radiation Effects Along a Porous Medium Bounded by Two Vertical Porous Plates Under the Influence of Hall Current And Heat Absorption With Chemical Reaction Volume, Issue, Year : 7(2)(2019) Pages : 157−170

Abstract: Magnetohydrodynamics oscillatory flow in between two vertical porous plates through porous medium in presence of hall current has been studied. One plate is kept stationary and other plate is kept as oscillating. The basic governing equations of the problem are transformed into a system of non dimensional differential equations. Effect of various parameters on velocity , temperature and concentration, skin friction and rate of heat and mass transfer were studied. The non dimensional parameters influences are discussed graphically using perturbation method.

Keywords: Hall Current, Chemical Reaction, MHD, Radiation, Porous Medium Oscillatory, Heat Source.

 Authors : P. Shanmugapriya and P. Maheswari Naik Title : Spectral Properties of M-class $A_{k}^{*}$ Operator Volume, Issue, Year : 7(2)(2019) Pages : 171−176

Abstract: The Banach algebra on a non-zero complex Hilbert space H of all bounded linear operators are denoted by $B(H)$. An operator T is defined as an element in $B(H)$. If T belongs to $B(H)$, then $T^{*}$ means the adjoint of T in $B(H)$. An operator T is called class $A(k)$ if $\left|T\right|^{2} \le \left(T^*\left|T\right|^{2k} T\right)^{\frac{1}{k+1} }$ for $k > 0$. An operator T is called class $A_{k}$ if $\left|T\right|^{2} \le \left(\left|T^{k+1} \right|^{\frac{2}{k+1} } \right)$ for some positive integer k. S. Panayappan \cite{11} introduced class $A_{k}^{* }$ operator as an operator T is called class $A_{k}^{*}$ if $\left|T^{k} \right|^{\frac{2}{k} } \ge \left|T^*\right|^{2}$ where k is a positive integer'' and studied Weyl and Weyl type theorems for the operator \cite{9}. In this paper we introduced extended class $A_{k}^{* }$ operator and studied some of its spectral properties. We also show that extended class $A_{k}^{*}$ operators are closed under tensor product.

Keywords: Class $A_{k}^{*}$, Quasi Class $A_{k}^{*}$, Weyl's theorem.

 Authors : S. K. Kalra, H. Kaur, J. K. Matharoo and S. Virdi Title : Commerce Executive v/s Mathematical Modeling Volume, Issue, Year : 7(2)(2019) Pages : 177−182

Abstract: Mathematics can be second-hand to represent real-world situations. Mathematical Models~are used that scrutinize historical data and use probability distribution as input for predicting the future principles. For the Commerce administrative~statistical or quantitative aspects of the various components of the dilemma are the most important. When we build a mathematical model and put into symbols for constants and variables, which for the most part stand for numbers in Commerce executive. Break-even analysis/Cost-volume-profit model, quantitative model, inventory models are very useful for the Commerce enrichment. In processing executive accounting business, the combination of mathematical models and the actual stipulation of enterprises and communal institutions can effectively solve various organization problems and evade different outfitted risks, But according to the Commerce executive theory, scientific executive accounting is not post-executive, but need the establishment of highly-adaptive mathematical models according to certain mathematical management ideas and principles to measure relevant parameter indexes, solve various difficult problems relating to enterprise supervision, and achieve effective executive. This is of great connotation to the prophecy, planning and control of enterprise procedure tricks.

Keywords: Commerce, Executive, Mathematical Modeling.

 Authors : R. Sivaraman Title : The Machine Interference Model; $(m, n)$ Systems with Balking and Spares Volume, Issue, Year : 7(2)(2019) Pages : 183−188

Abstract: In this paper, we have obtained an analytical solution of the queue: (m, n) system for machine interference with balking and spares considering the discipline FIFO. The probabilities have been calculated for the transient case, we have calculated the system availability and up time ratio. They had studied $(m, n)$ system with spares only. It has been discussed the truncated Poissonion queue: $MIM/C/k/N$ for machine interference but without assumption of balking, reneging or spares, They considered the system; MIMICm m with spares only. Medhi obtained a solution for the system: $MIMIC/mn/rn$ without assumption of balking, reneging or spares, and derived an analytical solution of the queue: $M/MJC/k/N$ for machine interference with balking, reneging and spares.

Keywords: Poisson Queue, Birth-Death coefficients, Probability differential difference equations, Up Time Ratio (UTR).