Journal of Indian Mathematical Society
http://www.i-scholar.in/index.php/JIMSIMS
<div id="i-scholarabout">The Society began publishing Progress Reports right from 1907 and then the Journal from 1908 (The 1908 and 1909 issues of the Journal are entitled "The Journal of the Indian Mathematical Club"). From 1910 onwards,it is published as its current title 'the Journal of Indian Mathematical Society. The four numbers of the Journal constitute a single volume and it is published in two parts: numbers 1 and 2 (January to June) as one part and numbers 3 and 4 (July to December) as the second part. The four numbers of the Student are published as a single yearly volume. Only the research papers of high quality are published in the Journal.</div>The Indian Mathematical Societyen-USJournal of Indian Mathematical Society0019-5839On the Uniqueness of Power of a Meromorphic Function Sharing a Set with its k-th Derivative
http://www.i-scholar.in/index.php/JIMSIMS/article/view/166160
<p>In the existing literature, many researchers consider the uniqueness of the power of a meromorphic function with its derivative counterpart share certain values or small functions. Here we consider the same problem under the aegis of a more general settings namely set sharing.</p>Abhijit BanerjeeBikash Chakraborty2018-01-012018-01-0185Effects of Rotation, Radiation and Hall Current on MHD Flow of a Viscoelastic Fluid Past an Infinite Vertical Porous Plate through Porous Medium with Heat Absorption, Chemical Reaction and Variable Suction
http://www.i-scholar.in/index.php/JIMSIMS/article/view/166161
The present study analyses the effects of Hall current and heat absorption on a viscous, incompressible, optically thick and electrically conducting viscoelastic fluid flow past an infinite vertical porous plate through porous medium in rotating system with variable suction, thermal radiation and chemical reaction in the presence of uniform magnetic field. The perturbation technique is employed to solve the governing nonlinear partial differential equations to obtain the expressions for velocity, temperature and concentration profile. With the help of graphs and tables, the effects of pertinent flow parameters on the velocity, temperature and concentration fields, shear stress, Nusselt number and Sherwood number within the boundary layer are discussed. The results reveal that the observed parameters in rotating system have a noteworthy influence on the ow, heat and mass transfer.Khem ChandNidhi Thakur2018-01-012018-01-0185New Approach to Minkowski Fractional Inequalities Using Generalized K-Fractional Integral Operator
http://www.i-scholar.in/index.php/JIMSIMS/article/view/166162
In this paper, we obtain results related to Minkowski fractional integral inequality using generalized k-fractional integral operator is in terms of the Gauss hypergeometric function.Vaijanath L. Chinchane2018-01-012018-01-0185On Rough Convergence of Fuzzy Numbers Based on α-Level Sets
http://www.i-scholar.in/index.php/JIMSIMS/article/view/166163
In this paper we have established some basic properties of rough convergence for fuzzy number sequences. Also introduce the set of rough limit points of a sequence of fuzzy number using α-level set and prove some results associated with this set.Shyamal DebnathDebjani Rakshit2018-01-012018-01-0185Modified Adomian Decomposition Method for Solving Fuzzy Volterra-Fredholm Integral Equation
http://www.i-scholar.in/index.php/JIMSIMS/article/view/166164
In this paper, a modied Adomian decomposition method has been applied to approximate the solution of the fuzzy Volterra-Fredholm integral equations of the first and second Kind. That, a fuzzy Volterra-Fredholm integral equation has been converted to a system of Volterra-Fredholm integral equations in crisp case. We use MADM to find the approximate solution of this system and hence obtain an approximation for the fuzzy solution of the Fuzzy Volterra-Fredholm integral equation. A nonlinear evolution model is investigated. Moreover, we will prove the existence, uniqueness of the solution and convergence of the proposed method. Also, some numerical examples are included to demonstrate the validity and applicability of the proposed technique.Ahmed A. HamoudKirtiwant P. Ghadle2018-01-012018-01-0185Sturm-Liouville Problems with Discontinuities at Two Interior Points
http://www.i-scholar.in/index.php/JIMSIMS/article/view/166165
<p>In this paper, we study the Sturm-Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions at two interior points. We establish a new operator <em>A</em> associated with the problem, prove the operator <em>A</em> is self-adjoint in an appropriate space <em>H</em>, construct the basic solutions and investigate some properties of the eigenvalues and corresponding eigenfunctions, then obtain asymptotic formulas for the eigenvalues and eigenfunctions, its Green function and the resolvent operator are also involved.</p>Hongmei Han2018-01-012018-01-0185Path Connected Components in the Spaces of Weighted Composition Operators with the Strong Operator Topology II
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The path connected components are determined in the space of weighted composition operators on the space of bounded harmonic functions with the strong operator topology.Kei Ji IzuchiYuko Izuchi2018-01-012018-01-0185On the Rate of Convergence of Wavelet Expansions
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In this paper we estimate the rate of convergence of wavelet expansion of functions <em>f</em> ∈ <em>L<sup>p</sup></em>, 1 ≤ <em>p</em> ≤ ∞ at a point x. The pointwise and <em>L<sup>p</sup></em> results were obtained by Kelly, S. [4]. Our result generalizes her result.Varsha Karanjgaokar2018-01-012018-01-0185Heat Potentials Method in the Treatment of One-Dimensional Free Boundry Problems Applied in Cryomedicine
http://www.i-scholar.in/index.php/JIMSIMS/article/view/166168
Free boundary problems are considered to be the most difcult and the least researched in the eld of mathematical physics. The present article is concerned with the research of the following issue: treatment of one-dimensional free boundary problems. The treated problem contains a nonlinear evolutionary equation, which occurs within the context of mathematical modeling of cryosurgery problems. In the course of the research, an integral expression has been obtained. The obtained integral expression presents a general solution to the non-homogeneous evolutionary equation which contains the functions that represent simple-layer and double-layer heat potential density. In order to determine the free boundary and the density of potential a system of nonlinear, the second kind of Fredholm integral equations was obtained within the framework of the given work. The treated problem has been reduced to the system of integral equations. In order to reduce the problem to the integral equation system, a method of heat potentials has been used. In the obtained system of integral equations instead of K(ξ; x; τ - t) in case of Dirichlet or Neumann conditions the corresponding Greens functions G(ξ; x; τ - t) or N(ξ; x; τ - t) have been applied. Herewith the integral expression contains fewer densities, but the selection of arbitrary functions is reserved. The article contains a number of results in terms of building a mathematical model of cooling and freezing processes of biological tissue, as well as their effective solution development.Fatimat K. KudayevaArslan A. KaigermazovElizaveta K. EdgulovaMariya M. TkhabisimovaAminat R. Bechelova2018-01-012018-01-0185Solution of Integral Equations by Dunkl and Distributional Dunkl Transform
http://www.i-scholar.in/index.php/JIMSIMS/article/view/166169
The paper investigates the Dunkl transform and distributional Dunkl transform and the basic properties as convolution. The integral equations such as Volterra integral equation of first and second kind and Abel integral equation are solved by using dunkl transform. Further, solution obtained is considered in distributional sense by employing integral equations to distribution spaces and as well as using the distributional Dunkl transform for its solution.Deshna Loonker2018-01-012018-01-0185An Appraisal of the Greek and Indian Approaches in Determining the Surface Area of a Sphere
http://www.i-scholar.in/index.php/JIMSIMS/article/view/166170
While both the Greek and Indian civilisations have made immense contributions to the development of mathematics, their approaches to various problems widely differ, both in terms of the techniques employed by them and in their scope. We demonstrate this in the context of determining the surface area of a sphere. While the solution to this problem is attributed to Archimedes (3rd cent. BCE) in the Greek tradition, the first surviving proof in the Indian tradition can be found in Bhāskara’s Siddhāntaśiromaṇi (12th cent. CE). In this paper, we discuss the approaches taken by Archimedes and Bhāskara and compare their techniques from a mathematical as well as a pedagogical standpoint.K. MaheshAditya KolachanaK. Ramasubramanian2018-01-012018-01-0185On the Uniqueness of Certain Type of Difference Polynomial Sharing a Small Function
http://www.i-scholar.in/index.php/JIMSIMS/article/view/166171
The purpose of this paper is to study the uniqueness problems of certain type of difference polynomial sharing a small function. In this paper, we not only point out some gaps in the proof of the main results in [14], but also rectify the errors and present our main results in a more compact way. Also we exhibit two examples to show that one of the conditions of our result is the best possible.Sujoy MajumderSomnath Saha2018-01-012018-01-0185Monoid and Topological Groupoid
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Here we introduce some new results which are relative to the concept of topological monoid-groupoid and prove that the category of topological monoid coverings of X is equivalent to the category covering groupoids of the monoid-groupoid π<sub>1</sub>(X). Also, it is shown that the monoid structure of monoid-groupoid lifts to a universal covering groupoid.Mohammad Qasim Mann'a2018-01-012018-01-0185Atom Bond Connectivity Indices of Jahangir Graphs (J<sub>n,m</sub>)
http://www.i-scholar.in/index.php/JIMSIMS/article/view/166173
In this paper, we determine the first four types of atom bond connectivity indices of Jahangir graphs.Keerthi G. MirajkarBhagyashri R. Doddamani2018-01-012018-01-01852-Inner Product which Takes Values in a Locally <i>C*</i> - Algebras
http://www.i-scholar.in/index.php/JIMSIMS/article/view/166174
<p>In this paper we introduce the new concept of 2-inner product map that takes values on locally<i>C*</i>-algebras. Then we prove some results on Schwarz inequality, the polarization identity and related important properties.</p>B. Mohebbi NajmabadiTayebe Lal Shateri2018-01-012018-01-0185p-Deformation of a General Class of Polynomials and its Properties
http://www.i-scholar.in/index.php/JIMSIMS/article/view/166175
The work incorporates the extension of the Srivastava-Pathan’s generalized polynomial by means of p-generalized gamma function: Γ<sub>p</sub> and Pochhammer p-symbol (x)<sub>n,p</sub> due to Rafael Dıaz and Eddy Pariguan [Divulgaciones Mathematicas Vol.15, No. 2(2007), pp. 179-192]. We establish the inverse series relation of this extended polynomial with the aid of general inversion theorem. We also obtain the generating function relations and the differential equation. Certain <em>p</em>-deformed combinatorial identities are illustrated in the last section.Rajesh V. SavaliaB. I. Dave2018-01-012018-01-0185Four-Dimensional Conformally Flat Berwald and Landsberg Spaces
http://www.i-scholar.in/index.php/JIMSIMS/article/view/166176
The problem of conformal transformation and conformal flatness of Finsler spaces has been studied in [6], [16], [17], [20], [21]. Recently, Prasad et. al [19] have studied three dimensional conformally flat Landsberg and Berwald spaces and have obtained some important results. The purpose of the present paper is to extend the idea of conformal change to four dimensional Finsler spaces and find the suitable conditions under which a four dimensional conformally at Landsberg space becomes a Berwald space.Gauree Shanker2018-01-012018-01-0185Bernstein Operator of Rough λ-Statistically and ρ Cauchy Sequences Convergence on Triple Sequence Spaces
http://www.i-scholar.in/index.php/JIMSIMS/article/view/166177
<p>In this article, using the concept of natural density, we introduce the notion of Bernstein polynomials of rough λ−statistically and ρ−Cauchy triple sequence spaces. We deﬁne the set of Bernstein polynomials of rough statistical limit points of a triple sequence spaces and obtain to λ−statistical convergence criteria associated with this set. We examine the relation between the set of Bernstein polynomials of rough λ−statistically and ρ−Cauchy triple sequences.</p><p> </p><p> </p>S. VelmuruganN. Subramanian2018-01-012018-01-0185