The Journal of the 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>Informatics Publishing Limited and The Indian Mathematical Societyen-USThe Journal of the Indian Mathematical Society0019-5839Generalization on the Question of C. C. Yang in the Light of Weighted Shared Sets
http://www.i-scholar.in/index.php/JIMSIMS/article/view/177917
In this paper, with the help of weighted sharing method, we have extended the question of Yang [8] from value sharing to set sharing which in turn have improved the results of Li-Gu [6] and Yi [10, 11] to a large extent.Abhijit BanerjeeMolla Basir Ahamed2019-01-012019-01-0186Weighted β−absolute Convergence of Single and Double Walsh−Fourier Series of Functions of Φ − ∧ −BV
http://www.i-scholar.in/index.php/JIMSIMS/article/view/177918
For one variable function of Φ − ∧−bounded variation on [0,1] the sufficient condition for the weighted β−absolute convergence of its Walsh−Fourier series ∑<sub>m</sub> γ<sub>m</sub>| ˆ f(m)|<sup>β</sup>, where 0 < β < 2 and {γ<sub>m</sub>} is a weighted sequence, is obtained and is extended for two dimensional analogue.Kiran N. DarjiRajendra G. Vyas2019-01-012019-01-01863-Absorbing Principal <I>T</I>-Ideals in the Ternary Semiring of Non-positive Integers
http://www.i-scholar.in/index.php/JIMSIMS/article/view/177919
Since the product of even number of elements of ternary semiring S may not be element of <em>S</em>, the concept of 2-absorbing ideal in <em>S</em> can not be defined. In this paper, we introduce the concept of 3-absorbing ideals in a commutative ternary semiring with identity element and obtain characterizations of 3-absorbing principal ideals and 3-absorbing principal <em>T</em>-ideals in the ternary semiring of non-positive integers.K. J. IngaleJ. N. Chaudhari2019-01-012019-01-0186On Nagata’s Result about Height One Maximal Ideals and Depth One Minimal Prime Ideals (II)
http://www.i-scholar.in/index.php/JIMSIMS/article/view/177920
We expand the theory of height one maximal ideals and depth one minimal prime ideals initiated by M. Nagata and continued by the authors in part I. A local ring is doho in case its completion has at least one depth one minimal prime ideal. We establish several families of doho local rings, prove that certain local rings associated with Rees valuation rings are doho, and complement a famous construction of Nagata by proving that each doho local domain (<I>R,M</I>) of altitude α ≥ 2 has a quadratic integral extension over-domain with precisely two maximal ideals, one of height α and the other of height one.Paula KempLouis J. RatliffKishor Shah2019-01-012019-01-0186Asymptotic Behaviour of Distributional Mexican Hat Wavelet Transform
http://www.i-scholar.in/index.php/JIMSIMS/article/view/177921
Theory of Weierstrass transform is ventured to derive properties of the Mexican hat wavelet transform by Pathak <em>et al</em>. [3]. In this paper, distributional Mexican hat wavelet transform is studied and an asymptotic behaviour for the same is established. Further, tauberian result of Mexican hat wavelet transform is derived.Anshu MalaAbhishek SinghDeepali Saxena2019-01-012019-01-0186Uniqueness for Q-shift of Meromorphic Functions of Zero Order Sharing Small Function
http://www.i-scholar.in/index.php/JIMSIMS/article/view/177922
To study the uniqueness results for <em>q</em>-shift differential-difference polynomials of meromorphic functions of zero order sharing a small function, we consider the problems in [12] and [8]. We point out a number of gaps in its main proof and rectify these. Then present an improved as well as generalized result in a more compact form. Also, exhibit some examples to show that one of the conditions of the obtained result is best possible.Rajib Mandal2019-01-012019-01-0186Approximate Controllability Results for Neutral Stochastic Differential Equations of Sobolev Type with Unbounded Delay in Hilbert Spaces
http://www.i-scholar.in/index.php/JIMSIMS/article/view/177923
In this paper, we discuss the approximate controllability of the neutral stochastic differential equations of Sobolev type with unbounded delay in Hilbert Spaces. A set of sufficient conditions are established for the existence and approximate controllability of the mild solutions using Krasnoselskii-Schaefer-type fixed point theorems and stochastic analysis theory. An application involving partial differential equation with unbounded delay is addressed.R. NirmalkumarR. Murugesu2019-01-012019-01-0186Elliptic Partial Differential Equation Involving a Singularity and a Radon Measure
http://www.i-scholar.in/index.php/JIMSIMS/article/view/177924
The aim of this paper is to prove the existence of solution for a partial differential equation involving a singularity with a general nonnegative, Radon measure μ as its nonhomogenous term which is given as<p>−Δu = f(x)h(u) + μ in Ω,</p><p>u = 0 on ∂Ω,</p><p>u > 0 on Ω,</p>where Ω is a bounded domain of R<sup>N</sup>, <em>f</em> is a nonnegative function over Ω.Akasmika PandaSekhar GhoshDebajyoti Choudhuri2019-01-012019-01-0186Revisiting Some Pal Type Birkhoff Interpolation Problems
http://www.i-scholar.in/index.php/JIMSIMS/article/view/177925
In this paper we revisit Pal type Birkhoff interpolation for the sets consisting of zeros of polynomials with complex coefficients with two or more additional nodes at value nodes. We also evaluate regularity of (0, 2) Pal type Birkhoff interpolation on the zeros of the polynomials obtained by applying mobius transform to the zeros of roots of unity with one additional complex node at value nodes.A. K. PathakPoornima Tiwari2019-01-012019-01-0186Stability Analysis of a Three Species Non-linear Eco-system with Restricted Resources
http://www.i-scholar.in/index.php/JIMSIMS/article/view/177926
The aim of this paper is to introduce the model and the study of a three species non linear ecosystem with restricted resources. In this paper, the system comprises of two species hosts S<sub>1</sub>, S<sub>2</sub> and one commensal species S<sub>3</sub>. Further, S<sub>1</sub> and S<sub>2</sub> are neutral and all the three species posses restricted resources. Commensalism is a symbiotic interaction between two or more populations which live together, and in which only one of the populations (commensalism) is beneted while the other (host) is not effected. The model equations constitute a set of three first order non-linear simultaneous differential equations. Criteria for the asymptotic stability of all the eight equilibrium states are established. The system would be stable if all the characteristic roots are negative, in case they are real, and have negative real parts, in case they are complex. Trajectories of the perturbations over the equilibrium states are illustrated. Further the global stability of the system is established with the aid of suitably constructed Liapunov's function.B. Hari Prasad2019-01-012019-01-0186Sum Formulas Involving Powers of Balancing and Lucas-balancing Numbers
http://www.i-scholar.in/index.php/JIMSIMS/article/view/177927
In this article, we obtain the closed form expressions for different types of summation formulas involving certain powers of balancing and Lucas-balancing numbers using the telescoping summation formula.S. G. RayaguruG. K. Panda2019-01-012019-01-0186Generalized Mittag-Leffler Matrix Function and Associated Matrix Polynomials
http://www.i-scholar.in/index.php/JIMSIMS/article/view/177928
The Mittag-Leffler function has been found useful in solving certain problems in Science and Engineering. On the other hand, noticing the occurrence of certain matrix functions in Special functions’ theory in general and in Statistics and Lie group theory in particular, we introduce here a matrix analogue of a recently generalized form of Mittag-Leffler function. This function yields the matrix analogues of the Saxena-Nishimoto’s function, Bessel-Maitland function, Dotsenko function and the Elliptic Function. We obtain matrix differential equation and eigen matrix function property for the proposed matrix function. Also, a generalized Konhauser matrix polynomial is deduced and its inverse series relations and generating function are derived.Reshma SanjhiraB. V. NathwaniB. I. Dave2019-01-012019-01-0186Elliptic WP-Bailey Transform and its Applications
http://www.i-scholar.in/index.php/JIMSIMS/article/view/177929
In this paper, idea of WP-Bailey transform has been extended to elliptic WP-Bailey transform and it has been applied to establish certain interesting summation and transformation formulas for elliptic and theta hypergeometric series.Satya Prakash SinghVijay Yadav2019-01-012019-01-0186Hypercyclicity, Supercyclicity and Cyclicity of Composition Operators on L<sup>p</sup> Spaces
http://www.i-scholar.in/index.php/JIMSIMS/article/view/177930
In this paper, we discuss hypercyclicity, supercyclicity and cyclicity of composition operators on <em>l<sup>p</sup></em>(1 ≤ p < ∞). We prove that no composition operator is hypercyclic on <em>l</em><sup>p</sup>. Further, we also prove that <em>C<sub>Φ</sub></em> : <em>l<sup>p</sup></em> → <em>l<sup>p</sup></em> is supercyclic if and only if <em>Φ</em> is injective and <em>Φ</em><sup>n</sup> has no fixed point in N, for any n ∈ N. We also give a sufficient condition and some necessary conditions for cyclicity of composition operator.Vijay Kumar SrivastavaHarish Chandra2019-01-012019-01-0186On Some Categories of Riemannian Manifolds
http://www.i-scholar.in/index.php/JIMSIMS/article/view/177931
In this article we introduce two categories of Riemannian manifolds. We also study some properties of such categories and compare them with the previously known categories.R. B. Yadav2019-01-012019-01-0186