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 Society0019-5839An Estimate of the Growth of Cohomology with Coefficients
http://www.i-scholar.in/index.php/JIMSIMS/article/view/209100
For a connected reductive algebraic group over an arbitrary number eld, we consider a nite dimensional algebraic, irreducible representation of the group of its real points. Each adelic locally symmetric space corresponding to a level structure constructed using the group has an associated sheaf induced by this representation. The purpose of this note is to estimate the rate of growth of the total dimension of the pertinent cohomology with coecients as either of the level structure or the associated sheaf varies. We obtain an upper bound on this total dimension. We also obtain a lower bound under certain topological conditions. Both the bounds are consistent with several classical dimension formulae as well as other known results.Chaitanya Ambi2021-07-012021-07-0188Uniqueness of Meromorphic Functions Ordinarily and Partially Sharing Values With Reduced Linear <i>C</i>-shift Operators
http://www.i-scholar.in/index.php/JIMSIMS/article/view/209101
In this paper, we investigate the uniqueness problem of meromorphic functions ordinarily and partially sharing values with the reduced linear c-shift operators governed by them, which practically provide an extensions and improvements of a number of recent results at a large extent.Abhijit BanerjeeArpita Roy2021-07-012021-07-0188Some Biharmonic Problems on the Tangent Bundle with a Berger-type Deformed Sasaki Metric
http://www.i-scholar.in/index.php/JIMSIMS/article/view/209102
Let (M<sub>2k</sub>,Φ,g) be an almost anti-paraKahler manifold and TM its tangent bundle equipped with the Berger type deformed Sasaki metric gBS and the paracomplex structure Φ<sub>˜</sub>. In this paper, we deal with the biharmonicity of canonical projection π : TM →M and a vector field X which is considered as a map X : M → TM.Abdallah MedjadjHichem ElhendiLakehal Belarbi2021-07-012021-07-0188Growth Properties of Solutions of Complex Linear Differential-difference Equations with Coefficients having the Same Logarithmic Order in the Unit Disc
http://www.i-scholar.in/index.php/JIMSIMS/article/view/209103
In this paper, we investigate the relations between the growth of meromorphic coefficients and that of meromorphic solutions of complex linear differential-difference equations with meromorphic cofficients of finite logarithmic order in the unit disc. Our results can be viewed as the generalization for both the cases of complex linear differential equations and complex linear difference equations.Nityagopal BiswasSanjib Kumar DattaGorachand Chakraborty2021-07-012021-07-0188On α-prime Ideals in the Semiring of Non-Negative Integers
http://www.i-scholar.in/index.php/JIMSIMS/article/view/209104
Characterizations of α-prime ideals in the semiring of non- negative integers are investigated.Dipak Ravindra BondeJayprakash Ninu Chaudhari2021-07-012021-07-0188Approximation of Functions in <i>H(α; p)</i>-space By Taylor Means
http://www.i-scholar.in/index.php/JIMSIMS/article/view/209105
In 2014, the authors [Mat. Vesnik, 66(1)(2014),46{57], among the other results, obtained the Jackson order: O(n<sup>-α</sup>) for 0 < α < 1 as the degree of approximation of functions in a subspace of H(α; p), 0 < α ≤ 1, 1 ≤ p ≤ ∞ space. In the present paper, among the other re- sults, we extend the subspace of H(α; p), used earlier by the authors[ibid], to obtain the Jackson order: O(n<sup>-α</sup>) for 0 < α ≤ 1 and relax the hypothesis imposed upon the functions in H(α; p) space.Prem Chandra2021-07-012021-07-0188On Subtractive Ideals of (m; n)-semirings
http://www.i-scholar.in/index.php/JIMSIMS/article/view/209106
Let <em>R</em> be a commutative (m, n)-semiring with an identity element. It is proved that every partitioning ideal of <em>R</em> is a subtractive ideal. Also if <em>I</em> is a partitioning ideal of R, then a relation between the set of subtractive ideals (subtractive prime ideals) of <em>R</em> containing <em>I</em> and the set of subtractive ideals (subtractive prime ideals) of the quotient (m, n)-semiring <em>R/I(Q</em>) is obtained.J. N. ChaudhariHarish Nemade2021-07-012021-07-0188Note on the <i><sub>p</sub>R<sub>q</sub>(α; β; z)</i> Function
http://www.i-scholar.in/index.php/JIMSIMS/article/view/209107
The aim of this paper is to give some convergence conditions of the <em><sub>p</sub>R<sub>q</sub>(α; β; z)</em> function. We also derive the integral representation of the function <em><sub>p</sub>R<sub>q</sub>(α; β; z)</em> in the form of Mellin-Barnes Integral including its analytic property.Rachana DesaiA. K. Shukla2021-07-012021-07-0188Irreducibility of A Formal Power Series with Integer Coefficients
http://www.i-scholar.in/index.php/JIMSIMS/article/view/209108
In this article, we have established a relation between total number of partitions of a positive integer n and all possible factorizations of a power series with constant term prime power<em> p<sup>n</sup></em>, into irreducible power series. Finally we try to develop an irreducibility criterion for power series whose constant term is a prime power.Mriganka S. DuttaHelen K. Saikia2021-07-012021-07-0188A Lusternik-Schnirelmann Type Theorem for C<sup>1</sup>-Frechet Manifolds
http://www.i-scholar.in/index.php/JIMSIMS/article/view/209109
We prove a Lusternik-Schnirelmann type theorem for a <em>C</em><sup>1</sup>- function φ : M → R, where M is a connected infinite dimensional Frechet manifold of class <em>C</em><sup>1</sup>. To this end, in this context we prove the so-called Deformation Lemma and by using it we derive the result generalizing the Minimax Principle.Kaveh EftekharinasabIvan Lastivka2021-07-012021-07-0188Oscillation for Certain Third Order Functional Delay Difference Equation
http://www.i-scholar.in/index.php/JIMSIMS/article/view/209110
This paper is concerned with the third order functional delay difference equation of the form Δ(C<sub>n</sub>Δ(a<sub>n</sub>Δx<sub>n</sub>)) + <sup>m</sup>Σ<sub>i=1</sub>pn<sub>i</sub>Δxσ<sub>i(n-r)</sub> + <sup>m</sup>Σ<sub>i=1</sub>qn<sub>i</sub>f (xσ<sub>i(n-r)</sub>) = 0. We obtain some new oscillation criteria by using Riccati transformation technique. Examples are given to illustrate the results.I. Mohammed Ali JafferR. Shanmugapriya2021-07-012021-07-0188The Closure Operator, Flats and Hyperplanes of es-Splitting Matroid
http://www.i-scholar.in/index.php/JIMSIMS/article/view/209111
The es-splitting operation on binary matroids is a natural generalization of Slater's <em>n</em>-line splitting operation on graphs. In this paper, we characterize the closure operator of the es-splitting binary matroid M<sup>e</sup><sub>X</sub> in terms of the closure operator of the original binary matroid M. We also describe the ats and the hyperplanes of the es-splitting bi- nary matroid M<sup>e</sup><sub>X</sub> in terms of the ats and the hyperplanes, respectively of the original binary matroid M.P. P. MalavadkarS. B. DhotreM. M. Shikare2021-07-012021-07-0188On a Generalization of Incomplete Fibonacci Quaternions
http://www.i-scholar.in/index.php/JIMSIMS/article/view/209112
The aim of this article is to introduce a new class of quater- nions, namely, incomplete Horadam quaternions that are based on in- complete Horadam numbers which generalize the previously introduced incomplete Fibonacci and Lucas quaternions. Further, some identities including summation formulas and generating functions concerning these quaternions are also established.Bijan Kumar PatelNarmada Behera2021-07-012021-07-0188Power of a Meromorphic Function Sharing A Set with Least Cardinality and Weight with its Derivative
http://www.i-scholar.in/index.php/JIMSIMS/article/view/209113
In this paper we deal with the uniqueness problem of the power of a meromorphic function when it shares a set with its derivative. We also relax the nature of sharing of the set and reduce the cardinality of the shared set in some cases.Arindam Sarkar2021-07-012021-07-0188Escaping Sets of Composition of Transcendental Entire Functions
http://www.i-scholar.in/index.php/JIMSIMS/article/view/209114
If <em>f</em> and <em>g</em> are transcendental entire functions, then so are <em>f</em> o <em>g</em> and <em>g</em> o<em> f.</em> We discuss here the dynamics of various types of escaping sets and also non-escaping sets of composition of transcendental entire functions <em>f</em> o <em>g</em> and <em>g</em> o <em>f</em> and also its relations with regard to its factors<em> f</em> and <em>g</em>.Anand P. SinghGarima Tomar2021-07-012021-07-0188