https://www.i-scholar.in/index.php/JIMSIMS/issue/feed The Journal of the Indian Mathematical Society 2023-07-13T05:47:56+00:00 Peeyush Chandra sudhirghorpade@gmail.com Open Journal Systems <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> https://www.i-scholar.in/index.php/JIMSIMS/article/view/222472 Preference Intuitionistic Fuzzy Rough Relation and its Theoretical Approach 2023-07-13T05:47:53+00:00 Ajoy Kanti Das ajoykantidas@gmail.com Carlos Granados carlosgranadosortiz@outlook.es Relations on intuitionistic fuzzy sets (IFSs) and rough sets (RSs) have recently received a lot of attention for uncertainty. IFSs can effectively represent and simulate the uncertainty and diversity of judgment information offered by decision-makers. In comparison to fuzzy sets (FSs), IFSs are highly beneficial for expressing vagueness and uncertainty more accurately. In this paper, we introduce a novel concept of preference intuitionistic fuzzy rough relation (PIFRR) as an extension of intuitionistic fuzzy rough relation (IFRR) and partially included intuitionistic fuzzy rough relation (PIIFRR). Based on the concepts of IFRR and PIIFRR a theoretical approach of the PIFRR is established and some useful properties are investigated. Finally, we introduce the concepts of Semi-connected and totally semi-connected IFRRs and study under which assumptions PIFRRs fulfil these properties. 2023-07-01T00:00:00+00:00 https://www.i-scholar.in/index.php/JIMSIMS/article/view/222473 Depth One Homogeneous Prime Ideals in Polynomial Rings over a Field 2023-07-13T05:47:56+00:00 Paula Kemp PaulaKemp@MissouriState.edu Louis J. Ratliff ratliff@math.ucr.edu Kishor Shah KishorShah@MissouriState.edu <span>This paper concerns the question: Which depth one homogeneous prime ideals N in a polynomial ring H are of the principal class? In answer to this question, we introduce acceptable bases of ideals in polynomial rings, and then use a known one-to-one correspondence between the ideals N in H := F[X</span><span>1</span><span>, . . . , X</span><span>n</span><span>] such that X</span><span>n</span><span> ∉ N and the maximal ideals P in the related polynomial ring G := F[X</span><span>1</span><span>/X</span><span>n</span><span>, . . . , X</span><span>n−1</span><span>/X</span><span>n</span><span>] to show that the acceptable bases of the maximal ideals P in G transform to homogeneous bases. This is used to determine several necessary and sufficient conditions for a given depth one homogeneous prime ideal N in H to be an ideal of the principal class, thus answering, in part, our main question. Then it is shown that the Groebner-grevlex bases of ideals are acceptable bases. Finally, we construct several examples to illustrate our results, and we delve deeper into an example first studied by Macaulay.</span> 2023-07-01T00:00:00+00:00 https://www.i-scholar.in/index.php/JIMSIMS/article/view/222476 On Topological Bihyperbolic Modules 2023-07-13T05:47:56+00:00 Soumen Mondal mondalsoumen79@gmail.com Chinmay Ghosh chinmayarp@gmail.com Sanjib Kumar Datta sanjibdatta05@gmail.com <span>In this paper, we introduce topological modules over the ring of bihyperbolic numbers. We discuss bihyperbolic convexity, bihyperbolic-valued seminorms and bihyperbolic-valued Minkowski functionals in topological bihyperbolic modules. Finally we introduce locally bihyperbolic convex modules.</span> 2023-07-01T00:00:00+00:00 https://www.i-scholar.in/index.php/JIMSIMS/article/view/222479 Independent Vertices Inserted Graph of Grid and Leftmost Child Joined Graph of a Subdivided Extreme-Sides Leave Tree are Graceful 2023-07-13T05:47:56+00:00 N. Shanmugapriya shanmugapriya.vec@gmail.com <span>A graceful labeling of a graph G with n edges is an injection f : V (G) → {0, 1, 2, . . . , n} with the property that the resulting edge labels are distinct where an edge incident with the vertices u and v is assigned the label |f(u) − f(v)|. The main focus of graph labeling is essentially understanding the nature of graceful graphs. The characterization of graceful graphs is one of the most difficult problems in graph theory. In this paper two new classes of graceful graphs are obtained using the graph operation, called insertion of independent vertices in a graph. More precisely, for every grid graph P</span><span>m</span><span>¤P</span><span>n</span><span>, with m, n ≥ 2, the independent vertices inserted graph G</span><span>*</span><span>(P</span><span>m</span><span>¤P</span><span>n</span><span>) of P</span><span>m</span><span>¤P</span><span>n</span><span> is shown to be graceful. Also for a given extreme-sides leave tree T, the independent vertices inserted graph of leftmost child joined graph of the subdivided extreme-sides leave tree, denoted [LC(Tˆ)]</span><span>*</span><span> is also shown to be graceful.</span> 2023-07-01T00:00:00+00:00 https://www.i-scholar.in/index.php/JIMSIMS/article/view/222481 Centrality betweenness in Some Join of Graphs 2023-07-13T05:47:56+00:00 Sunil Kumar sunilstands@gmail.com Kannan Balakrishnan mullayilkannan@gmail.com <span>Centrality measures the status of a vertex in a graph. Centrality betweenness determines how often a vertex comes in between pairs of other vertices. Since shortest paths are considered here, the centrality betweenness of a vertex is proportional to the number of shortest paths passing through it. Join is an important graph operation which interconnects two graphs. The centrality betweenness of some derived graphs generated by this operation is presented here.</span> 2023-07-01T00:00:00+00:00 https://www.i-scholar.in/index.php/JIMSIMS/article/view/222483 Entire Solutions of Certain Non-Linear Differential-Difference Equations 2023-07-13T05:47:56+00:00 Garima Pant garimapant.m@gmail.com Sanjay Kumar Pant skpant@ddu.du.ac.in <span>We study existence and non-existence of finite order transcendental entire solutions of some non-linear differential-difference equations.</span> 2023-07-01T00:00:00+00:00 https://www.i-scholar.in/index.php/JIMSIMS/article/view/222482 Fifth Hankel Determinant for Multivalent Bounded Turning Functions of Order 2023-07-13T05:47:56+00:00 Biswajit Rath brath@gitam.edu K. Sanjay Kumar skarri9@gitam.in D. Vamshee Krishna vamsheekrishna1972@gmail.com Ch. Vijaya Kumar vijay.chalumuri123@gmail.com N. Vani vnallmot@gitam.in <span>The objective of this paper is to estimate an upper bound for the third, fourth and fifth Hankel determinants for the class of multivalent holomorphic functions, whose derivative has a positive real part of order α(0 ≤ α &lt; 1). Further we investigate bound for 2-fold symmetric functions.</span> 2023-07-01T00:00:00+00:00 https://www.i-scholar.in/index.php/JIMSIMS/article/view/222485 On the Faithfulness of the Extension of Lawrence-Krammer Representation of the Group of Conjugating Automorphisms C3 2023-07-13T05:47:56+00:00 Mohamad N. Nasser m.nasser@bau.edu.lb Mohammad N. Abdulrahim mna@bau.edu.lb <span>Let C</span><span>n</span><span> be the group of conjugating automorphisms. We study the representation ρ of Cn, an extension of Lawrence-Krammer representation of the braid group Bn. It is known that the representation ρ is unfaithful for n ≥ 5, the cases n = 3, 4 remain open. In our work, we make attempts towards the faithfulness of ρ in the case n = 3.</span> 2023-07-01T00:00:00+00:00 https://www.i-scholar.in/index.php/JIMSIMS/article/view/222494 Projective Change between Matsumoto Metric and Generalized Kropina Metric 2023-07-13T05:47:56+00:00 Renu renu3119@gmail.com Ramdayal Singh Kushwaha bhuramdayal@gmail.com <span>In the present paper, we find the conditions to characterize the projective change between Finsler spaces with (α, β)-metrics such as Matsumoto metric and generalized Kropina metric on a manifold with dimension n &gt; 2. Moreover, we consider this Projective change when Matsumoto metric has some special curvature properties.</span> 2023-07-01T00:00:00+00:00 https://www.i-scholar.in/index.php/JIMSIMS/article/view/222495 Some Results Involving the pRq(α,β,z) Function 2023-07-13T05:47:56+00:00 Yogesh M. Thakkar ajayshukla2@rediffmail.com Ajay Shukla ajayshukla2@rediffmail.com <span>The main aim of this paper is to discuss some classical properties of the </span><span>p</span><span>R</span><span>q</span><span>(α, β; z) function such as integrals involving </span><span>p</span><span>R</span><span>q</span><span>(α, β; z) function and its product with some algebraic functions and higher Tanscendental function viz, Hermite polynomial, Legendre polynomial, Legendre function, Jacobi polynomial, Galue type Struve function, six summation formulas of </span><span>p</span><span>R</span><span>q</span><span>(α, β; z) function and relation between</span><span>p</span><span>R</span><span>q</span><span>(α, β; z) and </span><span>p</span><span>R</span><span>q</span><span>(α, β;- z) functions.</span> 2023-07-01T00:00:00+00:00 https://www.i-scholar.in/index.php/JIMSIMS/article/view/222496 Sensitivity Analysis in Multiobjective Solid Transportation Problem 2023-07-13T05:47:56+00:00 P. M. Paratane A. K. Bit <span>In this paper, we have discussed ordinary sensitivity analysis and tolerance analysis for supply, demand and conveyance capacity values of MSTP. Our aim to develop a method to obtain the sensitivity analysis for supply, demand and conveyance capacity values of MSTP by applying tolerance approach. It allows the variations in more than one parameter simultaneously and independently without altering the current optimal basis. The method is illustrated by a numerical example.</span> 2023-07-01T00:00:00+00:00 https://www.i-scholar.in/index.php/JIMSIMS/article/view/222497 Certain Supercongruences Deriving from Hypergeometric Series Identities 2023-07-13T05:47:56+00:00 Arijit Jana jana94arijit@gmail.com <span>In this paper, we deduce some supercongruences for sums involving third power of certain rising factorials using hypergeometric series identities and evaluations. In particular, we first relate a truncated hypergeometric sum with the coefficients of the modular form of weight 3. Further, we confirm certain supercongruence conjectures related to truncated hypergeometric series.</span> 2023-07-01T00:00:00+00:00 https://www.i-scholar.in/index.php/JIMSIMS/article/view/222498 On Certain Basic Hypergeometric Series Identities 2023-07-13T05:47:56+00:00 Satya Prakash Singh snsp39@gmail.com Vijay Yadav vijaychottu@yahoo.com <span>In this paper, making use of an identity, certain Rogers-Ramanujan type identities have been established.</span> 2023-07-01T00:00:00+00:00 https://www.i-scholar.in/index.php/JIMSIMS/article/view/222499 3-Isogonal Planar Tilings are not 3-Isogonal on the Torus 2023-07-13T05:47:56+00:00 Marbarisha M. Kharkongor marbarisha.kharkongor@gmail.com Debashis Bhowmik debashisiitg@gmail.com Dipendu Maity dipendumaity@gmail.com <span>A 3-isogonal tiling is an edge-to-edge tiling by regular polygons having 3 distinct transitivity classes of vertices. We know that there are sixty-one distinct 3-isogonal tilings on the plane. In this article, we discuss and determine the bounds of the vertex orbits of the plane’s 3-isogonal lattices on the torus and will show that these bounds are sharp.</span> 2023-07-01T00:00:00+00:00 https://www.i-scholar.in/index.php/JIMSIMS/article/view/222500 New Types of Metrics Deformations and Applications to p-Biharmonic Maps 2023-07-13T05:47:56+00:00 Bouchra Merdji bouchra.merdji@univ-mascara.dz Ahmed Mohammed Cherif a.mohammedcherif@univ-mascara.dz <span>We construct p-biharmonic non p-harmonic maps between Riemannian manifolds (M, g) and (N, h) by first making the ansatz that φ : (M, g) → (N, h) be a p-biharmonic map and then deforming the metric on N by h˜ = h − df ⊗ df to render φ p-biharmonic, where f is a smooth function on N satisfying some conditions. We construct a new example of p-biharmonic non p-harmonic map.</span> 2023-07-01T00:00:00+00:00 https://www.i-scholar.in/index.php/JIMSIMS/article/view/222501 On the Structure of Pronormal Subgroups of Dihedral Groups 2023-07-13T05:47:56+00:00 Shrawani Mitkari shrawaniin@gmail.com Vilas Kharat laddoo1@yahoo.com Manish Agalave manishagalave@gmail.com <span>In this paper, we study the structure of the collection of pronormal subgroups of dihedral groups D</span><span>n</span><span> for different values of n. We enumerate the number of pronormal subgroups of D</span><span>n</span><span> when n is some power of 2. Also, the relation of the collection of all pronormal subgroups with normal subgroups and all subgroups of D</span><span>n</span><span> for different values of n are studied.</span> 2023-07-01T00:00:00+00:00 https://www.i-scholar.in/index.php/JIMSIMS/article/view/222502 Harmonic Homomorphisms between Riemannian Three Dimensional Unimodular Lie Groups 2023-07-13T05:47:56+00:00 Nada Osamnia nada.osamnia@univ-mascara.dz kaddour Zegga zegga.kadour@univ-mascara.dz Abdelkader Zagane abdelkader.zaagane@univ-mascara.dz <span>In this paper, we give some results of harmonic homomorphisms φ : (G, g) → (H, h), where G, H are connected and simply connected three dimensional unimodular Lie groups and g, h are left invariant Riemannian metrics.</span> 2023-07-01T00:00:00+00:00