The Journal of the Indian Mathematical Society
https://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 Society0019-5839Preference Intuitionistic Fuzzy Rough Relation and its Theoretical Approach
https://www.i-scholar.in/index.php/JIMSIMS/article/view/222472
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.Ajoy Kanti DasCarlos Granados2023-07-012023-07-0190Depth One Homogeneous Prime Ideals in Polynomial Rings over a Field
https://www.i-scholar.in/index.php/JIMSIMS/article/view/222473
<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>Paula KempLouis J. RatliffKishor Shah2023-07-012023-07-0190On Topological Bihyperbolic Modules
https://www.i-scholar.in/index.php/JIMSIMS/article/view/222476
<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>Soumen MondalChinmay GhoshSanjib Kumar Datta2023-07-012023-07-0190Independent Vertices Inserted Graph of Grid and Leftmost Child Joined Graph of a Subdivided Extreme-Sides Leave Tree are Graceful
https://www.i-scholar.in/index.php/JIMSIMS/article/view/222479
<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>N. Shanmugapriya2023-07-012023-07-0190Centrality betweenness in Some Join of Graphs
https://www.i-scholar.in/index.php/JIMSIMS/article/view/222481
<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>Sunil KumarKannan Balakrishnan2023-07-012023-07-0190Entire Solutions of Certain Non-Linear Differential-Difference Equations
https://www.i-scholar.in/index.php/JIMSIMS/article/view/222483
<span>We study existence and non-existence of finite order transcendental entire solutions of some non-linear differential-difference equations.</span>Garima PantSanjay Kumar Pant2023-07-012023-07-0190Fifth Hankel Determinant for Multivalent Bounded Turning Functions of Order
https://www.i-scholar.in/index.php/JIMSIMS/article/view/222482
<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 < 1). Further we investigate bound for 2-fold symmetric functions.</span>Biswajit RathK. Sanjay KumarD. Vamshee KrishnaCh. Vijaya KumarN. Vani2023-07-012023-07-0190On the Faithfulness of the Extension of Lawrence-Krammer Representation of the Group of Conjugating Automorphisms C3
https://www.i-scholar.in/index.php/JIMSIMS/article/view/222485
<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>Mohamad N. NasserMohammad N. Abdulrahim2023-07-012023-07-0190Projective Change between Matsumoto Metric and Generalized Kropina Metric
https://www.i-scholar.in/index.php/JIMSIMS/article/view/222494
<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 > 2. Moreover, we consider this Projective change when Matsumoto metric has some special curvature properties.</span>Renu Ramdayal Singh Kushwaha2023-07-012023-07-0190Some Results Involving the pRq(α,β,z) Function
https://www.i-scholar.in/index.php/JIMSIMS/article/view/222495
<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>Yogesh M. ThakkarAjay Shukla2023-07-012023-07-0190Sensitivity Analysis in Multiobjective Solid Transportation Problem
https://www.i-scholar.in/index.php/JIMSIMS/article/view/222496
<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>P. M. ParataneA. K. Bit2023-07-012023-07-0190Certain Supercongruences Deriving from Hypergeometric Series Identities
https://www.i-scholar.in/index.php/JIMSIMS/article/view/222497
<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>Arijit Jana2023-07-012023-07-0190On Certain Basic Hypergeometric Series Identities
https://www.i-scholar.in/index.php/JIMSIMS/article/view/222498
<span>In this paper, making use of an identity, certain Rogers-Ramanujan type identities have been established.</span>Satya Prakash SinghVijay Yadav2023-07-012023-07-01903-Isogonal Planar Tilings are not 3-Isogonal on the Torus
https://www.i-scholar.in/index.php/JIMSIMS/article/view/222499
<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>Marbarisha M. KharkongorDebashis BhowmikDipendu Maity2023-07-012023-07-0190New Types of Metrics Deformations and Applications to p-Biharmonic Maps
https://www.i-scholar.in/index.php/JIMSIMS/article/view/222500
<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>Bouchra MerdjiAhmed Mohammed Cherif2023-07-012023-07-0190On the Structure of Pronormal Subgroups of Dihedral Groups
https://www.i-scholar.in/index.php/JIMSIMS/article/view/222501
<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>Shrawani MitkariVilas KharatManish Agalave2023-07-012023-07-0190Harmonic Homomorphisms between Riemannian Three Dimensional Unimodular Lie Groups
https://www.i-scholar.in/index.php/JIMSIMS/article/view/222502
<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>Nada Osamniakaddour ZeggaAbdelkader Zagane2023-07-012023-07-0190