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Bijections between different combinatorial models for q-Whittaker and modified Hall-Littlewood polynomials Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-04-24 T. V. Ratheesh
We consider the monomial expansion of the q-Whittaker polynomials and the modified Hall-Littlewood polynomials arising from specialization of the modified Macdonald polynomial. The two combinatorial formulas for the latter, due to Haglund, Haiman, and Loehr and Ayyer, Mandelshtam and Martin, give rise to two different parameterizing sets in each case. We produce bijections between the parameterizing
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Asymptotic behavior of entire solutions in space and time media Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-04-24 Jingjing Cai, Xiaoguo Yuan, Huayu Deng, Kaijun Zhang
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What is the gradient of a scalar function defined on a subspace of square matrices ? Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-04-24 Shriram Srinivasan, Nishant Panda
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Positive solutions to nonhomogeneous quasilinear problems with singular and supercritical nonlinearities Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-04-23 Ambesh Kumar Pandey, Rasmita Kar
In this article, we establish the existence of nonnegative solutions to the following quasilinear and singular elliptic problems with supercritical nonlinearity: $$\begin{aligned} \left\{ \begin{aligned} {} -\Delta _p z-\Delta _q z&{}= \lambda \frac{h(x)}{z^\gamma }+z^\theta , \ z>0&\quad \text{ in } \, \Omega , \\ z&{}= 0&\quad \text{ on } \partial \Omega , \end{aligned} \right. \end{aligned}$$ where
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Homogenization of the Neumann boundary value problem: polygonal domains Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-04-20 Jie Zhao, Juan Wang, Jianlin Zhang
In this paper, we study the convergence rates for homogenization problems for solutions of partial differential equations with rapidly oscillating Neumann boundary data in the convex polygonal domains. As a consequence, we obtain the pointwise and \(L^{p}\) convergence results. Our techniques are based on using Fourier analysis method as well as Diophantine condition on the boundary
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Hamilton and Souplet–Zhang type estimations on semilinear parabolic system along geometric flow Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-04-20 Sujit Bhattacharyya, Shahroud Azami, Shyamal Kumar Hui
In this article we derive both Hamilton type and Souplet–Zhang type gradient estimations for a system of semilinear equations along a geometric flow on a weighted Riemannian manifold.
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Congruence relation between Stirling numbers of the first and second kinds Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-04-20 A. Lalchhuangliana, S. S. Singh
This paper consists of certain congruence properties of Stirling numbers of the first and second kinds. Some congruence relations between s(n, k) and S(n, k) for different modulo are obtained through their generating functions. We also present some exact p-adic valuations of s(n, k) and S(n, k) for some cases, mainly when \(n-k\) is divisible by \(p-1\) for odd prime p. Some estimates of the p-adic
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Point-wise time-space estimates for a class of oscillatory integrals and their applications Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-04-20 JinMyong Kim, JinMyong An
This paper investigates the point-wise time-space estimates for a class of oscillatory integrals given by \(\int _{\mathbb R^{n} }e^{i\pm itP^{\frac{1}{2} } (\xi )} P^{-\frac{\alpha }{2} } (\xi )d\xi \), where P is a real non-degenerate elliptic polynomial of order \(m\ge 4\) on \(\mathbb R^{n} \). These estimates are applied to obtain time-space integrability estimates with regularity for solutions
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On a diophantine inequality involving prime numbers of a special form Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-04-18 Yuhui Liu
Let N be a sufficiently large real number. In this paper, we prove that for \(20\) , the Diophantine inequality $$\begin{aligned} \left| p_{1}^{c}+p_{2}^{c}+p_{3}^{c}+p_{4}^{c}+p_{5}^{c}-N\right| <\left( \log N\right) ^{-E} \end{aligned}$$ is solvable in prime variables \(p_1,p_2,p_3,p_4,p_5\) such that, each of the numbers \(p_{i}+2\,\, (1\le i\le 5)\) has at most \(\big [\frac{214467}{136000-66000c}\big
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Integer partitions with restricted odd and even parts Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-04-17 Nipen Saikia
In this note, two generalized partition functions \(p_o^\alpha (n)\) and \(p_e^\beta (n)\) are considered, where for any odd positive integer \(\alpha \), \(p_o^\alpha (n)\) denotes the number of partitions of n into odd parts such that no parts is congruent to \(\alpha \) modulo \(2\alpha \), and for any even positive integer \(\beta \), \(p_e^\beta (n)\) denotes the number of partitions of n into
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Joint Functional Independence of the Riemann Zeta-Function Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-04-16 Maxim Korolev, Antanas Laurinčikas
By the Ostrowski theorem, the Riemann zeta-function \(\zeta (s)\) does not satisfy any algebraic-differential equation. Voronin proved that the function \(\zeta (s)\) does not satisfy algebraic-differential equation with continuous coefficients. In the paper, a joint generalization of the Voronin theorem is given, i. e., that a collection \((\zeta (s_1), \dots , \zeta (s_r))\) does not satisfy a certain
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Higher order numerical methods for fractional delay differential equations Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-04-05 Manoj Kumar, Aman Jhinga, Varsha Daftardar-Gejji
In this paper, we present a new family of higher-order numerical methods for solving non-linear fractional delay differential equations (FDDEs) along with the error analysis. Further, we solve various non-trivial systems of FDDEs to illustrate their applicability and utility. By using the proposed numerical methods, computational time is reduced drastically. These methods take only 5 to 10 percent
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Clear graph of a ring Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-04-04 Shabir Ahmad Mir, Cihat Abdioğlu, Nadeem ur Rehman, Mohd Nazim, Muhammed Akkafa, Ece Yetkin Çelikel
This research article introduces the concept of the clear graph associated with a ring \({\mathcal {R}}\) with identity, denoted as \(Cr({\mathcal {R}})\). This graph comprises vertices of the form \(\{(x,u):\) x is a unit regular element of R and u is a unit of \({\mathcal {R}}\)} and two distinct vertices (x, u) and (y, v) are adjacent if and only if either \(xy=yx=0\) or \(uv=vu=1\). This research
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Convergence properties of new $$\alpha $$ -Bernstein–Kantorovich type operators Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-04-04 Ajay Kumar, Abhishek Senapati, Tanmoy Som
In the present paper, we introduce a new sequence of \(\alpha -\)Bernstein-Kantorovich type operators, which fix constant and preserve Korovkin’s other test functions in a limiting sense. We extend the natural Korovkin and Voronovskaja type results into a sequence of probability measure spaces. Then, we establish the convergence properties of these operators using the Ditzian-Totik modulus of smoothness
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Stratified bundles on the Hilbert Scheme of n points Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-04-04 Saurav Holme Choudhury
Let k be an algebraically closed field of characteristic \(p > 3\) and S be a smooth projective surface over k with k-rational point x. For \(n \ge 2\), let \(S^{[n]}\) denote the Hilbert scheme of n points on S. In this note, we compute the fundamental group scheme \(\pi ^{\text {alg}}(S^{[n]}, {\tilde{nx}})\) defined by the Tannakian category of stratified bundles on \(S^{[n]}\).
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On some super-congruences for the coefficients of analytic solutions of certain differential equations Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-04-03 Guo-Shuai Mao, Hao Zhang
In this paper, we prove some congruences involving the coefficients \(\{A_{n}\}_{n=0,1,2,\ldots }\) of the analytic solution \(y_0(z)=\sum _{n=0}^\infty A_nz^n\) of certian differential eqution \({\mathcal {D}}y=0\) normalized by the condition \(y_0(0)=A_0=1\), where \({\mathcal {D}}\) is a 4th-order linear differential operator.
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Ground state solutions to critical Schrödinger–Possion system with steep potential well Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-04-02 Xiuming Mo, Mengyao Li, Anmin Mao
We study the following critical Schrödinger-Possion system with steep potential well $$\begin{aligned} \left\{ \begin{aligned}&-\Delta u+(1+\lambda V(x))u+\phi u=f(u)+|u|^4u,&\text {in}\ {\mathbb {R}}^{3},\\&-\Delta \phi =u^2,&\text {in}\ {\mathbb {R}}^{3}, \end{aligned}\right. \end{aligned}$$ where \(\lambda >0\) is a positive parameter, \(V:{\mathbb {R}}^{3}\rightarrow {\mathbb {R}}\) is a continuous
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Total graph of a lattice Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-03-28 Pravin Gadge, Vinayak Joshi
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Compressed Cayley graph of groups Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-03-26
Abstract Let G be a group and let S be a subset of \(G \setminus \{e\}\) with \(S^{-1} \subseteq S\) , where e is the identity element of G. The Cayley graph \(\mathrm {{{\,\textrm{Cay}\,}}}(G,S)\) is a graph whose vertices are the elements of G and two distinct vertices \(g,h\in G\) are adjacent if and only if \(g^{-1} h\in S\) . Let \(S \subseteq Z(G)\) . Then the relation \( \sim \) on G, given
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On L(2, 1)-labeling of zero-divisor graphs of finite commutative rings Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-03-22 Annayat Ali, Rameez Raja
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Sufficient conditions for component factors in a graph Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-03-22 Hongzhang Chen, Xiaoyun Lv, Jianxi Li
Let G be a graph and \(\mathcal {H}\) be a set of connected graphs. A spanning subgraph H of G is called an \(\mathcal {H}\)–factor if each component of H is isomorphic to a member of \(\mathcal {H}\). In this paper, we first present a lower bound on the size (resp. the spectral radius) of G to guarantee that G has a \(\{P_2,\, C_n: n\ge 3\}\)–factor (or a perfect k–matching for even k) and construct
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Ramanujan-type congruences for partition k-tuples with 5-cores Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-03-21 Manjil P. Saikia, Abhishek Sarma, Pranjal Talukdar
We prove several Ramanujan-type congruences modulo powers of 5 for partition k-tuples with 5-cores, for \(k=2, 3, 4\). We also prove some new infinite families of congruences modulo powers of primes for k-tuples with p-cores, where p is a prime.
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Tracking the mean of a piecewise stationary sequence Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-03-18 Ghurumuruhan Ganesan
In this paper we study the problem of tracking the mean of a piecewise stationary sequence of independent random variables. First we consider the case where the transition times are known and show that a direct running average performs the tracking in short time and with high accuracy. We then use a single valued weighted running average with a tunable parameter for the case when transition times are
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On the line graph structure of the cozero-divisor graph of a commutative ring Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-03-16 Mojgan Afkhami, Zahra Barati
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Laplacian eigenvalues and eigenspaces of cographs generated by finite sequence Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-03-12 Santanu Mandal, Ranjit Mehatari, Zoran Stanić
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Sufficient conditions for fractional [a, b]-deleted graphs Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-03-12 Sizhong Zhou, Yuli Zhang
Let a and b be two positive integers with \(a\le b\), and let G be a graph with vertex set V(G) and edge set E(G). Let \(h:E(G)\rightarrow [0,1]\) be a function. If \(a\le \sum \limits _{e\in E_G(v)}{h(e)}\le b\) holds for every \(v\in V(G)\), then the subgraph of G with vertex set V(G) and edge set \(F_h\), denoted by \(G[F_h]\), is called a fractional [a, b]-factor of G with indicator function h
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Characterization of $$*$$ -(strongly) regular rings in terms of $${\mathcal {G}}$$ -projections Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-03-09 Tufan Özdin
A unit-picker is a map \({\mathcal {G}}\) that associates to every ring R a well-defined set \({\mathcal {G}}(R)\) of central units in R which contains \(1_R\) and is invariant under isomorphisms of rings and closed under taking inverses, and which satisfies certain set containment conditions for quotient rings, corner rings and matrix rings. Let \({\mathcal {G}}\) be a unit-picker. An element q of
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Nonlinear (skew-)centralizing mappings on unital algebras with nontrivial idempotents Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-03-06 Xinfeng Liang, Haonan Guo
Let \(\mathcal {R}\) be a commutative ring with unity, and \(\mathcal {A}\) be a unital \(\mathcal {R}\)-algebra with a nontrivial idempotent. Under some mild conditions, we prove that every nonlinear centralizing mapping on \(\mathcal {A}\) is proper. Nonlinear skew-centralizing mapping on \(\mathcal {A}\) is also studied in this paper.
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More efficient algorithms for searching for several edges in a hypergraph Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-03-04 Ting Chen
The edge searching problem is a generalization of the classical group testing problem. Chen and Hwang studied the problem of searching for many edges in a hypergraph with rank r. They provided a competitive algorithm to identify all d defective edges in a hypergraph with d unknown. Recently, Hwang first gave a competitive algorithm to find all defective edges in a graph. Chen proposed a revised algorithm
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Pachpatte type inequalities and their nabla unifications via convexity Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-03-04 Zeynep Kayar, Billur Kaymakçalan
Nabla unifications of the discrete and continuous Pachpatte type inequalities, which are convex generalizations of Hardy-Copson type inequalities, are established. These unifications also yield dual results, namely delta Pachpatte type inequalities. Some of the dual results and some discrete and continuous versions of nabla Pachpatte type inequalities have appeared in the literature for the first time
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A note on the normal complement problem in semisimple group algebras Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-03-02 Manju Khan, Himanshu Setia
Let FG be the semisimple group algebra of a finite group G over a finite field F. In this article, we obtain a sufficient condition for which G does not have a normal complement in the unit group of FG. In particular, we have studied the normal complement problem for semisimple group algebras of dihedral groups, quaternion groups and groups of order \(p^n\), where \(n=3,4\) and p is an odd prime.
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On LCD codes over $$\mathbb {Z}_4$$ Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-03-02
Abstract Linear Complementary Dual (LCD) code is a linear code with a trivial intersection with its dual. In this paper, we prove that non-free LCD codes do not exist over \(\mathbb {Z}_4\) and obtain a necessary and sufficient condition for the existence of LCD codes over \(\mathbb {Z}_4\) . Later, we investigate free LCD cyclic codes of odd lengths over \(\mathbb {Z}_4\) and find a relation between
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Intersection results for general classes of maps Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-03-02
Abstract In this paper we use new coincidence theorems of the author to obtain a variety of Ky Fan matching type theorems for open coverings related to the map or maps. To establish our new matching results, we consider maps which are of KKM or BPK type (these include the Kakutani maps, the acyclic maps and more generally the admissible maps of Gorniewicz) together with maps which generate HLPY type
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Revisiting J-semicommutative rings Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-03-01 Tikaram Subedi, Debraj Roy
Let J(R) denote the Jacobson radical of a ring R. R is called J-semicommutative if for any \(a,b\in R, ab=0\) implies \(aRb\subseteq J(R)\). We observe that the class of J -semicommutative rings contains the class of left (right) quasi-duo rings and various existing versions of semicommutative rings, symmetric rings and reversible rings. We provide some conditions for J-semicommutative rings to be
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Fractal generation via generalized Fibonacci–Mann iteration with s-convexity Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-02-05
Abstract Recently, the generalized Fibonacci–Mann iteration scheme has been defined and used to develop an escape criterion to study mutants of the classical fractals for a function \(\sin \left( z^{n}\right) +az+c\) , \(a,c\in \mathbb {C}\) , \(n\ge 2\) , and z is a complex variable. In the current work, we use generalized Fibonacci–Mann iteration extended further via the notion of s-convex combination
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Cubic residues and their new distributive properties Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-02-03 Xiaoge Liu, Tianping Zhang
Let \(M_{k}(p)\) denote the number of all integers \(1\le a \le p-1\) such that \(a+a^{k}\) and \(a-a^{k}\) are cubic residues modulo p. We obtain some identities or asymptotic formulae for \(M_{2}(p)\) and \(M_{3}(p)\) by using the properties of Gauss sums and third-order Dirichlet character. Through these results, the distributive properties of cubic residues have been fully characterized.
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15 Order types in 36 packages Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-02-02 V. Kannan, Swapnil Malegaonkar
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Approximate solution of KdV-Burgers equation using improved PINNs algorithm Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-01-31
Abstract Finding solutions to partial differential equations (PDEs) has long been a challenging endeavor. Despite various proposed methods, there isn’t a universal approach capable of solving all types of PDEs. Recently, deep learning methods have emerged as a powerful tool for the solution of PDEs. Among them, the physics-informed neural networks (PINNs) stand out, integrating fundamental physical
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On mock theta functions of Gordon and McIntosh Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-01-29
Abstract A new approach involving the concept of modular Ferrers diagram is employed to interpret the Gordon and McIntosh’s mock theta functions in terms of \({(n+t)}\) -color partitions. We then provide the generalized versions of the mock theta functions and their interpretations. We further found some arithmetic properties for two of the mock theta functions \(\beta (q)\) and \(\xi (q)\) .
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Multi-step inertial algorithms for equilibrium, fixed point, general systems of variational inequalities and split feasibility problems Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-01-27 Haiying Li, Jiaoying He, Fenghui Wang
In this paper, we present two novel multi-step inertial iterative methods to approximate a common element that combines equilibrium problems with other problems in real Hilbert spaces. Firstly, by combining equilibrium problems, fixed point problems and a general system of variational inequalities, we adopt a conjugate gradient method to solve them. Secondly, by integrating equilibrium problems, fixed
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Distinguishing labelling of sets under the wreath product action of $$\overrightarrow{A_{n}}$$ Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-01-27 Madhu Dadhwal, Pankaj
In this article, it is proved that the distinguishing number for the action of \(\overrightarrow{A_{n}}\) on the set \([2n]=\{1, 2,\ldots , 2n\}\) is the \(n^{th}\) term of the sequence “1, 2, 3, 3, 4, 4, 4, 5, ... (n appears \(n-1\) times prepended with 1)”. An optimal iterative algorithm to establish a closed formula to compute a distinguishing labelling of [2n] under the natural action of \(\ov
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A note on the energy critical inhomogeneous Hartree equation Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-01-26 Tarek Saanouni, Congming Peng
This note studies the inhomogeneous generalized Hartree equation $$\begin{aligned} i\dot{u}+\Delta u=\pm |x|^{-\rho }|u|^{p-2}(J_\gamma *|\cdot |^{-\rho }|u|^p)u,\quad \rho>0,\, p>2. \end{aligned}$$ The goal of this work is two-fold. First, one obtains the existence of a local solution in \(C_T(H^{s_c})\), where the critical Sobolev exponent is given by the equality \(\lambda ^\frac{2-2\rho +\gamma
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A note on the class number of certain real cyclotomic fields Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-01-25
Abstract We construct an infinite family of real cyclotomic fields with non-trivial class group. This result generalizes some results of [6] in the sense that our family includes theirs.
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Computing the 2-nilpotent multiplier of 2-generator p-groups of class 2 Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-01-25
Abstract The complete classification of 2-generator p-groups of class 2 has been achieved by Ahmad et al. (2012). The various homological functors of these groups, such as the nonabelian tensor square, the nonabelian exterior square and the Schur multiplier, are computed in recent past by Bacon and Kappe (1993), Kappe et al. (1999), and Magidin and Morse (2010). It is also specified which of these
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On extension of isometries between the positive unit spheres of $$c_0(\Gamma )$$ Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-01-24
Abstract Let \(\Gamma , \Delta \) be two index sets and let \(S_{c_0(\Gamma )}^+=\{x=(x_\gamma )_{\gamma \in \Gamma }\in c_0(\Gamma ): \Vert x\Vert =1; x_\gamma \ge 0,\; \forall \;\gamma \in \Gamma \}\) . In this paper, we show that every surjective isometry \(f:S_{c_0(\Gamma )}^+\rightarrow S_{c_0(\Delta )}^+\) can be extended to a linear surjective isometry from \(c_0(\Gamma )\) onto \(c_0(\Delta
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A generalization of Piatetski–Shapiro sequences (II) Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-01-22 Jinjiang Li, Jinyun Qi, Min Zhang
Suppose that \(\alpha ,\beta \in \mathbb {R}\). Let \(\alpha \geqslant 1\) and c be a real number in the range \(1
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On some representation numbers by $$a\sum x_i^2+b\sum x_ix_j$$ representing one Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-01-13 Ick Sun Eum
Let \(Q=a\sum x_i^2+b\sum x_ix_j\) be an integral positive definite quadratic form of level N in \(r(\ge 2)\) variables and \(r_Q(n)\) the representation number by Q for nonnegative integers n. First, we provide a necessary and sufficient condition that Q represents one and find the exact value of \(r_Q(1)\). Second, for such forms, we show that \(r_Q(n)\) satisfies a certain congruence relation for
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On series involving sine, cosine, and k-colored partition function Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-01-12 Mateus Alegri, Elen Viviani Pereira Spreafico
In this paper, we explore sine and cosine functions and also a relation involving these functions to establish identities involving convergent series in terms of the k-colored partition function and the set of the integer compositions of a positive integer n. Combinatorial interpretations are provided and some special cases are studied.
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Critical probabilistic characteristics of the Cramér model for primes and arithmetical properties Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-01-08 Michel J. G. Weber
This work is a probabilistic study of the ‘primes’ of the Cramér model, which consists with sums \(S_n =\sum _{i=3}^n \xi _i\), \(n\ge 3\), where \(\xi _i\) are independent random variables such that \(\mathbb {P}\{\xi _i= 1\}= 1-\mathbb {P}\{\xi _i= 1\}=1/{\log i}\), \(i\ge 3\). We prove that there exists a set of integers \(\mathscr {S} \) of density 1 such that $$\begin{aligned} \liminf _{ \mathscr
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On spectral spread and trace norm of Sombor matrix Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-01-03 Bilal Ahmad Rather, Muhammad Imran, Adama Diene
For a simple graph G with vertex set \( \{v_{1},\dots ,v_{n}\} \) and degree sequence \( \{d_{1},\dots ,d_{n}\} \), the Sombor matrix S(G) of G is an \( n\times n \) matrix, whose (i, j) -th entry is \( \sqrt{d_{i}^{2}+d_{j}^{2}} \), if \(v_{i}\) and \(v_{j}\) are adjacent and 0, otherwise. The multi-set of the eigenvalues of S(G) is known as the Sombor spectrum of G, denoted by \( \mu _{1}\ge \mu
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The r-bi $$^{q}$$ nomial coefficient and some properties Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2024-01-02
Abstract In this paper we give a new generalization of the binomial coefficient: the r-bi \(^{q}\) nomial coefficient \(\left( {\begin{array}{c}L\\ k\end{array}}\right) _{q,r}\) defined as the coefficient of \(x^{k}\) in the expansion of $$\begin{aligned} \left( 1+x+\cdots +x^{q}\right) ^{L}\left( 1+2x+\cdots +qx^{q-1}\right) ^{r}. \end{aligned}$$ We establish a connection between these coefficients
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On a theorem of Kanold on odd perfect numbers Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-12-29 Tomohiro Yamada
We shall prove that if \(N=p^\alpha q_1^{2\beta _1} q_2^{2\beta _2} \cdots q_{r-1}^{2\beta _{r-1}}\) is an odd perfect number such that \(p, q_1, \ldots , q_{r-1}\) are distinct primes, \(p\equiv \alpha \equiv 1\ \left( \textrm{mod}\ 4\right) \) and t divides \(2\beta _i+1\) for all \(i=1, 2, \ldots , r-1\), then \(t^5\) divides N, improving an eighty-year old result of Kanold.
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Padovan numbers as difference of two repdigits Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-12-22 Merve Güney Duman
In this paper, we find all Padovan numbers which can be written as are difference of two repdigits. It is shown that all Padovan numbers which can be written as a difference of two repdigits are \(P_{k}\in \{2,3,4,5,7,9,12\), \(16,21,28,37,49,65,86,200,3329\}\).
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Quaternary affine variety codes over a Klein-like curve Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-12-21 Nupur Patanker, Sanjay Kumar Singh
In this note, we study primary monomial affine variety codes defined from the Klein-like curve \(x^{2}y+y^{2}+x\) over \(\mathbb {F}_{4}\). Implementing the techniques suggested by Geil and Özbudak in [3], we estimate the minimum distance of various considered codes. In a few cases, we obtain the exact value of the symbol-pair distance of these codes. Furthermore, we determine lower bounds on the generalized
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On two generalized Ramanujan–Nagell equations Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-12-20 Yasutsugu Fujita, Maohua Le, Nobuhiro Terai
Let c be a positive integer. Then we conjecture that the equations \(x^2+2(2c)^m=(c^2+2)^n\) and \(x^2+2(2c)^m=(2c^2+1)^n\) have only the trivial positive integer solution (x, m, n) with explicit exceptional cases. In this paper, we verify that these conjectures are true under certain assumptions on c.
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The number of representations of arithmetic progressions by integral quadratic forms Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-12-19 Seoyeong Han, Kyoungmin Kim
Let f be a positive definite integral quadratic forms and let r(n, f) be the number of representations of an integer n by f. In this article, we prove that if f(z) is a modular form of weight \(\frac{k}{2}\) and level N, then \(f_{(m,r)}(z)\) is a modular form of weight \(\frac{k}{2}\) and level \(Nm^2\) (see Definition 2.3 for the definition of \(f_{(m,r)}(z)\)). As applications, we prove that if
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On hyponormality on the Bergman space of an annulus Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-12-18
Abstract A bounded operator S on a Hilbert space is hyponormal if \(S^{*}S-SS^{*}\) is positive. In this work we find necessary conditions for the hyponormality of the Toeplitz operator \(T_{\varphi +{\overline{\psi }}}\) on the Bergman space of the annulus \(\left\{ 1/2<|z|<1\right\} \) where both \(\varphi \) and \(\psi \) are bounded and analytic on the annulus and are of the form \(\displaystyle
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Numerical radius and spectral radius inequalities with an estimation for roots of a polynomial Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-12-15 Pintu Bhunia
Suppose A is a bounded linear operator defined on a complex Hilbert space. Among other numerical radius inequalities, it is proved (by using the Aluthge transform \({\widetilde{A}}\) of A) that $$\begin{aligned} w^2(A)\le & {} \frac{1}{2} {\left( \left\| A{\widetilde{A}}A^* \right\| \left\| {\widetilde{A}} \right\| \right) ^{1/2} } + \frac{1}{4} \Big \Vert A^*A+AA^* \Big \Vert , \end{aligned}$$ where
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Autocenral series and n-autoisoclinism of groups Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-12-15 Zohreh Sepehrizadeh, Mohammad Reza Rismanchian
In 1976 Bioch introduced the concept of n-isoclinism of groups. Using the definition of absolute centre and autocommutator subgroup of a group introduced by Hegarty, the notion of autoisoclinism has been studied in the recent years. In this article we first derive some results from definition of Hegarty. Then we introduce the concept of n-autoisoclinism, and obtain some basic results similar to n-isoclinism
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Existence and blow-up results for a weak-viscoelastic plate equation involving $$p(x)-$$ Laplacian operator and variable-exponent nonlinearities Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-12-14 Mohammad Shahrouzi, Faramarz Tahamtani
This paper is concerned with a weak viscoelastic \(p(x)-\)Laplacian plate equation with variable-exponent nonlinearities. By using the faedo-Galerkin method and the well-known contraction mapping theorem, we prove the local existence of solutions. Moreover, the blow up of solutions has been proved with negative initial energy as well as positive when the variable exponents and weak viscoelastic terms