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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
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Inequalities involving energy and Laplacian energy of non-commuting graphs of finite groups Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-12-13 Walaa Nabil Taha Fasfous, Rajat Kanti Nath
Let G be a finite non-abelian group and \({\Gamma }_{nc}(G)\) be its non-commuting graph. In this paper, we compute spectrum and energy of \({\Gamma }_{nc}(G)\) for certain classes of finite groups. As a consequence of our results we construct infinite families of integral complete r-partite graphs. We compare energy and Laplacian energy (denoted by \(E({\Gamma }_{nc}(G))\) and \(LE({\Gamma }_{nc}(G))\)
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The uniqueness of some singular Kirchhoff equations with non-homogeneous material Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-12-12 Baoqiang Yan, Donal O’Regan, Ravi P. Agarwal
In this paper, on the one hand, we prove a new theorem of sub-supersolution method for a generalized Kirchhoff equations with non-homogeneous material; on the other hand, based on the method of lower and upper solution, we consider the existence and uniqueness of the positive solution of some singular Kirchhoff equations.
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k-rotundity of Orlicz-Lorentz sequence spaces Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-12-07 Zichen Wang, Wanzhong Gong
The criteria for Orlicz-Lorentz sequence spaces endowed with Luxemburg norm as well as Orlicz norm being k-rotund were provided in this article, which generalized the similar results in Orlicz space.
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Inverse Coefficient Problem for Fractional Wave Equation with the Generalized Riemann–Liouville Time Derivative Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-12-06 Durdimurod Durdiev, Halim Turdiev
This paper considers the inverse problem of determining the time-dependent coefficient in the fractional wave equation with Hilfer derivative. In this case, the direct problem is initial-boundary value problem for this equation with Cauchy type initial and nonlocal boundary conditions. As overdetermination condition nonlocal integral condition with respect to direct problem solution is given. By the
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On $${\varvec{q}}$$ -congruences related to $${\varvec{H}}_{\varvec{n}}\left( {\varvec{x;q}}\right) $$ and $${\varvec{M}}_{{\varvec{n}}}\left( {\varvec{x;q}}\right) $$ Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-12-02 Sibel Koparal, Neşe Ömür, Laid Elkhiri
In this paper, we examine \(\sum \limits _{k=m}^{p-1}q^{k} {k \brack m} _{q}H_{k}\left( x;q\right) \pmod {\left[ p\right] _{q}}\) and \(M_{p-1}\left( x;q\right) \pmod {\left[ p\right] _{q}},\) where for real number x, \(H_{n}\left( x;q\right) =\sum \limits _{k=1}^{n}\frac{x^{k}}{\left[ k\right] _{q}}\) and \(M_{n}\left( x;q\right) =\sum \limits _{k=1}^{n}k\frac{x^{k}}{\left[ k\right] _{q}}.\) For example
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Finiteness properties of Ind-Sheaves with Ring Actions Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-12-01 Yohei Ito
In this paper, we shall consider some finiteness of ind-sheaves with ring actions. As the main result of this paper, there exists an equivalence of categories between the abelian category of coherent ind-\(\beta _X\mathcal {A}\)-modules and the one of coherent \(\mathcal {A}\)-modules, where \(\mathcal {A}\) is a sheaf of \(\Bbbk _X\)-algebras and \(\Bbbk \) is a field.
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On $$\varepsilon $$ -phase-isometries between the positive cones of continuous function spaces Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-11-29 Wenting Wang, Aimin An
Let K and T be compact Hausdorff spaces, \(C_+(K)=\{f\in C(K): f(k)\ge 0\; \mathrm{for\; all\;}\; k\in K\}\) be the positive cone of C(K). In this paper, we prove that if K is a compact Hausdorff perfectly normal space, then for every \(\varepsilon \)-phase-isometry \(F:C_+(K)\rightarrow C_+(T)\), there are nonempty closed subset \(S\subset T\) and an additive isometry \(V:C_+(K)\rightarrow C_+(S)\)
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On Ramanujan expansions with additive coefficients Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-11-23 Maurizio Laporta
The Ramanujan series attached to a complex-valued arithmetic function \(\widehat{g}\) in a fixed integer a is the series \(\sum _n\widehat{g}(n)c_n(a)\), where \(c_n(a)\) is the so-called Ramanujan sum. Assuming that \(\widehat{g}\) is additive or, more generally, a product of a multiplicative function with an additive one, we study the relationships between the Ramanujan series attached to \(\widehat{g}\)
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Feebly Baer N-groups and Nearrings Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-11-25 Ram Parkash Sharma, Shalini Chandel
In [8], the condition of commutativity was relaxed and certain results of [7] regarding regular rings, feebly Baer rings and weakly complemented rings were proved for reversible rings. We further ease some conditions and prove these results for nearrings with no non-zero nilpotent elements.
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Stabilization and blow-up for a class of weakly damped Kirchhoff plate equation with logarithmic nonlinearity Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-11-27 Qingqing Peng, Zhifei Zhang
In this paper, we consider the initial value problem for weakly damped Kirchhoff plate equation with logarithmic nonlinearity in a bounded domain. We investigate the existence, uniqueness and polynomial or exponential energy decay estimates of global weak solutions under initial energy less than the depth of the potential well and some appropriate conditions. Moreover, we derive the finite time blow
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Annular regions containing all the zeros of a polynomial Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-11-17 Suhail Gulzar, N. A. Rather, K. A. Thakur
A result due to Tôya, Montel and Kuniyeda concerning the location of the zeros of a polynomial states that if \(P(z)=a_{n}z^n+a_{n-1}z^{n-1}+a_{n-2}z^{n-2}+\cdots +a_0\) is a polynomial of degree n then all its zeros lie in the disk \( |z|\le \left( 1+A_{p}^{q}\right) ^{1/q} \) where \(p>1,\) \(q>1\) with \(1/p+1/q=1\) and \(A_{p}=\left( \sum _{j=0}^{n-1}\left| \frac{a_j}{a_n}\right| ^p\right) ^{1/p}
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Limit theory for an AR(1) model with intercept and a possible infinite variance Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-11-13 Qing Liu, Chiyu Xia, Xiaohui Liu
In this paper, we derive the limit distribution of the least squares estimator for an AR(1) model with a non-zero intercept and a possible infinite variance. It turns out that the estimator has a quite different limit for the cases of \(|\rho | < 1\), \(|\rho | > 1\), and \(\rho = 1 + \frac{c}{n^\alpha }\) for some constant \(c \in R\) and \(\alpha \in (0, 1]\), and whether or not the variance of the
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On the behaviour of analytic representation of the multivalent $$\alpha $$ -convex functions Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-11-14 Vali Soltani Masih, Jahangir Cheshmavar, Saeideh Maghsoudi
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Identities related to a pair of generalized skew derivations on Lie ideals Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-11-12 Vincenzo De Filippis, Junaid Nisar, Nadeem ur Rehman
Let \(\mathfrak {S}\) be a prime ring with \(char({\mathfrak {S}}) \ne 2\), \({\mathcal {Q}}_r\) its right Martindale quotient ring, \({\mathcal {C}}\) its extended centroid, L a non-central Lie ideal of \({\mathfrak {S}}\), \({\mathcal {F}}\) and \({\mathcal {G}}\) two generalized skew derivations of \({\mathfrak {S}}\). If \({\mathcal {F}}({\mathfrak {r}}{\mathfrak {s}})\pm {\mathcal {G}}({\mathfrak
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Enumeration of doubly semi-equivelar maps on the Klein bottle Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-11-11 Yogendra Singh, Anand Kumar Tiwari
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Total coloring of graphs associated with algebraic structures and ordered structures Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-11-05 Nilesh Khandekar, Vinayak Joshi
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On nonhomogeneous biharmonic problem involving Rellich-type potentials and a critical Sobolev exponent Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-11-04 Sofiane Messirdi, Abdelaziz Bennour, Atika Matallah
This paper is concerned with the existence of multiple solutions for a biharmonic problem involving multi-polar Rellich type potentials and Sobolev critical nonlinearity in an open bounded domain of \({\mathbb {R}}^{N}\), \(N\ge 5\). The method used here is based on the Nehari manifold.
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Dispersion matrix comparisons among estimators under two competing restricted linear regression models Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-10-31 Xingwei Ren, Qian Zhou
We consider two restricted linear regression models \({\mathscr {M}}_{1}\) and \({\mathscr {M}}_{2}\), and obtain some conditons for the superiorities of the ordinary least squares estimators (OLSEs) and best linear unbiased estimators (BLUEs) under \({\mathscr {M}}_{1}\) and \({\mathscr {M}}_{2}\) with respect to the dispersion matrix criterion. Via these conditions, we provide an answer the question
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Reducibility type of polynomials modulo a prime Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-10-25 Joshua Harrington, Lenny Jones
Let \(f(x)\in {\mathbb Z}[x]\) be a monic polynomial that is irreducible over \({\mathbb Q}\), and suppose that \(\deg (f)=N\ge 2\). For a prime p not dividing the discriminant of f(x), we define the reducibility type of f(x) modulo p to be \((d_1,d_2,\ldots ,d_t)_p\) if f(x) factors into distinct irreducibles \(g_i(x)\in {\mathbb F}_p[x]\) as $$\begin{aligned} f(x)=g_1(x)g_2(x)\cdots g_t(x), \end{aligned}$$
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On the signless Laplacian energy of a digraph Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-10-25 Hilal A. Ganie
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Bernstein-type inequalities for a polynomial not vanishing in a disk Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-10-11 Abdullah Mir, Firdose Ahmad
We establish some Bernstein-type inequalities which are point-wise estimates for the modulus of the derivative and polar derivative of a polynomial. The obtained results produce various generalizations and refinements of the classical Erdős-Lax inequality and related inequalities.
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An investigation of an inverse problem for second-order abstract differential equation Indian J. Pure Appl. Math. (IF 0.7) Pub Date : 2023-10-12 Muslim Malik, Santosh Ruhil, Rajesh Dhayal
In this manuscript, we consider an inverse problem for a second-order abstract differential equation in a Banach space and identify the parameter using an over-determined condition on a mild solution. A direct approach using Volterra integral equation for sufficiently regular data and an optimal control approach for less regular data are the main techniques to find the solution pair of the considered