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Some properties of generalized distance eigenvalues of graphs Czechoslov. Math. J. (IF 0.5) Pub Date : 2024-04-01
Abstract Let G be a simple connected graph with vertex set V(G) = {v1, v2, …, vn} and edge set E(G), and let \({d_{{v_i}}}\) be the degree of the vertex vi. Let D(G) be the distance matrix and let Tr(G) be the diagonal matrix of the vertex transmissions of G. The generalized distance matrix of G is defined as Dα(G) = αTr(G) + (1 − α)D(G), where 0 ⩽ α ⩽ 1. Let λ1(Dα(G)) ⩾ λ2(Dα(G)) ⩾ … ⩾ λn(Dα(G)) be
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Bilinear fractional Hardy-type operators with rough kernels on central Morrey spaces with variable exponents Czechoslov. Math. J. (IF 0.5) Pub Date : 2024-02-16
Abstract We introduce a type of n-dimensional bilinear fractional Hardy-type operators with rough kernels and prove the boundedness of these operators and their commutators on central Morrey spaces with variable exponents. Furthermore, the similar definitions and results of multilinear fractional Hardy-type operators with rough kernels are obtained.
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Rings in which elements are sum of a central element and an element in the Jacobson radical Czechoslov. Math. J. (IF 0.5) Pub Date : 2024-02-13 Guanglin Ma, Yao Wang, André Leroy
An element in a ring R is called CJ if it is of the form c+j, where c belongs to the center and j is an element from the Jacobson radical. A ring R is called CJ if each element of R is CJ. We establish the basic properties of CJ rings, give several characterizations of these rings, and connect this notion with many standard elementwise properties such as clean, uniquely clean, nil clean, CN, and CU
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Lipschitz constants for a hyperbolic type metric under Möbius transformations Czechoslov. Math. J. (IF 0.5) Pub Date : 2024-02-12
Abstract Let D be a nonempty open set in a metric space (X, d) with ∂D ≠ Ø. Define $$h_{D,c}(x,y)=\log\left(1+c{{{d(x,y)}}\over{{\sqrt{d_{D}(x)d_{D}(y)}}}}\right).$$ where dD(x) = d(x, ∂D) is the distance from x to the boundary of D. For every c ⩾ 2, hD,c is a metric. We study the sharp Lipschitz constants for the metric hD,c under Möbius transformations of the unit ball, the upper half space, and
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Representation functions for binary linear forms Czechoslov. Math. J. (IF 0.5) Pub Date : 2024-02-12 Fang-Gang Xue
Let \(\mathbb{Z}\) be the set of integers, \(\mathbb{N}_{0}\) the set of nonnegative integers and F(x1,x2) = u1x1 + u2x2 be a binary linear form whose coefficients u1, u2 are nonzero, relatively prime integers such that u1u2 ≠ ±1 and u1u2 ≠ −2. Let \(f : \mathbb{Z}\rightarrow \mathbb{N}_{0}\ \cup\{\infty\}\) be any function such that the set f−1(0) has asymptotic density zero. In 2007, M. B. Nathanson
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Complete monotonicity of the remainder in an asymptotic series related to the psi function Czechoslov. Math. J. (IF 0.5) Pub Date : 2024-02-12 Zhen-Hang Yang, Jing-Feng Tian
Let p, q ∈ ℝ with p − q ≽ 0, \(\sigma = {1 \over 2}(p + q - 1)\) and \(s = {1 \over 2}(1 - p + q)\), and let $${{\cal D}_m}(x;p,q) = {{\cal D}_0}(x;p,q) + \sum\limits_{k = 1}^m {{{{B_{2k}}(s)} \over {2k{{(x + \sigma )}^{2k}}}},} $$ where $${{\cal D}_0}(x;p,q) = {{\psi (x + p) + \psi (x + q)} \over 2} - \ln (x + \sigma ).$$ We establish the asymptotic expansion $${{\cal D}_0}(x;p,q) \sim - \sum\limits_{n
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On certain GL(6) form and its Rankin-Selberg convolution Czechoslov. Math. J. (IF 0.5) Pub Date : 2024-02-09
Abstract We consider LG(s) to be the L-function attached to a particular automorphic form G on GL(6). We establish an upper bound for the mean square estimate on the critical line of Rankin-Selberg L-function LG×G(s). As an application of this result, we give an asymptotic formula for the discrete sum of coefficients of LG×G(s).
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The generalized Toeplitz operators on the Fock space $$F_\alpha ^2$$ Czechoslov. Math. J. (IF 0.5) Pub Date : 2024-02-08 Chunxu Xu, Tao Yu
Let μ be a positive Borel measure on the complex plane ℂn and let j = (j1, …, jn) with ji ∈ ℕ. We study the generalized Toeplitz operators \(T_\mu ^{(j)}\) on the Fock space \(F_\alpha ^2\). We prove that \(T_\mu ^{(j)}\) is bounded (or compact) on \(F_\alpha ^2\) if and only if μ is a Fock-Carleson measure (or vanishing Fock-Carleson measure). Furthermore, we give a necessary and sufficient condition
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Symmetric and reversible properties of bi-amalgamated rings Czechoslov. Math. J. (IF 0.5) Pub Date : 2024-02-05
Abstract Let f: A → B and g: A → C be two ring homomorphisms and let K and K′ be two ideals of B and C, respectively, such that f−1(K) = g−1(K′). We investigate unipotent, symmetric and reversible properties of the bi-amalgamation ring A ⋈f,g (K, K′) of A with (B, C) along (K, K′) with respect to (f, g).
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Green-Liouville approximation and correct solvability in Lp(ℝ) of the general Sturm-Liouville equation Czechoslov. Math. J. (IF 0.5) Pub Date : 2024-02-01 Nina Chernyavskaya, Leonid Shuster
We consider the equation$$-(r(x) y^{\prime}(x))^{\prime}+q(x)y(x)=f(x),\quad x\in\mathbb R,$$ where f ∈ Lp(ℝ), p ∈ (1, ∞) and$$r>0,\quad{{1}\over{{r}}}\in L_1^{\text{loc}}(\mathbb R),\quad q\in L_1^{\text{loc}}(\mathbb R).$$ For particular equations of this form, we suggest some methods for the study of the question on requirements to the functions r and q under which the above equation is correctly
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Condition numbers of Hessenberg companion matrices Czechoslov. Math. J. (IF 0.5) Pub Date : 2024-01-26 Michael Cox, Kevin N. Vander Meulen, Adam Van Tuyl, Joseph Voskamp
The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion matrices that can be characterized by a Hessenberg form. We demonstrate that the Hessenberg form of the Fiedler companion matrices provides a straight-forward way to compare the condition numbers of these matrices. We also
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More on the strongly 1-absorbing primary ideals of commutative rings Czechoslov. Math. J. (IF 0.5) Pub Date : 2024-01-22 Ali Yassine, Mohammad Javad Nikmehr, Reza Nikandish
Let R be a commutative ring with identity. We study the concept of strongly 1-absorbing primary ideals which is a generalization of n-ideals and a subclass of 1-absorbing primary ideals. A proper ideal I of R is called strongly 1-absorbing primary if for all nonunit elements a,b,c ∈ R such that abc ∈ I, it is either ab ∈ I or \(c \in \sqrt 0 \). Some properties of strongly 1-absorbing primary ideals
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Lie perfect, Lie central extension and generalization of nilpotency in multiplicative Lie algebras Czechoslov. Math. J. (IF 0.5) Pub Date : 2024-01-19 Dev Karan Singh, Mani Shankar Pandey, Shiv Datt Kumar
This paper aims to introduce and explore the concept of Lie perfect multiplicative Lie algebras, with a particular focus on their connections to the central extension theory of multiplicative Lie algebras. The primary objective is to establish and provide proof for a range of results derived from Lie perfect multiplicative Lie algebras. Furthermore, the study extends the notion of Lie nilpotency by
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A conjecture on minimum permanents Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-12-11 Gi-Sang Cheon, Seok-Zun Song
We consider the permanent function on the faces of the polytope of certain doubly stochastic matrices, whose nonzero entries coincide with those of fully indecomposable square (0, 1)-matrices containing the identity submatrix. We show that a conjecture in K. Pula, S. Z. Song, I. M. Wanless (2011), is true for some cases by determining the minimum permanent on some faces of the polytope of doubly stochastic
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Boundary value problems with bounded ϕ-Laplacian and nonlocal conditions of integral type Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-12-08 Daria Bugajewska, Jean Mawhin
We study the existence of solutions to nonlinear boundary value problems for second order quasilinear ordinary differential equations involving bounded ϕ-Laplacian, subject to integral boundary conditions formulated in terms of Riemann-Stieltjes integrals.
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On feebly nil-clean rings Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-12-07 Marjan Sheibani Abdolyousefi, Neda Pouyan
A ring R is feebly nil-clean if for any a ∈ R there exist two orthogonal idem-potents e, f ∈ R and a nilpotent w ∈ R such that a = e − f + w. Let R be a 2-primal feebly nil-clean ring. We prove that every matrix ring over R is feebly nil-clean. The result for rings of bounded index is also obtained. These provide many classes of rings over which every matrix is the sum of orthogonal idempotent and
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Non-existence of global classical solutions to 1D compressible heat-conducting micropolar fluid Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-12-05 Jianwei Dong, Junhui Zhu, Litao Zhang
We study the non-existence of global classical solutions to 1D compressible heat-conducting micropolar fluid without viscosity. We first show that the life span of the classical solutions with decay at far fields must be finite for the 1D Cauchy problem if the initial momentum weight is positive. Then, we present several sufficient conditions for the non-existence of global classical solutions to the
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Global classical solutions in a self-consistent chemotaxis(-Navier)-Stokes system Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-12-04 Yanjiang Li, Zhongqing Yu, Yumei Huang
The self-consistent chemotaxis-fluid system $$\left\{ {\matrix{{{n_t} + u \cdot \nabla n = \Delta n - \nabla \cdot (n\nabla c) + \nabla \cdot (n\nabla \phi )} \hfill & {x \in \Omega ,\,\,t > 0,} \hfill \cr {{c_t} + u \cdot \nabla c = \Delta c - nc,} \hfill & {x \in \Omega ,\,\,t > 0,} \hfill \cr {{u_t} + \kappa (u \cdot \nabla )u + \nabla P = \Delta u - n\nabla \phi + n\nabla c,} \hfill & {x \in \Omega
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The origin and developments of Kurzweil’s generalized Riemann integral Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-12-04 Jean Mawhin
The paper describes to origin and motivation of Kurzweil in introducing a Riemann-type definition for generalized Perron integrals and his further contributions to the topics.
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Two results of n-exangulated categories Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-11-29 Jian He, Jing He, Panyue Zhou
M. Herschend, Y. Liu, H. Nakaoka introduced n-exangulated categories, which are a simultaneous generalization of n-exact categories and (n + 2)-angulated categories. This paper consists of two results on n-exangulated categories: (1) we give an equivalent characterization of axiom (EA2); (2) we provide a new way to construct a closed subfunctor of an n-exangulated category.
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Run-length function of the Bolyai-Rényi expansion of real numbers Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-11-29 Rao Li, Fan Lü, Li Zhou
By iterating the Bolyai-Rényi transformation T(x) = (x + 1)2 (mod 1), almost every real number x ∈ [0, 1) can be expanded as a continued radical expression$$x = - 1 + \sqrt {{x_1} + \sqrt {{x_2} + \ldots + \sqrt {{x_n} + \ldots}}}$$ with digits xn ∈ {0, 1, 2} for all n ∈ ℕ. For any real number n ∈ [0, 1) and digit i ∈ {0, 1, 2}, let rn(x, i) be the maximal length of consecutive i’s in the first n digits
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Hall algebras of two equivalent extriangulated categories Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-11-29 Shiquan Ruan, Li Wang, Haicheng Zhang
For any positive integer n, let An be a linearly oriented quiver of type A with n vertices. It is well-known that the quotient of an exact category by projective-injectives is an extriangulated category. We show that there exists an extriangulated equivalence between the extriangulated categories \({{\cal M}_{n + 1}}\) and \({{\cal F}_n}\), where \({{\cal M}_{n + 1}}\) and \({{\cal F}_n}\) are the
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Polyanalytic Besov spaces and approximation by dilatations Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-11-29 Ali Abkar
Using partial derivatives ∂f/∂z and \(\partial f/\partial\bar{z}\), we introduce Besov spaces of polyanalytic functions in the open unit disk, as well as in the upper half-plane. We then prove that the dilatations of functions in certain weighted polyanalytic Besov spaces converge to the same functions in norm. When restricted to the open unit disk, we prove that each polyanalytic function of degree
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A twisted class number formula and Gross’s special units over an imaginary quadratic field Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-11-07 Saad El Boukhari
Let F/k be a finite abelian extension of number fields with k imaginary quadratic. Let OF be the ring of integers of F and n ⩾ 2 a rational integer. We construct a submodule in the higher odd-degree algebraic K-groups of OF using corresponding Gross’s special elements. We show that this submodule is of finite index and prove that this index can be computed using the higher “twisted” class number of
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Parametric representations of BiHom-Hopf algebras Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-11-03 Xiaohui Zhang, Wei Wang, Juzhen Chen
The main purpose of the present paper is to study representations of BiHom-Hopf algebras. We first introduce the notion of BiHom-Hopf algebras, and then discuss BiHom-type modules, Yetter-Dinfeld modules and Drinfeld doubles with parameters. We get some new n-monoidal categories via the category of BiHom-(co)modules and the category of BiHom-Yetter-Drinfeld modules. Finally, we obtain a center construction
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Results related to Huppert’s ϱ-σ conjecture Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-11-02 Xia Xu, Yong Yang
We improve a few results related to Huppert’s ϱ-σ conjecture. We also generalize a result about the covering number of character degrees to arbitrary finite groups.
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Periodic linear groups factorized by mutually permutable subgroups Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-11-02 Maria Ferrara, Marco Trombetti
The aim is to investigate the behaviour of (homomorphic images of) periodic linear groups which are factorized by mutually permutable subgroups. Mutually permutable subgroups have been extensively investigated in the finite case by several authors, among which, for our purposes, we only cite J. C. Beidleman and H. Heineken (2005). In a previous paper of ours (see M. Ferrara, M. Trombetti (2022)) we
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The clean elements of the ring $${\cal R}(L)$$ Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-10-27 Ali Akbar Estaji, Maryam Taha
We characterize clean elements of \({\cal R}(L)\) and show that \(\alpha \in {\cal R}(L)\) is clean if and only if there exists a clopen sublocale U in L such that \({\mathfrak{c}_L}({\rm{coz}}(\alpha - {\bf{1}})) \subseteq U \subseteq {_L}({\rm{coz}}(\alpha))\). Also, we prove that \({\cal R}(L)\) is clean if and only if \({\cal R}(L)\) has a clean prime ideal. Then, according to the results about
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1-planar graphs with girth at least 6 are (1,1,1,1)-colorable Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-10-18 Lili Song, Lei Sun
A graph is 1-planar if it can be drawn in the Euclidean plane so that each edge is crossed by at most one other edge. A 1-planar graph on n vertices is optimal if it has 4n − 8 edges. We prove that 1-planar graphs with girth at least 6 are (1,1,1,1)-colorable (in the sense that each of the four color classes induces a subgraph of maximum degree one). Inspired by the decomposition of 1-planar graphs
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Special modules for R(PSL(2, q)) Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-10-13 Liufeng Cao, Huixiang Chen
Let R be a fusion ring and Rℂ:= R ⊗ℤ ℂ be the corresponding fusion algebra. We first show that the algebra Rℂ has only one left (right, two-sided) cell and the corresponding left (right, two-sided) cell module. Then we prove that, up to isomorphism, Rℂ admits a unique special module, which is 1-dimensional and given by the Frobenius-Perron homomorphism FPdim. Moreover, as an example, we explicitly
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Global solvability in the parabolic-elliptic chemotaxis system with singular sensitivity and logistic source Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-10-13 Xiangdong Zhao
We study the chemotaxis system with singular sensitivity and logistic-type source: ut = Δu − χ∇ · (u∇v/v) + ru − μuk, 0 = Δv − v + u under the non-flux boundary conditions in a smooth bounded domain Ω ⊂ ℝn, χ, r, μ > 0, k > 1 and n ⩾ 1. It is shown with k ∈ (1, 2) that the system possesses a global generalized solution for n ⩾ 2 which is bounded when χ > 0 is suitably small related to r > 0 and the
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Kernels of Toeplitz operators on the Bergman space Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-10-12 Young Joo Lee
A Coburn theorem says that a nonzero Toeplitz operator on the Hardy space is one-to-one or its adjoint operator is one-to-one. We study the corresponding problem for certain Toeplitz operators on the Bergman space.
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On pairs of Goldbach-Linnik equations with unequal powers of primes Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-10-12 Enxun Huang
It is proved that every pair of sufficiently large odd integers can be represented by a pair of equations, each containing two squares of primes, two cubes of primes, two fourth powers of primes and 105 powers of 2.
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On Π-property of some maximal subgroups of Sylow subgroups of finite groups Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-09-08 Zhengtian Qiu, Jianjun Liu, Guiyun Chen
Let H be a subgroup of a finite group G. We say that H satisfies the Π-property in G if for any chief factor L/K of G, ∣G/K: NG/K(HK/K ∩ L/K)∣ is a π(HK/K∩L/K)-number. We study the influence of some p-subgroups of G satisfying the Π-property on the structure of G, and generalize some known results.
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A class of quantum doubles of pointed Hopf algebras of rank one Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-09-06 Hua Sun, Yueming Li
We construct a class of quantum doubles \(D({H_{{D_n}}})\) of pointed Hopf algebras of rank one \({H_{\cal D}}\). We describe the algebra structures of \(D({H_{{D_n}}})\) by generators with relations. Moreover, we give the comultiplication ΔD, counit εD and the antipode SD, respectively.
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Exact multiplicity and bifurcation curves of positive solutions of generalized logistic problems Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-09-05 Shao-Yuan Huang, Ping-Han Hsieh
We study the exact multiplicity and bifurcation curves of positive solutions of generalized logistic problems $$\left\{ {\matrix{{ - {{[\varphi ({u^\prime })]}^\prime } = \lambda {u^p}\left( {1 - {u \over N}} \right)} \hfill & {{\rm{in}}\,\,( - L,L),} \hfill \cr {u( - L) = u(L) = 0,} \hfill & {} \hfill \cr } } \right.$$ where p > 1, N > 0, λ > 0 is a bifurcation parameter, L > 0 is an evolution parameter
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Function algebras of Besov and Triebel-Lizorkin-type Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-07-25 Fares Bensaid, Madani Moussai
We prove that in the homogeneous Besov-type space the set of bounded functions constitutes a unital quasi-Banach algebra for the pointwise product. The same result holds for the homogeneous Triebel-Lizorkin-type space.
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Large time behaviour of a conservation law regularised by a Riesz-Feller operator: the sub-critical case Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-07-20 Carlota Maria Cuesta, Xuban Diez-Izagirre
We study the large time behaviour of the solutions of a nonlocal regularisation of a scalar conservation law. This regularisation is given by a fractional derivative of order 1 + α, with α ∈ (0, 1), which is a Riesz-Feller operator. The nonlinear flux is given by the locally Lipschitz function ∣u∣q−1u/q for q > 1. We show that in the sub-critical case, 1 < q < 1 + α, the large time behaviour is governed
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On the zeros of a quaternionic polynomial: An extension of the Eneström-Kakeya theorem Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-06-22 Abdullah Mir
We present some results on the location of zeros of regular polynomials of a quaternionic variable. We derive new bounds of Eneström-Kakeya type for the zeros of these polynomials by virtue of a maximum modulus theorem and the structure of the zero sets of a regular product established in the newly developed theory of regular functions and polynomials of a quaternionic variable. Our results extend
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Commutative rings whose certain modules decompose into direct sums of cyclic submodules Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-06-21 Farid Kourki, Rachid Tribak
We provide some characterizations of rings R for which every (finitely generated) module belonging to a class \(\cal{C}\) of R-modules is a direct sum of cyclic submodules. We focus on the cases, where the class \(\cal{C}\) is one of the following classes of modules: semiartinian modules, semi-V-modules, V-modules, coperfect modules and locally supplemented modules.
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Majority choosability of 1-planar digraph Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-06-21 Weihao Xia, Jihui Wang, Jiansheng Cai
A majority coloring of a digraph D with k colors is an assignment π: V(D) → {1, 2, …, k} such that for every v ∈ V(D) we have π(w) = π(v) for at most half of all out-neighbors w ∈ N+(v). A digraph D is majority k-choosable if for any assignment of lists of colors of size k to the vertices, there is a majority coloring of D from these lists. We prove that if U(D) is a 1-planar graph without a 4-cycle
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Equations for the set of overrings of normal rings and related ring extensions Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-06-20 Mabrouk Ben Nasr, Ali Jaballah
We establish several finiteness characterizations and equations for the cardinality and the length of the set of overrings of rings with nontrivial zero divisors and integrally closed in their total ring of fractions. Similar properties are also obtained for related extensions of commutative rings that are not necessarily integral domains. Numerical characterizations are obtained for rings with some
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Tensor products of higher almost split sequences in subcategories Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-06-19 Xiaojian Lu, Deren Luo
We introduce the algebras satisfying the (\({\cal B}\), n) condition. If Λ, Γ are algebras satisfying the (\({\cal B}\), n), (\({\cal E}\), m) condition, respectively, we give a construction of (m+n)-almost split sequences in some subcategories \({({\cal B} \otimes {\cal E})^{({i_0},{j_0})}}\) of mod(Λ ⊗ Γ) by tensor products and mapping cones. Moreover, we prove that the tensor product algebra Λ ⊗
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Convergence of ap-Henstock-Kurzweil Integral on Locally Compact Spaces Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-06-19 Hemanta Kalita, Ravi P. Agarwal, Bipan Hazarika
We introduce an ap-Henstock-Kurzweil type integral with a non-atomic Radon measure and prove the Saks-Henstock type lemma. The monotone convergence theorem, μap-Henstock-Kurzweil equi-integrability, and uniformly strong Lusin condition are discussed.
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Conditional Fourier-Feynman transform given infinite dimensional conditioning function on abstract Wiener space Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-06-12 Jae Gil Choi, Sang Kil Shim
We study a conditional Fourier-Feynman transform (CFFT) of functionals on an abstract Wiener space (H, B, v). An infinite dimensional conditioning function is used to define the CFFT. To do this, we first present a short survey of the conditional Wiener integral concerning the topic of this paper. We then establish evaluation formulas for the conditional Wiener integral on the abstract Wiener space
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Finitely silting comodules in quasi-finite comodule category Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-06-07 Qianqian Yuan, Hailou Yao
We introduce the notions of silting comodules and finitely silting comodules in quasi-finite category, and study some properties of them. We investigate the torsion pair and dualities which are related to finitely silting comodules, and give the equivalences among silting comodules, finitely silting comodules, tilting comodules and finitely tilting comodules.
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Sobolev type inequalities for fractional maximal functions and Riesz potentials in Morrey spaces of variable exponent on half spaces Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-05-24 Yoshihiro Mizuta, Tetsu Shimomura
Our aim is to establish Sobolev type inequalities for fractional maximal functions \({M_{\mathbb{H},\nu }}f\) and Riesz potentials \({I_{\mathbb{H},\alpha}}f\) in weighted Morrey spaces of variable exponent on the half space \(\mathbb{H}\). We also obtain Sobolev type inequalities for a C1 function on \(\mathbb{H}\). As an application, we obtain Sobolev type inequality for double phase functionals
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Annihilator ideals of finite dimensional simple modules of two-parameter quantized enveloping algebra $${U_{r,s}}({\mathfrak{s}\mathfrak{l}_2})$$ Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-05-22 Yu Wang, Xiaoming Li
Let U be the two-parameter quantized enveloping algebra \({U_{r,s}}({\mathfrak{s}\mathfrak{l}_2})\) and F(U) the locally finite subalgebra of U under the adjoint action. The aim of this paper is to determine some ring-theoretical properties of F(U) in the case when rs−1 is not a root of unity. Then we describe the annihilator ideals of finite dimensional simple modules of U by generators.
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The topology of the space of $$\mathcal{H}\mathcal{K}$$ integrable functions in $${\mathbb{R}^n}$$ Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-05-22 Varayu Boonpogkrong
It is known that there is no natural Banach norm on the space \(\mathcal{H}\mathcal{K}\) of n-dimensional Henstock-Kurzweil integrable functions on [a, b]. We show that the \(\mathcal{H}\mathcal{K}\) space is the uncountable union of Fréchet spaces \(\mathcal{H}\mathcal{K}(X)\). On each \(\mathcal{H}\mathcal{K}(X)\) space, an F-norm ‖·‖X is defined. A ‖·‖X-convergent sequence is equivalent to a control-convergent
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Fredholmness of pseudo-differential operators with nonregular symbols Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-05-19 Kazushi Yoshitomi
We establish the Fredholmness of a pseudo-differential operator whose symbol is of class C0,σ, 0 < σ < 1, in the spatial variable. Our work here refines the work of H. Abels, C. Pfeuffer (2020).
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The Picard-Lindelöf Theorem and continuation of solutions for measure differential equations Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-05-15 Gastón Beltritti, Stefania Demaria, Graciela Giubergia, Fernando Mazzone
We obtain, by means of Banach’s Fixed Point Theorem, convergence for the Picard iterations associated to a general nonlinear system of measure differential equations. We study the existence of left-continuous solutions defined on maximal intervals and we establish some properties of these maximal solutions.
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A new approach to antisymmetric infinitesimal bialgebras Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-05-15 Tianshui Ma, Bei Li, Jie Li, Miaoshuang Chen
We present a notion of an anti-covariant bialgebra extending the anti-symmetric infinitesimal bialgebra and also provide some equivalent characterizations of it. We also prove that an anti-associative Yang-Baxter pair can produce a special Rota-Baxter system.
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Linear preserver of n × 1 Ferrers vectors Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-05-09 Leila Fazlpar, Ali Armandnejad
Let A = [aij]m×n be an m × n matrix of zeros and ones. The matrix A is said to be a Ferrers matrix if it has decreasing row sums and it is row and column dense with nonzero (1,1)-entry. We characterize all linear maps perserving the set of n × 1 Ferrers vectors over the binary Boolean semiring and over the Boolean ring \({\mathbb{Z}_2}\). Also, we have achieved the number of these linear maps in each
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On optimal parameters involved with two-weighted estimates of commutators of singular and fractional operators with Lipschitz symbols Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-05-09 Gladis Pradolini, Jorgelina Recchi
We prove two-weighted norm estimates for higher order commutator of singular integral and fractional type operators between weighted Lp and certain spaces that include Lipschitz, BMO and Morrey spaces. We also give the optimal parameters involved with these results, where the optimality is understood in the sense that the parameters defining the corresponding spaces belong to a certain region out of
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On the r-free values of the polynomial x2 + y2 + z2 + k Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-05-04 Gongrui Chen, Wenxiao Wang
Let k be a fixed integer. We study the asymptotic formula of R(H,r,k), which is the number of positive integer solutions 1 ⩽ x, y, z ⩽ H such that the polynomial x2 + y2 + z2 + k is r-free. We obtained the asymptotic formula of R(H, r, k) for all r ⩾ 2. Our result is new even in the case r = 2. We proved that R(H, 2, k) = ckH3 + O(H9/4+ε), where ck > 0 is a constant depending on k. This improves upon
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Symmetries in connected graded algebras and their PBW-deformations Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-04-27 Yongjun Xu, Xin Zhang
We focus on connected graded algebras and their PBW-deformations endowed with additional symmetric structures. Many well-known algebras such as negative parts of Drinfeld-Jimbo’s quantum groups, cubic Artin-Schelter algebras and three-dimensional Sklyanin algebras appear in our research framework. As an application, we investigate a \({{\cal K}_2}\) algebra \({\cal A}\) which was introduced to compute
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On the class number of the maximal real subfields of a family of cyclotomic fields Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-04-27 Mahesh Kumar Ram
For any square-free positive integer m ≡ 10 (mod 16) with m ⩾ 26, we prove that the class number of the real cyclotomic field ℚ(ζ4m +ζ −14m ) is greater than 1, where ζ4m is a primitive 4mth root of unity.
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On the average behavior of the Fourier coefficients of jth symmetric power L-function over certain sequences of positive integers Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-04-27 Anubhav Sharma, Ayyadurai Sankaranarayanan
We investigate the average behavior of the nth normalized Fourier coefficients of the jth (j ≽ 2 be any fixed integer) symmetric power L-function (i.e., L(s,symjf)), attached to a primitive holomorphic cusp form f of weight k for the full modular group \(SL(2,\mathbb{Z})\) over certain sequences of positive integers. Precisely, we prove an asymptotic formula with an error term for the sum $$S_j^ *:
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The tangent function and power residues modulo primes Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-04-13 Zhi-Wei Sun
Let p be an odd prime, and let a be an integer not divisible by p. When m is a positive integer with p ≡ 1 (mod 2m) and 2 is an mth power residue modulo p, we determine the value of the product \(\prod\limits_{k \in {R_m}(p)} {(1 + \tan (\pi ak/p))} \), where $${R_m}(p) = \{0 < k < p:k \in \mathbb{Z}\,\,{\rm{is}}\,\,{\rm{an}}\,\,m{\rm{th}}\,\,{\rm{power}}\,\,{\rm{residue}}\,\,{\rm{modulo}}\,p\} .$$
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Ding projective and Ding injective modules over trivial ring extensions Czechoslov. Math. J. (IF 0.5) Pub Date : 2023-04-13 Lixin Mao
Let R ⋉ M be a trivial extension of a ring R by an R-R-bimodule M such that MR, RM, (R, 0)R⋉ M and R⋉M(R, 0) have finite flat dimensions. We prove that (X, α) is a Ding projective left R ⋉ M-module if and only if the sequence \(M{\otimes _R}M{\otimes _R}X\mathop \to \limits^{M \otimes \alpha} M{\otimes _R}X\mathop \to \limits^\alpha X\) is exact and coker(α) is a Ding projective left R-module. Analogously