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Summands of finite group algebras Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-12-14 Carsten Dietzel, Gaurav Mittal
We study the inverse problem of the determination of a group algebra from the knowledge of its Wedderburn decomposition. We show that a certain class of matrix rings always occur as summands of finite group algebras.
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Stability of certain Engel-like distributions Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-12-18 Aritra Bhowmick
We introduce a higher dimensional analogue of the Engel structure, motivated by the Cartan prolongation of contact manifolds. We study the stability of such structure, generalizing the Gray-type stability results for Engel manifolds. We also derive local normal forms defining such a distribution.
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The boundedness of two classes of integral operators Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-12-18 Xin Wang, Ming-Sheng Liu
The aim of this paper is to characterize the Lp — Lq boundedness of two classes of integral operators from Lp(\({\cal U}\), dVα) to Lq(\({\cal U}\), dVβ) in terms of the parameters a, b, c, p, q and α, β, where \({\cal U}\) is the Siegel upper half-space. The results in the presented paper generalize a corresponding result given in C. Liu, Y. Liu, P. Hu, L. Zhou (2019).
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Constructing modular forms from harmonic Maass Jacobi forms Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-12-18 Ran Xiong, Haigang Zhou
We construct a family of modular forms from harmonic Maass Jacobi forms by considering their Taylor expansion and using the method of holomorphic projection. As an application we present a certain type Hurwitz class relations which can be viewed as a generalization of Mertens’ result in M. H. Mertens (2016).
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Algebraic properties of Toeplitz operators on weighted Bergman spaces Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-12-17 Amila Appuhamy
We study algebraic properties of two Toeplitz operators on the weighted Bergman space on the unit disk with harmonic symbols. In particular the product property and commutative property are discussed. Further we apply our results to solve a compactness problem of the product of two Hankel operators on the weighted Bergman space on the unit bidisk.
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On the Waring-Goldbach problem for one square and five cubes in short intervals Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-12-11 Fei Xue, Min Zhang, Jinjiang Li
Let N be a sufficiently large integer. We prove that almost all sufficiently large even integers n ∈ [N − 6U, N + 6U] can be represented as $$\left\{ {\matrix{ {n = p_1^2 + p_2^3 + p_3^3+ p_4^3 + p_5^3 + p_6^3,} \hfill \;\;\; {} \hfill \cr {\left| {p_1^2 - {N \over 6}} \right| \leqslant U,\,\,\,\,\,\left| {p_i^3 - {N \over 6}} \right| \leqslant U,\,\,} \hfill \;\;\; {i = 2,3,4,5,6,} \hfill \cr } }
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Ideal class (semi)groups and atomicity in Prüfer domains Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-12-10 Richard Erwin Hasenauer
We explore the connection between atomicity in Prüfer domains and their corresponding class groups. We observe that a class group of infinite order is necessary for non-Noetherian almost Dedekind and Prüfer domains of finite character to be atomic. We construct a non-Noetherian almost Dedekind domain and exhibit a generating set for the ideal class semigroup.
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Chebyshev polynomials and Pell equations over finite fields Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-12-09 Boaz Cohen
We shall describe how to construct a fundamental solution for the Pell equation x2 — my2 = 1 over finite fields of characteristic p ≠ 2. Especially, a complete description of the structure of these fundamental solutions will be given using Chebyshev polynomials. Furthermore, we shall describe the structure of the solutions of the general Pell equation x2 — my2 = n.
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Row Hadamard majorization on M m,n Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-12-07 Abbas Askarizadeh, Ali Armandnejad
An m × n matrix R with nonnegative entries is called row stochastic if the sum of entries on every row of R is 1. Let Mm,n be the set of all m × n real matrices. For A, B ∈ Mm,n, we say that A is row Hadamard majorized by B (denoted by A ≺ RHB) if there exists an m × n row stochastic matrix R such that A = R ο B, where X ο Y is the Hadamard product (entrywise product) of matrices X, Y ∈ Mm,n. In this
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Coleman Automorphisms of Finite Groups with a Self-Centralizing Normal Subgroup Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-09-24 Jinke Hai
Let G be a finite group with a normal subgroup N such that CG(N) ⩽ N. It is shown that under some conditions, Coleman automorphisms of G are inner. Interest in such automorphisms arose from the study of the normalizer problem for integral group rings.
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Erratum to ( δ , 2)-primary ideals of a commutative ring Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-11-02 Gülşen Ulucak, Ece Yetkin Çelikel
In Theorem 6 of [1], if R is a von Neumann regular ring, then every 2-prime ideal of R is a prime ideal. But the converse of this implication does not hold. Thus, we correct Theorem 6 of [1] as follows:
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S -depth on ZD -modules and local cohomology Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-10-29 Morteza Lotfi Parsa
Let R be a Noetherian ring, and I and J be two ideals of R. Let S be a Serre subcategory of the category of R-modules satisfying the condition CI and M be a ZD-module. As a generalization of the S-depth(I, M) and depth(I, J, M), the S-depth of (I, J) on M is defined as \(S{\rm{ - depth}}\left( {I,J,M} \right) = \inf \left\{ {S{\rm{ - depth}}\left( {\mathfrak{a},M} \right): \mathfrak{a}\in \widetilde{W}\left(
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On generalized Douglas-Weyl Randers metrics Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-10-29 Tayebeh Tabatabaeifar, Behzad Najafi, Mehdi Rafie-Rad
We characterize generalized Douglas-Weyl Randers metrics in terms of their Zermelo navigation data. Then, we study the Randers metrics induced by some important classes of almost contact metrics. Furthermore, we construct a family of generalized Douglas-Weyl Randers metrics which are not R-quadratic. We show that the Randers metric induced by a Kenmotsu manifold is a Douglas metric which is not of
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Monotonicity of first eigenvalues along the Yamabe flow Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-10-29 Liangdi Zhang
We construct some nondecreasing quantities associated to the first eigenvalue of \(-\Delta_{\varphi}+cR(c\geqslant\frac{1}{2}(n-2)/(n-1))\) along the Yamabe flow, where Δφ is the Witten-Laplacian operator with a C2 function φ. We also prove a monotonic result on the first eigenvalue of \(-\Delta_{\varphi}+\frac{1}{4}(n/(n-1))R\) along the Yamabe flow. Moreover, we establish some nondecreasing quantities
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The module of vector-valued modular forms is Cohen-Macaulay Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-10-27 Richard Gottesman
Let H denote a finite index subgroup of the modular group Γ and let ϱ denote a finite-dimensional complex representation of H. Let M(ϱ) denote the collection of holomorphic vector-valued modular forms for ϱ and let M(H) denote the collection of modular forms on H. Then M(ϱ) is a ℤ-graded M(H)-module. It has been proven that M(ϱ) may not be projective as a M(H)-module. We prove that M(ϱ) is Cohen-Macaulay
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On the Hilbert 2-class field tower of some imaginary biquadratic number fields Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-10-27 Mohamed Mahmoud Chems-Eddin, Abdelmalek Azizi, Abdelkader Zekhnini, Idriss Jerrari
Let \(\mathbb{k}=\mathbb{Q}(\sqrt{2},\sqrt{d})\) be an imaginary bicyclic biquadratic number field, where d is an odd negative square-free integer and \(\mathbb{k}_{2}^{(2)}\) its second Hilbert 2-class field. Denote by \(G=\text{Gal}(\mathbb{k}_{2}^{(2)}/\mathbb{k})\) the Galois group of \(\mathbb{k}_{2}^{(2)}/\mathbb{k}\). The purpose of this note is to investigate the Hilbert 2-class field tower
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Drinfeld doubles via derived Hall algebras and Bridgeland’s Hall algebras Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-10-20 Fan Xu, Haicheng Zhang
Let \(\mathcal{A}\) be a finitary hereditary abelian category. We give a Hall algebra presentation of Kashaev’s theorem on the relation between Drinfeld double and Heisenberg double. As applications, we obtain realizations of the Drinfeld double Hall algebra of \(\mathcal{A}\) via its derived Hall algebra and Bridgeland’s Hall algebra of m-cyclic complexes.
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On p -Adic Euler Constants Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-10-09 Abhishek Bharadwaj
The goal of this article is to associate a p-adic analytic function to the Euler constants γp(a, F), study the properties of these functions in the neighborhood of s = 1 and introduce a p-adic analogue of the infinite sum \(\sum\limits_{n \geqslant 1} {f(n)/n} \) for an algebraic valued, periodic function f. After this, we prove the theorem of Baker, Birch and Wirsing in this setup and discuss irrationality
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Annihilators and Attached Primes of Top Local Cohomology Modules Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-09-30 Shahram Rezaei
Let \(\mathfrak{a}\) be an ideal of Noetherian ring R and M a finitely generated R-module. In this paper we determine \({\rm{An}}{{\rm{n}}_R}({\rm{H}}_{\mathfrak{a}}^{{\rm{cd}}(\mathfrak{a},M)}(M))\) and \({\rm{At}}{{\rm{t}}_R}({\rm{H}}_{\mathfrak{a}}^{{\rm{cd}}(\mathfrak{a},M)}(M))\), which are two important problems concerning the last nonzero local cohomology module \({\rm{H}}_{\mathfrak{a}}^{{
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A Solvability Criterion for Finite Groups Related to Character Degrees Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-09-18 Babak Miraali, Sajjad Mahmood Robati
Let m > 1 be a fixed positive integer. In this paper, we consider finite groups each of whose nonlinear character degrees has exactly m prime divisors. We show that such groups are solvable whenever m > 2. Moreover, we prove that if G is a non-solvable group with this property, then m = 2 and G is an extension of A7 or S7 by a solvable group.
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Recollement of Colimit Categories and Its Applications Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-09-18 Ju Huang, Qinghua Chen, Chunhuan Lai
We give an explicit recollement for a cocomplete abelian category and its colimit category. We obtain some applications on Leavitt path algebras, derived equivalences and K-groups.
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Exponent of Class Group of Certain Imaginary Quadratic Fields Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-09-15 Kalyan Chakraborty, Azizul Hoque
Let n > 1 be an odd integer. We prove that there are infinitely many imaginary quadratic fields of the form \(\mathbb{Q}\left( {\sqrt {{x^2} - 2{y^n}} } \right)\) whose ideal class group has an element of order n. This family gives a counterexample to a conjecture by H. Wada (1970) on the structure of ideal class groups.
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Polynomial Expansiveness and Admissibility of Weighted Lebesgue Spaces Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-08-18 Pham Viet Hai
The paper investigates the interaction between the notions of expansiveness and admissibility. We consider a polynomially bounded discrete evolution family and define an admissibility notion via the solvability of an associated difference equation. Using the admissibility of weighted Lebesgue spaces of sequences, we give a characterization of discrete evolution families which are polynomially expansive
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Attractors for Stochastic Reaction-Diffusion Equation with Additive Homogeneous Noise Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-08-18 Jakub Slavík
We study the asymptotic behaviour of solutions of a reaction-diffusion equation in the whole space ℝd driven by a spatially homogeneous Wiener process with finite spectral measure. The existence of a random attractor is established for initial data in suitable weighted L2-space in any dimension, which complements the result from P. W. Bates, K. Lu, and B. Wang (2013). Asymptotic compactness is obtained
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On g -Natural Conformal Vector Fields on Unit Tangent Bundles Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-08-17 Mohamed Tahar Kadaoui Abbassi, Noura Amri
We study conformal and Killing vector fields on the unit tangent bundle, over a Riemannian manifold, equipped with an arbitrary pseudo-Riemannian g-natural metric. We characterize the conformal and Killing conditions for classical lifts of vector fields and we give a full classification of conformal fiber-preserving vector fields on the unit tangent bundle endowed with an arbitrary pseudo-Riemannian
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Compression of Slant Toeplitz Operators on the Hardy Space of n -Dimensional Torus Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-07-21 Gopal Datt, Shesh Kumar Pandey
This paper studies the compression of a kth-order slant Toeplitz operator on the Hardy space \({H^2}\left({\mathbb{T}{^n}} \right)\) for integers k ⩾ 2 and n ⩾ 1. It also provides a characterization of the compression of a kth-order slant Toeplitz operator on \({H^2}\left({\mathbb{T}{^n}} \right)\). Finally, the paper highlights certain properties, namely isometry, eigenvalues, eigenvectors, spectrum
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Decomposition of Finitely Generated Modules Using Fitting Ideals Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-07-09 Somayeh Hadjirezaei, Sina Hedayat
Let R be a commutative Noetherian ring and M be a finitely generated R-module. The main result of this paper is to characterize modules whose first nonzero Fitting ideal is a product of maximal ideals of R, in some cases.
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Generalized Symmetry Classes of Tensors Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-07-08 Gholamreza Rafatneshan, Yousef Zamani
Let V be a unitary space. For an arbitrary subgroup G of the full symmetric group Sm and an arbitrary irreducible unitary representation Λ of G, we study the generalized symmetry class of tensors over V associated with G and Λ. Some important properties of this vector space are investigated.
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Controlling Products of Currents by Higher Powers of Plurisubharmonic Functions Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-07-07 Ahmad K. Al Abdulaali, Hassine El Mir
We discuss the existence of the current gkT, k ∈ ℕ for positive and closed currents T and unbounded plurisubharmonic functions g. Furthermore, a new type of weighted Lelong number is introduced under the name of weight k Lelong number.
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Formal Deformations and Principal Series Representations of SL(2, ℝ) and SL(2, ℂ) Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-07-01 Benjamin Cahen
In this note, we study formal deformations of derived representations of the principal series representations of SL(2, ℝ). In particular, we recover all the representations of the derived principal series by deforming one of them. Similar results are also obtained for SL(2, ℂ).
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Homogenization of a Three-Phase Composites of Double-Porosity Type Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-07-01 Ahmed Boughammoura, Yousra Braham
In this work we consider a diffusion problem in a periodic composite having three phases: matrix, fibers and interphase. The heat conductivities of the medium vary periodically with a period of size εγ (ε > 0 and β > 0) in the transverse directions of the fibers. In addition, we assume that the conductivity of the interphase material and the anisotropy contrast of the material in the fibers are of
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On Sectional Newtonian Graphs Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-08-17 Zening Fan; Suo Zhao
In this paper, we introduce the so-called sectional Newtonian graphs for univariate complex polynomials, and study some properties of those graphs. In particular, we list all possible sectional Newtonian graphs when the degrees of the polynomials are less than five, and also show that every stable gradient graph can be realized as a polynomial sectional Newtonian graph.
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H-Conformal Anti-Invariant Submersions from Almost Quaternionic Hermitian Manifolds Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-08-04 Kwang Soon Park
We introduce the notions of h-conformal anti-invariant submersions and h-conformal Lagrangian submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds as a generalization of Riemannian submersions, horizontally conformal submersions, anti-invariant submersions, h-anti-invariant submersions, h-Lagrangian submersion, conformal anti-invariant submersions. We investigate their
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Strongly ( T , n )-Coherent Rings, ( T , n )-Semihereditary Rings and ( T , n )-Regular Rings Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-07-07 Zhanmin Zhu
Let T be a weak torsion class of left R-modules and n a positive integer. A left R-module M is called (T, n)-injective if ExtnR (C, M) = 0 for each (T, n + 1)-presented left R-module C; a right R-module M is called (T, n)-flat if TorRn (M, C) = 0 for each (T, n +1)-presented left R-module C; a left R-module M is called (T, n)-projective if ExtnR (M, N) = 0 for each (T, n)-injective left R-module N;
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A Note on L-Dunford-Pettis Sets in A Topological Dual Banach Space Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-04-30 Abderrahman Retbi
The present paper is devoted to some applications of the notion of L-Dunford-Pettis sets to several classes of operators on Banach lattices. More precisely, we establish some characterizations of weak Dunford-Pettis, Dunford-Pettis completely continuous, and weak almost Dunford-Pettis operators. Next, we study the relationships between LDunford-Pettis, and Dunford-Pettis (relatively compact) sets in
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A Note on Skolem-Noether Algebras Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-04-23 Juncheol Han, Tsiu-Kwen Lee, Sangwon Park
The paper was motivated by Kovacs’ paper (1973), Isaacs’ paper (1980) and a recent paper, due to Brešar et al. (2018), concerning Skolem-Noether algebras. Let K be a unital commutative ring, not necessarily a field. Given a unital K-algebra S, where K is contained in the center of S, n ∈ ℕ, the goal of this paper is to study the question: when can a homomorphism φ: Mn(K) → Mn(S) be extended to an inner
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Tridiagonal Matrices and Spectral Properties of Some Graph Classes Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-04-23 Milica Anđelić, Zhibin Du, Carlos M. da Fonseca, Slobodan K. Simić
A graph is called a chain graph if it is bipartite and the neighbourhoods of the vertices in each colour class form a chain with respect to inclusion. In this paper we give an explicit formula for the characteristic polynomial of any chain graph and we show that it can be expressed using the determinant of a particular tridiagonal matrix. Then this fact is applied to show that in a certain interval
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On Groups of Automorphisms of Nilpotent p -Groups of Finite Rank Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-04-22 Tao Xu, Heguo Liu
Let α and β be automorphisms of a nilpotent p-group G of finite rank. Suppose that 〈(αβ(g))(βα(g))–: g ∈G〉 is a finite cyclic subgroup of G, then, exclusively, one of the following statements holds for G and Γ, where Γ is the group generated by α and β. (i) G is finite, then Γ is an extension of a p-group by an abelian group. (ii) G is infinite, then Γ is soluble and abelian-by-finite.
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Squarefree Monomial Ideals with Maximal Depth Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-04-20 Ahad Rahimi
Let (R,m) be a Noetherian local ring and M a finitely generated R-module. We say M has maximal depth if there is an associated prime p of M such that depth M = dim R/p. In this paper we study squarefree monomial ideals which have maximal depth. Edge ideals of cycle graphs, transversal polymatroidal ideals and high powers of connected bipartite graphs with this property are classified.
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P-Injective Group Rings Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-04-17 Liang Shen
A ring R is called right P-injective if every homomorphism from a principal right ideal of R to RR can be extended to a homomorphism from RR to RR. Let R be a ring and G a group. Based on a result of Nicholson and Yousif, we prove that the group ring RG is right P-injective if and only if (a) R is right P-injective; (b) G is locally finite; and (c) for any finite subgroup H of G and any principal right
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Rigidity of the Holomorphic Automorphism of the Generalized Fock-Bargmann-Hartogs Domains Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-04-17 Ting Guo, Zhiming Feng, Enchao Bi
We study a class of typical Hartogs domains which is called a generalized Fock-Bargmann-Hartogs domain. \(D_{n,m}^p(\mu ).\) The generalized Fock-Bargmann-Hartogs domain is defined by inequality \({e^{\mu z{^2}}}\sum\limits_{j = 1}^m {{\omega _j}{^{2p}}} 1,\) where (z, ω) ∈ ℂn × ℂn. In this paper, we will establish a rigidity of its holomorphic automorphism group. Our results imply that a holomorphic
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( δ , 2)-Primary Ideals of a Commutative Ring Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-04-17 Gülşen Ulucak, Ece Yetkin Çelikel
Let R be a commutative ring with nonzero identity, let I(R) be the set of all ideals of R and δ: I(R) → I(R) an expansion of ideals of R defined by I ↦ δ(I). We introduce the concept of (δ, 2)-primary ideals in commutative rings. A proper ideal I of R is called a (δ, 2)-primary ideal if whenever a, b ∈ R and ab ∈ I, then a2 ∈ I or b2 ∈ δ(I). Our purpose is to extend the concept of 2-ideals to (δ, 2)-primary
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Avoidance Principle and Intersection Property for A Class of Ring Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-04-16 Rahul Kumar, Atul Gaur
Let R be a commutative ring with identity. If a ring R is contained in an arbitrary union of rings, then R is contained in one of them under various conditions. Similarly, if an arbitrary intersection of rings is contained in R, then R contains one of them under various conditions.
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A Certain Tensor on Real Hypersurfaces in a Nonflat Complex Space Form Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-04-14 Kazuhiro Okumura
In a nonflat complex space form (namely, a complex projective space or a complex hyperbolic space), real hypersurfaces admit an almost contact metric structure (φ, ξ, η, g) induced from the ambient space. As a matter of course, many geometers have investigated real hypersurfaces in a nonflat complex space form from the viewpoint of almost contact metric geometry. On the other hand, it is known that
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Main Eigenvalues of Real Symmetric Matrices with Application to Signed Graphs Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-04-14 Zoran Stanić
An eigenvalue of a real symmetric matrix is called main if there is an associated eigenvector not orthogonal to the all-1 vector j. Main eigenvalues are frequently considered in the framework of simple undirected graphs. In this study we generalize some results and then apply them to signed graphs.
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Increasing Sequences of Sectorial Forms Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-04-14 Hendrik Vogt, Jürgen Voigt
We prove convergence results for ‘increasing’ sequences of sectorial forms. We treat both the case of closed forms and the case of non-closable forms.
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The Torsion Subgroup of a Family of Elliptic Curves Over the Maximal Abelian Extension of ℚ Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-04-02 Jerome Tomagan Dimabayao
We determine explicitly the structure of the torsion group over the maximal abelian extension of ℚ and over the maximal p-cyclotomic extensions of ℚ for the family of rational elliptic curves given by y2 = x3 + B, where B is an integer.
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Maximal non Valuation Domains in an Integral Domain Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-04-01 Rahul Kumar, Atul Gaur
Let R be a commutative ring with unity. The notion of maximal non valuation domain in an integral domain is introduced and characterized. A proper subring R of an integral domain S is called a maximal non valuation domain in S if R is not a valuation subring of S, and for any ring T such that R ⊂ T ⊂ S, T is a valuation subring of S. For a local domain S, the equivalence of an integrally closed maximal
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Fermionic Novikov Algebras Admitting Invariant Non-Degenerate Symmetric Bilinear Forms Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-03-31 Zhiqi Chen, Xueqing Chen, Ming Ding
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and Hamiltonian operators in the formal variational calculus. Fermionic Novikov algebras correspond to a certain Hamiltonian superoperator in a supervariable. In this paper, we show that fermionic Novikov algebras equipped with invariant non-degenerate symmetric bilinear forms are Novikov algebras.
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The Bicrossed Products of H 4 and H 8 Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-03-30 Daowei Lu, Yan Ning, Dingguo Wang
Let H4 and H8 be the Sweedler’s and Kac-Paljutkin Hopf algebras, respectively. We prove that any Hopf algebra which factorizes through H8 and H4 (equivalently, any bicrossed product between the Hopf algebras H8 and H4) must be isomorphic to one of the following four Hopf algebras: H8 ⊗ H4,H32,1,H32,2,H32,3. The set of all matched pairs (H4,H4, ⊳, ⊲) is explicitly described, and then the associated
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When is the Order Generated by a Cubic, Quartic or Quintic Algebraic Unit Galois Invariant: Three Conjectures Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-03-30 Stéphane R. Louboutin
Let ε be an algebraic unit of the degree n ⩾ 3. Assume that the extension ℚ(ε)/ℚ is Galois. We would like to determine when the order ℤ[ε] of ℚ(ε) is Gal(ℚ(ε)/ℚ)-invariant, i.e. when the n complex conjugates ε1, …, εn of ε are in ℤ[ε], which amounts to asking that ℤ[ε1, …, εn] = ℤ[ε], i.e., that these two orders of ℚ(ε) have the same discriminant. This problem has been solved only for n = 3 by using
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Some Results on Poincaré Sets Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-03-27 Min-wei Tang; Zhi-Yi Wu
It is known that a set H of positive integers is a Poincaré set (also called intersective set, see I. Ruzsa (1982)) if and only if \({\dim _\mathcal{H}}({X_H}) = 0\), where$${X_H}: = \left\{ {x = \sum\limits_{n = 1}^\infty {\frac{{{x_n}}}{{{2^n}}}:{x_n} \in \{ 0,1\} ,{x_n}{x_n} + h = 0\,for\,all\,n \geqslant 1,\,h \in H} } \right\}$$and \({\dim _\mathcal{H}}\) denotes the Hausdorff dimension (see C
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Complex Symmetric Weighted Composition Operators on the Hardy Space Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-03-23 Cao Jiang; Shi-An Han; Ze-Hua Zhou
This paper identifies a class of complex symmetric weighted composition operators on H2(D) that includes both the unitary and the Hermitian weighted composition operators, as well as a class of normal weighted composition operators identified by Bourdon and Narayan. A characterization of algebraic weighted composition operators with degree no more than two is provided to illustrate that the weight
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Weighted Estimates for Commutators of Multilinear Hausdorff Operators on Variable Exponent Morrey-Herz Type Spaces Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-02-28 Dao Van Duong; Kieu Huu Dung; Nguyen Minh Chuong
We establish the boundedness for the commutators of multilinear Hausdorff operators on the product of some weighted Morrey-Herz type spaces with variable exponent with their symbols belonging to both Lipschitz space and central BMO space. By these, we generalize and strengthen some previously known results.
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Solutions to Conjectures on a Nonlinear Recursive Equation Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-02-24 Özkan Öcalan; Oktay Duman
We obtain solutions to some conjectures about the onlinear difference equation$${x_{n + 1}} = \alpha + \beta {x_{n - 1}}{e^{ - x}}^{_n},n = 0,1, \ldots,\,\alpha,\beta >0.$$More precisely, we get not only a condition under which the equilibrium point of the above equation is globally asymptotically stable but also a condition under which the above equation has a unique positive cycle of prime period
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New Estimates for the First Eigenvalue of the Jacobi Operator on Closed Hypersurfaces in Riemannian Space Forms Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-02-24 Jiancheng Liu; Rong Mi
We study the first eigenvalue of the Jacobi operator on closed hypersurfaces with constant mean curvature in non-flat Riemannian space forms. Under an appropriate constraint on the totally umbilical tensor of the hypersurfaces and following Meléndez’s ideas in J. Meléndez (2014) we obtain a new sharp upper bound of the first eigenvalue of the Jacobi operator.
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Criterion of the Reality of Zeros in a Polynomial Sequence Satisfying a Three-Term Recurrence Relation Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-02-24 Innocent Ndikubwayo
This paper establishes the necessary and sufficient conditions for the reality of all the zeros in a polynomial sequence \(\{P_i\}=_{i=1}^\infty\) generated by a three-term recurrence relation Pi(x) + Q1(x)Pi−1(x) + Q2(x)Pi−2(x) = 0 with the standard initial conditions P0(x) = 1, P−1(x) = 0, where Q1(x) and Q2(x) are arbitrary real polynomials.
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The p -Nilpotency of Finite Groups with Some Weakly Pronormal Subgroups Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-02-21 Jianjun Liu; Jian Chang; Guiyun Chen
For a finite group G and a fixed Sylow p-subgroup P of G, Ballester-Bolinches and Guo proved in 2000 that G is p-nilpotent if every element of P ∩ G′ with order p lies in the center of NG(P) and when p = 2, either every element of P ∩ G′ with order 4 lies in the center of NG(P) or P is quaternion-free and NG(P) is 2-nilpotent. Asaad introduced weakly pronormal subgroup of G in 2014 and proved that
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On the Binary System of Factors of Formal Matrix Rings Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-02-19 Weining Chen; Guixin Deng; Huadong Su
We investigate the formal matrix ring over R defined by a certain system of factors. We give a method for constructing formal matrix rings from non-negative integer matrices. We also show that the principal factor matrix of a binary system of factors determine the structure of the system.
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On Dual Ramsey Theorems for Relational Structures Czechoslov. Math. J. (IF 0.412) Pub Date : 2020-02-07 Dragan Mašulović
We discuss dual Ramsey statements for several classes of finite relational structures (such as finite linearly ordered graphs, finite linearly ordered metric spaces and finite posets with a linear extension) and conclude the paper with another rendering of the Nešetřil-Rödl Theorem for relational structures. Instead of embeddings which are crucial for “direct” Ramsey results, for each class of structures
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