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Visibility Properties Of Lattice Points In Multiple Random Walks Acta Math. Hungar. (IF 0.9) Pub Date : 2024-03-13 M. Lu
This paper concerns the visibility properties of lattice points in multiple random walks on \(\mathbb{N}^k\), where \(k\geq 2\) is an integer. We study two aspects of the visibility: simultaneous visibility in multiple random walkers; and that only some of these walkers are visible. Combining tools from number theory and probability theory, we prove the corresponding densities of the above two parts
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Coleman automorphisms of finite groups with semidihedral Sylow 2-subgroups Acta Math. Hungar. (IF 0.9) Pub Date : 2024-03-13 R. Aragona
We study some families of finite groups having inner class-preserving automorphisms. In particular, let G be a finite group and S be a semidihedral Sylow 2-subgroup. Then, in both cases when either Sym(4) is not a homomorphic image of G and \(Z(S) < Z(G)\) or G is nilpotent-by-nilpotent, we have that all the Coleman automorphisms of G are inner. As a consequence, these groups satisfy the normalizer
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Central limit theorem for the average closure coefficient Acta Math. Hungar. (IF 0.9) Pub Date : 2024-03-13
Abstract Many real-world networks exhibit the phenomenon of edge clustering,which is typically measured by the average clustering coefficient. Recently,an alternative measure, the average closure coefficient, is proposed to quantify local clustering. It is shown that the average closure coefficient possesses a number of useful properties and can capture complementary information missed by the classical
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A Bounded Below, Noncontractible, Acyclic Complex Of Projective Modules Acta Math. Hungar. (IF 0.9) Pub Date : 2024-03-13 L. Positselski
We construct examples of bounded below, noncontractible, acyclic complexes of finitely generated projective modules over some rings S, as well as bounded above, noncontractible, acyclic complexes of injective modules. The rings S are certain rings of infinite matrices with entries in the rings of commutative polynomials or formal power series in infinitely many variables. In the world of comodules
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Numbers expressible as a difference of two Pisot numbers Acta Math. Hungar. (IF 0.9) Pub Date : 2024-03-04 A. Dubickas
We characterize algebraic integers which are differences of two Pisot numbers. Each such number \(\alpha\) must be real and its conjugates over \(\mathbb{Q}\) must all lie in the union of the disc \(|z|<2\) and the strip \(|\Im(z)|<1\). In particular, we prove that every real algebraic integer \(\alpha\) whose conjugates over \(\mathbb{Q}\), except possibly for \(\alpha\) itself, all lie in the disc
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On common index divisors and monogenity of septic number fields defined by trinomials of type $$x^7+ax^2+b$$ Acta Math. Hungar. (IF 0.9) Pub Date : 2024-03-04 H. Ben Yakkou
We study the index \(i(K)\) of any septic number field \(K\) generated by a root of an irreducible trinomial of type \(F(x)=x^7+ax^2+b \in \mathbb{Z}[x]\). We show that the unique prime which can divide \(i(K)\) is \(2\). Moreover, we give necessary and sufficient conditions on \(a\) and \(b\) so that \(2\) is a common index divisor of \(K\). Further, we show that \(i(K)=2\) whenever \(2\) divides
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Martingale Orlicz-Hardy spaces for continuous-time Acta Math. Hungar. (IF 0.9) Pub Date : 2024-03-01
Abstract We introduce several martingale Orlicz-Hardy spaces with continuous time. By use of the atomic decomposition, we establish some martingale inequalities and characterize the dualities of these spaces.
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Compatible relative open books on relative contact pairs via generalized square bridge diagrams Acta Math. Hungar. (IF 0.9) Pub Date : 2024-03-01 M. F. Arıkan, İ. Ö. Taşpınar
Using square bridge position, Akbulut-Ozbagci and later Arikan gave algorithms both of which construct an explicit compatible open book decomposition on a closed contact 3-manifold which results from a contact \((\pm 1)\)-surgery on a Legendrian link in the standard contact 3-sphere. In this article, we introduce the “generalized square bridge position” for a Legendrian link in the standard contact
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Linear independence of the real numbers generated by the square and cube subsequences of Thue–Morse Acta Math. Hungar. (IF 0.9) Pub Date : 2024-02-29 E. Miyanohara
Let \((t(m))_{m \ge0}\) be Thue-Morse sequence and \(b>2\) be an integer. In this paper, we prove that the real numbers \(1\), \(\sum_{m=0}^\infty {\frac{t(m^2)}{{b}^{m+1}}}\) and \(\sum_{m=0}^\infty {\frac{t(m^3)}{{b}^{m+1}}}\) are linearly independent over \(\mathbb{Q}\).
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Level aspect exponential sums involving Fourier coefficients of symmetric-square lifts Acta Math. Hungar. (IF 0.9) Pub Date : 2024-02-29 F. Hou
Fix an integer \(\kappa\ge 2\). Let \(P\ge 2\) be a prime, and \(F\) be the symmetric-square lift of a Hecke newform \(f\in \mathcal{S}^ {\ast} _\kappa(P)\). We study the exponential sum $$\begin{aligned}\mathscr{L}_F(\alpha)=\sum_{n\sim N} A_F(n,1)e(n \alpha) \end{aligned}$$ by implementing an average over a family in such a way to investigate the best possible magnitude of the level aspect bound
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On locally compact groups of small topological entropy Acta Math. Hungar. (IF 0.9) Pub Date : 2024-02-28 F. G. Russo, O. Waka
We discuss the finiteness of the topological entropy of continuous endomorphims for some classes of locally compact groups. Firstly, we focus on the abelian case, imposing the condition of being compactly generated, and note an interesting behaviour of slender groups. Secondly, we remove the condition of being abelian and consider nilpotent periodic locally compact p-groups (p prime), reducing the
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Characterizing Inverse Sequences For Which Their Inverse Limits Are Homeomorphic Acta Math. Hungar. (IF 0.9) Pub Date : 2024-02-20 M. Črepnjak, T. Sovič
In [11], Mioduszewski characterized inverse sequences of polyhedra for which their inverse limits are homeomorphic. In this article, we obtain a more general characterization: we characterize inverse sequences of arbitrary compact metric spaces and continuous single-valued functions for which their inverse limits are homeomorphic. In our approach, set-valued functions are used instead of continuous
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Local cohomology and Foxby classes Acta Math. Hungar. (IF 0.9) Pub Date : 2024-02-15 M. Ahmadi, A. Rahimi
Let R be a commutative Noetherian ring and I a proper ideal of R. In this paper, we study finitely generated R-modules M with only one non-vanishing local cohomology module \({H}_I^c(M)\) where \(c=cd(I,M)\). Let C be a semidualizing R-module. We investigate the conditions under which \({H}_I^c(M)\) belongs to either the Auslander class \(\mathscr{A}_C(R)\) or the Bass class \(\mathscr{B}_C(R)\).
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Egerváry's theorems for harmonic trinomials Acta Math. Hungar. (IF 0.9) Pub Date : 2024-02-15
Abstract We study the arrangements of the roots in the complex plane for the lacunary harmonic polynomials called harmonic trinomials. We provide necessary and sufficient conditions so that two general harmonic trinomials have the same set of roots up to a rotation around the origin in the complex plane, a reflection over the real axis, or a composition of the previous both transformations. This extends
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Singular Modifications Of A Classical Function Acta Math. Hungar. (IF 0.9) Pub Date : 2024-02-15
Abstract The present article deals with properties of one class of functions with complicated local structure. These functions can be modeled by certain operators of digits. Such operators were considered by the author earlier (for example, see [27,39] and references therein). This research is a generalization of investigations presented in the last-mentioned papers.
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Parallel covering a parallelogram with squares Acta Math. Hungar. (IF 0.9) Pub Date : 2024-02-01 Z.-J. Su, J. Zhang
Suppose that \(R(h, \alpha)\) is a parallelogram with the longer side 1, with acute angle \(\alpha\) and with height h. Let S be a square with a side parallel to the longer side of \(R(h, \alpha)\) and let \(\{S_{n}\}\) be a collection of the homothetic copies of S. In this note a tight lower bound of the sum of the areas of squares from \(\{S_{n}\}\) that can parallel cover \(R(h, \alpha)\) is given
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Geometric Condition For Dependent Choice Acta Math. Hungar. (IF 0.9) Pub Date : 2024-01-31 A. Karagila, J. Schilhan
We provide a geometric condition which characterises when the Principle of Dependent Choice holds in a Fraenkel-Mostowski-Specker permutation model. This condition is a slight weakening of requiring the filter of groups to be closed under countable intersections. We show that this condition holds nontrivially in a new permutation model we call "the nowhere dense model" and we study its extensions to
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Explicit upper bounds for Touchard polynomials and Bell numbers Acta Math. Hungar. (IF 0.9) Pub Date : 2024-01-31 A.-M. Acu, J. A. Adell, I. Raşa
We obtain explicit upper bounds for the Touchard polynomials \(T_n(x)\), for \(x>0\). When applied to the Bell numbers \(B_n=T_n(1)\), such bounds are asymptotically sharp. A simple probabilistic approach based on estimates of moments of nonnegative random variables is used. Applications giving upper bounds for the moments of a certain subset of Jakimovski-Leviatan operators are also provided.
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Coupled fixed point results for new classes of functions on ordered vector metric space Acta Math. Hungar. (IF 0.9) Pub Date : 2024-01-31
Abstract The contraction condition in the Banach contraction principle forces a function to be continuous. Many authors overcome this obligation and weaken the hypotheses via metric spaces endowed with a partial order. In this paper, we present some coupled fixed point theorems for the functions having mixed monotone properties on ordered vector metric spaces, which are more general spaces than partially
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Mean value characterizations of the Dunkl polyharmonic functions Acta Math. Hungar. (IF 0.9) Pub Date : 2024-01-31 G. Łysik
We give characterizations of the Dunkl polyharmonic functions, i.e., solutions to the iteration of the Dunkl-Laplace operator \(\Delta_\kappa\) which is a differential-reflection operator associated with a Coxeter–Weil group \(W\) generated by a finite set of reflections and an invariant multiplicity function \(\kappa\), in terms of integral means over Euclidean balls and spheres.
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Finite beta-expansions of natural numbers Acta Math. Hungar. (IF 0.9) Pub Date : 2024-01-31 F. Takamizo
Let \(\beta>1\). For \(x \in [0,\infty)\), we have so-called a beta-expansion of \(x\) in base \(\beta\) as follows: $$x= \sum_{j \leq k} x_{j}\beta^{j} = x_{k}\beta^{k}+ \cdots + x_{1}\beta+x_{0}+x_{-1}\beta^{-1} + x_{-2}\beta^{-2} + \cdots$$ where \(k \in \mathbb{Z}\), \(\beta^{k} \leq x < \beta^{k+1}\), \(x_{j} \in \mathbb{Z} \cap [0,\beta)\) for all \(j \leq k\) and \(\sum_{j \leq n}x_{j}\beta^{j}<\beta^{n+1}\)
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The uncountable Hadwiger conjecture and characterizations of trees using graphs Acta Math. Hungar. (IF 0.9) Pub Date : 2024-01-31 D. Uhrik
We prove that the existence of a non-special tree of size \(\lambda\) is equivalent to the existence of an uncountably chromatic graph with no \(K_{\omega1}\) minor of size \(\lambda\), establishing a connection between the special tree number and the uncountable Hadwiger conjecture. Also characterizations of Aronszajn, Kurepa and Suslin trees using graphs are deduced. A new generalized notion of connectedness
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On totally semipermutable products of finite groups Acta Math. Hungar. (IF 0.9) Pub Date : 2024-01-31 A. Ballester-Bolinches, J. Cossey, S. Y. Madanha , M. C. Pedraza-Aguilera
We say a group G = AB is the totally semipermutable product of subgroups A and B if every Sylow subgroup P of A is totally permutable with every Sylow subgroup Q of B whenever \( \gcd(|P|,|Q|)=1 \). Products of pairwise totally semipermutable subgroups are studied in this article. Let \( \mathfrak{U} \) denote the class of supersoluble groups and \( \mathfrak{D} \) denote the formation of all groups
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Applications of $$T^r$$ -strongly convergent sequences to Fourier series by means of modulus functions Acta Math. Hungar. (IF 0.9) Pub Date : 2024-01-31 S. Devaiya, S. K. Srivastava
Recently, Devaiya and Srivastava [3] studied the \(T^r\)-strong convergence of numerical sequences and Fourier series using a lower triangular matrix \(T=(b_{m,n})\), and generalized the results of Kórus [8]. The main objective of this paper is to introduce \([T^r,G,u,q]\)-strongly convergent sequence spaces for \(r\in\mathbb{N}\), and defined by a sequence of modulus functions. We also provide a relationship
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Inequalities for polynomials satisfying $$p(z)\equiv z^np(1/z)$$ Acta Math. Hungar. (IF 0.9) Pub Date : 2024-01-31 A. Dalal, N. K. Govil
Finding the sharp estimate of \(\max_{|z|=1} |p'(z)|\) in terms of \(\max_{|z|=1} |p(z)|\) for the class of polynomials p(z) satisfying \(p(z) \equiv z^n p(1/z)\) has been a well-known open problem for a long time and many papers in this direction have appeared. The earliest result is due to Govil, Jain and Labelle [9] who proved that for polynomials p(z) satisfying \(p(z) \equiv z^n p(1/z)\) and having
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On pseudo-real finite subgroups of $$\mathrm{PGL}_3(\mathbb{C})$$ Acta Math. Hungar. (IF 0.9) Pub Date : 2023-12-13 E. Badr, A. El-Guindy
Let \(G\) be a finite subgroup of \( \rm PGL_3(\mathbb C)\), and let \(\sigma\) be the generator of Gal\((\mathbb C/ \mathbb R)\). We say that \(G\) has a real field of moduli if \(\sigma G\) and \(G\) are \( \rm PGL_3(\mathbb C)\)-conjugates. Furthermore, we say that \(\mathbb R\) is a field of definition for \(G\) or that \(G\) is definable over \(\mathbb R\) if \(G\) is \(\textrm{PGL}_3(\mathbb
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On p-Groups With Restricted Centralizers Acta Math. Hungar. (IF 0.9) Pub Date : 2023-12-13 E. Jabara
Let \(G\) be a \(p\) -group in which every centralizer is either finite or of finite index. It is shown that if the size of the \(FC\) -center of \(G\) is infinite and \(G\) is not an \(FC\) -group, then \(G\) is abelian-by-finite.
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Some New weak-( $$H_{p}-L_p$$ ) Type Inequalities For Weighted Maximal Operators Of Fejér Means Of Walsh–Fourier Series Acta Math. Hungar. (IF 0.9) Pub Date : 2023-12-13 D. Baramidze, G. Tephnadze
We introduce some new weighted maximal operators of the Fejér means of the Walsh–Fourier series. We prove that for some "optimal" weights these new operators are bounded from the martingale Hardy space \(H_{p}(G)\) to the space \(\text{weak-}L_{p}(G)\) , for \(0
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Hardy–Sobolev Inequalities For Riesz Potentials Of Functions In Orlicz Spaces Acta Math. Hungar. (IF 0.9) Pub Date : 2023-12-13 Y. Mizuta, T. Shimomura
We establish a Hardy–Sobolev inequality for Riesz potentials of functions in Orlicz spaces.
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Entropy on quasi-uniform spaces Acta Math. Hungar. (IF 0.9) Pub Date : 2023-12-13 P. Haihambo, O. Olela Otafudu
Quasi-uniform entropy \(h_{QU}(\psi)\) is defined for a uniformly continuous self-map \(\psi\) on a \(T_0\) quasi-uniform space \((X,\mathcal{U})\). Basic properties are proved about this entropy, and it is shown that the quasi-uniform entropy \(h_{QU}(\psi ,\mathcal{U})\) is less than or equal to the uniform entropy \(h_U(\psi, \mathcal{U}^s)\) of \(\psi\) considered as a uniformly continuous self-map
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Weighted inequalities for Fourier multiplier operators of Bochner–Riesz type on $$ \mathbb{R} ^2$$ Acta Math. Hungar. (IF 0.9) Pub Date : 2023-12-11 S. Sato
We consider Fourier multipliers in \( \mathbb{R} ^2\) with singularities on certain curves, which are closely related to the Bochner–Riesz Fourier multipliers. We prove weighted inequalities and vector valued inequalities for the Fourier multiplier operators which generalize some known results.
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On reciprocal sums of infinitely many arithmetic progressions with increasing prime power moduli Acta Math. Hungar. (IF 0.9) Pub Date : 2023-12-11 B. Borsos, A. Kovács, N. Tihanyi
Numbers of the form \(k\cdot p^n+1\) with the restriction \(k < p^n\) are called generalized Proth numbers. For a fixed prime p we denote them by \(\mathcal{T}_p\). The underlying structure of \(\mathcal{T}_2\) (Proth numbers) was investigated in [2]. In this paper the authors extend their results to all primes. An efficiently computable upper bound for the reciprocal sum of primes in \(\mathcal{T}_p\)
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Upper bounds for the size of set systems with a symmetric set of Hamming distances Acta Math. Hungar. (IF 0.9) Pub Date : 2023-11-03 G. Hegedüs
Let \( \mathcal{F} \subseteq 2^{[n]}\) be a fixed family of subsets. Let \(D( \mathcal{F} )\) stand for the following set of Hamming distances: $$D( \mathcal{F} ):=\{d_H(F,G) : F, G\in \mathcal{F} ,\ F\neq G\}$$ . \( \mathcal{F} \) is said to be a Hamming symmetric family, if \( \mathcal{F} \)X implies \(n-d\in D( \mathcal{F} )\) for each \(d\in D( \mathcal{F} )\). We give sharp upper bounds for the
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The Baire category method for intermittent convex integration Acta Math. Hungar. (IF 0.9) Pub Date : 2023-10-31 G. Sattig, L. Székelyhidi
We use a convex integration construction from [22] in a Baire category argument to show that weak solutions to the transport equation with incompressible vector fields with Sobolev regularity are generic in the Baire category sense. Using the construction of [7] we prove an analog statement for the 3D Navier–Stokes equations.
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On boundary discreteness of mappings with a modulus condition Acta Math. Hungar. (IF 0.9) Pub Date : 2023-11-01 E. Sevost’yanov
We study the boundary behavior of spatial mappings that distort the modulus of families of paths in the same way as the inverse Poletsky inequality. Under certain conditions on the boundaries of the corresponding domains, we have shown that such mappings have a continuous boundary extension. Separately, we study the problem of discreteness of the indicated extension. It is shown that under some requirements
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Spectrality of a class of Moran measures on the plane Acta Math. Hungar. (IF 0.9) Pub Date : 2023-10-31 Z.-S. Liu
Let \(\{(R_k,D_k)\}_{k=1}^\infty\) be a sequence of pairs, where $$D_k=\{0,1,\ldots,q_k-1\}(1,1)^T$$ is an integer vector set and \(R_k\) is an integer diagonal matrix or upper triangular matrix, i.e., \(R_k={\begin{pmatrix} s_k & 0\\ 0 & t_k \end{pmatrix}}\) or \(R_k={\begin{pmatrix} u_k & 1\\ 0 & v_k \end{pmatrix}}\). Associated with the sequence \(\{(R_k,D_k)\}_{k=1}^\infty\) , Moran measure \(\mu_{\{R_k\}
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Arithmetic properties of colored p-ary partitions Acta Math. Hungar. (IF 0.9) Pub Date : 2023-10-31 B. Żmija
We study divisibility properties of p-ary partitions colored with k(p − 1) colors for some positive integer k. In particular, we obtain a precise description of p-adic valuations in the case of \(k=p^{\alpha}\) and \(k=p^{\alpha}-1\). We also prove a general result concerning the case in which finitely many parts can be colored with a number of colors smaller than k(p − 1) and all others with exactly
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c-Normality and coprime action in finite groups Acta Math. Hungar. (IF 0.9) Pub Date : 2023-10-31 A. Beltrán, C. Shao
A subgroup H of a finite group G is called c-normal if there exists a normal subgroup N in G such that G = HN and \(H\cap N \leq core_G (H)\), the largest normal subgroup of G contained in H. c-Normality is a weaker form of normality, introduced by Y.M. Wang, that has led to interesting results and structural criteria of finite groups. In this paper we study c-normality in the coprime action setting
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The sum of squares of degrees of bipartite graphs Acta Math. Hungar. (IF 0.9) Pub Date : 2023-10-31 M. G. Neubauer
Let G be a subgraph of the complete bipartite graph \(K_{l,m},{l \leq m}\), with \(e=qm+p>0\), \(0 \leq p
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A small ultrafilter number at every singular cardinal Acta Math. Hungar. (IF 0.9) Pub Date : 2023-10-31 T. Benhamou, S. Jirattikansakul
We obtain a small ultrafilter number at \(\aleph_{\omega_1}\). Moreover, we develop a version of the overlapping strong extender forcing with collapses which can keep the top cardinal \(\kappa\) inaccessible. We apply this forcing to construct a model where \(\kappa\) is the least inaccessible and \( V_\kappa \) is a model of GCH at regulars, failures of SCH at singulars, and the ultrafilter numbers
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Properties of complex-valued power means of random variables and their applications Acta Math. Hungar. (IF 0.9) Pub Date : 2023-10-24 Y. Akaoka, K. Okamura, Y. Otobe
We consider power means of independent and identically distributed (i.i.d.) non-integrable random variables. The power mean is an example of a homogeneous quasi-arithmetic mean. Under certain conditions, several limit theorems hold for the power mean, similar to the case of the arithmetic mean of i.i.d. integrable random variables. Our feature is that the generators of the power means are allowed to
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A universal bound concerning t-intersecting families Acta Math. Hungar. (IF 0.9) Pub Date : 2023-09-21 P. Frankl
A very short inductive proof is given for the maximal size of a k-graph on n vertices in which any two edges overlap in at least t vertices.
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On transitive Cayley graphs of homogeneous inverse semigroups Acta Math. Hungar. (IF 0.9) Pub Date : 2023-09-21 E. Ilić-Georgijević
Let S be a pseudo-unitary homogeneous (graded) inverse semigroup with zero 0, that is, an inverse semigroup with zero, and with a family \(\{S_\delta\}_{\delta\in\Delta}\) of nonzero subsets of S, called components of S, indexed by a partial groupoid \(\Delta\), that is, by a set with a partial binary operation, such that \(S=\bigcup_{\delta\in\Delta}S_\delta\), and: i) \(S_\xi\cap S_\eta\subseteq\{0\}\)
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Nearly fibered links with genus one Acta Math. Hungar. (IF 0.9) Pub Date : 2023-09-12 A. Cavallo, I. Matkovič
We classify all the \(n\)-component links in the \(3\)-sphere that bound a Thurston norm minimizing Seifert surface \(\Sigma\) with Euler characteristic \(\chi(\Sigma)=n-2\) and that are nearly fibered, which means that the rank of their link Floer homology group \(\widehat{HFL}\) in the maximal (collapsed) Alexander grading \(s_{\text{top}}\) is equal to two. In other words, such a link \(L\) satisfies
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Quasi-periodicity of $$\mathbb {Z}_{p^an_0}$$ Acta Math. Hungar. (IF 0.9) Pub Date : 2023-09-06 W. Zhou
Let pa be a prime power and n0 a square-free number. We prove that any complementing pair in a cyclic group of order pan0 is quasi-periodic, with one component decomposable by the the subgroup of order p. The proof is by induction and reduction since the presence of the square-free factor n0 allows us to perform a Tijdeman decomposition. We also give an explicit example to show that \(\mathbb{Z}_{72}\)
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Interpolation on weak martingale Hardy-type spaces associated with quasi-Banach function lattice Acta Math. Hungar. (IF 0.9) Pub Date : 2023-09-06 N. Silas, H. Tian
We study the real interpolation spaces between weak martingale Hardy-type spaces \(WH_{X}^{s}(\Omega)\) and martingale Hardy space \(H_{\infty}^{s}(\Omega)\) associated with quasi-Banach function lattice by using atomic characterizations of weak martingale Hardy-type spaces. As applications, we obtain the corresponding results on the weighted Lorentz space and the generalized grand Lebesgue space.
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On the integrability of multi-dimensional rare maximal functions Acta Math. Hungar. (IF 0.9) Pub Date : 2023-09-06 I. Japaridze, G. Oniani
We characterize the translation invariant monotone collections of multi-dimensional intervals for which the analogue of Stein's criterion for the integrability of the Hardy--Littlewood maximal function is true. Namely, we characterize the collections \(B\) of the mentioned type for which the conditions \(\int_{[0,1]^d}M_B(f)<\infty\) and \(\int_{[0,1]^d}\vert f\vert \log^+\vert f\vert <\infty\) are
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On the asymptotics of coefficients of Rankin–Selberg L-functions Acta Math. Hungar. (IF 0.9) Pub Date : 2023-09-06 H. Lao, H. Zhu
Let f and g be two different holomorphic cusp froms or Maass cusp forms for the full modular group \(SL(2,\mathbb{Z})\). We are interested in coefficients of Rankin–Selberg L-functions, and establish some bounds for $$\begin{aligned}\sum_{n\leq x} \lambda_{{\rm sym}^if\times {\rm sym}^jg}(n),\quad \sum_{n\leq x}\lambda_f(n^i)\lambda_g(n^j), \\ \sum_{n\leq x} |\lambda_{{\rm sym}^if\times {\rm sym}^jg}(n)|
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Dedekind sums and class numbers of imaginary abelian number fields Acta Math. Hungar. (IF 0.9) Pub Date : 2023-09-06 S. R. Louboutin
As a consequence of their work, Bruce C. Berndt, Ronald J. Evans, Larry Joel Goldstein and Michael Razar obtained a formula for the square of the class number of an imaginary quadratic number field in terms of Dedekind sums. We give a short proof of it and also express the relative class numbers of imaginary abelian number fields in terms of Dedekind sums.
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Variable anisotropic fractional integral operators Acta Math. Hungar. (IF 0.9) Pub Date : 2023-09-04 B. D. Li, J. W. Sun, Z. Z. Yang
In 2011, Dekel et al. introduced a highly geometric Hardy spaces \(H^p(\Theta)\), for the full range \(0
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Fields $$\mathbb{Q}(i, \sqrt{2},\sqrt{p_1},\ldots ,\sqrt{p_n})$$ with cyclic 2-class group Acta Math. Hungar. (IF 0.9) Pub Date : 2023-09-04 S. Essahel, A. Mouhib
Let \(n\) be an integer \(\geq 1\) and \(p_1\), . . . , \(p_n\) distinct odd prime integers. In this article, we give the list of all imaginary multiquadratic number fields \( K_n=\mathbb{Q}(i,\sqrt 2,\sqrt{p_1},\ldots ,\sqrt{p_n})\) that have a cyclic 2-class group.
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On the zero-divisor hypergraph of a reduced ring Acta Math. Hungar. (IF 0.9) Pub Date : 2023-09-04 T. Asir, A. Kumar, A. Mehdi
The concept of zero-divisor graphs of rings is widely used for establishing relationships between the properties of graphs and the properties of the underlying ring. The zero-divisor graph of a ring is generalized to the k-zero-divisor hypergraph of a ring R for \(k\in \mathbb{N}\), which is denoted by \(\mathcal{H}_{k}(R)\). This paper is an endeavor to discuss some properties of zero-divisor hypergraphs
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The structure of the orthomorphism graph of $$\mathbb{Z}_2 \times \mathbb{Z}_4$$ Acta Math. Hungar. (IF 0.9) Pub Date : 2023-09-04 V. K. Jain, R. Pradhan
We give a theoretical proof of the fact that the orthomorphism graph of group \(\mathbb{Z}_2 \times \mathbb{Z}_4\) has maximal clique 2 by determining the structure of the graph.
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A note on the partial sum of Apostol's Möbius function Acta Math. Hungar. (IF 0.9) Pub Date : 2023-09-04 D. Banerjee, Y. Fujisawa, T. M. Minamide, Y. Tanigawa
T. M. Apostol introduced a certain Möbius function \(\mu_{k}(\cdot)\) of order k, where \(k\geq 2\) is a fixed integer. Let k=1, then \(\mu_{1}(\cdot)\) coincides with the Möbius function \(\mu(\cdot)\), in the usual sense. For any fixed \(k\geq 2\), he proved the asymptotic formula \(\sum_{n\leq x}\mu_{k}(n)=A_{k}x+O_{k}(x^{1/k}\log x)\) as \(x\to\infty\), where \(A_{k}\) is a positive constant. Later
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Discrete and disjoint shrinking properties of locally convex spaces Acta Math. Hungar. (IF 0.9) Pub Date : 2023-09-04 V. V. Tkachuk
Given a sequence \(\mathcal{U}= \{U_n: {n\in\omega} \}\) of non-empty open subsets of a space X, a family \(\{V_n: {n\in\omega} \}\) is a shrinking of \(\mathcal{U}\) if Vn is a non-empty open set and \(V_n\subset U_n\) for every \({n\in\omega}\). A space X has the disjoint (discrete) shrinking property if every sequence of non-empty open subsets of X has a disjoint (discrete) shrinking. We present
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On a Piatetski-Shapiro analog problem over almost-primes Acta Math. Hungar. (IF 0.9) Pub Date : 2023-09-04 W.-G. Zhai, Y.-T. Zhao
Let N be a sufficiently large number, \(\mathfrak{A}\) and \(\mathfrak{B}\) be subsets of \(\{N+1, \ldots , 2N\}\). We prove that if \(10\) is sufficiently small, then the equation $$ab=\lfloor n^c\rfloor,\quad a\in\mathfrak{A},\ b\in\mathfrak{B} $$ is solvable, which improves the result of Rivat and Sárközy [14]. We also investigate the solvability of the equation $$ab=\lfloor P_k^c\rfloor,\quad a\in\mathfrak{A}
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Certain invariant multiplicative subset of a simple Artinian ring with involution. II Acta Math. Hungar. (IF 0.9) Pub Date : 2023-08-29 M. Chacron
In the first part of the paper, we provide a fairly complete description of a simple ring R with involution f such that relative to f the traces of all elements of R form a commutative subset of R. This description is based on the characteristic of R. While the case of characteristic not 2 readily follows from current results in the literature, by contrast, the opposite case of characteristic 2 requires
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Resolvability and complete accumulation points Acta Math. Hungar. (IF 0.9) Pub Date : 2023-08-29 A. E. Lipin
We prove that: I. For every regular Lindelöf space X if \(|X|=\Delta(X)\) and \(\mathrm{cf}|X|\ne\omega\), then X is maximally resolvable; II. For every regular countably compact space X if \(|X|=\Delta(X)\) and \({\mathrm{cf}|X|=\omega}\), then X is maximally resolvable. Here \(\Delta(X)\), the dispersion character of X, is the minimum cardinality of a nonempty open subset of X. Statements I and II
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The influence of weakly pronormal subgroups on the supersolvability of finite groups Acta Math. Hungar. (IF 0.9) Pub Date : 2023-08-02 M. Asaad
Let G be a finite group and H a subgroup of G. We say that H is pronormal in G if for every \(g\in G\), the subgroups H and \(H^g\) are conjugate in \(\langle H,H^{g} \rangle\); H is called weakly pronormal in G if there exists a subgroup K of G such that G = HK and \(H\cap K\) is pronormal in G. In this paper, we investigate the structure of G under the assumption that certain subgroups of G are weakly
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On the index of the octic number field defined by $x^8+ax+b$ Acta Math. Hungar. (IF 0.9) Pub Date : 2023-07-31 H. Ben Yakkou, B. Boudine
Let K be an octic number field generated by a complex root \(\theta\) of a monic irreducible trinomial \(F(x)= x^{8}+ax+b \in \mathbb{Z}[x]\), where a and b are two non-zero rational integers. Let \(i(K)\) be the index of K. We show that i(K) is either 1 or a power of 2. Further, assuming that \((a,b) \notin (32+64\mathbb{Z})\times {(16+64\mathbb{Z}) } \) and \((a,b) \notin (64\mathbb{Z})\times(112+128\mathbb{Z})\)