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On Sjölin–Soria–Antonov type extrapolation for locally compact groups and a.e. convergence of Vilenkin–Fourier series Acta Math. Hungar. (IF 0.588) Pub Date : 2020-11-30 G. Oniani
A Sjölin–Soria–Antonov type extrapolation theorem for locally compact \(\sigma\)-compact non-discrete Hausdorff groups is proved. Applying this result it is shown that the Fourier series with respect to the Vilenkin orthonormal systems on the Vilenkin groups of bounded type converge almost everywhere for functions from the class \(L {\rm log}^{+} L {\rm log}^{+} {\rm log}^{+} {\rm log}^{+} L\).
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On regular $$\kappa$$ κ -bounded spaces admitting only constant continuous mappings into $$T_1$$ T 1 spaces of pseudocharacter $$\leq \kappa$$ ≤ κ Acta Math. Hungar. (IF 0.588) Pub Date : 2020-10-23 S. Bardyla, A. Osipov
For each cardinal \(\kappa\) we construct an infinite \(\kappa\)-bounded (and hence countably compact) regular space \(R_{\kappa}\) such that for any \(T_1\) space \(Y\) of pseudocharacter \(\leq\kappa\), each continuous function \(f : R_{\kappa}\rightarrow Y\) is constant. This result resolves two problems posted by Tzannes [13] and extends results of Ciesielski and Wojciechowski [4] and Herrlich
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Independence algebras, basis algebras and the distributivity condition Acta Math. Hungar. (IF 0.588) Pub Date : 2020-10-22 W. Bentz, V. Gould
Stable basis algebras were introduced by Fountain and Gould and developed in a series of articles. They form a class of universal algebras, extending that of independence algebras, and reflecting the way in which free modules over well-behaved domains generalise vector spaces. If a stable basis algebra \(\mathbb{B}\) satisfies the distributivity condition (a condition satisfied by all the previously
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Weighted Erdős–Kac Type Theorems Over Gaussian Field In Short Intervals Acta Math. Hungar. (IF 0.588) Pub Date : 2020-10-22 X.-L. Liu, Z.-S. Yang
Assume that \(\mathbb{K}\) is Gaussian field, and \({{a}_{\mathbb{K}}} (n) \) is the number of non-zero integral ideals in \(\mathbb{Z} [i] \) with norm \(n\). We establish an Erdős–Kac type theorem weighted by \({{a}_{\mathbb{K}}}( n^2 )^l (l\in \mathbb{Z}^{+})\) in short intervals. We also establish an asymptotic formula for the average behavior of \({{a}_{\mathbb{K}}}( n^2 )^l\) in short intervals
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On The Generalized Ramanujan–Nagell Equation $$x^2+(2c-1)^m=c^n$$ x 2 + ( 2 c - 1 ) m = c n Acta Math. Hungar. (IF 0.588) Pub Date : 2020-10-22 Y. Fujita, N. Terai
We show that if c is a positive integer satisfying \(2c-1=3p^l\ \hbox{or}\ 2c-1=5p^l\) with p prime and l positive integer, then the equation \({x^2 + (2c-1)^m}=c^n\) has only the positive integer solution \((x,m,n)=(c-1,1,2)\) without any congruence condition on a prime p.
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On linear combinations of products of consecutive integers Acta Math. Hungar. (IF 0.588) Pub Date : 2020-10-22 A. Bazsó
We investigate Diophantine problems concerning linear combinations of polynomials of the shape \(a_0 x+a_1x(x+1)+ a_2x(x+1)(x+2)+ \cdots + a_n x(x+1)\ldots (x+n)\) with \(n\in \mathbb{N}\cup\{0\}\). We provide effective finiteness results for the power, shifted power, and quadratic polynomial values of these linear combinations, generalizing the analogous results of Hajdu, Laishram and Tengely [10]
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Small exotic $$4$$ 4 -manifolds from lines and quadrics in $$\mathbb{CP}^{2}$$ CP 2 Acta Math. Hungar. (IF 0.588) Pub Date : 2020-10-22 S. Mihajlović
We construct potentially new manifolds homeomorphic but not diffeomorphic to \(\mathbb{CP}^{2} \) # \(8\overline{{\mathbb{CP}}^{2}}\) and \(\mathbb{CP}^{2}\)# \(9\overline{{\mathbb{CP}}^{2}}\) via rational blowdown surgery along certain 4-valent plumbing graphs. This way all the graph classes from [5] have a representative which admits a rational blowdown leading to an exotic manifold. We emphasize
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The Sets Of Positivity Of Sine Series With Monotone Coefficients Acta Math. Hungar. (IF 0.588) Pub Date : 2020-10-22 K. Oganesyan
We study the sums of nondegenerate sine series with monotone coefficients and consider the sets of positivity of such functions. We obtain the sharp lower estimate of the measure of such a set on \([\pi/2, \pi]\) and a new lower bound on its measure on \([0,\pi]\). It is shown that the latter measure is at least \(\pi/2 + 0.24\) and in the case of fulfilling special conditions it is at least \(2\pi/3\)
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On a problem of J. H. Fang and Z. K. Fang Acta Math. Hungar. (IF 0.588) Pub Date : 2020-10-08 B.-L. Wu, X.-H. Yan
Let A be a sequence of positive integers and P(A) be the set of all integers which are the finite sum of distinct terms of A. Let \(B=\{b_1
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Product Methods And G -Connectedness Acta Math. Hungar. (IF 0.588) Pub Date : 2020-10-08 L. Liu, Z. Ping
The generalized topology on the Cartesian product of sets can be defined by the generalized topology on the factors of the product. A G-method on a set can derive a generalized topology, which is called a G-generalized topology. On the one hand, we introduce the concept of product G-methods on sets which lead to a G-generalized topology on the Cartesian products that is different both from the Császár
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Generalized monotonically T 2 spaces Acta Math. Hungar. (IF 0.588) Pub Date : 2020-10-08 W. H. Sun
The notion of \(\mu\)-monotonically T2 spaces is introduced, which is a generation of monotone T2 separation in general topological spaces. The characterization and some properties of \(\mu\)-monotonically T2 spaces are given. Besides, the definition of the box product of the topologies is extended to generalized topologies, and we prove that the box product of \(\mu\)-monotonically T2 spaces is \
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A uniform set with fewer than expected arithmetic progressions of length 4 Acta Math. Hungar. (IF 0.588) Pub Date : 2020-07-23 W. T. Gowers
An example is constructed of a subset \(A \subset \mathbb {Z}_N\) of density \({1\over 2}+o(1)\) such that all the non-trivial Fourier coefficients of the characteristic function of A are very small, but if \(x,d \in \mathbb {Z}_N\) are chosen uniformly at random, then the probability that \(x, x+d, x+2d\) and \(x+3d\) all belong to A is at most \({1\over 16}-c\), where \(c>0\) is an absolute constant
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Congruence classes and maximal nonbases Acta Math. Hungar. (IF 0.588) Pub Date : 2020-07-22 M. B. Nathanson
The set A is an asymptotic nonbasis of order h for an additive abelian semigroup X if there are infinitely many elements of X not in the h-fold sumset hA. For all \(h \geq 2\), this paper constructs new classes of asymptotic nonbases of order h for Z and for N0 that are not subsets of maximal asymptotic nonbases.
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On monochromatic solutions to $$x-y=z^2$$ x - y = z 2 Acta Math. Hungar. (IF 0.588) Pub Date : 2020-07-22 T. Sanders
For \(k \in \mathbb {N}\), write S(k) for the largest natural number such that there is a k-colouring of \(\{1, \ldots ,S(k)\}\) with no monochromatic solution to \(x-y=z^2\). That S(k) exists is a result of Bergelson, and a simple example shows that \(S(k) \ge 2^{2^{k-1}}\). The purpose of this note is to show that \(S(k) \le 2^{2^{2^{O(k)}}}\) .
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Efficient, local and symmetric Markov chains that generate one-factorizations Acta Math. Hungar. (IF 0.588) Pub Date : 2020-07-22 M. Dotan, N. Linial, Y. Peled
It is well known that for every even integer n, the complete graph \(K_{n}\) has a one-factorization, namely a proper edge coloring with \(n-1\) colors. Unfortunately, not much is known about the possible structure of large one-factorizations. Also, at present we have only woefully few explicit constructions of large one-factorizations. In particular, we know essentially nothing about the typical properties
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The Frobenius postage stamp problem, and beyond Acta Math. Hungar. (IF 0.588) Pub Date : 2020-07-22 A. Granville, G. Shakan
Let A be a finite subset of \(\mathbb{Z}^n\), which generates \(\mathbb{Z}^n\) additively. We provide a precise description of the N-fold sumsets NA for N sufficiently large, with some explicit bounds on “sufficiently large.”
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Minimum pair degree condition for tight Hamiltonian cycles in 4-uniform hypergraphs Acta Math. Hungar. (IF 0.588) Pub Date : 2020-07-22 J. Polcyn, Chr. Reiher, V. Rödl, A. Ruciński, M. Schacht, B. Schülke
We show that every 4-uniform hypergraph with n vertices and minimum pair degree at least \((5/9+o(1))n^{2}/2\) contains a tight Hamiltonian cycle. This degree condition is asymptotically optimal.
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On 4-chromatic Schrijver graphs: their structure, non-3-colorability, and critical edges Acta Math. Hungar. (IF 0.588) Pub Date : 2020-07-22 G. Simonyi, G. Tardos
We investigate 4-chromatic Schrijver graphs from various points of view and color-critical edges in Schrijver graphs in general. In particular, we present the following results. We give an elementary proof for the non-3-colorability of 4-chromatic Schrijver graphs thus providing such a proof also for 4-chromatic Kneser graphs. We show that only certain types of edges of Schrijver graphs can be color-critical
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Nearly subadditive sequences Acta Math. Hungar. (IF 0.588) Pub Date : 2020-07-22 Z. Füredi, I. Z. Ruzsa
We show that the de Bruijn–Erdős condition for the error term in their improvement of Fekete's Lemma is not only sufficient but also necessary in the following strong sense. Suppose that given a sequence \(0\leq f(1)\leq f(2)\leq f(3) \leq \cdots\) such that $$(1) \qquad \qquad \sum_{ n=1}^{\infty} f(n)/n^2 = \infty. $$ Then, there exists a sequence \(\{b(n)\}_{n=1,2,\ldots }\) satisfying $$(2) \qquad
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Number on the Forehead Protocols yielding dense Ruzsa–Szemerédi graphs and hypergraphs Acta Math. Hungar. (IF 0.588) Pub Date : 2020-07-22 N. Alon, A. Shraibman
We describe algorithmic Number On the Forehead protocols that provide dense Ruzsa–Szemerédi graphs. One protocol leads to a simple and natural extension of the original construction of Ruzsa and Szemerédi. The graphs induced by this protocol have n vertices, \(\Omega(n^2/\log n)\) edges, and are decomposable into \(n^{1+O(1/\log \log n)}\) induced matchings. Another protocol is a somewhat simpler version
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Colorings with only rainbow arithmetic progressions Acta Math. Hungar. (IF 0.588) Pub Date : 2020-07-22 J. Pach, I. Tomon
If we want to color \(1,2,\ldots ,n\) with the property that all 3-term arithmetic progressions are rainbow (that is, their elements receive 3 distinct colors), then, obviously, we need to use at least n/2 colors. Surprisingly, much fewer colors suffice if we are allowed to leave a negligible proportion of integers uncolored. Specifically, we prove that there exist \(\alpha ,\beta <1\) such that for
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Regular partitions of gentle graphs Acta Math. Hungar. (IF 0.588) Pub Date : 2020-07-22 Y. Jiang, J. Nešetřil, P. Ossona de Mendez, S. Siebertz
Szemerédi's Regularity Lemma is a very useful tool of extremal combinatorics. Recently, several refinements of this seminal result were obtained for special, more structured classes of graphs. We survey these results in their rich combinatorial context. In particular, we stress the link to the theory of (structural) sparsity, which leads to alternative proofs, refinements and solutions of open problems
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Szemerédi’s proof of Szemerédi’s theorem Acta Math. Hungar. (IF 0.588) Pub Date : 2020-07-22 T. Tao
In 1975, Szemerédi famously established that any set of integers of positive upper density contained arbitrarily long arithmetic progressions. The proof was extremely intricate but elementary, with the main tools needed being the van der Waerden theorem and a lemma now known as the Szemerédi regularity lemma, together with a delicate analysis (based ultimately on double counting arguments) of limiting
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On Linnik’s approximation to Goldbach’s problem. II Acta Math. Hungar. (IF 0.588) Pub Date : 2020-07-22 J. Pintz, I. Z. Ruzsa
Linnik considered about 70 years ago the following approximation to the binary Goldbach problem. Is it possible to give a fixed integer K such that every sufficiently large even integer could be written as the sum of two primes and K powers of two? He solved the problem affirmatively with an unspecified large K. The first explicit result \((K=54\,000)\) appeared at the end of the 1990's. In the present
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Quadratic functions satisfying an additional equation Acta Math. Hungar. (IF 0.588) Pub Date : 2020-07-01 M. Amou
There is a result, due independently to Kurepa [14] and to Jurkat [12], which distinguishes linear functions or derivations from other additive functions as solutions to certain functional equations. The purpose of this paper is to prove an analogue of a part of this result, corresponding to derivations, for quadratic functions.
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L -functions and sum-free sets Acta Math. Hungar. (IF 0.588) Pub Date : 2020-07-01 T. Schoen, I. D. Shkredov
For set \(A\subset \mathbb{F}_p^*\) define by \(\mathsf{sf}(A)\) the size of the largest sum-free subset of A. Alon and Kleitman [3] showed that \(\mathsf{sf} (A) \ge |A|/3+O(|A|/p)\). We prove that if \(\mathsf{sf}(A)-|A|/3\) is small then the set A must be uniformly distributed on cosets of each large multiplicative subgroup. Our argument relies on irregularity of distribution of multiplicative subgroups
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On the addition of values of a quadratic polynomial at units modulo n Acta Math. Hungar. (IF 0.588) Pub Date : 2020-06-30 R. Xiong
Let \(\mathbb{Z}_{n}\) be the ring of residue classes modulo n, \(\mathbb{Z}_{n}^{*}\) be its unit group, and let \(f(z)=az^{2}+bz\) be an integral quadratic polynomial with \(b\neq0\) and \({\rm gcd}(a,b)=1\). In this paper, for any integer c and positive integer n we give a formula for the number of solutions of the congruence equation \(f(x)+f(y)\equiv c({\rm mod}\, n)\) with x, y units \(({\rm
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Spherical spectral synthesis on hypergroups Acta Math. Hungar. (IF 0.588) Pub Date : 2020-06-30 L. Székelyhidi
We introduce the basic concepts of spherical spectral synthesis on hypergroups, following the ideas of our paper [11]. The commutativity of the hypergroup X is not assumed, we suppose only that (X,K) is a Gelfand pair, that is, K is a compact subhypergroup in X and the convolution algebra of allK-invariant compactly supported complex Borel measures on X is commutative.
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On certain D (9) and D (64) Diophantine triples Acta Math. Hungar. (IF 0.588) Pub Date : 2020-06-30 B. Earp-Lynch, S. Earp-Lynch, O. Kihel
A set of m distinct positive integers \(\{a_{1} , \ldots a_{m}\}\) is called a \(D(q)-m\)-tuple for nonzero integer q if the product of any two increased by q, \(a_{i}a_{j}+q, i \neq j\) is a perfect square. Due to certain properties of the sequence, there are many D(q)-Diophantine triples related to the Fibonacci numbers. A result of Baćić and Filipin characterizes the solutions of Pellian equations
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On left ideal essential extensions of rings Acta Math. Hungar. (IF 0.588) Pub Date : 2020-06-30 M. Nowakowska, E. R. Puczyłowski
The main goal of this paper is to extend Flanigan’s theorem in [4] concerning ideal essential extensions of rings to left ideal essential extensions. Moreover, we give new proofs of two Flanigan’s theorems and answer a question raised by M. Petrich in [5] which is related to pure extensions of rings.
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On higher-power moments of $$\Delta_{(1)}(x)$$ Δ ( 1 ) ( x ) Acta Math. Hungar. (IF 0.588) Pub Date : 2020-06-30 D. Liu, Y. Sui
Let \(d_{(1)}(n)\) be the n-th coefficient of the Dirichlet series \((\zeta '(s))^{2}=\sum _{n=1}^{\infty }d_{(1)}(n)n^{-s}\) in \(\mathfrak {R}s>1\), and \(\Delta _{(1)}(x)\) be the error term of the sum \(\sum _{n\le x}d_{(1)}(n)\). In this paper, we study the higher power moments of \(\Delta _{(1)}(x)\) and derive asymptotic formulas for $$\int _{1}^{T}\Delta _{(1)}^{k}(x)\, dx , \quad k=3,\ldots
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A General Separation Theorem For Various Structures Acta Math. Hungar. (IF 0.588) Pub Date : 2020-06-30 F. Jordan, I. Kalantari, H. Pajoohesh
There are several important separation theorems in various areas; for example, theorems of Gordan, Stone, Mazur, Hahn–Banach, etc. In this paper, we give a general treatment, in ZFC, of separation results with several examples in old and new settings. In order to achieve some uniformity of the treatment, we define the notion of a solid operator that leads to the notion of separation. We also characterize
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Ramsey theory for highly connected monochromatic subgraphs Acta Math. Hungar. (IF 0.588) Pub Date : 2020-06-30 J. Bergfalk, M. Hrušák, S. Shelah
An infinite graph is highly connected if the complement of any subgraph of smaller size is connected. We consider weaker versions of Ramsey’s Theorem asserting that in any coloring of the edges of a complete graph there exist large highly connected subgraphs all of whose edges are colored by the same color.
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Linear independence results for sums of reciprocals of Fibonacci and Lucas numbers Acta Math. Hungar. (IF 0.588) Pub Date : 2020-06-30 D. Duverney, Y. Suzuki, Y. Tachiya
The aim of this paper is to give linear independence results for the values of Lambert type series. As an application, we derive arithmetical properties of the sums of reciprocals of Fibonacci and Lucas numbers associated with certain coprime sequences \(\{n_\ell\}_{\ell\geq1}\). For example, the three numbers $$1, \quad \sum_{p:{\rm prime}}\frac{1}{F_{p^2}}, \quad \sum_{p:{\rm prime}}\frac{1}{L_{p^2}}
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Hyperfinite graphings and combinatorial optimization Acta Math. Hungar. (IF 0.588) Pub Date : 2020-06-30 L. Lovász
We exhibit an analogy between the problem of pushing forward measurable sets under measure preserving maps and linear relaxations in combinatorial optimization. We show how invariance of hyperfiniteness of graphings under local isomorphism can be reformulated as an infinite version of a natural combinatorial optimization problem, and how one can prove it by extending wellknown proof techniques (linear
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The order of appearance of the product of two Fibonacci and Lucas numbers Acta Math. Hungar. (IF 0.588) Pub Date : 2020-06-30 N. Irmak, P. k. Ray
Let \(F_{n}\) and \(L_{n}\) be the nth Fibonacci and Lucas number, respectively. The order of appearance is defined as the smallest natural number k such that n divides \(F_{k}\) and denoted by z(n) . In this paper, we give explicit formulas for the terms \( z(F_{a}F_{b}) \), \( z( L_{a}L_{b}) \), \( z(F_{a}L_{b}) \) and \( z(F_{n}F_{n+p}F_{n+2p}) \) with \(p\ge 3\) prime.
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On the volume of hyperplane sections of a d -cube Acta Math. Hungar. (IF 0.588) Pub Date : 2020-06-30 I. Aliev
We obtain an optimal upper bound for the normalised volume of a hyperplane section of an origin-symmetric d-dimensional cube. This confirms a conjecture posed by Imre Bárány and Péter Frankl.
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Summability of Fourier series in periodic Hardy spaces with variable exponent Acta Math. Hungar. (IF 0.588) Pub Date : 2020-06-30 F. Weisz
Let \(p(\cdot ) \mathbb{T}\it ^n\rightarrow (0,\infty )\) be a variable exponent function satisfying the globally log-Hölder condition and \(0
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Monochromatic Partitions In Local Edge Colorings Acta Math. Hungar. (IF 0.588) Pub Date : 2020-06-30 G. N. Sárközy
An edge coloring of a graph is a local r-coloring if the edges incident to any vertex are colored with at most r distinct colors. In this paper, generalizing our earlier work, we study the following problem. Given a family of graphs \(\mathcal {F} \) (for example matchings, paths, cycles, powers of cycles and paths, connected subgraphs) and fixed positive integers s, r, at least how many vertices can
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Generating subgroups of the circle using statistical convergence of order α Acta Math. Hungar. (IF 0.588) Pub Date : 2020-06-30 K. Bose, P. Das, W. He
We introduce a new version of characterized subgroups of the circle group \(\mathbb{T}\) that we call "\(\alpha\)-statistically characterized subgroups", in line of the very recent work [11], using the notion of statistical convergence of order \(\alpha\) [4]. We show that for any arithmetic sequence \((a_n)\) and \(\alpha \in (0, 1)\), the \(\alpha\)-statistically characterized subgroups \(t^\alp
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Erdős covering systems Acta Math. Hungar. (IF 0.588) Pub Date : 2020-06-30 P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba
A covering system is a finite collection of arithmetic progressions whose union is the set of integers. The study of these objects was initiated by Erdős in 1950, and over the following decades he asked many questions about them. Most famously, he asked whether there exist covering systems with distinct moduli whose minimum modulus is arbitrarily large. This problem was resolved in 2015 by Hough, who
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Criteria of a multi-weight weak type inequality in Orlicz classes for maximal functions defined on homogeneous type spaces Acta Math. Hungar. (IF 0.588) Pub Date : 2020-06-30 S. Ding, Y. Ren
We obtain some new necessary and sufficient conditions for a multi-weight weak type maximal inequality of the form $$\begin{aligned} \int _{\{ {x: \mathcal {M} f(x) > \lambda } \}} {\varphi (\lambda {\omega _1}(x))} {\omega _2}(x) \,d\mu \le {c} \int _X \varphi ({c}f(x){\omega _3}(x)){\omega _4}(x) \,d\mu \end{aligned}$$ in Orlicz classes, where \(\mathcal {M} f\) is a Hardy–Littlewood maximal function
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On the Erlang loss function Acta Math. Hungar. (IF 0.588) Pub Date : 2020-06-30 H. Alzer, M. K. Kwong
We present various properties of the Erlang loss function $$B(x,a)=\Bigl( a \int_0^\infty e^{-at} (1+t)^x \,dt \Bigr) ^{-1} \quad{(x\geq 0,\ a>0)}.$$ Among other results, we prove: (1) The function \(x\mapsto B(x,a)^{\lambda}\) is convex on \([0,\infty)\) for every \(a>0\) if and only if \(\lambda\leq 0\) or \(\lambda \geq 1\). (2) The function \(x\mapsto ({1-B(1/x,a)})^{-1} \) is strictly convex on
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Extremal triangle-free and odd-cycle-free colourings of uncountable graphs Acta Math. Hungar. (IF 0.588) Pub Date : 2020-06-30 C. Lambie-Hanson, D. T. Soukup
The optimality of the Erdős–Rado theorem for pairs is witnessed by the colouring \(\Delta_\kappa : [2^\kappa]^2 \rightarrow \kappa\) recording the least point of disagreement between two functions. This colouring has no monochromatic triangles or, more generally, odd cycles. We investigate a number of questions investigating the extent to which \(\Delta_\kappa\) is an extremal such triangle-free or
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Random bipartite posets and extremal problems Acta Math. Hungar. (IF 0.588) Pub Date : 2020-06-30 C. Biró, P. Hamburger, H. A. Kierstead, A. Pór, W. T. Trotter, R. Wang
Previously, Erdős, Kierstead and Trotter [5] investigated the dimension of random height 2 partially ordered sets. Their research was motivated primarily by two goals: (1) analyzing the relative tightness of the Füredi–Kahn upper bounds on dimension in terms of maximum degree; and (2) developing machinery for estimating the expected dimension of a random labeled poset on n points. For these reasons
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Convergence to infinity for orthonormal spline series Acta Math. Hungar. (IF 0.588) Pub Date : 2020-06-30 G. G. Gevorkyan, K. A. Keryan, M. P. Poghosyan
We generalize an important property of trigonometric series to the case of series by orthonormal spline systems corresponding to the dyadic sequence of grid points. We prove that Ciesielski series cannot diverge to infinity on a set of positive measure.
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Erdős–Kakutani phenomena for paths Acta Math. Hungar. (IF 0.588) Pub Date : 2020-05-19 S. Todorcevic
We consider countable edge colourings of complete graphs and investigate the existence of monochromatic paths. We show how this depends on the sizes of the complete graphs whose edges are being coloured.
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Transference of L p bounds between symmetrized Jacobi expansions and Dunkl transform Acta Math. Hungar. (IF 0.588) Pub Date : 2020-05-19 W. Słomian
We prove two theorems showing connections between multipliers for the symmetrized Jacobi expansions and multipliers for the Dunkl transform on \(\mathbb{R}\). These results can be seen as generalizations of the classical Igari’s result relating Jacobi and Hankel multipliers. Moreover, we show a transference theorem relating Jacobi and Dunkl transplantations.
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Integral operators with rough kernels in variable Lebesgue spaces Acta Math. Hungar. (IF 0.588) Pub Date : 2020-05-19 M. Urciuolo, L. Vallejos
We study integral operators with kernels $$K(x,y)= k_{1}( x- A_1y) \cdots k_{m}( x-A_my),$$ \(k_{i}(x)=\frac{\Omega_{i}(x)}{|x|^{n/q_i}}\) where \(\Omega_{i} \colon \mathbb{R}^{n} \to \mathbb{R}\) are homogeneous functions of degree zero, satisfying a size and a Dini condition, Ai are certain invertible matrices, and \(\frac n{q_1}+\cdots+ \frac n{q_m} = n - \alpha, 0 \leq \alpha
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Best proximity point results for p -proximal contractions Acta Math. Hungar. (IF 0.588) Pub Date : 2020-05-19 I. Altun, M. Aslantas, H. Sahin
We introduce the concepts of p-proximal contraction and p-proximal contractive mappings on metric spaces. Then we give some best proximity point results for such mappings. Also we provide some illustrative examples to compare our results with some earliers.
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On the Diophantine equation $$\sum_{j=1}^{k}jP_j^p=P_n^q$$∑j=1kjPjp=Pnq Acta Math. Hungar. (IF 0.588) Pub Date : 2020-05-19 E. Tchammou, A. Togbé
We find all the solutions of the title Diophantine equation \(P_1^p+2P_2^p + \cdots +kP_k^p=P_n^q\) in positive integer variables \((k, n)\), where \(P_i\) is the \(i^{th}\) term of the Pell sequence if the exponents p, q are included in the set \(\{1,2\}\).
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Generalized quotient topologies and hereditary classes Acta Math. Hungar. (IF 0.588) Pub Date : 2020-05-19 P. Montagantirud, S. Phonrakkhet
We introduce a definition of \({\pi}\) being injective with respect to a generalized topology and a hereditary class where \({\pi}\) is a generalized quotient map between generalized topological spaces. This definition is mainly a sufficient condition to show several relations about a generalized topology and its induced generalized quotient topology when either is extended by a hereditary class or
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Mutual stationarity and singular Jonsson cardinals Acta Math. Hungar. (IF 0.588) Pub Date : 2020-05-19 S. Shelah
We prove that if the sequence \(\langle k_n:1 \le n < \omega\rangle\) contains a so-called gap then the sequence \(\langle S^{\aleph_n}_{\aleph_{k_n}}:1 \le n < \omega\rangle\) of stationary sets is not mutually stationary, provided that \(k_n
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Another regular Menon-type identity in residually finite Dedekind domains Acta Math. Hungar. (IF 0.588) Pub Date : 2020-05-13 Ch. Ji, Y. Wang
We give a regular extension of the Menon-type identity to residually finite Dedekind domains.
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Aczél’s iterations for three-variable means Acta Math. Hungar. (IF 0.588) Pub Date : 2020-05-13 G. E. Sbérgamo
We extend the notion of Aczél’s iterations of a mean to three-variable means and prove that these iterations can be used to define a continuous and scale invariant weigthing procedure on an extensive class of means.
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On the p -adic properties of Stirling numbers of the first kind Acta Math. Hungar. (IF 0.588) Pub Date : 2020-05-13 S. F. Hong, M. Qiu
Let n, k and a be positive integers. The Stirling numbers of the first kind, denoted by s(n, k), count the number of permutations of n elements with k disjoint cycles. Let p be a prime. Lengyel, Komatsu and Young, Leonetti and Sanna, Adelberg, Hong and Qiu made some progress in the study of the p-adic valuations of s(n, k). In this paper, by using Washington’s congruence on the generalized harmonic
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Digit frequencies of beta-expansions Acta Math. Hungar. (IF 0.588) Pub Date : 2020-03-31 Y.-Q. Li
Let \(\beta >1\) be a non-integer. First we show that Lebesgue almost every number has a \(\beta \)-expansion of a given frequency if and only if Lebesgue almost every number has infinitely many \(\beta \)-expansions of the same given frequency. Then we deduce that Lebesgue almost every number has infinitely many balanced \(\beta \)-expansions, where an infinite sequence on the finite alphabet \(\{0
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Power comparison theorems for oscillation problems for second order differential equations with p(t) -Laplacian Acta Math. Hungar. (IF 0.588) Pub Date : 2020-03-30 K. Fujimoto
This paper deals with the nonlinear differential equation $$(r(t)|x'|^{p(t)-2}x')'+c(t) |x|^{p(t)-2}x=0, $$ where r(t) > 0 and c(t) are continuous functions, and p(t) > 1 is a smooth function. We establish a comparison theorem for the oscillation problem for this equation with respect to the power p(t) . Using our result, we can utilize oscillation criteria given for half-linear differential equations
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Finite groups whose noncyclic graphs have positive genus Acta Math. Hungar. (IF 0.588) Pub Date : 2020-03-30 X. Ma, H. Su
For a finite noncyclic group G, let \({\rm Cyc} (G)\) be a set of elements a of G such that \(\langle a, b\rangle\) is cyclic for each b of G. The noncyclic graph of G is a graph with the vertex set \(G\setminus {\rm Cyc} (G)\), having an edge between two distinct vertices x and y if \(\langle x, y\rangle\) is not cyclic. In this paper, we show that, for a fixed nonnegative integer k, there are at
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The Thue–Morse and Rudin–Shapiro sequences at primes in principal number fields Acta Math. Hungar. (IF 0.588) Pub Date : 2020-03-30 S. Drappeau, G. Hanna
We consider a numeration system in the ring of integers \({\mathcal{O}}_K\) of a number field, which we assume to be principal. We prove that the property of being a prime in \({\mathcal{O}}_K\) is decorrelated from two fundamental examples of automatic sequences relative to the chosen numeration system: the Thue–Morse and the Rudin–Shapiro sequences. This is an analogue, in \({\mathcal{O}}_K\), of
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