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On a generalization of Schur theorem concerning resultants Period. Math. Hung. (IF 0.693) Pub Date : 2020-11-23 Maciej Ulas
Let K be a field and put \({\mathcal {A}}:=\{(i,j,k,m)\in \mathbb {N}^{4}:\;i\le j\;\text{ and }\;m\le k\}\). For any given \(A\in {\mathcal {A}}\) we consider the sequence of polynomials \((r_{A,n}(x))_{n\in \mathbb {N}}\) defined by the recurrence $$\begin{aligned} r_{A,n}(x)=f_{n}(x)r_{A,n-1}(x)-v_{n}x^{m}r_{A,n-2}(x),\;n\ge 2, \end{aligned}$$ where the initial polynomials \(r_{A,0}, r_{A,1}\in
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A new proof of a generalization of Gerzon’s bound Period. Math. Hung. (IF 0.693) Pub Date : 2020-11-22 Gábor Hegedüs
In this paper we give a short, new proof of a natural generalization of Gerzon’s bound. This bound improves the Delsarte, Goethals and Seidel’s upper bound in a special case. Our proof is a simple application of the linear algebra bound method.
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On the maximal unramified pro-2-extension of certain cyclotomic $$\mathbb {Z}_2$$ Z 2 -extensions Period. Math. Hung. (IF 0.693) Pub Date : 2020-11-20 Abdelmalek Azizi, Mohammed Rezzougui, Abdelkader Zekhnini
In this paper, we establish a necessary and sufficient criterion for a finite metabelian 2-group G whose abelianized \(G^{ab}\) is of type \((2, 2^m)\), with \(m\ge 2\), to be metacyclic. This criterion is based on the rank of the maximal subgroup of G which contains the three normal subgroups of G of index 4. Then, we apply this result to study the structure of the Galois group of the maximal unramified
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Direct estimates of the weighted simultaneous approximation by the Szász–Mirakjan operator Period. Math. Hung. (IF 0.693) Pub Date : 2020-11-17 Borislav R. Draganov
We establish direct estimates of the rate of weighted simultaneous approximation by the Szász–Mirakjan operator for smooth functions in the supremum norm on the non-negative semi-axis. We consider Jacobi-type weights. The estimates are stated in terms of appropriate moduli of smoothness or K-functionals.
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James type constants and fixed points for multivalued nonexpansive mappings Period. Math. Hung. (IF 0.693) Pub Date : 2020-11-17 Zhan-fei Zuo
In this paper, we give some sufficient conditions for the Domínguez–Lorenzo condition in terms of the James type constant \(J_{X,t}(\tau )\), the coefficient of weak orthogonality \(\mu (X)\) and the Domínguez Benavides coefficient R(1, X), which imply the existence of fixed points for multivalued nonexpansive mappings. Our results extend some well known results in the recent literature.
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A class of homogeneous superspaces associated to odd involutions Period. Math. Hung. (IF 0.693) Pub Date : 2020-10-30 Fereshteh Bahadorykhalily, Mohammad Mohammadi, Saad Varsaie
A new generalization of Grassmannians in supergeometry, called \(\nu \)-Grassmannians, are constructed by gluing \(\nu \)-domains. By a \(\nu \)-domain, we mean a superdomain with an odd involution say \(\nu \) on its structure sheaf, as morphism of modules. Then we show that \(\nu \)-Grassmannians are homogeneous superspaces. In addition, in the last section, a supergroup associated to the odd involution
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From biased coin to any discrete distribution Period. Math. Hung. (IF 0.693) Pub Date : 2020-10-29 Karol Gryszka
In this note we construct an algorithm generating any discrete distribution with an arbitrary coin (and, as a result, with arbitrary initial distribution). The coin need not be fair and the target distribution can be supported on a countable set.
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On a sum involving the Mangoldt function Period. Math. Hung. (IF 0.693) Pub Date : 2020-10-22 Jing Ma, Jie Wu
Let \(\Lambda (n)\) be the von Mangoldt function, and let [t] be the integral part of real number t. In this note we prove that the asymptotic formula $$\begin{aligned} \sum _{n\leqslant x} \Lambda \Big (\Big [\frac{x}{n}\Big ]\Big ) = x\sum _{d\geqslant 1}\frac{\Lambda (d)}{d(d+1)} + O_{\varepsilon }\big (x^{35/71+\varepsilon }\big ) \end{aligned}$$ holds as \(x\rightarrow \infty \) for any \(\varepsilon
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Continuous maps with the disjoint support property Period. Math. Hung. (IF 0.693) Pub Date : 2020-10-16 Snigdha Bharati Choudhury, Satya Deo
It is well known that for each \(n\ge 0\), there is a continuous map \( f :S^{n}\rightarrow \partial \bigtriangleup ^{n+1}\) with the disjoint support property. Since \(S^{n}\) and \(\partial \bigtriangleup ^{n+1}\) are homeomorphic, it is natural to ask whether or not there is a homeomorphism \( h :S^{n}\rightarrow \partial \bigtriangleup ^{n+1}\) with the disjoint support property. In this paper
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Deciding multiple tiling by polygons in polynomial time Period. Math. Hung. (IF 0.693) Pub Date : 2020-10-13 Mihail N. Kolountzakis
Suppose P is a symmetric convex polygon in the plane. We give an algorithm, running in polynomial time in the number of sides of the polygon, which decides if P can tile the plane by translations at some level (not necessarily at level one; this is multiple tiling). The main technical contribution is a polynomial time algorithm that selects, if this is possible, for each \(j=1,2,\ldots ,n\) one of
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A note on algebraic independence criterion for Laurent series in positive characteristic Period. Math. Hung. (IF 0.693) Pub Date : 2020-08-20 Mao-Sheng Li
We study the algebraic independence of Laurent series in positive characteristic which can be fast approximated by rational functions. This can be seen as a completion of the results obtained by Chaichana and Laohakosol (Period Math Hung 55(1):35–59, 2007).
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Wetzel’s sector covers unit arcs Period. Math. Hung. (IF 0.693) Pub Date : 2020-07-29 Chatchawan Panraksa, Wacharin Wichiramala
We settle J. Wetzel’s 1970’s conjecture and show that a \(30^{\circ }\) circular sector of unit radius can accommodate every planar arc of unit length. Leo Moser asked in 1966 for the (convex) region with the smallest area in the plane that can accommodate each arc of unit length. With area \(\pi /12,\) this sector is the smallest such set presently known. Moser’s question has prompted a multitude
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Diophantine quadruples in $$\mathbb {Z}[i][X]$$ Z [ i ] [ X ] Period. Math. Hung. (IF 0.693) Pub Date : 2020-07-27 Alan Filipin, Ana Jurasić
In this paper, we prove that every Diophantine quadruple in \(\mathbb {Z}[i][X]\) is regular. More precisely, we prove that if \(\{a, b, c, d\}\) is a set of four non-zero polynomials from \(\mathbb {Z}[i][X]\), not all constant, such that the product of any two of its distinct elements increased by 1 is a square of a polynomial from \(\mathbb {Z}[i][X]\), then $$\begin{aligned} (a+b-c-d)^2=4(ab+1)(cd+1)
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On local metric pressure of dynamical systems Period. Math. Hung. (IF 0.693) Pub Date : 2020-07-25 M. Rahimi, A. Assari
In this paper, a local version of the topological pressure of dynamical systems is presented. It is a function defined on the product space which does not depend on any measure. It is shown that, for any invariant measure, integration of the introduced function with respect to its corresponding diagonal measure results in the metric pressure of the dynamical system.
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On Ivády’s bounds for the gamma function and related results Period. Math. Hung. (IF 0.693) Pub Date : 2020-07-24 Horst Alzer, Man Kam Kwong
We prove that the inequality $$\begin{aligned} \Gamma (x+1)\le \frac{x^2+\beta }{x+\beta } \end{aligned}$$ holds for all \(x\in [0,1]\), \(\beta \ge {\beta ^{*}}\), with the best possible constant $$\begin{aligned} \beta ^*=\max _{0.1\le x\le 0.3} f(x)=1.75527\ldots , \end{aligned}$$ where f is given by $$\begin{aligned} f(x)=\frac{x\Gamma (x+1)-x^2}{1-\Gamma (x+1)}. \end{aligned}$$ This refines bounds
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Inequalities for generalized eigenvalues of quaternion matrices Period. Math. Hung. (IF 0.693) Pub Date : 2020-07-21 Yan Hong, Feng Qi
Studying eigenvalues of square matrices is a traditional and fundamental direction in linear algebra. Quaternion matrices constitute an important and extensively useful subclass of square matrices. In the paper, the authors (1) introduce the concept of “generalized eigenvalues of quaternion matrix”; (2) give some properties of generalized eigenvalues for a regular quaternion matrix pair; (3) establish
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The mixed conformable partial derivatives Period. Math. Hung. (IF 0.693) Pub Date : 2020-06-12 Chang-Jian Zhao, Wing-Sum Cheung
In this paper we introduce a new conformable derivative call it mixed conformable partial derivative, which obeys classical properties, including linearity, product rule, quotient rule and vanishing derivatives for constant functions. As an application, we establish an Opial type inequality for the mixed second order conformable partial derivatives.
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On approximately monotone and approximately Hölder functions Period. Math. Hung. (IF 0.693) Pub Date : 2020-06-11 Angshuman R. Goswami; Zsolt Páles
A real valued function f defined on a real open interval I is called \(\Phi \)-monotone if, for all \(x,y\in I\) with \(x\le y\) it satisfies$$\begin{aligned} f(x)\le f(y)+\Phi (y-x), \end{aligned}$$where \( \Phi :[0,\ell (I) [ \rightarrow \mathbb {R}_+\) is a given nonnegative error function, where \(\ell (I)\) denotes the length of the interval I. If f and \(-f\) are simultaneously \(\Phi \)-monotone
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On the structure of partition which the difference of their representation function is a constant Period. Math. Hung. (IF 0.693) Pub Date : 2020-06-05 Xiao-Hui Yan
Let \(\mathbb {N}\) be the set of nonnegative integers. For any set \(A \subset \mathbb {N}\), let \(R_1(A, n)\), \(R_2(A, n)\) and \(R_3(A, n)\) be the number of representations of n as \(n=a+a',a, a'\in A\); \(n=a+a',a, a'\in A\), \(a
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Integral points on curves of genus zero over totally real number fields Period. Math. Hung. (IF 0.693) Pub Date : 2020-06-03 Dimitrios Poulakis
In this paper, we consider plane algebraic curves of genus zero defined over number fields having three simple points at infinity such that their minimal fields of definition are totally real, and we determine an upper bound of polynomial type for the size of their integral points.
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A note on $$AP_3$$AP3 -covering sequences Period. Math. Hung. (IF 0.693) Pub Date : 2020-06-01 Jin-Hui Fang
For a given integer \(k\ge 3\), a sequence A of nonnegative integers is called an \(AP_k\)-covering sequence if there exists an integer \(n_0\) such that, if \(n>n_0\), then there exist \(a_1\in A\), \(\ldots \), \(a_{k-1}\in A\), \(a_1
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Non-characteristic Heisenberg group domains Period. Math. Hung. (IF 0.693) Pub Date : 2020-05-29 Nadia Alamri, Najoua Gamara
In this work, we study non-characteristic domains of Heisenberg groups. We prove that bounded domains which are diffeomorphic to the solid torus having the center of the group as rotation axis, are non-characteristic. Then we state the following conjecture: the bounded non-characteristic domains of the Heisenberg group of dimension 1 are diffeomorphic to a solid torus having the center of the group
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On $${\mathcal {I}}_{ Period. Math. Hung. (IF 0.693) Pub Date : 2020-05-28 József Bukor, Ferdinánd Filip, János T. Tóth, László Zsilinszky
Let \(\mathbb N\) be the set of positive integers, and denote by $$\begin{aligned} \lambda (A)=\inf \{t>0:\sum _{a\in A} a^{-t}<\infty \} \end{aligned}$$ the convergence exponent of \(A\subset \mathbb N\). For \(0
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On perfect powers that are sums of two Pell numbers Period. Math. Hung. (IF 0.693) Pub Date : 2020-05-22 Hyacinthe Aboudja, Mohand Hernane, Salah Eddine Rihane, Alain Togbé
Let \(P_k\) denote the kth term of the Pell sequence. In this paper we find all solutions of the exponential Diophantine equation \(P_n+P_m = y^s\) in positive integer variables (m, n, y, s) under the assumption \(n \equiv m \pmod 2\).
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Irreducibility of analytic arc-sections of hypersurface singularities Period. Math. Hung. (IF 0.693) Pub Date : 2020-05-21 Miguel Angel Marco-Buzunariz, Maria Pe Pereira
We explore the existence of irreducible and reducible arc-sections in an irreducible hypersurface singularity germ along finite projections. In particular we provide examples of irreducible isolated hypersurface singularities for which no irreducible arc-sections exist, and show that reducible ones always exist. Moreover, we give an algorithm to check if a given projection allows irreducible arc-sections
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Strongly quasipositive quasi-alternating links and Montesinos links Period. Math. Hung. (IF 0.693) Pub Date : 2020-05-17 Idrissa Ba
The aim of this article is to give a characterization of strongly quasipositive quasi-alternating links and detect new classes of strongly quasipositive Montesinos links and non-strongly quasipositive Montesinos links. In this direction, we show that, if L is an oriented quasi-alternating link with a quasi-alternating crossing c such that \(L_0\) is alternating (where \(L_0\) has the induced orientation)
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Sumsets associated with Wythoff sequences and Fibonacci numbers Period. Math. Hung. (IF 0.693) Pub Date : 2020-05-15 Sutasinee Kawsumarng, Tammatada Khemaratchatakumthorn, Passawan Noppakaew, Prapanpong Pongsriiam
Let \(\alpha = (1+\sqrt{5})/2\) be the golden ratio, and let \(B(\alpha ) = (\left\lfloor n\alpha \right\rfloor )_{n\ge 1}\) and \(B(\alpha ^2) = \left( \left\lfloor n\alpha ^2\right\rfloor \right) _{n\ge 1}\) be the lower and upper Wythoff sequences, respectively. In this article, we obtain a new estimate concerning the fractional part \(\{n\alpha \}\) and study the sumsets associated with Wythoff
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A note on the simultaneous Pell equations $$x^2-(a^2-1)y^2=1$$x2-(a2-1)y2=1 and $$y^2-bz^2=1$$y2-bz2=1 Period. Math. Hung. (IF 0.693) Pub Date : 2020-04-14 Xing-Wang Jiang
Let \(a>1,b\) be two positive integers where the square-free part of b is 2pq with p, q two distinct odd primes. Recently, Cipu (Proc Am Math Soc 146:983–992, 2018) proved that if one of the following conditions holds: (i) \(2a^2-1\) is not a perfect square, (ii) \(\{p\pmod 8,q\pmod 8\}\ne \{1,3\}\), then the equations $$\begin{aligned} x^2-(a^2-1)y^2=1 \quad \text {and} \quad y^2-bz^2=1 \end{aligned}$$
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An introduction to knot Floer homology and curved bordered algebras Period. Math. Hung. (IF 0.693) Pub Date : 2020-04-13 Antonio Alfieri; Jackson Van Dyke
We survey Ozsváth–Szabó’s bordered approach to knot Floer homology. After a quick introduction to knot Floer homology, we introduce the relevant algebraic concepts (\(\mathcal {A}_\infty \)-modules, type D-structures, box tensor product, etc.), we discuss partial Kauffman states, the construction of the boundary algebra, and sketch Ozsváth and Szabó’s analytic construction of the type D-structure associated
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Two q -congruences from Carlitz’s formula Period. Math. Hung. (IF 0.693) Pub Date : 2020-04-06 Cheng-Yang Gu, Victor J. W. Guo
Recently, using a formula of Carlitz, the second author proved a q-congruence conjectured by Tauraso. In this note we utilize Carlitz’s formula to prove two more similar q-congruences. We also propose a conjectural q-congruence that refines one of our q-congruences.
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Weighted $$L^p$$Lp -spaces on locally compact nilpotent groups Period. Math. Hung. (IF 0.693) Pub Date : 2020-04-06 Mateusz Krukowski
Our paper begins with a revision of the spectral theory for commutative Banach algebras, which enables us to prove the \(L^p_{\omega }\)-conjecture for locally compact abelian groups. We follow an alternative approach to the one known in the literature. In particular, we do not resort to any structural theorems for locally compact groups at this stage. Subsequently, we discuss nilpotent, locally compact
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Jeśmanowicz’ conjecture for polynomials Period. Math. Hung. (IF 0.693) Pub Date : 2020-04-06 Jerome T. Dimabayao
Let (a, b, c) be pairwise relatively prime integers such that \(a^2 + b^2 = c^2\) . In 1956, Jeśmanowicz conjectured that the only solution of \(a^x + b^y = c^z\) in positive integers is \((x,y,z)=(2,2,2)\). In this note we prove a polynomial analogue of this conjecture.
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Optimality of barrier dividend strategy in a jump-diffusion risk model with debit interest Period. Math. Hung. (IF 0.693) Pub Date : 2020-04-05 Wei Wang, Jingmin He
This paper investigates the optimal dividend problem in a jump-diffusion risk model with debit interest. In this model, the insurer could borrow money at a debit interest when the surplus turns negative. However, when the negative surplus attains a certain critical level, the business stops and absolute ruin happens at this moment. A sufficient condition under which the optimal dividend strategy is
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Stable Pontryagin–Thom construction for proper maps Period. Math. Hung. (IF 0.693) Pub Date : 2020-04-01 András Csépai
We will present proofs for two conjectures stated in Rot (Homotopy classes of proper maps out of vector bundles, 2020. arXiv:1808.08073). The first one is that for an arbitrary manifold W, the homotopy classes of proper maps \(W\times \mathbb {R}^n\rightarrow \mathbb {R}^{k+n}\) stabilise as \(n\rightarrow \infty \), and the second one is that in a stable range there is a Pontryagin–Thom type bijection
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Knots not concordant to L-space knots Period. Math. Hung. (IF 0.693) Pub Date : 2020-03-30 Ramazan Yozgyur
In this short note we use methods of Friedl, Livingston and Zentner to show that there are knots that are not algebraically concordant to a connected sum of positive and negative L-space knots.
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The locus of the representation of logarithmic connections by Fuchsian equations Period. Math. Hung. (IF 0.693) Pub Date : 2020-03-30 Péter Ivanics
The generic element of the moduli space of logarithmic connections with parabolic points on holomorphic vector bundle over the Riemann sphere can be represented by a Fuchsian equation with some singularities and some apparent singularities. We analyze the case of rank 3 vector bundle which leads to third order Fuchsian equation. We find coordinates on an open subset of the moduli space and we construct
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Convergence of linking Baskakov-type operators Period. Math. Hung. (IF 0.693) Pub Date : 2020-03-26 Ulrich Abel; Margareta Heilmann; Vitaliy Kushnirevych
In this paper we consider a link \(B_{n,\rho }\) between Baskakov type operators \(B_{n,\infty }\) and genuine Baskakov–Durrmeyer type operators \( B_{n,1}\) depending on a positive real parameter \(\rho \). The topic of the present paper is the pointwise limit relation \(\left( B_{n,\rho }f\right) \left( x\right) \rightarrow \left( B_{n,\infty }f\right) \left( x\right) \) as \(\rho \rightarrow \infty
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Fibonacci numbers and real quadratic p -rational fields Period. Math. Hung. (IF 0.693) Pub Date : 2020-03-24 Zakariae Bouazzaoui
We characterize p-rational real quadratic fields in terms of generalized Fibonacci numbers. We then use this characterization to give numerical evidence to a conjecture of Greenberg asserting the existence of p-rational multi-quadratic fields of arbitrary degree \(2^{t}\), \(t\ge 1\).
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On Lau–Loy’s decomposition of a measure algebra on CHART groups Period. Math. Hung. (IF 0.693) Pub Date : 2020-03-23 Z. Bahramian; A. Jabbari
By using the Furstenberg–Ellis–Namioka structure theorem, we give a decomposition theorem for the Banach algebra \({\mathcal {M}}(G)\), i.e. the Banach algebra of those complex regular Borel measures on a compact Hausdorff admissible right topological (or simply CHART) group G for which the natural convolution product makes sense, generalizing an existing result due to Lau and Loy. Next, we characterize
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Diophantine triples with largest two elements in common Period. Math. Hung. (IF 0.693) Pub Date : 2020-03-23 Mihai Cipu, Andrej Dujella, Yasutsugu Fujita
In this paper we prove that if \(\{a,b,c\}\) is a Diophantine triple with \(a
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3-rank of ambiguous class groups of cubic Kummer extensions Period. Math. Hung. (IF 0.693) Pub Date : 2020-03-19 S. Aouissi, D. C. Mayer, M. C. Ismaili, M. Talbi, A. Azizi
Let \(k=k_0(\root 3 \of {d})\) be a cubic Kummer extension of \(k_0=\mathbb {Q}(\zeta _3)\) with \(d>1\) a cube-free integer and \(\zeta _3\) a primitive third root of unity. Denote by \(C_{k,3}^{(\sigma )}\) the 3-group of ambiguous classes of the extension \(k/k_0\) with relative group \(G={\text {Gal}}(k/k_0)=\langle \sigma \rangle \). The aims of this paper are to characterize all extensions \(k/k_0\)
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Multiplicative dependence between k -Fibonacci and k -Lucas numbers Period. Math. Hung. (IF 0.693) Pub Date : 2020-03-19 Carlos A. Gómez, Jhonny C. Gómez, Florian Luca
A generalization of the well-known Fibonacci and Lucas sequences are the k-Fibonacci and k-Lucas sequences with some fixed integer \(k\ge 2\). For these sequences the first k terms are \(0,\ldots ,0,1\) and \(0,\ldots ,0,2,1\), respectively, and each term afterwards is the sum of the preceding k terms. Here we find all pairs of k-Fibonacci and k-Lucas numbers multiplicatively dependent.
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Online packing of d -dimensional boxes into the unit cube Period. Math. Hung. (IF 0.693) Pub Date : 2020-03-19 Janusz Januszewski; Łukasz Zielonka
Any sequence of d-dimensional boxes of edge length smaller than or equal to 1 with total volume not greater than \((3-2\sqrt{2})\cdot 3^{-d}\) can be packed online into the d-dimensional unit cube.
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Closure of an exponential system in some Hardy–Smirnov spaces Period. Math. Hung. (IF 0.693) Pub Date : 2020-03-19 Elias Zikkos, Gajath Gunatillake
Let \(\Omega \) be an open, simply connected, bounded subset of the complex plane \(\mathbb {C}\) with a rectifiable boundary \({\partial {\Omega }}\). We investigate the relation between the Hardy–Smirnov space \(H^2(\Omega )\) and the closed span of the exponential system \(\{e^{nz}\}_{n=1}^{\infty }\) with respect to the Hardy–Smirnov norm \(\Vert \cdot \Vert _\Omega \). Depending on the “height”
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Some particular properties of general orthonormal systems Period. Math. Hung. (IF 0.693) Pub Date : 2020-03-18 V. Tsagareishvili
The present paper deals with some particular properties of special series of Fourier coefficients of the class of functions with bounded variation with respect to general orthonormal systems (ONS). The obtained results demonstrate that the properties of the general ONS and of the classical ONSs (trigonometric, Haar, Walsh system) are different in some cases.
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Coproducts in the category $${{\mathcal {S}}}(B)$$S(B) of Segal topological algebras, revisited Period. Math. Hung. (IF 0.693) Pub Date : 2020-03-18 Mart Abel
In this paper we generalize the result (obtained by the author earlier in the paper titled “Products and coproducts in the category \({{\mathcal {S}}}(B)\) of Segal topological algebras”) about the existence of the coproduct of objects of the category \({\mathcal S}(B)\) from finite collection of objects of \({{\mathcal {S}}}(B)\) to any collection of objects of \({{\mathcal {S}}}(B)\).
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A note on the exceptional solutions of Jeśmanowicz’ conjecture concerning primitive Pythagorean triples Period. Math. Hung. (IF 0.693) Pub Date : 2020-03-18 Ruiqin Fu, Hai Yang
Let \((m,\ n)\) be fixed positive integers such that \(m>n,\ \gcd (m,\ n)=1\) and \( mn\equiv 0 \pmod 2\). Then the triple \((m^2-n^2,\ 2mn,\ m^2+n^2)\) is called a primitive Pythagorean triple. In 1956, Jeśmanowicz (Wiadom Math 1(2):196–202, 1955/1956 ) conjectured that the equation \((m^2-n^2)^x+(2mn)^y=(m^2+n^2)^z\) has only the positive integer solution \((x,\ y,\ z)=(2,\ 2,\ 2)\). This problem
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On the Diophantine equation $$x^2+3^a41^b=y^n $$ x 2 + 3 a 41 b = y n Period. Math. Hung. (IF 0.693) Pub Date : 2020-03-17 Murat Alan, Uğur Zengin
In this paper we find all positive integer solutions (x, y, n, a, b) of the equation in the title for non negative integers a and b under the condition that the integers x and y are relatively prime and \( n \ge 3\).
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The $${\mathbb {Q}}$$ Q -Korselt set of $$\mathrm {pq}$$ pq Period. Math. Hung. (IF 0.693) Pub Date : 2020-03-17 Nejib Ghanmi
Let N be a positive integer, \({\mathbb {A}}\) be a nonempty subset of \({\mathbb {Q}}\) and \(\alpha =\dfrac{\alpha _{1}}{\alpha _{2}}\in {\mathbb {A}}{\setminus } \{0,N\}\). \(\alpha \) is called an N-Korselt base (equivalently N is said an \(\alpha \)-Korselt number) if \(\alpha _{2}p-\alpha _{1}\) is a divisor of \(\alpha _{2}N-\alpha _{1}\) for every prime p dividing N. The set of all Korselt
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Martingale transforms and fractional integrals on rearrangement-invariant martingale Hardy spaces Period. Math. Hung. (IF 0.693) Pub Date : 2020-03-17 Kwok-Pun Ho
We establish an interpolation result for the rearrangement-invariant martingale Hardy spaces. By using this interpolation result, we extend the mapping properties of the martingale transforms and the fractional integrals on martingale function spaces. In particular, we obtain the mapping properties on the martingale Hardy–Orlicz spaces, the grand martingale Hardy spaces and the martingale Hardy–Lorentz–Karamata
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Von Neumann–Davis type theorems for HLPK and Sherman functionals on Eaton triples Period. Math. Hung. (IF 0.693) Pub Date : 2020-03-17 Marek Niezgoda
In this work, we generalize the von Neumann and Davis theorems on the extension of the convexity of a group-invariant norm (resp. function) from the subspace of diagonal matrices to the whole space of complex (resp. hermitian) matrices. Our generalizations go in two directions: (1) We replace the space of complex (hermitian) matrices and its subspace of diagonal matrices by an Eaton triple and its
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Arithmetic properties of polynomials Period. Math. Hung. (IF 0.693) Pub Date : 2020-03-17 Yong Zhang; Zhongyan Shen
First, we prove that the Diophantine system$$\begin{aligned} f(z)=f(x)+f(y)=f(u)-f(v)=f(p)f(q) \end{aligned}$$has infinitely many integer solutions for \(f(X)=X(X+a)\) with nonzero integers \(a\equiv 0,1,4\pmod {5}\). Second, we show that the above Diophantine system has an integer parametric solution for \(f(X)=X(X+a)\) with nonzero integers a, if there are integers m, n, k such that$$\begin{aligned}
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Convergence rate for Rényi-type continued fraction expansions Period. Math. Hung. (IF 0.693) Pub Date : 2020-03-16 Gabriela Ileana Sebe, Dan Lascu
This paper continues our investigation of Rényi-type continued fractions studied in Lascu and Sebe (A dependence with complete connections approach to generalized Rényi continued fractions, Acta Math. Hungar. 160, 292–313, 2020). A Wirsing-type approach to the Perron–Frobenius operator of the Rényi-type continued fraction transformation under its invariant measure allows us to study the optimality
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Weakly Douglas Finsler metrics Period. Math. Hung. (IF 0.693) Pub Date : 2020-03-16 M. Atashafrouz, B. Najafi, A. Tayebi
In this paper, we define a weaker notion of Douglas metrics, namely weakly Douglas metrics. A Finsler metric satisfies a projectively invariant equation \(D^i_{\,\,jkl}=T_{jkl} y^i\) for some tensor \(T_{jkl}\) is called a weakly Douglas metric. We show that every Randers manifold of dimension \(n\ge 3\) is a weakly Douglas metric if and only if it is a Douglas metric. Then, we prove that every Kropina
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Flag curvatures on Berwald submersions Period. Math. Hung. (IF 0.693) Pub Date : 2020-03-16 Rongmu Yan
In this paper, we give some fundamental equations of curvature tensors on Berwald submersions, which imply the relationship of flag curvatures of the associated manifolds and the fibers.
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Maximal inequalities and their applications to orthogonal and Hadamard matrices Period. Math. Hung. (IF 0.693) Pub Date : 2020-03-16 George Giorgobiani; Vakhtang Kvaratskhelia
Maximal inequalities for the signed vector summands are established. Probabilistic estimations for the sets of appropriate signs are given. By use of the “transference technique” appropriate maximal inequalities are derived for the permutations. One application for orthogonal and Hadamard matrices is suggested.
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An Ehresmann–Schein–Nambooripad theorem for locally Ehresmann P -Ehresmann semigroups Period. Math. Hung. (IF 0.693) Pub Date : 2020-01-14 Shoufeng Wang
Lawson has obtained an Ehresmann–Schein–Nambooripad theorem (ESN theorem for short) for Ehresmann semigroups which states that the category of Ehresmann semigroups together with (2,1,1)-homomorphisms is isomorphic to the category of Ehresmann categories together with admissible mappings. Recently, Jones introduced P-Ehresmann semigroups as generalizations of Ehresmann semigroups. In this paper, we
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On the non-tangential convergence of Poisson and modified Poisson semigroups at the smoothness points of $$L_{p}$$Lp -functions Period. Math. Hung. (IF 0.693) Pub Date : 2020-01-13 Simten Bayrakci; M. F. Shafiev; Ilham A. Aliev
The high-dimensional version of Fatou’s classical theorem asserts that the Poisson semigroup of a function \(f\in L_{p}(\mathbb {R}^{n}), \ 1\le p \le \infty \), converges to f non-tangentially at Lebesque points. In this paper we investigate the rate of non-tangential convergence of Poisson and metaharmonic semigroups at \(\mu \)-smoothness points of f.
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On q -analogues of quadratic Euler sums Period. Math. Hung. (IF 0.693) Pub Date : 2020-01-11 Zhonghua Li; Ce Xu
In this paper we study q-analogues of Euler sums and present a new family of identities by using the method of Jackson q-integral representations of series. We then apply it to obtain a family of identities relating quadratic Euler sums to linear sums and q-polylogarithms. Furthermore, we use certain stuffle products to evaluate several q-series with q-harmonic numbers. Some interesting new results
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On the $$\chi ^2$$χ2 statistics of leading digits of irrational rotations with a large first or second partial quotient Period. Math. Hung. (IF 0.693) Pub Date : 2020-01-04 Toshifumi Nagayoshi; Keizo Takashima
We derive exact formulas for the \(\chi ^2\) statistics of the distribution of the leading digit of \(a^n\), where \(\log _{10} a\) has a large first or second partial quotient in its continued fraction expansion. We also give a mathematical explanation for the difference between the behavior of the discrepancy and that of the distribution of leading digits.
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