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Browse Our Mathematics and Statistics Journals

Mathematics and statistics journals publish papers on the theory and application of mathematics, statistics, and probability. Most mathematics journals have a broad scope that encompasses most mathematical fields. These commonly include logic and foundations, algebra and number theory, analysis (including differential equations, functional analysis and operator theory), geometry, topology, combinatorics, probability and statistics, numerical analysis and computation theory, mathematical physics, etc.

When it comes to mathematics, we can classify it into pure and applied mathematics. Pure mathematics studies mathematical concepts separately from any form of mathematical application. It focuses on exploring basic ideas that make up mathematics and providing a deeper understanding of the field. It encompasses number theory, algebra, combinatorics, geometry, topology, and mathematical analysis.

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Atom Canonicity and First Order Definability in Classes of Algebras of Relations

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 3
DOI:: https://doi.org/10.1556/012.2020.57.3.1467

Author:

Tarek Sayed Ahmed

Abstract

Fix 2 < n < ω and let CA _n denote the class of cyindric algebras of dimension n. Roughly CA _n is the algebraic counterpart of the proof theory of first order logic restricted to the first n variables which we denote by L_n . The variety RCA _n of representable CA _n s reflects algebraically the semantics of L_n . Members of RCA _n are concrete algebras consisting of genuine n-ary relations, with set theoretic operations induced by the nature of relations, such as projections referred to as cylindrifications. Although CA _n has a finite equational axiomatization, RCA _n is not finitely axiomatizable, and it generally exhibits wild, often unpredictable and unruly behavior. This makes the theory of CA _n substantially richer than that of Boolean algebras, just as much as L_ω,ω is richer than propositional logic. We show using a so-called blow up and blur construction that several varieties (in fact infinitely many) containing and including the variety RCA _n are not atom-canonical. A variety V of Boolean algebras with operators is atom canonical, if whenever $A$ ∈ V is atomic, then its Dedekind-MacNeille completion, sometimes referred to as its minimal completion, is also in V. From our hitherto obtained algebraic results we show, employing the powerful machinery of algebraic logic, that the celebrated Henkin-Orey omitting types theorem, which is one of the classical first (historically) cornerstones of model theory of L_ω,ω , fails dramatically for L_n even if we allow certain generalized models that are only locallly classical. It is also shown that any class K such that Nr _n CA _ω ∩ CRCA _n $\underline{\subseteq}$ K $\underline{\subseteq}$ S _c Nr _n CA _n ₊₃, where CRCA _n is the class of completely representable CA _n s, and S _c denotes the operation of forming dense (complete) subalgebras, is not elementary. Finally, we show that any class K such that S _d RaCA _ω $\underline{\subseteq}$ K $\underline{\subseteq}$ S _c RaCA₅ is not elementary, where S _d denotes the operation of forming dense subalgebra.

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Banach algebras satisfying certain chain conditions on closed ideals

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 3
DOI:: https://doi.org/10.1556/012.2020.57.3.1465

Authors:

Abdullah Alahmari

Falih A. Aldosray

, and

Mohamed Mabrouk

Abstract

Let 𝔄 be a unital Banach algebra and ℜ its Jacobson radical. This paper investigates Banach algebras satisfying some chain conditions on closed ideals. In particular, it is shown that a Banach algebra 𝔄 satisfies the descending chain condition on closed left ideals then 𝔄/ℜ is finite dimensional. We also prove that a C ^*-algebra satisfies the ascending chain condition on left annihilators if and only if it is finite dimensional. Moreover, other auxiliary results are established.

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Characterizations of the Cauchy distribution associated with integral transforms

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 3
DOI:: https://doi.org/10.1556/012.2020.57.3.1469

Author:

Kazuki Okamura

Abstract

We give two new simple characterizations of the Cauchy distribution by using the Möbius and Mellin transforms. They also yield characterizations of the circular Cauchy distribution and the mixture Cauchy model.

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Integral inequalities in a generalized context

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 3
DOI:: https://doi.org/10.1556/012.2020.57.3.1464

Authors:

Péter Kórus

Luciano M. Lugo

, and

Juan E. Nápoles Valdés

Abstract

In this paper we present different variants of the well-known Hermite–Hadamard inequality, in a generalized context. We consider general fractional integral operators for h-convex and r-convex functions.

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Lemniscate and exponential starlikeness of regular Coulomb wave functions

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 3
DOI:: https://doi.org/10.1556/012.2020.57.3.1468

Author:

İbrahim Aktaş

Abstract

In this study, a normalized form of regular Coulomb wave function is considered. By using the differential subordinations method due to Miller and Mocanu, we determine some conditions on the parameters such that the normalized regular Coulomb wave function is lemniscate starlike and exponential starlike in the open unit disk, respectively. In additon, by using the relationship between the regular Coulomb wave function and the Bessel function of the first kind we give some conditions for which the classical Bessel function of the first kind is lemniscate and exponential starlike in the unit disk 𝔻.

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Ninety years of k-tridiagonal matrices

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 3
DOI:: https://doi.org/10.1556/012.2020.57.3.1466

Authors:

Carlos M. da Fonseca

Victor Kowalenko

, and

László Losonczi

Abstract

This survey revisits Jenő Egerváry and Otto Szász’s article of 1928 on trigonometric polynomials and simple structured matrices focussing mainly on the latter topic. In particular, we concentrate on the spectral theory for the first type of the matrices introduced in the article, which are today referred to as k-tridiagonal matrices, and then discuss the explosion of interest in them over the last two decades, most of which could have benefitted from the seminal article, had it not been overlooked.

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On power integral bases for certain pure number fields defined by x ²⁴ – m

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 3
DOI:: https://doi.org/10.1556/012.2020.57.3.1472

Author:

Lhoussain El Fadil

Abstract

Let K = ℚ(α) be a number field generated by a complex root α of a monic irreducible polynomial f(x) = x ²⁴ – m, with m ≠ 1 is a square free rational integer. In this paper, we prove that if m ≡ 2 or 3 (mod 4) and m ≢∓1 (mod 9), then the number field K is monogenic. If m ≡ 1 (mod 4) or m ≡ 1 (mod 9), then the number field K is not monogenic.

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Quadrilateral cell graphs of the normalizer with signature (2,4,∞)

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 3
DOI:: https://doi.org/10.1556/012.2020.57.3.1473

Authors:

Nazli Yazici Gözütok

and

Bahadir Özgür Güler

Abstract

In this study, we investigate suborbital graphs G _u,n of the normalizer Γ_B (N) of Γ₀ (N) in PSL(2, ℝ) for N = 2^α3^β where α = 1, 3, 5, 7, and β = 0 or 2. In these cases the normalizer becomes a triangle group and graphs arising from the action of the normalizer contain quadrilateral circuits. In order to obtain graphs, we first define an imprimitive action of Γ_B (N) on $\overset{\land}{ℚ}$ using the group $Г_{Β}^{+}$ (N) and then obtain some properties of the graphs arising from this action.

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The unit balls of $ℒ (^{n} l_{\infty}^{m})$ and $ℒ_{s} (^{n} l_{\infty}^{m})$

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 3
DOI:: https://doi.org/10.1556/012.2020.57.3.1470

Author:

Sung Guen Kim

Abstract

For n,m≥ 2 this paper is devoted to the description of the sets of extreme and exposed points of the closed unit balls of

ℒ ({}^{n}l_{\infty}^{m})

and

ℒ_{s} ({}^{n}l_{\infty}^{m})

, where

ℒ ({}^{n}l_{\infty}^{m})

is the space of n-linear forms on

ℝ^{m}

with the supremum norm, and

ℒ_{s} ({}^{n}l_{\infty}^{m})

is the subspace of

ℒ ({}^{n}l_{\infty}^{m})

consisting of symmetric n-linear forms. First we classify the extreme points of the unit balls of

ℒ ({}^{n}l_{\infty}^{m})

and

ℒ_{s} ({}^{n}l_{\infty}^{m})

, respectively. We show that ext

B_{ℒ ({}^{n}l_{\infty}^{m})}

⊂ ext

B_{ℒ ({}^{n}l_{\infty}^{m} + 1)}

, which answers the question in [32]. We show that every extreme point of the unit balls of

ℒ ({}^{n}l_{\infty}^{m})

and

ℒ_{s} ({}^{n}l_{\infty}^{m})

is exposed, correspondingly. We also show that

ext B_{ℒ_{s} ({}^{n}l_{\infty}^{2})} = ext B_{ℒ ({}^{n}l_{\infty}^{2})} \cap ℒ_{s} ({}^{n}l_{\infty}^{2}),

ext B_{ℒ_{s} ({}^{2}l_{\infty}^{m + 1})} \neq ext B_{ℒ ({}^{2}l_{\infty}^{m + 1})} \cap ℒ_{s} ({}^{2}l_{\infty}^{m + 1}),

exp B_{ℒ_{S} ({}^{n}l_{\infty}^{2})} = exp B_{ℒ ({}^{n}l_{\infty}^{2})} \cap ℒ_{s} ({}^{n}l_{\infty}^{2})

and $exp B_{ℒ_{s} ({}^{2}l_{\infty}^{m + 1})} \neq exp B_{ℒ ({}^{2}l_{\infty}^{m + 1})} \cap ℒ_{s} ({}^{2}l_{\infty}^{m + 1}),$

which answers the questions in [31].

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Descartes’ rule of signs, Rolle’s theorem and sequences of compatible pairs

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 2
DOI:: https://doi.org/10.1556/012.2020.57.2.1463

Authors:

Hassen Cheriha

Yousra Gati

, and

Vladimir Petrov Kostov

Abstract

Consider the sequence s of the signs of the coefficients of a real univariate polynomial P of degree d. Descartes’ rule of signs gives compatibility conditions between s and the pair (r ⁺ ,r ⁻), where r ⁺ is the number of positive roots and r ⁻ the number of negative roots of P. It was recently asked if there are other compatibility conditions, and the answer was given in the form of a list of incompatible triples (s; r ⁺ ,r ⁻) which begins at degree d = 4 and is known up to degree 8. In this paper we raise the question of the compatibility conditions for $(s; r_{0}^{+}, r_{0}^{-}; r_{1}^{+}, r_{1}^{-}; \dots; r_{d - 1}^{+}, r_{d - 1}^{-})$ , where $r_{i}^{+}$ (resp. $r_{i}^{-}$ ) is the number of positive (resp. negative) roots of the i-th derivative of P. We prove that up to degree 5, there are no other compatibility conditions than the Descartes conditions, the above recent incompatibilities for each i, and the trivial conditions given by Rolle’s theorem.

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A note on the ternary purely exponential diophantine equation A ^x + B ^y = C ^z with A + B = C ²

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 2
DOI:: https://doi.org/10.1556/012.2020.57.2.1457

Authors:

Elif kizildere

Maohua le

, and

Gökhan Soydan

Abstract

Let l,m,r be fixed positive integers such that 2 $∤$ | l, 3 $∤$ lm, l > r and 3 | r. In this paper, using the BHV theorem on the existence of primitive divisors of Lehmer numbers, we prove that if min{rlm ² − 1,(l − r)lm ² + 1} > 30, then the equation (rlm ² − 1)^x + ((l − r)lm ² + 1)^y = (lm)^z has only the positive integer solution (x,y,z) = (1,1,2).

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Numerical solution of linear differential equations by Walsh polynomials approach

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 2
DOI:: https://doi.org/10.1556/012.2020.57.2.1459

Authors:

György Gát

and

Rodolfo Toledo

Abstract

In 1975 C. F. Chen and C. H. Hsiao established a new procedure to solve initial value problems of systems of linear differential equations with constant coefficients by Walsh polynomials approach. However, they did not deal with the analysis of the proposed numerical solution. In a previous article we study this procedure in case of one equation with the techniques that the theory of dyadic harmonic analysis provides us. In this paper we extend these results through the introduction of a new procedure to solve initial value problems of differential equations with not necessarily constant coefficients.

Open access

On sharpening of inequalities for a class of polynomials satisfying $p (z) \equiv z^{n} p (1 / z)$

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 2
DOI:: https://doi.org/10.1556/012.2020.57.2.1461

Authors:

Ritu Dhankhar

Narendra Kumar Govil

, and

Prasanna Kumar

Abstract

Let $p (z) = \sum_{j = 0}^{n} a_{j} z^{j}$ be a polynomial of degree n. Further, let $M (p, R) = \max_{| z | = R \geq 1} | p (z) |,$ and $‖ p ‖ = M (p, 1)$ . Then according to the well-known Bernstein inequalities, we have $‖ p^{'} ‖ \leq n ‖ p ‖$ and $M (p, R) \leq R^{n} ‖ p ‖$ . It is an open problem to obtain inequalities analogous to these inequalities for the class of polynomials satisfying p(z) ≡ z ⁿ p(1/z). In this paper we obtain some inequalites in this direction for polynomials that belong to this class and have all their coefficients in any sector of opening γ, where 0 $\leq_$ γ < π. Our results generalize and sharpen several of the known results in this direction, including those of Govil and Vetterlein [3], and Rahman and Tariq [12]. We also present two examples to show that in some cases the bounds obtained by our results can be considerably sharper than the known bounds.

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On star Lindelöf spaces

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 2
DOI:: https://doi.org/10.1556/012.2020.57.2.1462

Authors:

Wei-Feng Xuan

and

Yan-Kui Song

Abstract

In this paper, we prove that if X is a space with a regular G _δ-diagonal and X ² is star Lindelöf then the cardinality of X is at most 2^c. We also prove that if X is a star Lindelöf space with a symmetric g-function such that $\cap$ {g ²(n, x): n ∈ ω} = {x} for each x ∈ X then the cardinality of X is at most 2^c. Moreover, we prove that if X is a star Lindelöf Hausdorff space satisfying Hψ(X) = κ then e(X) $≦$ 2^2κ; and if X is Hausdorff and we(X) = Hψ(X) = κsubset of a space then e(X) $≦$ 2^κ. Finally, we prove that under V = L if X is a first countable DCCC normal space then X has countable extent; and under MA+¬CH there is an example of a first countable, DCCC and normal space which is not star countable extent. This gives an answer to the Question 3.10 in Spaces with property (DC(ω ₁)), Comment. Math. Univ. Carolin., 58(1) (2017), 131-135.

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Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 2
DOI:: https://doi.org/10.1556/012.2020.57.2.1454

Authors:

Gert Vegter

and

Mathijs Wintraecken

Abstract

Fejes Tóth [3] studied approximations of smooth surfaces in three-space by piecewise flat triangular meshes with a given number of vertices on the surface that are optimal with respect to Hausdorff distance. He proves that this Hausdorff distance decreases inversely proportional with the number of vertices of the approximating mesh if the surface is convex. He also claims that this Hausdorff distance is inversely proportional to the square of the number of vertices for a specific non-convex surface, namely a one-sheeted hyperboloid of revolution bounded by two congruent circles. We refute this claim, and show that the asymptotic behavior of the Hausdorff distance is linear, that is the same as for convex surfaces.

Open access

Some properties of harmonic numbers

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 2
DOI:: https://doi.org/10.1556/012.2020.57.2.1458

Authors:

Bing-Ling Wu

and

Xiao-Hui Yan

Abstract

Let H _n be the n-th harmonic number and let v _n be its denominator. It is known that v _n is even for every integer $n \underset{=}{>} 2$ . In this paper, we study the properties of H _n and prove that for any integer n, v _n = e ^n(1+o(1)). In addition, we obtain some results of the logarithmic density of harmonic numbers.

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Some remarks on the midrange crossing constant

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 2
DOI:: https://doi.org/10.1556/012.2020.57.2.1453

Authors:

Éva Czabarka

Inne Singgih

Laszlό Székely

, and

Zhiyu Wang

Abstract

We verify an upper bound of Pach and Tóth from 1997 on the midrange crossing constant. Details of their $\frac{8}{9 π^{2}}$ upper bound have not been available. Our verification is different from their method and hinges on a result of Moon from 1965. As Moon’s result is optimal, we raise the question whether the midrange crossing constant is $\frac{8}{9 π^{2}}$ .

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Zeros of the Riemann zeta-function in the discrete universality of the Hurwitz zeta-function

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 2
DOI:: https://doi.org/10.1556/012.2020.57.2.1460

Author:

Antanas Laurinčikas

Abstract

Let 0 < γ ₁ < γ ₂ < ··· ⩽ ··· be the imaginary parts of non-trivial zeros of the Riemann zeta-function. In the paper, we consider the approximation of analytic functions by shifts of the Hurwitz zeta-function ζ(s + iγ _k h, α), h > 0, with parameter α such that the set {log(m + α): m ∈ $ℕ_{0}$ } is linearly independent over the field of rational numbers. For this, a weak form of the Montgomery conjecture on the pair correlation of {γ _k} is applied.

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Characterization of automorphisms of twisted tensor biproducts

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 1
DOI:: https://doi.org/10.1556/012.2020.57.1.1451

Authors:

Wang Xing

Chen Quanguo

, and

Wang Dingguo

Abstract

We study certain subgroups of the full group of Hopf algebra automorphisms of twisted tensor biproducts.

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The Dirichlet problem for the uniformly elliptic equation in generalized weighted Morrey spaces

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 1
DOI:: https://doi.org/10.1556/012.2020.57.1.1449

Authors:

Tahir S. Gadjiev

Vagif S. Guliyev

, and

Konul G. Suleymanova

Abstract

In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class A_p by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝ ⁿ are obtained.

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The first cohomology group of some operator algebras on Hilbert C*-modules

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 1
DOI:: https://doi.org/10.1556/012.2020.57.1.1455

Authors:

Hoger Ghahramani

and

Saman Sattari

Abstract

Let X be a Hilbert C*-module over a C*-algebra B. In this paper we introduce two classes of operator algebras on the Hilbert C*-module X called operator algebras with property $k$ and operator algebras with property ℤ, and we study the first (continuous) cohomology group of them with coefficients in various Banach bimodules under several conditions on B and X. Some of our results generalize the previous results. Also we investigate some properties of these classes of operator algebras.

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Integral bases of pure fields with square-free parameter

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 1
DOI:: https://doi.org/10.1556/012.2020.57.1.1450

Author:

László Remete

Abstract

Let m ≠ 0, ±1 and n ≥ 2 be integers. The ring of algebraic integers of the pure fields of type $ℚ (\frac{n}{m})$ is explicitly known for n = 2, 3,4. It is well known that for n = 2, an integral basis of the pure quadratic fields can be given parametrically, by using the remainder of the square-free part of m modulo 4. Such characterisation of an integral basis also exists for cubic and quartic pure fields, but for higher degree pure fields there are only results for special cases.

In this paper we explicitly give an integral basis of the field $ℚ (\frac{n}{m})$ , where m ≠ ±1 is square-free. Furthermore, we show that similarly to the quadratic case, an integral basis of $ℚ (\frac{n}{m})$ is repeating periodically in m with period length depending on n.

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Jordan's totient function and trigonometric sums

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 1
DOI:: https://doi.org/10.1556/012.2020.57.1.1452

Author:

Wenchang Chu

Abstract

Two classes of trigonometric sums about integer powers of secant function are evaluated that are closely related to Jordan's totient function.

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An L-function free proof of Hua's Theorem on sums of five prime squares

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 1
DOI:: https://doi.org/10.1556/012.2020.57.1.1456

Author:

Claus Bauer

Abstract

We provide a new proof of Hua's result that every sufficiently large integer N ≡ 5 (mod 24) can be written as the sum of the five prime squares. Hua's original proof relies on the circle method and uses results from the theory of L-functions. Here, we present a proof based on the transference principle first introduced in[5]. Using a sieve theoretic approach similar to ([10]), we do not require any results related to the distributions of zeros of L- functions. The main technical difficulty of our approach lies in proving the pseudo-randomness of the majorant of the characteristic function of the W-tricked primes which requires a precise evaluation of the occurring Gaussian sums and Jacobi symbols.

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Character varieties of even classical pretzel knots

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 4
DOI:: https://doi.org/10.1556/012.2019.56.4.1439

Author:

Haimiao Chen

Abstract

For each even classical pretzel knot P(2k ₁ + 1, 2k ₂ + 1, 2k ₃), we determine the character variety of irreducible SL (2, ℂ)-representations, and clarify the steps of computing its A-polynomial.

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A Construction of Cohen-Macaulay Graphs

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 4
DOI:: https://doi.org/10.1556/012.2019.56.4.1437

Authors:

Safyan Ahmad

and

Shamsa Kanwal

Abstract

We present a technique to construct Cohen–Macaulay graphs from a given graph; if this graph fulfills certain conditions. As a consequence, we characterize Cohen–Macaulay paths.

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Domain representable Lindelöf spaces are cofinally Polish

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 4
DOI:: https://doi.org/10.1556/012.2019.56.4.1442

Author:

Vladimir V. Tkachuk

Abstract

We prove that, for any cofinally Polish space X, every locally finite family of non-empty open subsets of X is countable. It is also established that Lindelöf domain representable spaces are cofinally Polish and domain representability coincides with subcompactness in the class of σ-compact spaces. It turns out that, for a topological group G whose space has the Lindelöf Σ-property, the space G is domain representable if and only if it is Čech-complete. Our results solve several published open questions.

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Korselt rational bases of prime powers

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 4
DOI:: https://doi.org/10.1556/012.2019.56.4.1444

Author:

Nejib Ghanmi

Abstract

Let N be a positive integer, $A$ be a subset of ℚ and $α = \frac{α_{1}}{α_{2}} \in A \ {0, N}$ . N is called an α-Korselt number (equivalently α is said an N-Korselt base) if α ₂ p − α ₁ divides α ₂ N − α ₁ for every prime divisor p of N. By the Korselt set of N over $A$ , we mean the set $A - K S (N)$ of all $α \in A \ {0, N}$ such that N is an α-Korselt number.

In this paper we determine explicitly for a given prime number q and an integer l ∈ ℕ \{0, 1}, the set $A - K S (q^{l})$ and we establish some connections between the q^l -Korselt bases in ℚ and others in ℤ. The case of $A = ℚ \cap [- 1, 1 [$ is studied where we prove that $(ℚ \cap [- 1, 1 [) - K S (q^{l})$ is empty if and only if l = 2.

Moreover, we show that each nonzero rational α is an N-Korselt base for infinitely many numbers N = q^l where q is a prime number and l ∈ ℕ.

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Lemniscate convexity of generalized Bessel functions

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 4
DOI:: https://doi.org/10.1556/012.2019.56.4.1445

Authors:

Vibha Madaan

Ajay Kumar

, and

V. Ravichandran

Abstract

Sufficient conditions on associated parameters p, b and c are obtained so that the generalized and “normalized” Bessel function u_p (z) = u_p,b,c (z) satisfies the inequalities ∣(1 + (zu″ _p (z)/u′ _p (z)))² − 1∣ < 1 or ∣((zu _p(z))′/u_p (z))² − 1∣ < 1. We also determine the condition on these parameters so that $- (4 (p + (b + 1) / 2) / c) u_{p}^{'} (x) ≺ \sqrt{1 + z}$ . Relations between the parameters μ and p are obtained such that the normalized Lommel function of first kind h_μ,p (z) satisfies the subordination $1 + (z h_{μ, p}^{''} (z) / h_{μ, q}^{'} (z)) ≺ \sqrt{1 + z}$ . Moreover, the properties of Alexander transform of the function h_μ,p (z) are discussed.

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On exponential decay of the variance of BLUE for the mean of a stationary sequence

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 4
DOI:: https://doi.org/10.1556/012.2019.56.4.1448

Authors:

Nikolay Babayan

and

Mamikon S. Ginovyan

Abstract

In this paper, we obtain necessary as well as sufficient conditions for exponential rate of decrease of the variance of the best linear unbiased estimator (BLUE) for the unknown mean of a stationary sequence possessing a spectral density. In particular, we show that a necessary condition for variance of BLUE to decrease to zero exponentially is that the spectral density vanishes on a set of positive Lebesgue measure in any vicinity of zero.

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On the multi-dimensional modal logic of substitutions

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 4
DOI:: https://doi.org/10.1556/012.2019.56.4.1447

Authors:

Tarek Sayed Ahmed

and

Mohammad Assem Mahmoud

Abstract

We prove completeness, interpolation, decidability and an omitting types theorem for certain multi-dimensional modal logics where the states are not abstract entities but have an inner structure. The states will be sequences. Our approach is algebraic addressing varieties generated by complex algebras of Kripke semantics for such logics. The algebras dealt with are common cylindrification free reducts of cylindric and polyadic algebras. For finite dimensions, we show that such varieties are finitely axiomatizable, have the super amalgamation property, and that the subclasses consisting of only completely representable algebras are elementary, and are also finitely axiomatizable in first order logic. Also their modal logics have an N P complete satisfiability problem. Analogous results are obtained for infinite dimensions by replacing finite axiomatizability by finite schema axiomatizability.

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Perfect Pell and Pell–Lucas numbers

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 4
DOI:: https://doi.org/10.1556/012.2019.56.4.1440

Authors:

Jhon J. Bravo

and

Florian Luca

Abstract

The Pell sequence ${(P_{n})}_{n = 0}^{\infty}$ is given by the recurrence P_n = 2P_n ₋₁ + P_n ₋₂ with initial condition P ₀ = 0, P ₁ = 1 and its associated Pell-Lucas sequence ${(Q_{n})}_{n = 0}^{\infty}$ is given by the same recurrence relation but with initial condition Q ₀ = 2, Q ₁ = 2. Here we show that 6 is the only perfect number appearing in these sequences. This paper continues a previous work that searched for perfect numbers in the Fibonacci and Lucas sequences.

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A remark on large gaps between primes in arithmetic progressions

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 4
DOI:: https://doi.org/10.1556/012.2019.56.4.1443

Author:

Deniz Ali Kaptan

Abstract

We record an implication between a recent result due to Li, Pratt and Shakan and large gaps between arithmetic progressions.

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Ruin probability for discrete risk processes

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 4
DOI:: https://doi.org/10.1556/012.2019.56.4.1441

Author:

Ivana Geček Tuden

Abstract

We study the discrete time risk process modelled by the skip-free random walk and derive results connected to the ruin probability and crossing a fixed level for this type of process. We use the method relying on the classical ballot theorems to derive the results for crossing a fixed level and compare them to the results known for the continuous time version of the risk process. We generalize this model by adding a perturbation and, still relying on the skip-free structure of that process, we generalize the previous results on crossing the fixed level for the generalized discrete time risk process. We further derive the famous Pollaczek-Khinchine type formula for this generalized process, using the decomposition of the supremum of the dual process at some special instants of time.

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Stronger forms of sensitivity on product dynamical system via Furstenberg families

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 4
DOI:: https://doi.org/10.1556/012.2019.56.4.1446

Authors:

Rahul Thakur

and

Ruchi Das

Abstract

In this paper, it has been investigated that how various stronger notions of sensitivity like 𝓕-sensitive, multi-𝓕-sensitive, (𝓕₁, 𝓕₂)-sensitive, etc., where 𝓕, 𝓕₁, 𝓕₂ are Furstenberg families, are carried over to countably infinite product of dynamical systems having these properties and vice versa. Similar results are also proved for induced hyperspaces.

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A variant of the Fejér–Jackson inequality

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 4
DOI:: https://doi.org/10.1556/012.2019.56.4.1438

Authors:

Horst Alzer

and

Man Kam Kwong

Abstract

We prove: For all natural numbers n and real numbers x ∈ [0, π] we have $- \frac{5}{48} \sqrt{130 - 58 \sqrt{5}} \leq \sum_{k = 1}^{n} {(- 1)}^{k + 1} (\frac{\sin ((2 k - 1) x)}{2 k - 1} + \frac{\sin (2 k x)}{2 k})$ .

The sign of equality holds if and only if n = 2 and x = 4π/5.

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Cohomology of the vector fields lie algebras on ℝℙ¹ acting on bilinear differential operators

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 3
DOI:: https://doi.org/10.1556/012.2019.56.3.1433

Author:

Abdaoui Meher

Abstract

Let Vect (ℝℙ¹) be the Lie algebra of smooth vector fields on ℝℙ¹. In this paper, we classify $a f f (1)$ -invariant linear differential operators from Vect (ℝℙ¹) to $D_{λ, μ; ν}$ vanishing on $a f f (1)$ , where $D_{λ, μ; ν} : = {Hom}_{diff} (ℱ_{λ} \otimes ℱ_{μ}; ℱ_{ν})$ is the space of bilinear differential operators acting on weighted densities. This result allows us to compute the first differential $a f f (1)$ -relative cohomology of Vect (ℝℙ¹) with coefficients in $D_{λ, μ; ν}$ .

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Counting surface branched covers

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 3
DOI:: https://doi.org/10.1556/012.2019.56.3.1431

Authors:

Carlo Petronio

and

Filippo Sarti

Abstract

To a branched cover f between orientable surfaces one can associate a certain branch datum $D (f)$ , that encodes the combinatorics of the cover. This $D (f)$ satisfies a compatibility condition called the Riemann-Hurwitz relation. The old but still partly unsolved Hurwitz problem asks whether for a given abstract compatible branch datum $D$ there exists a branched cover f such that $D (f) = D$ . One can actually refine this problem and ask how many these f's exist, but one must of course decide what restrictions one puts on such f’s, and choose an equivalence relation up to which one regards them. As it turns out, quite a few natural choices for this relation are possible. In this short note we carefully analyze all these choices and show that the number of actually distinct ones is only three. To see that these three choices are indeed different from each other we employ Grothendieck's dessins d'enfant.

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Good congruences on abundant semigroups with quasi-ideal adequate transversals

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 3
DOI:: https://doi.org/10.1556/012.2019.56.3.1434

Author:

Aifa Wang

Abstract

The aim of this paper is to study the congruences on abundant semigroups with quasi-ideal adequate transversals. The good congruences on an abundant semigroup with a quasi-ideal adequate transversal S° are described by the equivalence triple abstractly which consists of equivalences on the structure component parts I, S° and Λ. Also, it is shown that the set of all good congruences on this kind of semigroup forms a complete lattice.

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Monomorphisms in categories of firm acts

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 3
DOI:: https://doi.org/10.1556/012.2019.56.3.1432

Authors:

Valdis Laan

and

Ülo Reimaa

Abstract

We prove that in the category of firm acts over a firm semigroup monomorphisms co-incide with regular monomorphisms and we give an example of a non-injective monomorphism in this category. We also study conditions under which monomorphisms are injective and we prove that the lattice of subobjects of a firm act over a firm semigroup is isomorphic to the lattice unitary subacts of that act.

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On the problem of Pillai with Padovan numbers and powers of 3

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 3
DOI:: https://doi.org/10.1556/012.2019.56.3.1435

Author:

Mahadi Ddamulira

Abstract

Let {P _n }_n≥0 be the sequence of Padovan numbers defined by P ₀ = 0, P ₁ = 1, P ₂ = 1, and P_n ₊₃ = P_n ₊₁ + P_n for all n ≥ 0. In this paper, we find all integers c admitting at least two representations as a difference between a Padovan number and a power of 3.

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Pre-Schwarzian norm for linear operators of uniformly convex functions of order α and type β

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 3
DOI:: https://doi.org/10.1556/012.2019.56.3.1429

Authors:

Jacek Dziok

and

Hanaa M. Zayed

Abstract

By making use of the pre-Schwarzian norm given by

‖ f ‖ = \sup_{z \in U} (1 - | z |^{2}) | \frac{f^{''} (z)}{f^{'} (z)} |,

we obtain such norm estimates for Hohlov operator of functions belonging to the class of uniformly convex functions of order α and type β. We also employ an entirely new method to generalize and extend the results of Theorems 1, 2 and 3 in [3]. Finally, some inequalities concerning the norm of the pre-Schwarzian derivative for Dziok-Srivastava operator are also considered.

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Various notions of represetability for cylindric and polyadic algebras

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 3
DOI:: https://doi.org/10.1556/012.2019.56.3.1436

Author:

Tarek Sayed Ahmed

Abstract

For β an ordinal, let PEA_β (SetPEA_β) denote the class of polyadic equality (set) algebras of dimension β. We show that for any infinite ordinal α, if $A \in {PEA}_{α}$ is atomic, then for any n < ω, the n-neat reduct of $A$ , in symbols $ℜ r_{n} A \to B$ , is a completely representable PEA_n (regardless of the representability of $A$ ). That is to say, for all non-zero $a \in ℜ r_{n} A$ , there is a $B_{a} \in {SetPEA}_{n}$ and a homomorphism $f_{a} : ℜ r_{n} A \to B$ such that f_a (a) ≠ 0 and $f_{a} (\sum X) = \cup_{x \in X} f_{a} (x)$ for any $X \underset{=}{\subset} A$ for which $\sum X$ exists. We give new proofs that various classes consisting solely of completely representable algebras of relations are not elementary; we further show that the class of completely representable relation algebras is not closed under ≡_∞,ω. Various notions of representability (such as ‘satisfying the Lyndon conditions’, weak and strong) are lifted from the level of atom structures to that of atomic algebras and are further characterized via special neat embeddings. As a sample, we show that the class of atomic CA_ns satisfying the Lyndon conditions coincides with the class of atomic algebras in ElS _c Nr _n CA _ω, where El denotes ‘elementary closure’ and S _c is the operation of forming complete subalgebras.

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Almost sure central limit theorems for weighted dependent sequences

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 2
DOI:: https://doi.org/10.1556/012.2019.56.2.1426

Author:

Khurelbaatar Gonchigdanzan

Abstract

Let {X_n : n ≧ 1} be a sequence of dependent random variables and let {w_nk : 1 ≦ k ≦ n, n ≧ 1} be a triangular array of real numbers. We prove the almost sure version of the CLT proved by Peligrad and Utev [7] for weighted partial sums of mixing and associated sequences of random variables, i.e.

\lim_{n \to \infty} \frac{1}{\log n} \sum_{k = 1}^{n} \frac{1}{k} I (\sum_{i = 1}^{k} w_{k i} X_{i} ≦ x) = \frac{1}{\sqrt{2 π}} \int_{- \infty}^{x} e^{- \frac{1}{2} t^{2}} d t a .s ..

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Associative rings in which nilpotents form an ideal

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 2
DOI:: https://doi.org/10.1556/012.2019.56.2.1428

Author:

Orest D. Artemovych

Abstract

It is shown that if N(R) is a Lie ideal of R (respectively Jordan ideal and R is 2-torsion-free), then N(R) is an ideal. Also, it is presented a characterization of Noetherian NR rings with central idempotents (respectively with the commutative set of nilpotent elements, the Abelian unit group, the commutative commutator set).

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Commutators of sublinear operators in grand morrey spaces

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 2
DOI:: https://doi.org/10.1556/012.2019.56.2.1425

Authors:

Vakhtang Kokilashvili

Alexander Meskhi

, and

Humberto Rafeiro

Abstract

In this paper we establish the boundedness of commutators of sublinear operators in weighted grand Morrey spaces. The sublinear operators under consideration contain integral operators such as Hardy-Littlewood and fractional maximal operators, Calderón-Zygmund operators, potential operators etc. The operators and spaces are defined on quasi-metric measure spaces with doubling measure.

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Eigenstructure for binomial operators *

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 2
DOI:: https://doi.org/10.1556/012.2019.56.2.1423

Authors:

Shifen Wang

and

Chungou Zhang

Abstract

In this article, the eigenvalues and eigenvectors of positive binomial operators are presented. The results generalize the previously obtained ones related to Bernstein operators. Illustrative examples are supplied.

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Groups with restrictions on proper uncountable subgroups

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 2
DOI:: https://doi.org/10.1556/012.2019.56.2.1427

Authors:

Francesco De Giovanni

and

Marco Trombetti

Abstract

A group G is called metahamiltonian if all its non-abelian subgroups are normal. The aim of this paper is to investigate the structure of uncountable groups of cardinality ℵ in which all proper subgroups of cardinality ℵ are metahamiltonian. It is proved that such a group is metahamiltonian, provided that it has no simple homomorphic images of cardinality ℵ. Furthermore, the behaviour of elements of finite order in uncountable groups is studied in the second part of the paper.

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The odd Nadarajah-Haghighi family of distributions: properties and applications

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 2
DOI:: https://doi.org/10.1556/012.2019.56.2.1416

Authors:

Abraão D. C. Nascimento

Kássio F. Silva

Gauss M. Cordeiro

Morad Alizadeh

Haitham M. Yousof

, and

G. G. Hamedani

Abstract

We study some mathematical properties of a new generator of continuous distributions called the Odd Nadarajah-Haghighi (ONH) family. In particular, three special models in this family are investigated, namely the ONH gamma, beta and Weibull distributions. The family density function is given as a linear combination of exponentiated densities. Further, we propose a bivariate extension and various characterization results of the new family. We determine the maximum likelihood estimates of ONH parameters for complete and censored data. We provide a simulation study to verify the precision of these estimates. We illustrate the performance of the new family by means of a real data set.

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On quasi-radical of near-ring of polynomials

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 56: Issue 2
DOI:: https://doi.org/10.1556/012.2019.56.2.1430

Authors:

Ebrahim Hashemi

Fatemeh Shokuhifar

, and

Abdollah Alhevaz

Abstract

The intersection of all maximal right ideals of a near-ring N is called the quasi-radical of N. In this paper, first we show that the quasi-radical of the zero-symmetric near-ring of polynomials R ₀[x] equals to the set of all nilpotent elements of R ₀[x], when R is a commutative ring with Nil (R)² = 0. Then we show that the quasi-radical of R ₀[x] is a subset of the intersection of all maximal left ideals of R ₀[x]. Also, we give an example to show that for some commutative ring R the quasi-radical of R ₀[x] coincides with the intersection of all maximal left ideals of R ₀[x]. Moreover, we prove that the quasi-radical of R ₀[x] is the greatest quasi-regular (right) ideal of it.

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