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A note on the maximal operators of Vilenkin—Nörlund means with non-increasing coefficients

Studia Scientiarum Mathematicarum Hungarica

In [14] we investigated some Vilenkin—Nörlund means with non-increasing coefficients. In particular, it was proved that under some special conditions the maximal operators of such summabily methods are bounded from the Hardy space H 1/(1+α) to the space weak-L 1/(1+α), (0 < α ≦ 1). In this paper we construct a martingale in the space H 1/(1+α), which satisfies the conditions considered in [14], and so that the maximal operators of these Vilenkin—Nörlund means with non-increasing coefficients are not bounded from the Hardy space H 1/(1+α) to the space L 1/(1+α). In particular, this shows that the conditions under which the result in [14] is proved are in a sense sharp. Moreover, as further applications, some well-known and new results are pointed out.

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On characterizations and infinite divisibility of recently introduced distributions

Studia Scientiarum Mathematicarum Hungarica
Author: G. G. Hamedani

We present here characterizations of the most recently introduced continuous univariate distributions based on: (i) a simple relationship between two truncated moments; (ii) truncated moments of certain functions of the 1th order statistic; (iii) truncated moments of certain functions of the n th order statistic; (iv) truncated moment of certain function of the random variable. We like to mention that the characterization (i) which is expressed in terms of the ratio of truncated moments is stable in the sense of weak convergence. We will also point out that some of these distributions are infinitely divisible via Bondesson’s 1979 classifications.

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On M p -embedded primary subgroups of finite groups

Studia Scientiarum Mathematicarum Hungarica
Authors: Jia Zhang and Long Miao

A subgroup H of G is called M p-embedded in G, if there exists a p-nilpotent subgroup B of G such that H p ∈ Sylp(B) and B is M p-supplemented in G. In this paper, we use M p-embedded subgroups to study the structure of finite groups.

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On the approximation properties of Cesàro means of negative order of Vilenkin—Fourier series

Studia Scientiarum Mathematicarum Hungarica

In this paper we establish approximation properties of Cesàro (C, −α) means with α ∈ (0, 1) of Vilenkin—Fourier series. This result allows one to obtain a condition which is sufficient for the convergence of the means σ n α(f, x) to f(x) in the L p-metric.

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The principal ideal theorem for w-Noetherian rings

Studia Scientiarum Mathematicarum Hungarica
Authors: Huayu Yin and Fanggui Wang

In this paper, we concern the Principal Ideal Theorem (PIT) for w-Noetherian rings. Let R be a w-Noetherian ring and a be a nonzero nonunit element of R. If p is a prime ideal of R minimal over (a), then ht p ≦ 1.

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Approximation by k-th order modifications of Szász—Mirakyan operators

Studia Scientiarum Mathematicarum Hungarica
Authors: Tuncer Acar, Ali Aral, and Ioan Raşa

In this paper, we study the k-th order Kantorovich type modication of Szász—Mirakyan operators. We first establish explicit formulas giving the images of monomials and the moments up to order six. Using this modification, we present a quantitative Voronovskaya theorem for differentiated Szász—Mirakyan operators in weighted spaces. The approximation properties such as rate of convergence and simultaneous approximation by the new constructions are also obtained.

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Characterization of stably simple curve singularities

Studia Scientiarum Mathematicarum Hungarica
Authors: Muhammad Ahsan Binyamin, Junaid Alam Khan, Faira Kanwal Janjua, and Naveed Hussain

In this article we characterize the classification of stably simple curve singularities given by V. I. Arnold, in terms of invariants. On the basis of this characterization we describe an implementation of a classifier for stably simple curve singularities in the computer algebra system SINGULAR.

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On the convergence of double Fourier integrals of functions of bounded variation on ℝ2

Studia Scientiarum Mathematicarum Hungarica
Authors: Bhikha Lila Ghodadra and Vanda Fülöp

We investigate the pointwise and uniform convergence of the symmetric rectangular partial (also called Dirichlet) integrals of the double Fourier integral of a function that is Lebesgue integrable and of bounded variation over ℝ2. Our theorem is a two-dimensional extension of a theorem of Móricz (see Theorem 3 in [10]) concerning the single Fourier integrals, which is more general than the two-dimensional extension given by Móricz himself (see Theorem 3 in [11]).

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On the refinements of Hadamard-type inequalities and their applications for cubature formulas

Studia Scientiarum Mathematicarum Hungarica
Author: Kai-Chen Hsu

In this paper, we shall establish some Hadamard-type inequalities for differentiable coordinated convex functions in a rectangle from the plane in two variables. Through these inequalities, more precise estimates could be obtained. Some examples and applications to cubature formulas are also provided.

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Yet some more non-finite axiomatizability results for algebras of relations and ways to avoid them

Studia Scientiarum Mathematicarum Hungarica
Author: Tarek Sayed Ahmed

Let α be an infinite ordinal. Let RCAα denote the variety of representable cylindric algebras of dimension α. Modifying Andréka’s methods of splitting, we show that the variety RQEAα of representable quasi-polyadic equality algebras of dimension α is not axiomatized by a set of universal formulas containing only finitely many variables over the variety RQAα of representable quasi-polyadic algebras of dimension α. This strengthens a seminal result due to Sain and Thompson, answers a question posed by Andréka, and lifts to the transfinite a result of hers proved for finite dimensions > 2. Using the modified method of splitting, we show that all known complexity results on universal axiomatizations of RCAα (proved by Andréka) transfer to universal axiomatizations of RQEAα. From such results it can be inferred that any algebraizable extension of L ω,ω is severely incomplete if we insist on Tarskian square semantics. Ways of circumventing the strong non-negative axiomatizability results hitherto obtained in the first part of the paper, such as guarding semantics, and /or expanding the signature of RQEAω by substitutions indexed by transformations coming from a finitely presented subsemigroup of (ω ω, ○) containing all transpositions and replacements, are surveyed, discussed, and elaborated upon.

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