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# On a second order coercive dirichlet problem with a non-differentiable action functional

Studia Scientiarum Mathematicarum Hungarica
Author: Marek Galewski

Applying certain convexity arguments we investigate the existence of a classical solution for a Dirichlet problem for which the Euler action functional is not necessarily differentiable in the sense of Gâteaux.

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# On semifields of order q 4 with center \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{F}_q$$ \end{document}, admitting a Klein 4-group of automorphisms

Studia Scientiarum Mathematicarum Hungarica
Authors: Mashhour Bani-Ata and Ra’ed Al-Nouty

The aim of this paper is to investigate the semifields of order q 4 over a finite field of order q, q an odd prime power, admitting a Klein 4-group of automorphisms.

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# On the maximal operators of Riesz logarithmic means of Vilenkin-Fourier series

Studia Scientiarum Mathematicarum Hungarica

The main aim of this paper is to investigate (H p, L p) and (H p, L p,∞) type inequalities for maximal operators of Riesz logarithmic means of one-dimensional Vilenkin—Fourier series.

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# Riesz decomposition for super-polyharmonic functions in the punctured unit ball

Studia Scientiarum Mathematicarum Hungarica
Authors: Toshihide Futamura, Yoshihiro Mizuta, and Takao Ohno
We consider a Riesz decomposition theorem for super-polyharmonic functions satisfying certain growth condition on surface integrals in the punctured unit ball. We give a condition that super-polyharmonic functions u have the bound
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$u\left( x \right) = O\left( {\mathcal{R}_2 \left( x \right)} \right),$$ \end{document}
where
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{R}_2$$ \end{document}
denotes the fundamental solution for −Δu in ℝn.
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# On Devaney chaotic generalized shift dynamical systems

Studia Scientiarum Mathematicarum Hungarica
Authors: Fatemah Shirazi, Javad Sarkooh, and Bahman Taherkhani

In the following text we prove that in a generalized shift dynamical system (X Г, σ φ) for infinite countable Г and discrete X with at least two elements the following statements are equivalent:

1. the dynamical system (X Г, σ φ) is chaotic in the sense of Devaney
2. the dynamical system (X Г, σ φ) is topologically transitive
3. the map φ: Г → Г is one to one without any periodic point.
Also for infinite countable Г and finite discrete X with at least two elements (X Г, σ φ) is exact Devaney chaotic, if and only if φ: Г → Г is one to one and φ: Г → Г has niether periodic points nor φ-backwarding infinite sequences.

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# C-coherent rings, C-semihereditary rings and C-regular rings

Studia Scientiarum Mathematicarum Hungarica
Author: Zhanmin Zhu

Let C be a class of some finitely presented left R-modules. A left R-module M is called C-injective, if ExtR 1(C, M) = 0 for each CC. A right R-module M is called C-flat, if Tor1 R(M, C) = 0 for each CC. A ring R is called C-coherent, if every CC is 2-presented. A ring R is called C-semihereditary, if whenever 0 → KPC → 0 is exact, where CC and P is finitely generated projective and K is finitely generated, then K is also projective. A ring R is called C-regular, if whenever P/KC, where P is finitely generated projective and K is finitely generated, then K is a direct summand of P. Using the concepts of C-injectivity and C-flatness of modules, we present some characterizations of C-coherent rings, C-semihereditary rings, and C-regular rings.

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# Bernstein-type operators which preserve exactly two test functions

Studia Scientiarum Mathematicarum Hungarica
Authors: Ovidiu Pop, Dan Bǎrbosu, and Petru Braica

A general class of linear and positive operators dened by nite sum is constructed. Some of their approximation properties, including a convergence theorem and a Voronovskaja-type theorem are established. Next, the operators of the considered class which preserve exactly two test functions from the set {e 0, e 1, e 2} are determined. It is proved that the test functions e 0 and e 1 are preserved only by the Bernstein operators, the test functions e 0 and e 2 only by the King operators while the test functions e 1 and e 2 only by the operators recently introduced by P. I. Braica, O. T. Pop and A. D. Indrea in [4].

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# The beta generalized half-normal geometric distribution

Studia Scientiarum Mathematicarum Hungarica
Authors: Thiago Ramires, Edwin Ortega, Gauss Cordeiro, and Gholamhoss Hamedani

The beta generalized half-normal distribution is commonly used to model lifetimes. We propose a new wider distribution called the beta generalized half-normal geometric distribution, whose failure rate function can be decreasing, increasing or upside-down bathtub. Its density function can be expressed as a linear combination of beta generalzed half-normal density functions. We derive quantile function, moments and generating unction. We characterize the proposed distribution using a simple relationship between wo truncated moments. The method of maximum likelihood is adapted to estimate the model parameters and its potentiality is illustrated with an application to a real fatigue data set. Further, we propose a new extended regression model based on the logarithm of the new distribution. This regression model can be very useful for the analysis of real data and provide more realistic fits than other special regression models.

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# Characterizations of selfadjoint operators

Studia Scientiarum Mathematicarum Hungarica
Authors: Zoltán Sebestyén and Zsigmond Tarcsay

The purpose of this paper is to revise von Neumann’s characterizations of selfadjoint operators among symmetric ones. In fact, we do not assume that the underlying Hilbert space is complex, nor that the corresponding operator is densely defined, moreover, that it is closed. Following Arens, we employ algebraic arguments instead of the geometric approach of von Neumann using the Cayley transform.

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# Comment on the paper of J. Mills: “certain congruences on orthodox semigroups”

Studia Scientiarum Mathematicarum Hungarica
Author: Roman Gigoń

In the paper we give some remarks on the article of Janet Mills. In particular, the proof of Lemma 1.2 (in her work) is incorrect, and so the proof of Theorem 3.5 is not valid, too. Using different methods we show the mentioned theorem. Moreover, we find a new equivalent condition to the statements in Theorem 3.5. In particular, an explicit definition of a new class of orthodox semigroups is introduced.

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