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# Commutators of sublinear operators in grand morrey spaces

Studia Scientiarum Mathematicarum Hungarica
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
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
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
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
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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# On weakly ℌ-embedded subgroups and p-nilpotence of finite groups

Studia Scientiarum Mathematicarum Hungarica

## Abstract

Let G be a finite group and H a subgroup of G. We say that H is an -subgroup of G if NG (H) ∩ HgH for all gG; H is called weakly -embedded in G if G has a normal subgroup K such that HG = HK and HK is an -subgroup of G, where HG is the normal clousre of H in G, i. e., HG = 〈Hg|gG〉. In this paper, we study the p-nilpotence of a group G under the assumption that every subgroup of order d of a Sylow p-subgroup P of G with 1 < d < |P| is weakly -embedded in G. Many known results related to p-nilpotence of a group G are generalized.

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# Polynomial index in discrete valuation rings

Studia Scientiarum Mathematicarum Hungarica
Authors: Mohamed E. Charkani and Abdulaziz Deajim

## Abstract

Let R be a discrete valuation ring, $p$ its nonzero prime ideal, PR[X] a monic irreducible polynomial, and K the quotient field of R. We give in this paper a lower bound for the $p$-adic valuation of the index of P over R in terms of the degrees of the monic irreducible factors of the reduction of P modulo $p$. By localization, the same result holds true over Dedekind rings. As an important immediate application, when the lower bound is greater than zero, we conclude that no root of P generates a power basis for the integral closure of R in the field extension of K defined by P.

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# Rings in which every regular locally principal ideal is projective

Studia Scientiarum Mathematicarum Hungarica
Authors: Rachida El Khalfaoui and Najib Mahdou

## Abstract

In this article, we study the class of rings in which every regular locally principal ideal is projective called LPP-rings. We investigate the transfer of this property to various constructions such as direct products, amalgamation of rings, and trivial ring extensions. Our aim is to provide examples of new classes of commutative rings satisfying the above-mentioned property.

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# Approximation of functions by some exponential operators of max-product type

Studia Scientiarum Mathematicarum Hungarica

## Abstract

In this paper we study the uniform approximation of functions by a generalization of the Picard and Gauss-Weierstrass operators of max-product type in exponential weighted spaces. We estimate the rate of approximation in terms of a suitable modulus of continuity. We extend and improve previous results.

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# Existence and uniqueness of solutions of an A-harmonic elliptic equation

Studia Scientiarum Mathematicarum Hungarica
Author: Mouna Kratou

## Abstract

This paper deals with the existence and uniqueness of weak solution of a problem which involves a class of A-harmonic elliptic equations of nonhomogeneous type. Under appropriate assumptions on the function f, our main results are obtained by using Browder Theorem.

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