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# Automorphisms of Finite Order of Soluble Groups of Finite Rank

Studia Scientiarum Mathematicarum Hungarica
Author: Bertram A. F. Wehrfritz

We study the effect on sections of a soluble-by-finite group G of finite rank of an almost fixed-point-free automorphism φ of G of finite order. We also elucidate the structure of G if φ has order 4 and if G is also (torsion-free)-by-finite. The latter extends recent work of Xu, Zhou and Liu.

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# Borel Directions and the Uniqueness of Algebroid Functions Dealing with Multiple Values

Studia Scientiarum Mathematicarum Hungarica
Authors: Yang Tan and Qingcai Zhang

In this paper, we investigate the uniqueness of algebroid functions in angular domain by the method of conformal mapping. We discuss the relations between the Borel directions and uniquenss with the multiple values of algebroid functions and obtain some results which extend some uniqueness results of meromorphic functions to that of algebroid functions.

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# Estimates of Functions with Transformed Double Fourier Series

Studia Scientiarum Mathematicarum Hungarica
Author: Boris V. Simonov

The paper provides a detailed study of inequalities of complete moduli of smoothness of functions with transformed Fourier series by moduli of smoothness of initial functions. Upper and lower estimates of the norms and best approximations of the functions with transformed Fourier series by the best approximations of initial functions are also obtained.

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# Exceptional Set in Waring–Goldbach Problem Involving Squares, Cubes and Sixth Powers

Studia Scientiarum Mathematicarum Hungarica
Authors: Jinjiang Li, Min Zhang, and Haonan Zhao

Let N be a sufficiently large integer. In this paper, it is proved that, with at most O(N 119/270+ s) exceptions, all even positive integers up to N can be represented in the form $p12+p22+p33+p43+p56+p66,$

where p 1 , p 2 , p 3 , p 4 , p 5 , p 6 are prime numbers.

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# Existence Results for a Class of p(x)-Kirchhoff Problems

Studia Scientiarum Mathematicarum Hungarica
Author: Mostafa Allaoui

This paper is concerned with the existence of solutions to a class of p(x)-Kirchhoff-type equations with Robin boundary data as follows:

$−M∫Ω1p(x)∇up(x)dx+∫∂Ωβ(x)p(x)∇up(x)dσdiv(∇up(x)-2∇u)=f(x,u)inΩ,$

Where $β∈L∞(∂Ω)$ and $f:Ω×ℝ→ℝ$ satisfies Carathéodory condition. By means of variational methods and the theory of the variable exponent Sobolev spaces, we establish conditions for the existence of weak solutions.

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# A Note on Weakly 𐒎 -Subgroups

Studia Scientiarum Mathematicarum Hungarica
Author: Changwen Li

The major aim of the note is to give new brief proofs of the results in the paper “The influence of weakly H -subgroups on the structure of finite groups” [Studia Scientiarum Mathematicarum Hungarica, 51 (1), 27–40 (2014)].

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# On the Maximal Operators of T Means with Respect to Walsh–Kaczmarz System

Studia Scientiarum Mathematicarum Hungarica
Authors: Nata Gogolashvili and George Tephnadze

In this paper we prove and discuss some new (Hp, Lp,∞) type inequalities of the maximal operators of T means with monotone coefficients with respect to Walsh–Kaczmarz system. It is also proved that these results are the best possible in a special sense. As applications, both some well-known and new results are pointed out. In particular, we apply these results to prove a.e. convergence of such T means.

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# Sticky Polymatroids on At Most Five Elements

Studia Scientiarum Mathematicarum Hungarica
Author: László Csirmaz

The sticky polymatroid conjecture states that any two extensions of the polymatroid have an amalgam if and only if the polymatroid has no non-modular pairs of flats. We show that the conjecture holds for polymatroids on five or less elements.

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Mathematica Pannonica
Author: Péter Berkics

A linear operator on a Hilbert space $ℍ$, in the classical approach of von Neumann, must be symmetric to guarantee self-adjointness. However, it can be shown that the symmetry could be omitted by using a criterion for the graph of the operator and the adjoint of the graph. Namely, S is shown to be densely defined and closed if and only if $k+l:k,l∈GS∩GS*=ℍ$.

In a more general setup, we can consider relations instead of operators and we prove that in this situation a similar result holds. We give a necessary and sufficient condition for a linear relation to be densely defined and self-adjoint.

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# Conceptions of Topological Transitivity on Symmetric Products

Mathematica Pannonica
Authors: Franco Barragán, Sergio Macías, and Anahí Rojas

Let X be a topological space. For any positive integer n, we consider the n-fold symmetric product of X, ℱn(X), consisting of all nonempty subsets of X with at most n points; and for a given function ƒ : XX, we consider the induced functions ℱn(ƒ): ℱn(X) → ℱn(X). Let M be one of the following classes of functions: exact, transitive, ℤ-transitive, ℤ+-transitive, mixing, weakly mixing, chaotic, turbulent, strongly transitive, totally transitive, orbit-transitive, strictly orbit-transitive, ω-transitive, minimal, I N, T T ++, semi-open and irreducible. In this paper we study the relationship between the following statements: ƒM and ℱn(ƒ) ∈ M.

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