# Browse

## You are looking at 131 - 140 of 11,145 items for :

• Mathematics and Statistics
• Refine by Access: All Content
Clear All

# On star Lindelöf spaces

Studia Scientiarum Mathematicarum Hungarica
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 2c. We also prove that if X is a star Lindelöf space with a symmetric g-function such that $∩$ {g 2(n, x): nω} = {x} for each xX then the cardinality of X is at most 2c. Moreover, we prove that if X is a star Lindelöf Hausdorff space satisfying (X) = κ then e(X) $≦$ 22κ ; and if X is Hausdorff and we(X) = (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.

Restricted access

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

Studia Scientiarum Mathematicarum Hungarica
Authors:
Gert Vegter
and
Mathijs Wintraecken

## Abstract

Fejes Tóth [] 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
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 $n > = 2$ . 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.

Restricted access

# Some remarks on the midrange crossing constant

Studia Scientiarum Mathematicarum Hungarica
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 $8 9 π 2$ 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 $8 9 π 2$ .

Restricted access

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

Studia Scientiarum Mathematicarum Hungarica
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 + 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.

Restricted access

# Characterization of automorphisms of twisted tensor biproducts

Studia Scientiarum Mathematicarum Hungarica
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.

Restricted access

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

Studia Scientiarum Mathematicarum Hungarica
Authors:
,
Vagif S. Guliyev
, and
Konul G. Suleymanova

## Abstract

In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap 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.

Restricted access

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

Studia Scientiarum Mathematicarum Hungarica
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.

Restricted access

# Integral bases of pure fields with square-free parameter

Studia Scientiarum Mathematicarum Hungarica
Author:
László Remete

## Abstract

Let m ≠ 0, ±1 and n ≥ 2 be integers. The ring of algebraic integers of the pure fields of type $ℚ ( n m )$ 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 $ℚ ( n m )$ , where m ≠ ±1 is square-free. Furthermore, we show that similarly to the quadratic case, an integral basis of $ℚ ( n m )$ is repeating periodically in m with period length depending on n.

Full access

# Jordan's totient function and trigonometric sums

Studia Scientiarum Mathematicarum Hungarica
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.

Restricted access