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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
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.
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
Abstract
We verify an upper bound of Pach and Tóth from 1997 on the midrange crossing constant. Details of their
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 + iγ
k
h, α), h > 0, with parameter α such that the set {log(m + α): m ∈
Abstract
We study certain subgroups of the full group of Hopf algebra automorphisms of twisted tensor biproducts.
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.
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
Abstract
Let m ≠ 0, ±1 and n ≥ 2 be integers. The ring of algebraic integers of the pure fields of type
In this paper we explicitly give an integral basis of the field
Abstract
Two classes of trigonometric sums about integer powers of secant function are evaluated that are closely related to Jordan's totient function.
