Weighted Young Inequalities for Convolutions

Sufficient conditions for some weighted Young inequalities type are obtained.AMS Subject Classification (1991): 42A85, 42B20, 47G10     

Asymptotics of Differentiated Bernstein Polynomials

It is shown that the m th-order derivative of the n th-order Bernstein polynomial of a function f satisfying a certain Lipschitz condition, can be written for n\rightarrow +∈fty as a singular integral of Gauss—Weierstrass type, m times differentiated (in a certain sense) under the integral sign. The theorem is applied to yield an overdifferentiation formula, involving p times differentiated Bernstein polynomials of functions that are not C ^p . December 1, 1998. Dates revised: July 22, 1999 and January 11, 2000. Date accepted: February 1, 2000.     

Derived Lengths of Solvable Groups Having Five Irreducible Character Degrees I

Let G be a solvable group with five character degrees. We show that the derived length of G is at most 5. This verifies that the Taketa inequality, dl(G)|cd(G)|, is valid for solvable groups with at most five character degrees.     

Bounds for solutions of a differential inequality

This work compares the solutions of an th order differential inequality plus boundary conditions with the solution of the related differential equation with boundary conditions. The differential operator is assumed to be disconjugate. It is proved that under suitable conditions the ratio of these solutions is monotone. The solution of the inequality can be replaced by the corresponding Green's function.

     

Chern-Osserman inequality for minimal surfaces in H

We obtain Chern-Osserman's inequality of a complete properly immersed minimal surface in hyperbolic -space, provided the -norm of the second fundamental form of the surface is finite.

     

On the structure of the class A(ϕ)

In this paper, we study whether the set A(?) is closed under multiplication f · g, where f and g belong to the class A(?). We also study the problem of the existence of a solution of the equation Bx = C (where B,C ∈ A(?) and B ≠ 0) on the set A(?).     

数值积分求解均匀带电圆环平面上的电场分布

本文用数值积分的方法计算椭圆积分，求出在均匀带电圆环平面上的场强与电势．     

Harnack inequality for two‐weight subelliptic p ‐Laplace operators

In this note, we prove a Harnack inequality for two‐weight subelliptic p ‐Laplace operators together with an upper bound of the Harnack constant associated with such inequality. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

关于量子力学的基本原理

文章抽选关于量子力学基本原理的几个题目,包括量子力学与经典物理学的对比、量子概念的产生、薛定谔方程的出现、全同性原理和量子路径积分等,作些说明。目的在于激发读者思考量子力学的本质在哪里。     

Some Hardy Type Inequalities in R~n

Some Hardy type inequalities on the ball and its complementary set in the Euclidean space are established by using the Picone type identity and constructing suitable auxiliary functions.