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ON A GENERALIZED WARING PROBLEM II
2007/12/12
<正> Introduction.Let P(h) be an integral-valued polynomial of theK-th degree and with positive first coefficient,Let G(P(h.)) be theleast value of integers such that the Diophantine equation
The Fractional Derives of a Fractal Function
Weierstrass function fractional derivatives dimensions of graphs of functions
2007/12/12
The present paper investigates the fractional derivatives of Weierstrass function, proves that there exists some linear connection between the order of the fractional derivatives and the dimension of ...
具二次约束的最小平方解问题
2007/12/12
本文用广义逆矩阵与正交投影算子的方法,讨论了下述具二次约束的最小平方解问题:$\|A_x-b\|\leq \tau,\|C_x-d\|=\min$,研究了问题的可解性条件与存在显然解的判别方法,在不存在显然解的正则情形下,建立了上述问题解唯一的必要充分条件,给出了存在定理,解法与解的基本结构等理论结果,最后进行了一些讨论.
对偶根和F.A.SZASZ问题21
2007/12/11
本文证明了根 R 的补根是由所有非 R-半单的亚直既约环确定的上根.对半遗传根,给出了补根的进一步刻划,证明了遗传根是对偶根,当且仅当它是由一个亚直既约环环类确定的上根,每个遗传对偶根或者是超幂零的,或者是次幂等的.
On the Semivalues and the Least Square Values, Average per capita formulas and relationships
Shapley value Semivalues Least Square Values Average per capita formulas Banzhaf value
2007/12/11
In this paper, it is shown that both the Semivalues and the Least Square Values of cooperative transferable utilities games can be expressed in terms of $n^2$ averages of values of the characteristic ...
Poisson Equation on Some Complete Noncompact Manifolds
Poisson equation heat equation Green's function
2007/12/11
We study the Poisson equation on some complete noncompact manifolds with asymptotically nonnegative curvature. We will also study the limiting behavior of the nonhomogeneous heat equation on some comp...
Mean value on the difference between a quadratic residue and its inverse modulo p
An integer and its inverse Bernoulli numbers Cochrane sums
2007/12/11
The main purpose of this paper is to use the generalized Bernoulli numbers, Gauss sums and the mean value theorems of Dirichlet $L$-functions to study the asymptotic property of the difference between...
Positive Solutions for Second-Order $m$-Point Boundary Value Problems on Time Scales
time scales positive solution Schauder fixed point theorem
2007/12/11
Let $\Bbb{T}$ be a time scale such that $0,T\in \Bbb{T}$. By means of the Schauder fixed point theorem and analysis method, we establish some existence criteria for positive solutions of the $m$-point...
Pseudo almost periodic solutions of a singularly perturbed differential equation with piecewise constant argument
Singular perturbation Pseudo-almost periodic solutions Pseudo-almost periodic sequences Piecewise constant argument
2007/12/11
Under suitable assumptions, the existence and the uniqueness of the pseudo-almost periodic solution for a singularly perturbed differential equation with piecewise constant argument are obtained. In a...
Some Results Related to a Question of Hinkkanen
meromorphic functions uniqueness sharing values
2007/12/11
In this paper, we prove several results concerning meromorphic functions $f$ and $g$ of hyper-order less than one such that $f^{(j)}$ and $g^{(j)}$ have the same zeros and poles for $j = 0, 1, 2.$ We ...
In this paper, the authors study some properties of Littlewood--Paley $g$-functions $g_\psi(f)$, Lusin area functions $S_{\psi,\alpha}(f)$ and Littlewood--Paley $g_{\psi, \lambda}^*(f)$ functions defi...
On Bounded Variation Functions by General MKZD Operators
approximation by positive operators rate of convergence degree of approximation functions of bounded variation total variation
2007/12/11
In this paper, we study the rate of convergence for functions of bounded variation for the recently introduced Bzier variant of the Meyer--Knig--Zeller--Durrmeyer operators.
Interpolation of Ideal Measures by Abstract $K$ and $J$ Spaces
real interpolation ideal measures operator ideals shift operators
2007/12/10
We work with the abstract K and J interpolation method generated by a sequence lattice $\Gamma$. We investigate the deviation of an interpolated operator from a given operator ideal by establishing fo...
Normal Families and Uniqueness of Entire Functions and Their Derivatives
entire function normal family unicity theorem
2007/12/10
Let $f$ be a nonconstant entire function; let $k\ge 2$ be a positive integer; and let $a$ be a nonzero complex number. If $f(z)=a$ $\Longrightarrow $ $f'(z)=a$, and $f'(z)=a$ $\Longrightarrow $ $f^{(k...
典型 Gibbs 态与可逆测度
典型 Gibbs 态 可逆测度
2007/12/10
本文给出[1]提出的一类一般的无穷质点系的随机演化模型作为 Feller 过程的一个充分条件,证明了在某些条件下,可逆随机场(从而典型 Gibbs 态)与可逆测度等价.在势为有界可测的条件下构造出全部典型 Gibbs 态、可逆随机场和可逆测度.证明了若存在正可逆测度,则速度函数有势,且正可逆测度集与正典型 Gibbs 态集相等.