Weighted pseudo almost periodic solutions of N-th order neutral differential equations with piecewise constant arguments

In this work, we present some existence theorems of weighted pseudo almost periodic solutions for N-th order neutral differential equations with piecewise constant argument by means of weighted pseudo almost periodic solutions of relevant difference equations.     

Geometry of manifolds with densities

We study the geometry of complete Riemannian manifolds endowed with a weighted measure, where the weight function is of quadratic growth. Assuming the associated Bakry–Émery curvature is bounded from below, we derive a new Laplacian comparison theorem and establish various sharp volume upper and lower bounds. We also obtain some splitting type results by analyzing the Busemann functions. In particular, we show that a complete manifold with nonnegative Bakry–Émery curvature must split off a line if it is not connected at infinity and its weighted volume entropy is of maximal value among linear growth weight functions.     

Global classical solution of the Cauchy problem to 1D compressible Navier–Stokes equations with large initial data

In this paper, we prove that the 1D Cauchy problem of the compressible Navier–Stokes equations admits a unique global classical solution (ρ,u)$(\rho ,\mathrm{u})$ if the viscosity μ(ρ)=1+ρ^β$\mu (\rho )=1+{\rho }^{\beta }$ with β?0$\beta ?0$. The initial data can be arbitrarily large and may contain vacuum. Some new weighted estimates of the density and velocity are obtained when deriving higher order estimates of the solution.     

Tractability results for the weighted star-discrepancy

The weighted star-discrepancy has been introduced by Sloan and Wo?niakowski to reflect the fact that in multidimensional integration problems some coordinates of a function may be more important than others. It provides upper bounds for the error of multidimensional numerical integration algorithms for functions belonging to weighted function spaces of Sobolev type. In the present paper, we prove several tractability results for the weighted star-discrepancy. In particular, we obtain rather sharp sufficient conditions under which the weighted star-discrepancy is strongly tractable. The proofs are probabilistic, and use empirical process theory.     

加权全能量最小的圆环形变北大核心CSCD

主要考虑如下加权全能量极值问题:h∈■^(inf)(A_(1),A_(2))α∫∫A_(1)(|h_(N)|^(2)+|h_(T)|^(2))1/(|h_(z)|^(2))dz+β∫∫A_(1)|h_(N)|^(2)+|h_(T)|^(2)/J(z,h)1/|z|^(2)dz,其中■(A_(1),A_(2))代表从圆环A_(1)到圆环A_(2)的所有保向同胚映射的集合.研究得到唯一的极值映射为径向拉伸映射.这将[Iwaniec T,Onninen J.Hyperelastic deformations of smallest total energy[J].Arch Rational Mech Anal,2009,194:927-986.]的结果推广至非欧情形.同时,也分别研究了圆环上的加权调和能量的极值问题与加权偏差的极值问题.     

多圆柱上Bloch型空间之间加权复合算子的本性范数

设φ(z)=(φ1(z),…,φ_n(z))是D~n到自身的一个全纯映射,ψ(z)是D~n上的全纯函数,其中D~n是C~n中的单位多圆柱.研究了单位多圆柱上Bloch型空阊之间的加权复合算子ψC_φ的本性范数,并给出了其上下界估计.     

加权p-Laplace方程解的整体分叉问题

该文利用指标理论，谱理论以及标准分叉定理，研究了加权索伯列夫空间中的p Laplace方程初值问题的解的整体分叉现象。     

On general summability factor theorem of infinite series

A lower triangular matrix with nonzero principal diagonal entries is called a triangle. In this paper we obtain the sufficient conditions for ∑a_nλ_n to be summable ∣A∣_k whenever ∑a_n is summable ∣T∣_k for a triangle T.     

Compactness of Iterated Commutators on Weighted Bergman Spaces

Compactness of Iterated Commutators on Weighted Bergman Spaces@刘永民&&     

加权Lebesgue空间的对偶和嵌入

本文建立了加权Lebesgue空间的对偶空间，并且给出了在这些空间之间嵌入的必要条件。