Sinc-regularized techniques to compute eigenvalues of schrödinger operators on L 2 ( I ) ⊕ ℂ 2 $L^{2}(I)oplus mathbb {C}^{2}$

Numerical Algorithms - We introduced two different sinc-regularized techniques to compute eigenvalues of Schrödinger operators defined on the Hilbert space $L^{2}(0,1)oplus mathbb {C}^{2}$...     

一类$L^2(mathbb{R}^n)$的紧支撑不可分正交小波

本篇文章给出一类$L^{2}(mathbb{R}^{n})$, $ngeq2$的紧支撑不可分正交小波基的具体构造算法,其中正交小波的伸缩矩阵为$alpha I_{n}~(alphageq2, alpha in mathbb{Z})$, $I_{n}$是$n$阶单位矩阵.最后给出两个不可分正交小波基的构造算例.     

一类具间断系数退化椭圆型方程的$L^{p,lambda}$正则性

得到一类退化椭圆型方程弱解梯度在其拟线性系数矩阵$A(cdot,u)$对任意$u$关于$x$一致满足VMO条件下在Morrey空间$L^{p,lambda}$的内部正则性.     

$T_{2}(T)$的几乎可裂序列及几乎$mathcal {D}$-可裂序列

The AR-quiver and derived equivalence are two important subjects in the representation theory of finite dimensional algebras, and for them there are two important research tools-AR-sequences and D-split sequences. So in order to study the representations of triangular matrix algebra T2 (T ) = T0TT where T is a finite dimensional algebra over a field, it is important to determine its AR-sequences and D-split sequences. The aim of this paper is to construct the right(left) almost split morphisms, irreducible morphisms, almost split sequences and D-split sequences of T2 (T) through the corresponding morphisms and sequences of T. Some interesting results are obtained.     

再论仿射不变量$W_{i}(K)W_{i}(K^{})$的下界估计

对于所有凸体与每一个$i$, 寻找仿射不变量$W_{i}(K)W_{i}(K^{*})$下界的问题是一个至今未能完全解决的公开问题. 最近,赵长健考虑了仿射不变量$W_{i}(K)W_{i}(K^{*})$的下界是与凸体$K$本身有关的常数的情形, 并利用混合体积与对偶混合体积的关系理论, 对仿射不变量$W_{i}(K)W_{i}(K^{*})$的下界进行了讨论. 本文进一步讨论仿射不变量$W_{i}(K)W_{i}(K^{*})$的下界估计, 并对具有正的连续曲率且包含原点为其内点的凸体!$K$, 获得了仿射不变量$W_{i}(K)W_{i}(K^{*})$的几个不同精度的下界, 同时给出了著名的Bourgain-Milman不等式中通用常数$c$的具体表示值.最后提出了两个公开问题.     

椭圆方程在Orlicz类中的正则估计(英文)

The purpose of this paper is to give the element proof of the regularity estimates in Orlicz classes for the second order derivatives of the solutions to the general second order elliptic equations.The global regularities in Orlicz for the second order derivatives of the solutions of the Dirichlet problems are also given.     

系数在模李超代数~$W(m,3,underline{1})$ 上的~$frak{gl}(2,mathbb{F})$ 的一维上同调

研究了系数在模李超代数~$W(m,3,underline{1})$上的~$frak{gl}(2,mathbb{F})$ 的一维上同调, 其中~$mathbb{F}$是一个素特征的代数闭域且~$frak{gl}(2,mathbb{F})$是系数在~$mathbb{F}$ 上的~$2times 2$ 阶矩阵李代数.计算出所有~$frak{gl}(2,mathbb{F})$到模李超代数~$W(m,3,underline{1})$ 的子模的导子和内导子.从而一维上同调~$textrm{H}^{1}(frak{gl}(2,mathbb{F}),W(m,3,underline{1}))$可以完全用矩阵的形式表示.     

赋Orlicz范数的Orlicz-Bochner空间E_M(μ,X)的对偶空间

本文研究了Orlicz-Bochner空间E_M(μ,X)的对偶空间的充分必要条件.运用Radon-Nikodym性质,给出Orlicz-Bochner空间L_((N))(μ,X~*)为E_M(μ,X)~*的对偶空间当且仅当X~*具Radon-Nikodym性质,提升了Orlicz空间及Lebesgue-Bochner空间的相关结论.     

(log,θ)-Calderon-Zygmund算子在H~p中的有界性(英文)

本文我们在条件∫１０θｐ（ｔ）／ｔ１＋ｎ（１－ｐ）ｄｔ＜＋∞下，讨论了（ｌｏｇ，θ）－Ｃａｌｄｅｒóｎ－Ｚｙｇｍｕｎｄ算子在Ｈｐ（Ｒｎ），（０＜ｐ≤１）中的有界性．     

关于完全二部图$K_{4, n}$和$K_{n, n}$的点可区别 $IE$-全染色的一些注记

Let G be a simple graph.An IE-total coloring f of G refers to a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color.Let C(u) be the set of colors of vertex u and edges incident to u under f.For an IE-total coloring f of G using k colors,if C(u)=C(v) for any two different vertices u and v of V(G),then f is called a k-vertex-distinguishing IE-total-coloring of G,or a k-VDIET coloring of G for short.The minimum number of colors required for a VDIET coloring of G is denoted by χ ie vt (G),and it is called the VDIET chromatic number of G.We will give VDIET chromatic numbers for complete bipartite graph K4,n (n≥4),K n,n (5≤ n ≤ 21) in this article.     

Best Simultaneous Approximation in LΦ(I,X)

Let X be a Banach space and Φ be an Orlicz function.Denote by LΦ(I,X)the space of X-valued Φ-integrable functions on the unit interval I equipped with the Luxemburg norm.For f1,f2,...,fm ∈ LΦ(I,X),a distance formula disΦ(f1,f2,...,fm,LΦ(I,G))is presented,where G is a close subspace of X.Moreover,some existence and characterization results concerning the best simultaneous approximation of LΦ(I,G)in LΦ(I,X)are given.     

Taylor's inequalities in Orlicz–Sobolev type spaces

In this paper, we obtain inequalities involving the Taylor polynomial and weak derivatives of a function in an Orlicz–Sobolev type space. Moreover, we show that any such function can be expanded in a finite Taylor series almost everywhere. As a consequence, we prove that the coefficients of any extended best polynomial -approximation of a function on a ball almost everywhere converge to the weak derivatives of such a function when the radius tends to 0. Lastly, we get a mean convergence result of such coefficients.     

赋Orlicz范数的Orlicz空间中最佳逼近算子

在赋Ｏｒｌｉｃｚ范数的Ｏｒｌｉｃｚ空间中,给出最佳逼近算子单调性的一个充分条件和最佳逼近元存在定理．     

Best Local Approximation in Orlicz Spaces

We get results in Orlicz spaces L ^φ about best local approximation on non-balanced neighborhoods when φ satisfies a certain asymptotic condition. This fact generalizes known previous results in L ^p spaces.     

一类Orlicz空间中复系数多项式的倒数逼近

定义了互余的N函数M（u）和N（v）的△条件,并研究了由这种N函数M（u）所生成的一类Orlicz空间中复系数多项式的倒数逼近问题．     

Orlicz空间中的多元光滑模及其应用

本文的目的是引进和应用Orlicz空间中一种新的多元光滑模，该光滑模是一元情形的一种自然推广．利用函数分解方法和归纳讨论证明它与K-泛函之间的等价关系．作为应用，给出定义在单纯形上Durrmeyer算子在Orlicz空间中的一个逼近逆定理．     

A Note on Pad ′e Approximants Pairs as Limits of Algebraic Polynomials Pairs of Weighted Best Approximation in Orlicz Spaces

In this short note, we show the behavior in Orlicz spaces of best approxima-tions by algebraic polynomials pairs on union of neighborhoods, when the measure of them tends to zero.