最坏框架与平均框架下区间[1,1]上带Jacobi权的函数逼近

本文研究最坏框架和平均框架下区间[1,1]上带Jocobi权(1 x)α(1+x)β,α,β1/2的函数逼近问题.在最坏框架下,本文得到加权Sobolev空间BWr p,α,β在Lq,α,β(1 q∞)空间尺度下的Kolmogorov n-宽度和线性n-宽度的渐近最优阶,其中Lq,α,β(1 q∞)表示区间[1,1]上带Jacobi权的加权Lq空间.在平均框架下,本文研究具有Gauss测度的加权Sobolev空间Wr2,α,β被多项式子空间和Fourier部分和算子在Lq,α,β(1 q∞)空间尺度下的最佳逼近问题,得到平均误差估计的渐近阶.我们发现,在平均框架下,多项式子空间和Fourier部分和算子在Lq,α,β(1 q2+22 max{α,β}+1)空间尺度下是渐近最优的线性子空间和渐近最优的线性算子.     

具有混合光滑性的Sobolev-Wiener类在L_q(R~d)中的平均宽度

本文研究了具有混合光滑性的Sobolev-Wiener类SpqrW在Lq(Rd)中的平均σ-K宽度(1相似文献   

具有混合光滑性的Holder-Nikolskii-Wiener类在Lq(Rd)中的平均宽度（英文）

本文研究了具有混合光滑性的Holder-Nikolskii-Wiener类SrpqH在Lq(Rd)中的平均σ-K宽度(2≤q≤p<∞),得到了该量的弱渐近估计.     

各向异性Besov-Wiener类由多重样本的最优恢复

研究各向异性Besov-Wiener类SrpqθB（R^n）在Lq（R^n）,（1＜q≤P＜∞）中由其函数和它们的导数样本的最优恢复问题,确定了误差界的精确阶.     

积分算子的n-逼近数

本文研究了积分算子ＴＫ：Ｌｑ［０，１］→Ｌｑ［０，１］，（ｑ≥１）当核 Ｋ（ｓ， ｔ）是 Ｓｏｂｏｌｅｖ空间 Ｗｐｒ（［０， １］２）中元素时ｎ－逼近数 ａｎ（ＴＫ： Ｌｑ→ Ｌｑ）的估计，并把这个估计应用于退化核方法解第二类线性Ｆｒｅｄｈｏｌｍ方程（Ｉ一ＴＫ）ｘ＝ｙ时，Ｂａｄｈｖａｌｏｖ［５］意义下最佳误差的讨论中，所得到的最佳误差之估计当ｑ＝１时，最优化了［１０］的结论．     

分数次积分算子交换子在Morrey 空间上的有界性特征

本文证明了: 如果分数次积分算子交换子[b, T_Ω,α] 从Morrey 空间L^p, ^λ(Rⁿ) 到L^q,^λ(Rⁿ) (1 n). 这个结果改进并推广了前人的结果.     

三维磁微极流体方程弱解的正则性

本文给出了磁微极流体方程弱解的一个新的正则性准则:如果u满足uz ∈Lq(0,T;Lp(R3)),其中p≥3且满足3/p+2/q≤1,那么弱解(u,ω,b)在(0,T)是光滑解.     

各向异性Besov类的最优恢复

本文讨论各向异性 Ｂｅｓｏｖ类 ＳＢ（Ｒd）在 Ｌp （Ｒd ）（１＜ p<∞）中及在Ｌｑ（Ｒｄ）（１＜ｐ≤ｑ≤２）中的最优恢复,得到了相应误差的弱渐近估计．     

q-类似Virasoro-like代数模的导子

记Lq为两个变量的量子环面上的斜导子李代数,当0≠q∈C为非单位时,Lq就是q-类似Virasoro-like代数.本文给出了文中构造的Lq的模上的导子及一上同调群H^1（Lq,M）.     

Rough multiple singular integrals along hypersurfaces

In this paper, the authors study the mapping properties of singular integrals on product domains with kernels in L(log+L)ε(Sm-1 × Sn-1) (ε = 1 or 2) supported by hyper-surfaces. The Lp bounds for such singular integral operators as well as the related Marcinkiewicz integral operators are established, provided that the lower dimensional maximal function is bounded on Lq(R3) for all q > 1. The condition on the integral kernels is known to be optimal.     

Lq(Ω)空间中C0-半群的一些结果

设T（t）是Lq（1＜q＜∞）空间上的C0-半群,A为其无穷小生成元．本文证明若T（t）是弱LP稳定的,则其生成元的谱界是负的。由LotzWeis最近得到的关于Lq（Ω）空间中正C0半群的增长界等于生成元的谱界这一结果得出,Lq（Ω）空间中正C0半群弱Lp稳定与指数稳定等价．     

On the Representation of Band-Dominant Functions on the Sphere Using Finitely Many Bits

A band-dominant function on the Euclidean sphere embedded in R ^q+1 is the restriction to this sphere of an entire function of q+1 complex variables having a finite exponential type in each of its variables. We develop a method to represent such a function using finitely many bits, using the values of the function at scattered sites on the sphere. The number of bits required in our representation is asymptotically the same as the metric entropy of the class of such functions with respect to any of the L ^p norms on the sphere.     

Some Aspects on the Geometry of the Tangent Bundles and Tangent Sphere Bundles of a Riemannian Manifold

In this paper we study a Riemannian metric on the tangent bundle T(M) of a Riemannian manifold M which generalizes Sasaki metric and Cheeger–Gromoll metric and a compatible almost complex structure which confers a structure of locally conformal almost K?hlerian manifold to T(M) together with the metric. This is the natural generalization of the well known almost K?hlerian structure on T(M). We found conditions under which T(M) is almost K?hlerian, locally conformal K?hlerian or K?hlerian or when T(M) has constant sectional curvature or constant scalar curvature. Then we will restrict to the unit tangent bundle and we find an isometry with the tangent sphere bundle (not necessary unitary) endowed with the restriction of the Sasaki metric from T(M). Moreover, we found that this map preserves also the natural contact structures obtained from the almost Hermitian ambient structures on the unit tangent bundle and the tangent sphere bundle, respectively. This work was also partially supported by Grant CEEX 5883/2006–2008, ANCS, Romania.     

Asymptotically optimal staffing of service systems with joint QoS constraints

We consider the problem of staffing large-scale service systems with multiple customer classes and multiple dedicated server pools under joint quality-of-service (QoS) constraints. We first analyze the case in which arrival rates are deterministic and the QoS metric is the probability a customer is queued, given by the Erlang-C formula. We use the Janssen–Van Leeuwaarden–Zwart bounds to obtain asymptotically optimal solutions to this problem. The second model considered is one in which the arrival rates are not completely known in advance (before the server staffing levels are chosen), but rather are known via a probability distribution. In this case, we provide asymptotically optimal solutions to the resulting stochastic integer program, leveraging results obtained for the case of deterministic arrivals.     

一类量子环面李代数的泛中心扩张

设Cq=Cq[x1^±1,x2^1]为复数域上的量子环面,其中q≠0是一个非单位根．D（Cq）为Cq的导子李代数．记Lq为Cq＋D（Cq）的导出子代数．本文研究李代数Lq的泛中心扩张．     

The central limit theorem without the condition of independence

Necessary and sufficient conditions are presented for sums of asymptotically independent random variables to converge to a normal random variable in the sense of total variation distance, uniform metric for characteristic functions. and mean metric of order q. Supported by the Russian Foundation for Fundamental Research (grant No. 96-01-01920). Proceedings of the Seminar on Stability Problems for Stochastic Models. Moscow. Russia. 1996. Part II.     

Measure Density and Extension of Besov and Triebel–Lizorkin Functions

We show that a domain is an extension domain for a Haj?asz–Besov or for a Haj?asz–Triebel–Lizorkin space if and only if it satisfies a measure density condition. We use a modification of the Whitney extension where integral averages are replaced by median values, which allows us to handle also the case \(0<p<1\). The necessity of the measure density condition is derived from embedding theorems; in the case of Haj?asz–Besov spaces we apply an optimal Lorentz-type Sobolev embedding theorem which we prove using a new interpolation result. This interpolation theorem says that Haj?asz–Besov spaces are intermediate spaces between \(L^p\) and Haj?asz–Sobolev spaces. Our results are proved in the setting of a metric measure space, but most of them are new even in the Euclidean setting, for instance, we obtain a characterization of extension domains for classical Besov spaces \(B^s_{p,q}\), \(0<s<1\), \(0<p<\infty \), \(0<q\le \infty \), defined via the \(L^p\)-modulus of smoothness of a function.     

分数次积分在局部Hardy空间上的有界性质

证明了当0<αn/(n-α)时,分数次积分Iα是局部Hardy空间hp(Rn)到空间hp(Rn)+Lq(Rn)的一个线性映射.     

Lp[0,1]空间中弱奇异积分算子性质的研究

首先讨论具有弱奇异核k(s,t)=g(s,t)/│s-t│α的积分算子当0＜α＜1/q(1/p+1/q=1)时在Lp[0,1]上是紧的,进一步得到对于任一给定的q当α＜1/q时,有α阶弱奇异积分算子K*(K的共轭算子)在Lq[0,1]中是紧算子.