On the Integration by Parts and Characterization of a Fractional Diffusion Process北大核心CSCD

本文研究分数扩散过程和其分部积分公式的关系.首先利用Bismut方法给出拉回公式,进而得到分数扩散过程的分部积分公式。反过来,证明了分数扩散过程可由其分部积分公式唯一刻画.     

一类带扰动的随机脉冲泛函微分方程解的渐近性北大核心CSCD

该文讨论了一类带扰动的随机脉冲泛函微分方程解的渐近性.通过比较扰动方程的解和原方程的解,得到了两者逼近的充分条件.首先,两者在有限的时间区间上相互逼近;其次,当扰动趋于零时,区间长度趋于无穷大,在这个区间上两个解仍然是相互逼近的.最后,举例说明了结果的有效性.     

Convolution semigroups and central limit theorem associated with a dual convolution structure

We consider hypergroups associated with Jacobi functions ⁽⁾ (x), (–1/2). We prove the existence of a dual convolution structure on [0,+[i(]0,s ₀]{{) =++1,s ₀=min(,–+1). Next we establish a Lévy-Khintchine type formula which permits to characterize the semigroup and the infinitely divisible probabilities associated with this dual convolution, finally we prove a central limit theorem.     

Rate conservation laws: A survey

We survey the rate conservation law, RCL for short, arising in queues and related stochastic models. RCL was recognized as one of the fundamental principles to get relationships between time and embedded averages such as the extended Little's formulaH=G, but we show that it has other applications. For example, RCL is one of the important techniques for deriving equilibrium equations for stochastic processes. It is shown that the various techniques, including Mecke's formula for a stationary random measure, can be formulated as RCL. For this purpose, we start with a new definition of the rate with respect to a random measure, and generalize RCL by using it. We further introduce the notion of quasi-expectation, which is a certain extension of the ordinary expectation, and derive RCL applicable to the sample average results. It means that the sample average formulas such asH=G can be obtained as the stationary RCL in the quasi-expectation framework. We also survey several extensions of RCL and discuss examples. Throughout the paper, we would like to emphasize how results can be easily obtained by using a simple principle, RCL.     

On the convergence of multipoint Padé-type approximants and quadrature formulas associated with the unit circle

We study the convergence of rational interpolants with prescribed poles on the unit circle to the Herglotz-Riesz transform of a complex measure supported on [–, ]. As a consequence, quadrature formulas arise which integrate exactly certain rational functions. Estimates of the rate of convergence of these quadrature formulas are also included.This research was performed as part of the European project ROLLS under contract CHRX-CT93-0416.     

Alternating Sign Matrices and Some Deformations of Weyl's Denominator Formulas

An alternating sign matrix is a square matrix whose entries are 1, 0, or –1, and which satisfies certain conditions. Permutation matrices are alternating sign matrices. In this paper, we use the (generalized) Littlewood's formulas to expand the products and 2 as sums indexed by sets of alternating sign matrices invariant under a 180° rotation. If we put t = 1, these expansion formulas reduce to the Weyl's denominator formulas for the root systems of type B _n and C _n. A similar deformation of the denominator formula for type D _n is also given.     

Phenolic Compounds of Plants of the Scutellaria L. Genus. Distribution, Structure, and Properties

Information on flavones, flavanones, flavanonols, flavonols, chalcones, isoflavones, biflavonoids, lignoflavonoids, and lignane glycosides and stilbenes isolated from plants of the Scutellaria L. genus was systematized and reviewed. A list of 208 phenolic compounds was given according to flavonoid type with an indication of the plant sources, structures, and physicochemical properties and citations of the original articles.     

γ-聚谷氨酸在细胞冻存中的作用

无DMSO、无血清细胞冻存液在临床级细胞产品的冷冻保存中具有重要的应用价值。本文以K562细胞为模型,设置含10%(v/v)DMSO及胎牛血清的冻存液为阳性对照,含10%(v/v)甘油的RPMI 1640培养基冻存液为阴性对照组,含10%(v/v)甘油及0.01%(w/v)γ-PGA的RPMI 1640培养基冻存液为实验组,考察了在无DMSO、无血清细胞冻存体系中γ-聚谷氨酸对细胞的冷冻保护作用。将K562细胞以1×10^6cells/mL的密度分别悬浮在上述冻存液中,置于液氮冻存10周,检测复苏后K562的细胞复苏率、细胞形态以及复苏后细胞的扩增情况,以评判γ-聚谷氨酸在无DMSO无血清冻存液中对K562细胞的冷冻保护作用。结果显示,实验组的细胞复苏率为(83.00±3.00)%,明显高于阴性对照组的(70.33±5.51)%(p<0.05)和阳性对照组的(71.00±2.65)%(p<0.05);且实验组冻存后的细胞形态完整,冻存前后细胞的平均直径及圆度基本一致,细胞复苏后培养24h后的细胞活性为(88.83±14.29)%,明显高于阴性对照组的(67.51±5.20)%(p<0.05),与阳性对照组的(78.75±3.31)%没有显著性差异,同时复苏后细胞扩增的延滞期明显缩短。可见,在无DMSO、无血清的甘油冻存体系中添加γ-PGA可显著提高细胞的冻存效果,具有良好的实际应用价值。     

Dibromomethane as one-carbon source in organic synthesis: total synthesis of (±)-canadensolide

A diastereoselective total synthesis of (±)-canadensolide is described. The key step is to introduce the α-methylene group by the ozonolysis of mono-substituted alkenes followed by reaction with a preheated mixture of CH₂Br₂-Et₂NH.