Special simplices and Gorenstein toric rings

Athanasiadis [Ehrhart polynomials, simplicial polytopes, magic squares and a conjecture of Stanley, J. Reine Angew. Math., to appear.] studies an effective technique to show that Gorenstein sequences coming from compressed polytopes are unimodal. In the present paper we will use such the technique to find a rich class of Gorenstein toric rings with unimodal h-vectors arising from finite graphs.     

局部对称共形平坦黎曼流形中具有平行平均曲率向量的子流形

本文把[1]的结论推广到了环绕空间是局部对称共形平坦的情形,即获得了:设M~是局部对称共形平坦黎曼流形N~+p(p>1)中具有平行平均曲率向量的紧致子流形,如果则M~位于N~+p的全测地子流形N~+1中。其中S,H分别是M~的第二基本形式长度的平方和M~的平均曲率,T_C、t_c分别是N~+p的Ricci曲率的上、下确界,K是N~+p的数量曲率。     

低速二维流动的粒子仿真研究

本文运用信息保存法对低速二维的流动现象进行模拟，考察了低速条件下的有限平板绕流以及微槽道气体流动问题。研究表明：在对低速流动的模拟过程中，运用IP法在能够获得较好的结果的同时，具有比DSMC方法更高的计算效率。     

Finite-Dimensional Simple Leibniz Pairs and Simple Poisson Modules

Simple modules over the Leibniz pairs are studied. Simple Poisson modules over Poisson algebras of the semisimple associative algebra structure are determined and they are nothing but simple bimodules over simple associative algebras with standard noncommutative Poisson algebra structure.     

Hopf Modules and Noncommutative Differential Geometry

We define a new algebra of noncommutative differential forms for any Hopf algebra with an invertible antipode. We prove that there is a one-to-one correspondence between anti-Yetter–Drinfeld modules, which serve as coefficients for the Hopf cyclic (co)homology, and modules which admit a flat connection with respect to our differential calculus. Thus, we show that these coefficient modules can be regarded as “flat bundles” in the sense of Connes’ noncommutative differential geometry.     

The core of zero-dimensional monomial ideals

The core of an ideal is the intersection of all its reductions. We describe the core of a zero-dimensional monomial ideal I as the largest monomial ideal contained in a general reduction of I. This provides a new interpretation of the core in the monomial case as well as an efficient algorithm for computing it. We relate the core to adjoints and first coefficient ideals, and in dimension two and three we give explicit formulas.     

Reducing system of parameters and the Cohen-Macaulay property

Let R be a local ring and let (x ₁, …, x _r) be part of a system of parameters of a finitely generated R-module M, where r < dim_R M. We will show that if (y ₁, …, y _r) is part of a reducing system of parameters of M with (y ₁, …, y _r) M = (x ₁, …, x _r) M then (x ₁, …, x _r) is already reducing. Moreover, there is such a part of a reducing system of parameters of M iff for all primes P ε Supp M ∩ V _R(x ₁, …, x _r) with dim_R R/P = dim_R M − r the localization M _P of M at P is an r-dimensional Cohen-Macaulay module over R _P. Furthermore, we will show that M is a Cohen-Macaulay module iff y _d is a non zero divisor on M/(y ₁, …, y _d−1) M, where (y ₁, …, y _d) is a reducing system of parameters of M (d:= dim_R M).     

Hopf代数上的扭曲模和(斜)余配对Hopf模

本文第一部分主要把扭曲的方法运用到模上,从而得到扭曲模．作为特例,我们构造了H  M的Smaush模和量子模．当K是有限维Hopf代数,证明K*  M是一个右D(K)-Hopf模,因此得到了一个基本同构定理．第二部分主要把斜余配对双代数进行推广,得到了斜余配对Hopf模,并且给出判断斜余配对Hopf模的一个充要条件．     

太阳CO 4.6微米红外成像观测

太阳红外光谱中蕴含着丰富的物理信息,其中CO 4.6μm波段是具有代表性的分子谱带,其形成于温度极小区附近,对研究太阳物理具有极其重要的意义。为获得CO 4.6μm波段太阳单色像,本文建立了一套全反射太阳红外成像观测系统。该系统采用定天镜跟踪引光,通过成像反射镜将太阳成像于3~5μm波段红外相机的焦平面上,该相机采用的是国产HgCdTe焦平面阵列器件。同时,为提高信噪比,提出了一种有效计算平场提取观测目标的方法,并利用该方法获得了CO 4.6μm波段的太阳单色像。     

Structure control within poly(amidoamine) dendrimers: size, shape and regio-chemical mimicry of globular proteins

This work describes the syntheses of a new poly(amidoamine) (PAMAM) dendrimer family possessing a disulfide function (cystamine) in its core. Traditional redox-chemistry associated with the disulfide core in these dendrimer structures, provides a versatile strategy for designing unique sizes, shapes and controlling the regio-disposition of chemical groups on the surface of these dendrimers. Various single site, sulfhydryl functionalized dendron reactants may be generated in situ, under standard reducing conditions (i.e. dithiothreitol (DTT)). Facile control of size, shape and chemical functionality placement involves covalent hybridization of these single point, sulfhydryl reactive dendron components. This is accomplished by re-oxidation in the presence of air, to yield generation/surface chemistry differentiated cross-over products which may be isolated by preparative thin layer or column chromatography. Differentiated cystamine core dendrimers derived from combination and permutation of lower generation (i.e. Gen.=0-3) sulfhydryl functionalized dendrons possessing amino, hydroxyl, acetamido or dansyl surface groups, were synthesized and isolated. They were characterized by a variety of methods including; ¹³C NMR, capillary electrophoresis (CE), gel electrophoresis (PAGE), thin layer chromatography (TLC) and electrospray (ES) or matrix assisted laser desorption ionization (MALDI-TOF) mass spectrometry. This general strategy has broad implications for the systematic size, shape and regio-chemical control of a wide range of dendritic nanostructures, many of which may be designed to mimic the sizes, shapes and regio specific chemo-domains observed for globular proteins.