On the Cayley-Bacharach Property

The Cayley-Bacharach Property (CBP), which has been classically stated as a property of a finite set of points in an affine or projective space, is extended to arbitrary 0-dimensional affine algebras over arbitrary base fields. We present characterizations and explicit algorithms for checking the CBP directly, via the canonical module, and in combination with the property of being a locally Gorenstein ring. Moreover, we characterize strict Gorenstein rings by the CBP and the symmetry of their affine Hilbert function, as well as by the strict CBP and the last difference of their affine Hilbert function.     

Synthesis of AN-g-casein copolymer in concentrated aqueous solution of sodium thiocyanate and AN-g-casein fiber's structure and property

The main products of graft copolymerization of acrylonitrile (AN) onto casein in concentrated aqueous solution of sodium thiocyanate in homogeneous phase were characterized as a graft copolymer (AN-g-casein) by Fourier transform infrared. The effects of the monomer concentration, initiator concentration, reaction temperature and reaction time on copolymerization were investigated. The result of WAXD showed that the major part of casein in graft copolymer is amorphous. The SDSC determination showed that the lateral order of PAN, the side chain of copolymer, decreases and the lateral order distribution becomes wider with the increase of the casein component in copolymer. It revealed that the two systems of AN-g-casein copolymer are incompatible by an investigation of DMTA, SEM. The two systems of AN-g-casein exist in separating phases, but tie up each other. So the phenomena of characteristic boundary relaxation occur.Direct spinning of graft copolymer in concentrated aqueous solution of sodium thiocyanate in homogeneous phase was successfully carried out. The skin-core layer structure of AN-g-casein fiber cross-section was observed by scanning electron microscope (SEM). In the core layer, the dimension of phase domain of casein is about from 20 to 60 nm. When the fiber was drawn into broken, microfibrillation occurs, the fiber skin layer is compact, and its broken section is flat. Many long and thin casein strips are formed in the surface of the fiber, respective crystalline grade of two components is scarcely effected by the change of the content of casein. AN-g-casein fibers have good hygroscopicity and dyeability, and more, they can be dyed by acidic dyestuff and cationic dyestuff. AN-g-casein fiber still has good mechanical properties, so AN-g-casein fiber is a new type modified “silk-like” fiber for wide application.     

模糊推理的变权综合算法及其构造的模糊系统响应能力分析

将变权综合原理应用于模糊推理,提出一种新的模糊推理算法-变权综合推理算法,并给出利用模糊蕴涵算子确定规则变权的方法。证明了由一些正常蕴涵算子如Lukasiewicz蕴涵、Goguen蕴涵、Godel蕴涵、Dubois-Prade蕴涵等确定的变权综合算法是相容的。进一步分析了该变权综合算法构造的模糊系统的响应能力,结果表明:基于这些正常蕴涵算子的变权综合算法构造的模糊系统具有泛逼近性。     

下方图度量下的非紧模糊数空间

证明了非紧模糊数空间E^～在下方图度量下关于模糊数的序是可逼近的。本文给出的证明方法是构造性的，从而说明了模糊数值积分如M-积分和G-积分等是可计算的。最后给出了E^～中关于下方图度量的一些分析性质。     

Herstein定理的推广

1955年Herstein将著名的Jacobson定理推广为:定理A.如果对R中任意x,y,存在可依赖于x,y的整系数多项式p(t),使[x-x2p(x),y]=0,则R是交换的.本文利用多项式的系数和定义了n元多项式,f(x1,x2…,xn)的Fk性质,并以此证明了一个环的交换性定理,当n=1时,即得到定理A.     

应用电化学方法研究α和βi(I=1,2,3)-K5SiAl(OH2)W11O39·nH2O的氧化还原性质

本文系统地研究了α和βi(i=1,2 ,3) - K5Si Al(OH2 ) W11O3 9· n H2 O的氧化还原性质 ,通过导数脉冲伏安、常规脉冲伏安确定了其氧化还原机理 ,并比较了其氧化还原性质的强弱。     

A 2‐fold Interpenetrated Framework based on Tetranuclear Heterometallic Cluster: Synthesis,Structure and Magnetic Properties

A 2‐fold parallel interpenetrated polymer, ZnCo(OH)(pheno)(p‐BDC)_1.5·H₂O ( 1 ) (pheno = phenanthrene‐9,10‐dione; p‐BDC = 1,4‐benzenedicarboxylate) has been prepared by hydrothermal synthesis and structurally characterized by IR, elemental analysis, ICP and single crystal X‐ray diffraction. Complex 1 crystallizes in the orthorhombic space group Pbca and affords a three‐dimensional (3D) six‐connected α‐Po network. The magnetic behavior for 1 was studied in the temperature range of 1.8‐300 K.     

On stationary equilibria of a single-controller stochastic game

We consider a two-person, general-sum, rational-data, undiscounted stochastic game in which one player (player II) controls the transition probabilities. We show that the set of stationary equilibrium points is the union of a finite number of sets such that, every element of each of these sets can be constructed from a finite number of extreme equilibrium strategies for player I and from a finite number of pseudo-extreme equilibrium strategies for player II. These extreme and pseudo-extreme strategies can themselves be constructed by finite (but inefficient) algorithms. Analogous results can also be established in the more straightforward case of discounted single-controller games.     

非自伴算子代数间的等距代数同构

设Ｇｉ是满足第二可数性公理的、Ｈａｕｓｄｏｒｆｆ的、顺从的、ｒ－离散的、主的局部紧群胚，并且有一个紧开Ｇ－集覆盖；设Ｐｉ是Ｇｉ中含Ｇ＿ｉ￣０的开闭集，且满足及相应的模是具有性质ＤＣ的Ｃ（Ｇｉ）的子代数（ｉ＝１，２）．本文证明从Ａ（Ｐ１）到Ａ（Ｐ２）上的每一个等距代数同构可以扩张成从Ｃ（Ｇ１）到Ｃ（Ｇ２）上的Ｃ－同构，进一步，可以对Ｃ（Ｇ２）重新坐标化，使得这个Ｃ－同构可由一个群胚同构生成．     

对-二甲氨基苯甲醛苯甲酰腙及其锌(Ⅱ)、镉(Ⅱ)配合物的合成与光学性质

合成了对-二甲氨基苯甲醛苯甲酰腙(配体)及其锌(Ⅱ)、镉(Ⅱ)配合物,通过元素分析、IR、MS对结构进行表征,研究了配体及锌(Ⅱ)、镉(Ⅱ)配合物的紫外光谱和荧光光谱。这些物质都有较强的荧光,适合掺入涂料中做成荧光涂料。