Score sets in oriented 3-partite graphs

Let D(U, V, W) be an oriented 3-partite graph with |U|=p, |V|=q and |W|= r. For any vertex x in D(U, V, W), let d x and d-x be the outdegree and indegree of x respectively. Define aui (or simply ai) = q r d ui - d-ui, bvj(or simply bj) = p r d vj - d-vj and Cwk (or simply ck) = p q d wk - d-wk as the scores of ui in U, vj in V and wk in Wrespectively. The set A of distinct scores of the vertices of D(U, V, W) is called its score set. In this paper, we prove that if a1 is a non-negative integer, ai(2≤i≤n - 1) are even positive integers and an is any positive integer, then for n≥3, there exists an oriented 3-partite graph with the score set A = {a1,2∑i=1 ai,…,n∑i=1 ai}, except when A = {0,2,3}. Some more results for score sets in oriented 3-partite graphs are obtained.     

Basis of the 'duplication' strategy for enhancing the enantiomeric excess in chiral resolutions: proof of the equivalence of rate and product ratios

The 'duplication' strategy for the further enrichment of an already enantiomerically-enriched mixture consists of the formation of all the three possible 'dimeric' diastereomers, i.e., (R)–X–(R), (R)–X–(S) and (S)–X–(S), where X is an appropriate spacer that can be readily cleaved to yield the original enantiomers. The mixture of (R)–X–(R) and (S)–X–(S) thus obtained would be of higher enantiomeric excess (e.e.) as compared to the original mixture, on the basis of a simple kinetic scheme. The success of the strategy is experimentally well-established, but is apparently based on the (unproven) assumption that the theoretically-derived rate ratios are identical to the experimentally observed product ratios. Although the detailed kinetic treatment for a system such as the above is extremely complex, it is possible to show (mathematically) that the above assumption is indeed justified when all the three diastereomers are formed without chiral discrimination (as assumed in the strategy).     

Entire functions decaying rapidly on strips

It has been known for many years that there exist non-constant entire functions f which decay to 0 along every infinite line. Recently it has been shown that if 0 < α < 1/2, then there exist entire functions f such that exp(|z| ^α )f(z) → 0 (z → ∞, z ? S) for every strip S; moreover there is a vector space M which consists of such functions and which is dense in the space of all entire functions with the topology of local uniform convergence. In this note the result is shown to hold for every α > 0. The proof depends upon a theorem about tangential harmonic approximation on unbounded sets. As a corollary, a new result is proved about the class of entire functions which have zero integral on every doubly infinite line.     

Singular integrals along surfaces on product domains

In this paper, we study the mapping properties of singular integral operator along surfaces of revolution. We prove Lp bounds (1 < p < ∞) for such singular integral operators as well as for their corresponding maximal truncated singular integrals if the singular kernels are allowed to be in certain block spaces.     

AgCl-CS(NH~2)~2-H~2O体系的研究

研究AgCl-CS(NH_2)_2-H_2O三元体系,对于用硫脲溶解、分离角银矿(AgCl)中的金、银显然是有意义的.但有关该三元体系的文献很少.等结合折光指数认为在AgCl-CS(NH_2)_2-KCl-H_2O系统中只生成配合物Ag[CS(NH_2)]_2Cl.我们的研究工作也证明可生成Ag[Cs(NH_2)_2]_2Cl.我们研究了AgCl-CS(NH_2)_2-H_2O三元体系在20℃及30℃时的溶度和折光指数.由于两个温度的溶度图图形基本相仿,故本文只报道30℃的工作.     

宽广温度范围的水离子积计算公式

宽广温度范围的水离子积是在理论上和实际应用上涉及面很广的重要物理化学性质之一.傅培鑫,Quist及Marshall等在总结实验数据的基础上提出了相应的计算水离子积的经验公式;Taylor还用热力学方法进行了计算.在饱和蒸气压及0～800℃范围内,以Marshall-Franck的经验公式准确度为最高,并由国际蒸气性质协会(IAPA)于1980年公布为计算宽广温度范围的水离子积公式.但是在温度较高(200～300℃)时,此公式的计算值与实验值之间的误差随温度升高而逐渐增大,平均误差为0.033pK_w单位.     

碱土金属的极谱研究 IV. 钡-钙-茜素配合剂双金属三元配合物的吸附波

本文研究了一个钡-钙-茜素配合剂(ALC)新体系的极谱波及其机理,此极谱波是一种双金属三元配合物吸附波,是由钡-钙-ALC配合物在电极上吸附还原而产生的,配合物的组成为:Ba:Ca:ALC=1:2:5,此方法可应用于硫酸钡溶积度的测定。     

L^P BOUNDS FOR SINGULAR INTEGRALS ASSOCIATED TO SURFACES OF REVOLUTION ON PRODUCT DOMAINS

In this paper, the authors establish Lp boundedness for several classes of multiple singular integrals along surfaces of revolution with kernels satisfying rather weak size condition. The results of the corresponding maximal truncated singular integrals are also obtained. The main results essentially improve and extend some known results.     

二硅烷的光解反应

本文介绍了杂环基二硅烷的光解反应，用捕捉技术来研究，二硅烷光解反应的机理和产物，随硅原子上的取代基而异。