The hard-sphere fluid: New exact results with applications

A theorem for convolution integrals is proved and then applied to extend the second zero-separation theorem to the bridge functionb(r) and direct-correlation tail functionsd(r). This theorem allows us to exactly relateb(r)/r andd(r)/ratr=0 for the hard-sphere fluid to the contact value of the radial distribution functiong(r) atr= ⁺. From this we obtain immediately the exact values of b(r)/r and d(r)/r atr=0 through second order in number density . Using our results to compare the exact and Percus-Yevick (PY) bridge function, we find that they differ significantly. After obtaining the bridge function and tail function and their derivatives atr=0 andr= through, we suggest new approximations forb(0) andd(0) as well as an analytical integral-equation theory to improve the PY approximation in the pure hard-sphere fluid. The major deficiency of that approximation has been its poor assessment of the cavity function inside the hard-core region. Our theory remedies this defect in a way that yields ay(r) that is self-consistent with respct to the virial and compressibility relations and also the two zero-separation relations involvingy(r) and its spatial derivative atr=0.     

沉淀法制备超细氧化铝粉末过程中的团聚机理和消除办法

采用沉淀法以Al(NO3)3.9H2O和NH3.H2O为原料制备了Al(OH)3干凝胶,经过高温煅烧合成纳米级的α-Al2O3粉末,分析了在制备过程中氧化铝粉末产生团聚的机理,推测了硬团聚的机理模型,并提出了几种消除硬团聚的方法,制备出的α-Al2O3粉末,粒径分布均匀,且无明显团聚,近似球形,平均粒径为70nm。     

A partial enumeration algorithm for pure nonlinear integer programming

In this paper, a partial enumeration algorithm is developed for a class of pure IP problems. Then, a computational algorithm, named PE_SPEEDUP (partial enumeration speedup), has been developed to use whatever explicit linear constraints are present to speedup the search for a solution. The method is easy to understand and implement, yet very effective in dealing with many pure IP problems, including knapsack problems, reliability optimization, and spare allocation problems. The algorithm is based on monotonicity properties of the problem functions, and uses function values only; it does not require continuity or differentiability of the problem functions. This allows its use on problems whose functions cannot be expressed in closed algebraic form. The reliability and efficiency of the proposed algorithm and the PE_SPEEDUP algorithm has been demonstrated on some integer optimization problems taken from the literature.     

Changing and unchanging of the domination number of a graph

Let G be a graph and γ(G) denote the domination number of G. A dominating set D of a graph G with |D|=γ(G) is called a γ-set of G. A vertex x of a graph G is called: (i) γ-fixed if x belongs to every γ-set, (ii) γ-free if x belongs to some γ-set but not to all γ-sets, (iii) γ-bad if x belongs to no γ-set, (iv) γ^--free if x is γ-free and γ(G-x)=γ(G)-1, (v) γ⁰-free if x is γ-free and γ(G-x)=γ(G), and (vi) γ^q-fixed if x is γ-fixed and γ(G-x)=γ(G)+q. In this paper we investigate for any vertex x of a graph G whether x is γ^q-fixed, γ⁰-free, γ^--free or γ-bad when G is modified by deleting a vertex or adding or deleting an edge.     

Thin position for knots and 3-manifolds

We prove that for 2-bridge knots and 3-bridge knots in thin position the double branched cover inherits a manifold decomposition in thin position. We also argue that one should not expect this sort of correspondence to hold in general.     

数字温度计制作实验及研究

本文介绍了设计性实验——数字温度计制作实验的开设,并对实验中存在的问题进行了研究和解决。     

Syntheses and Crystal Structures of Two Two-dimensional Coordination Polymers with 2,3-Dimethylpyrazine-1,4-dioxide and Thiocyanate as Mixed Bridge Ligands

Two two-dimensional coordination polymers,[Cd(μ1,3-SCN-)2(μ1,6-L)]n 1 and [Co(μ1,3-SCN-)2(μ1,6-L)]n 2,have been synthesized with 2,3-dimethylpyrazine-1,4-dioxide (L) and thiocyanate as mixed bridging ligands,and their crystal structures were determined by X-ray crystallography.Both crystals belong to monoclinic system,space group C2/c.The other crystal parameters are as follows:for complex 1:a = 9.732(3),b = 14.658(5),c = 8.811(3) (A),β =102.935(4)°,Z = 4,V = 1225.1(7)(A)3,CsHsCdN4O2S2,Mr = 368.71,Dc.-- 1.999 g/cm3,F(000) =720 andμ = 2.117 mm-1;for complex 2:a = 9.528(7),b = 14.563(11),c = 8.415(6) (A),β =102.195(9)°,V= 1141.3(14) (A)3,Z = 4,C8H8CoN4O2S2,Mr = 315.23,Dc = 1.835 g/cm3,F(000) =636 andμ = 1.863 mm-1.The two complexes show similar two-dimensional sheet structures.Along the c axis one-dimensional chains are constructed by the coordination of Cd(Ⅱ) (or Co(Ⅱ))ions with μ1,6-L bridging ligand,and the μ1,3-SCN- bridging ligands make the chains connect to each other,resulting in the formation of a two-dimensional sheet on the ac plane.     

Bridge-disubstituted calix[4]arenes obtained via a new preparative route. Synthesis and structural study

A series of calix[4]arenes bearing various substituents including alkyl, p-bromobenzyl, carboxy and allyl at opposite methylene bridges has been synthesized via successive metallation followed by nucleophilic substitution. In a first step, mono-lithiated calix[4]arenes react with terminal bromoalkanes to give 2-alkylated calix[4]arenes or with CO₂ the respective calixarene-2-carboxylic acid in good yields. A second lithiation step of the monosubstituted products with subsequent attachment of both polar and non-polar substituents yields several new diametrally bridge-disubstituted calix[4]arenes. 2D-NMR measurements establish the disubstituted calixarenes to predominantly adopt the 1,2-alternate conformation in solution. First examples of X-ray crystal structures of the new type of disubstituted calix[4]arenes are described featuring the calix[4]arene also in the rare 1,2-alternate conformation.