Effect of External Acidity of Mordenite-Supported Catalysts on the 2,2-Dimethylbutane Content in Hydroisomerization Products of n-Hexane

We have used potentiometric titration with tetrabutylammonium hydroxide to determine the acid center content on the outer surface of dealuminated natural and synthetic mordenites. We have established a symbatic relationship between the 2,2-dimethylbutane content in the hydroisomerization products of n-hexane on dealuminated palladium-containing mordenites and the number of their external acid centers. We have studied the possibility of partial deactivation of such centers during ion-exchange deposition of palladium on the catalysts, using a tetraammine palladium solution.     

有向全图的幂敛指数和周期

设G是有向图,T(G)表示G的有向全图.本文得到了它们的幂敛指数k(G)和k(T)之间的关系:对任何有向图G,周期p(T(G))=1;当G是本原图时,k(T)≤k(G)+1,文中给出了取得k(G)+1的两类图;当G是无圈图时,k(T)=2k(G)-1,当G是有向圈时,k(T)=2|V(G)|-1,当G是强连通时得到了k(T)的一些估计.     

Galactic Metrics

The paths of stars in galaxies have circular velocity independent of their distance from the centre of the galaxy. Newtonian mechanics with a logarithmic potential has such paths. In relativity these paths can be taken to be geodesics and this requirement places a restricting equation on the spacetime metric. This equation has a non-unique spherically symmetric solution that in the Newtonian limit has a logarithmic potential. It also can be solved in terms of a conformal factor. In particular it has solutions which are conformal to the vacuum-Einstein solutions and such spacetimes are solutions to the vacuum-Bach equations. Therefore it is suggested that the Bach equations describe dynamics on galactic length scales.     

Maximal σ‐polynomials of connected 3‐chromatic graphs

In the set of graphs of order n and chromatic number k the following partial order relation is defined. One says that a graph G is less than a graph H if c_i(G) ≤ c_i(H) holds for every i, k ≤ i ≤ n and at least one inequality is strict, where c_i(G) denotes the number of i‐color partitions of G. In this paper the first ? n/2 ? levels of the diagram of the partially ordered set of connected 3‐chromatic graphs of order n are described. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 210–222, 2003     

Spectral Analysis of Powers of the Operator (Vf)(x)=q(x)∫0 xw(t)f(t),dt

Mathematical Notes -     

On Two Theorems of Finite Solvable Groups

For a finite group G, let T（G） denote a set of primes such that a prime p belongs to T（G） if and only if p is a divisor of the index of some maximal subgroup of G. It is proved that if G satisfies any one of the following conditions： （1） G has a p-complement for each p∈T（G）; （2）│T（G）│= 2： （3） the normalizer of a Sylow p-subgroup of G has prime power index for each odd prime p∈T（G）; then G either is solvable or G/Sol（G）≌PSL（2, 7） where Sol（G） is the largest solvable normal subgroup of G.     

A Monte Carlo simulation of the heterogeneous adsorption of hydrogen ions on metal oxides: Effect of inert electrolyte

Charging of the surface of an oxide caused by the adsorption of hydrogen ions and ions of inert 1:1 electrolyte was investigated by using grand canonical Monte Carlo simulation technique. In particular, adsorption isotherms of protons as well as of ions of the electrolyte together with the resulting charge density of the surface were obtained for different system parameters. Also, the effect of the surface energetic heterogeneity and the concentration of the background electrolyte on the isotherms and the charge density curves was examined. Furthermore, lateral interactions in the mixed adsorbed phase were taken into account in the modeling of the system behavior. The obtained results, in general, suggest that the three factors mentioned above may have substantial influence on the charging mechanism at the liquid/oxide interface.     

非对称核物质中同位旋对称势的动量和密度依赖性

在Brueckner-Hartree-Fock理论框架内, 研究了同位旋非对称核物质中质子和中子单粒子势的动量相关性及其随同位旋非对称度的变化, 在此基础上计算了同位旋对称势, 并讨论了三体核力的影响. 结果表明同位旋对称势对于同位旋非对称度的依赖性很弱, 但对于动量和密度均有较强的依赖性. 当密度固定时, 同位旋对称势随动量增加而减小. 尽管三体核力对于质子和中子单粒子势的动量相关性有较大影响, 但对同位旋对称势的影响很小. 还与目前重离子碰撞输运理论模型中所使用的各种参数化的唯象对称势进行了比较.     

A strong law of large numbers for generalized random sets from the viewpoint of empirical processes

In this article we prove a strong law of large numbers for Borel measurable nonseparably valued random elements in the case of generalized random sets.