Factors affecting stability and equilibria of free radicals—IX: Non-equivalence of aryl groups in 1,1-diaryl-2-benzenesulphonyl-hydrazyls and related compounds

1,1-Bis-(3',5'-di-t-butylphenyl)-2-benzenesulphonyl-hydrazine 11 and the corresponding 2-picryl-hydrazine 13 were synthesized. Oxidation of 11 afforded the stable hydrazyl 12 whose ESR spectrum could be simulated in terms of three hyperfine coupling constants. These experimental data leave no alternative but to assign larger proton hyperfine coupling constants to one aryl group in 12 than to the other. This non-equivalence was interpreted in terms of the Linnett theory. The picrylhydrazyl 14 does not give completely resolved ESR spectra. Structures were ascertained by IR, UV-vis, ¹H NMR and ¹³C NMR spectra.     

顶点法在边坡稳定性评价中的应用

考虑到边坡稳定性分析中存在的测量数据的不确定性和确定计算参数的复杂性以及描述边坡稳定状态的模糊性, 本文介绍了-种新的适用于边坡稳定性分析的模糊数学方法—顶点法, 该法由不确定的土力学参数求得边坡稳定性系数的模糊集合, 然后运用对比法进行分类来确定边坡所处的稳定状态, 文章最后通过-个工程实例阐述了应用过程。     

中国八个城市居民食品摄入量与胃癌死亡率的对应分析

为探讨食品摄入量及胃癌死亡率与中国部分城市之间的关系,用对应分析方法对食品摄入量及胃癌死亡率与中国部分城市之间的关系进行分析.对应分析将8个城市16项食品摄入量及胃癌死亡率分成四个点群:点群族I城市包括上海、南京、苏州,食品包括大米、豆制品、绿色蔬菜、咸菜、猪肉、鱼虾类、绽粉类;点群族II城市包括北京、天津、西安,食品包括面粉、浅色蔬菜、水果、乳类、植物油;点群族III城市包括长春,食品包括干豆类、蛋类;点群族IV城市包括沈阳,食品包括薯类.说明中国部分城市与胃癌死亡率存在地区性差异,饮食中应减少精制米类及食盐的摄入,而增加面类和植物油的摄入.     

A continuous-state polynomial branching process

A continuous-state polynomial branching process is constructed as the pathwise unique solution of a stochastic integral equation with absorbing boundary condition. The process can also be obtained from a spectrally positive Lévy process through Lamperti type transformations. The extinction and explosion probabilities and the mean extinction and explosion times are computed explicitly. Some of those are also new for the classical linear branching process. We present necessary and sufficient conditions for the process to extinguish or explode in finite times. In the critical or subcritical case, we give a construction of the process coming down from infinity. Finally, it is shown that the continuous-state polynomial branching process arises naturally as the rescaled limit of a sequence of discrete-state processes.     

点传递图有向连通度的下界

本文研究点传递有向图与定向留连通度的下界，对达到此下界的Ｃｈｙｌｅｙ有向图与定向图进行了刻划。     

Vertex Angles of a Simplex in Hyperbolic Space H n

For an n-simplex in H ⁿ or S ⁿ , we give sine theorems and their results for kth-order vertex angles which are defined in this paper. The Gram and edge matrices, and polar simplex of n-simplex in H ⁿ or S ⁿ are used to prove the theorems and their results.     

Conformal designs based on vertex operator algebras

We introduce the notion of a conformal design based on a vertex operator algebra. This notation is a natural analog of the notion of block designs or spherical designs when the elements of the design are based on self-orthogonal binary codes or integral lattices, respectively. It is shown that the subspaces of an extremal self-dual vertex operator algebra of fixed degree form conformal 11-, 7-, or 3-designs, generalizing similar results of Assmus and Mattson and Venkov for extremal doubly-even codes and extremal even lattices. Other examples are coming from group actions on vertex operator algebras, the case studied first by Matsuo. The classification of conformal 6- and 8-designs is investigated. Again, our results are analogous to similar results for codes and lattices.     

Clustering of contingency table and mixture model

Basing cluster analysis on mixture models has become a classical and powerful approach. It enables some classical criteria such as the well-known k-means criterion to be explained. To classify the rows or the columns of a contingency table, an adapted version of k-means known as Mndki2, which uses the chi-square distance, can be used. Unfortunately, this simple, effective method which can be used jointly with correspondence analysis based on the same representation of the data, cannot be associated with a mixture model in the same way as the classical k-means algorithm. In this paper we show that the Mndki2 algorithm can be viewed as an approximation of a classifying version of the EM algorithm for a mixture of multinomial distributions. A comparison of the algorithms belonging in this context are experimentally investigated using Monte Carlo simulations.     

Untersuchung der Flammenemission von Metallhalogeniden und deren Nutzung zur Analytik der Halogene

Departing from the until now well known A and B systems of the indium and gallium halide emissions the authors tried to find further spectra of molecule bands in flames. The following band systems were observed: InF¹ (A, B and C systems), GaF¹ (A, B and C systems), A1F¹ (A system), T1C1¹, TlBr¹, TII¹ and the C systems of the GaCl, GaBr, InCl and InBr molecules.From the behaviour of the intensities of excited and nonexcited MeX species and the existence of InF-C bands (excitation energy 5.30 eV) in the hydrogen-nitrogen diffusion flame it could be derived that the excited state results from the reaction of metal and halogen atoms. Furthermore the experimental results of MeX intensity measurements indicate reactions of excited molecules with particles of flame gases. This is especially valid for the A and B systems of the indium and gallium halides (triplet states) which have as a result of the forbidden transitions a relatively long life time. Using other gas mixtures (Hr-air, propane-air) and observation of CuX and alkaline earth halide bands as well gave the possibility to set up a block diagram of optimum conditions for measuring the different MeX emissions.Examination of the analytical performance gave detection limits of 0.7 $\text{mg}\text{l}$ for F^?1 and about 4 $\text{mg}\text{l}$ for Cl^?, Br^? and I^? by means of InX emissions. The limits of the concentration ratios for the determination of traces were 1:640 (Cl^? in HBr) up to 1:60,000 (I^? in HF). The best determinations of other halogens are possible in HC1 and HF matrices.     

Some facets of the simple plant location polytope

We relate the simple plant location problem to the vertex packing problem and derive several classes of facets of their associated integer polytopes.This work was supported by NSF Grant ENG 79-02506.