The diagnonal multivariate natural exponential families and their classification

A natural exponential family (NEF)F in ? ⁿ ,n>1, is said to be diagonal if there existn functions,a ₁,...,a _n , on some intervals of ?, such that the covariance matrixV _F (m) ofF has diagonal (a ₁(m ₁),...,a _n (m _n )), for allm=(m ₁,...,m _n ) in the mean domain ofF. The familyF is also said to be irreducible if it is not the product of two independent NEFs in ? ^k and ? ^n-k , for somek=1,...,n?1. This paper shows that there are only six types of irreducible diagonal NEFs in ? ⁿ , that we call normal, Poisson, multinomial, negative multinomial, gamma, and hybrid. These types, with the exception of the latter two, correspond to distributions well established in the literature. This study is motivated by the following question: IfF is an NEF in ? ⁿ , under what conditions is its projectionp(F) in ? ^k , underp(x ₁,...,x _n )∶=(x ₁,...,x _k ),k=1,...,n?1, still an NEF in ? ^k ? The answer turns out to be rather predictable. It is the case if, and only if, the principalk×k submatrix ofV _F (m ₁,...,m _n ) does not depend on (m _k+1,...,m _n ).     

Banach spaces that admit support sets

It is shown that the existence of a closed convex set all of whose points are properly supported in a Banach space is equivalent to the existence of a certain type of uncountable ordered one-sided biorthogonal system. Under the continuum hypothesis, we deduce that this notion is weaker than the existence of an uncountable biorthogonal system.

     

Impossibility of a Certain Cyclotomic Equation with Applicationsto Difference Sets

Under certain conditions, we show the nonexistence ofan element in the p-th cyclotomicfield over , that satisfies . As applications, we establish the nonexistence ofsome difference sets and affine difference sets.     

Countable network weight and multiplication of Borel sets

A space Borel multiplies with a space if each Borel set of is a member of the -algebra in generated by Borel rectangles. We show that a regular space Borel multiplies with every regular space if and only if has a countable network. We give an example of a Hausdorff space with a countable network which fails to Borel multiply with any non-separable metric space. In passing, we obtain a characterization of those spaces which Borel multiply with the space of countable ordinals, and an internal necessary and sufficient condition for to Borel multiply with every metric space.

     

HYPERFINITE TRANSVERSAL THEORY. II

We continue the investigation of validity of Hall's theorem in the case of the Loeb space of an internal, uniformly distributed, hyperfinite measure space initiated in1992 by the author. Some new classes of graphs are introduced for which the measure theoretic version of Hall's theorem still holds.

     

Stochastic dominance with nonadditive probabilities

Choquet expected utility which uses capacities (i.e. nonadditive probability measures) in place of-additive probability measures has been introduced to decision making under uncertainty to cope with observed effects of ambiguity aversion like the Ellsberg paradox. In this paper we present necessary and sufficient conditions for stochastic dominance between capacities (i.e. the expected utility with respect to one capacity exceeds that with respect to the other one for a given class of utility functions). One wide class of conditions refers to probability inequalities on certain families of sets. To yield another general class of conditions we present sufficient conditions for the existence of a probability measureP with f dC= f dP for all increasing functionsf whenC is a given capacity. Examples includen-th degree stochastic dominance on the reals and many cases of so-called set dominance. Finally, applications to decision making are given including anticipated utility with unknown distortion function.     

烯烃聚合均相催化剂研究进展

均相催化剂产生于５０年代末期，但由于活性很低而末引起重视。８０年代初，由于发现ＭＡＯ具有良好的助催化能力而使均相催化剂得到了很大发展，涌现了多种催化体系，广泛地使α－烯烃及其衍生物立体选择性聚合，开辟了配位聚合研究的新领域，本文对均相催化剂的产生，发展及现状作了综述评述。     

An experimental and theoretical study of vibrational spectra of picolinamide, nicotinamide, and isonicotinamide

The molecular structures and vibrational spectra of the three isomers of pyridinecarboxamide (picolinamide, nicotinamide, isonicotinamide) were calculated with the Density Functional Theory (DFT) method using the B3LYP function and the 6-31++G(d,p), Z2PolX, Z3PolX basis sets. The calculations were performed by using the Gaussian98W packet program set. The total energy distributions (TED) of the vibrational modes of these molecules were calculated by using the Scale 2.0 program and the vibrational modes of the molecules were determined. The Scaled Quantum Mechanical (SQM) method was used in the scaling procedure. In the experimental part of the study, the solid phase FT-IR and Micro Raman spectra of the three isomers of pyridinecarboxamide have been recorded in the range of 4000-650 and 1200-100 cm⁻¹, respectively. The calculated wavenumbers were compared to the corresponding experimental values. As a result, the observed bands of the three isomers of pyridinecarboxamide were assigned with good accuracy.     

均相催化剂催化合成碳酸亚丙酯

分别就单组为催化剂和双组分催化剂对二氧化碳与环氧丙烷合成碳酸亚丙酯的催化活性进行了研究。实验结果表明，在单组分催化体系中，相转移催化剂，如十六烷基三甲基漠化按、四丁基演化铵对上述酯化反应具有较高的催化活性此外，盐酸羟胺、三苯基磷也有一定的催化活性；在双组分催化体系中，KI／PEG（聚乙二醇）体系具有很高的催化活性，能在较短时间内、较低的压力下高产率地得到碳酸亚丙酯，而某些金属盐、有机碱、季接盐的适当红合，也能有效地催化该反应。     

Preparation, structure and ethylene polymerization behavior of mixed-halide nickel(II) complexes and cobalt(II) complex containing imidazolium

Preparation of two imidazolium salts, two monomeric nickel(II) and one cobalt(II) complexes bearing imidazolium ligands is described, The solid-state structures of these compounds have determined by single-crystal X-ray diffraction. After activation with methylaluminoxane (MAO) the nickel complexes show moderate catalytic activities of up to 6 × 10⁵ g PE mol⁻¹Ni h⁻¹ for polymerization of ethylene. Catalytic activities, molecular weights have been investigated under the various reaction conditions.