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 ).     

关于B-凸空间及其上黎斯算子West分解

给出 Ｂａｎａｃｈ空间列｛Ｘｉ｝ｉ＝１∞的 ｌｐ乘积Ｂ－凸的特征刻划, 证明Ｂ－凸空间上的每个黎斯算子可Ｗｅｓｔ分解,即分解成一个紧算子和一个拟幂 零算子的和．     

Trigonometric wavelets for Hermite interpolation

The aim of this paper is to investigate a multiresolution analysis of nested subspaces of trigonometric polynomials. The pair of scaling functions which span the sample spaces are fundamental functions for Hermite interpolation on a dyadic partition of nodes on the interval . Two wavelet functions that generate the corresponding orthogonal complementary subspaces are constructed so as to possess the same fundamental interpolatory properties as the scaling functions. Together with the corresponding dual functions, these interpolatory properties of the scaling functions and wavelets are used to formulate the specific decomposition and reconstruction sequences. Consequently, this trigonometric multiresolution analysis allows a completely explicit algorithmic treatment.

     

Balancing domain decomposition for problems with large jumps in coefficients

The Balancing Domain Decomposition algorithm uses in each iteration solution of local problems on the subdomains coupled with a coarse problem that is used to propagate the error globally and to guarantee that the possibly singular local problems are consistent. The abstract theory introduced recently by the first-named author is used to develop condition number bounds for conforming linear elements in two and three dimensions. The bounds are independent of arbitrary coefficient jumps between subdomains and of the number of subdomains, and grow only as the squared logarithm of the mesh size . Computational experiments for two- and three-dimensional problems confirm the theory.

     

Thermal decomposition of transition metal carboxylates

Thermal solid-phase decomposition of anhydrous copper(ii) formate has been studied at 120–180 ° The rate of gas evolution during the decomposition depends on the depth of conversion and can be presented as the sum of first-order reaction rates and the rate of the autocatalytic process (a second-order reaction). The evolution of the solid phase during thermolysis has been observed by optical microscopy. The decomposition of copper formate is a complex topochemical process, a combination of homogeneous and heterogeneous transformations and dispersion of large crystals.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. l, pp. 72–76, January, 1996.     

High-temperature TG/DSC/QMS applications in environmental protection

The decomposition reactions of polystyrene, phenolic resin and a protective undercoating material for automobiles which contains PVC were tested using a new type of thermal analysis — mass spectrometry coupling system for measurements to 1500C or 2000C, which is based on the principle of a two-step skimmer orifice system. The results will be presented, with particular emphasis on the detection sensitivity of the new system for the products of decomposition.The capability of this coupling system to detect even heavy metals such as lead and silver in the waste gases from decomposition or after evaporation at high temperatures will also be demonstrated.     

A class of nonlinear relativistic partial differential equations in elementary particle theory

In mathematical approaches to elementary particle theory, the equation [² - ²/t²]=m² ;+g ³ has been of interest [1,2]; it describes a quartically self-coupled neutral scalar meson field. This paper applies the decomposition method [3-6] to obtain accurate non-perturbative timedevelopment of the field for this equation, or variations involving other nonlinear interactions, without the use of cutoff functions or truncations.     

Direct and stepwise intercalation of alkylalcohols intoα-zirconium phosphate

Intercalation of alkylalcohols into -zirconium phosphate was investigated at 25°C and/or under reflux.n-Alcohols having two to five carbons and 2-propanol were taken up at 25°C. These alcohols, andn-hexanol and heptanol, also intercalated under reflux.n-Alcohols having eight to eighteen carbon atoms intercalated when a stepwise method was employed. 2-Butanol and tertiary amylalcohols intercalated under reflux using a butanol intercalate as a starting material. Ethanol-to-butanol intercalates were unstable at room temperature, losing alcohols and changing to -zirconium phosphate. The particle size of the -zirconium phosphate did not affect the intercalation of alcohols.     

A characterization of discrete unimodality with applications to variance upper bounds

Bertin and Theodorescu (1984,Statist. Probab. Lett.,2, 23–30) developed a characterization of discrete unimodality based on convexity properties of a discretization of distribution functions. We offer a new characterization of discrete unimodality based on convexity properties of a piecewise linear extension of distribution functions. This reliance on functional convexity, as in Khintchine's classic definition, leads to variance dilations and upper bounds on variance for a large class of discrete unimodal distributions. These bounds are compared to existing inequalities due to Muilwijk (1966,Sankhy, Ser. B,28, p. 183), Moors and Muilwijk (1971,Sankhy, Ser. B,33, 385–388), and Rayner (1975,Sankhy, Ser. B,37, 135–138), and are found to be generally tighter, thus illustrating the power of unimodality assumptions.     

The properties of the metal complex hydrides

The essential features (geometries of the minima and of the saddle points, energy barriers) of the potential energy surface of the four hydrides YXH₄ mentioned in the title have been determined with two basis sets, of minimal and DZ quality respectively. The importance of the different extent of the deformation of the XH₄ group in the different structures of the four hydrides is brought out and discussed. The aspects of charge distribution and bonding are examined drawing on population analysis, comparison of the electrostatic molecular potentials and decomposition of the interaction energy (this last referred to the Y⁺ + XH ₄ ^– YXH₄ process). The capability of XH₃ in effecting the etherolytic disruption of the Y-H bond is finally brought out.