Exponential distributions on semigroups

Three fundamental characterizations of the standard exponential distribution on [0, ) are the remaining life, memoryless and constant failure properties. Analogs of these properties are studied for distributions on a class of semigroups in which the semigroup operation replaces addition, a compatible partial order replaces the ordinary order, and a left-invariant measure replaces Lebesgue measure. Partial characterizations of exponential distributions on such semigroups are obtained and the semigroup formulation provides new characterizations of certain aging properties studied in reliability-increasing failure rate, new better than used, and increasing failure rate average.     

Convolution semigroups and central limit theorem associated with a dual convolution structure

We consider hypergroups associated with Jacobi functions ⁽⁾ (x), (–1/2). We prove the existence of a dual convolution structure on [0,+[i(]0,s ₀]{{) =++1,s ₀=min(,–+1). Next we establish a Lévy-Khintchine type formula which permits to characterize the semigroup and the infinitely divisible probabilities associated with this dual convolution, finally we prove a central limit theorem.     

Rate conservation laws: A survey

We survey the rate conservation law, RCL for short, arising in queues and related stochastic models. RCL was recognized as one of the fundamental principles to get relationships between time and embedded averages such as the extended Little's formulaH=G, but we show that it has other applications. For example, RCL is one of the important techniques for deriving equilibrium equations for stochastic processes. It is shown that the various techniques, including Mecke's formula for a stationary random measure, can be formulated as RCL. For this purpose, we start with a new definition of the rate with respect to a random measure, and generalize RCL by using it. We further introduce the notion of quasi-expectation, which is a certain extension of the ordinary expectation, and derive RCL applicable to the sample average results. It means that the sample average formulas such asH=G can be obtained as the stationary RCL in the quasi-expectation framework. We also survey several extensions of RCL and discuss examples. Throughout the paper, we would like to emphasize how results can be easily obtained by using a simple principle, RCL.     

On the convergence of multipoint Padé-type approximants and quadrature formulas associated with the unit circle

We study the convergence of rational interpolants with prescribed poles on the unit circle to the Herglotz-Riesz transform of a complex measure supported on [–, ]. As a consequence, quadrature formulas arise which integrate exactly certain rational functions. Estimates of the rate of convergence of these quadrature formulas are also included.This research was performed as part of the European project ROLLS under contract CHRX-CT93-0416.     

The formation of the Ba(CuOx)1−y(CO3)y

Carbocuprate compounds are generally described as multiple perovskites with CO ₃ ² - and Cu-O alternating layers containing Ba and/or Sr; they have gained an unexpected importance in the high temperature superconductivity field, because many compounds with transition temperature above 100 K belong to this class of materials.We have started a systematic study on phase formation and stabilisation in the Ba-Cu-C-O system in the temperature range 20-600°C, by using thermal analysis techniques. Starting from a BaCO₃-BaO₂-CuO mixture (311 mol), a new phase isomorphic with BaCO₃ formed after heat treatment above 390°C in air. TG, DSC, EGA and high temperature XRD were employed to follow the complex interaction of the reactants with the atmosphere and the formation of the new phase.     

Alternating Sign Matrices and Some Deformations of Weyl's Denominator Formulas

An alternating sign matrix is a square matrix whose entries are 1, 0, or –1, and which satisfies certain conditions. Permutation matrices are alternating sign matrices. In this paper, we use the (generalized) Littlewood's formulas to expand the products and 2 as sums indexed by sets of alternating sign matrices invariant under a 180° rotation. If we put t = 1, these expansion formulas reduce to the Weyl's denominator formulas for the root systems of type B _n and C _n. A similar deformation of the denominator formula for type D _n is also given.     

A new catalyst for direct synthesis of dimethyl ether from synthesis gas

A new catalyst has been prepared by coprecipitation sedimentation method developed in our laboratory. It exhibits excellent catalytic activity, selectivity and stability for conversion of synthesis gas to dimethyl ether: conversion of CO 92%, selectivity of dimethyl ether 98%. Catalytic properties of the catalyst show no evident change after being used for 100 h.     

Phenolic Compounds of Plants of the Scutellaria L. Genus. Distribution, Structure, and Properties

Information on flavones, flavanones, flavanonols, flavonols, chalcones, isoflavones, biflavonoids, lignoflavonoids, and lignane glycosides and stilbenes isolated from plants of the Scutellaria L. genus was systematized and reviewed. A list of 208 phenolic compounds was given according to flavonoid type with an indication of the plant sources, structures, and physicochemical properties and citations of the original articles.     

New far infrared laser lines obtained by optically pumping13CD3OD

We have obtained laser action on 34 far infrared lines for the first time in fully deuterated methyl alcohol with the¹³C isotope (¹³CD₃OD), and we have measured the frequency of 13 lines. The molecule was pumped by a cw CO₂ laser. We have measured the wavelength, the relative polarization, the relative intensity of most lines, the frequency, and the CO₂ pump frequency offset of the strongest lines. The new lines are distributed in the wavelength region from 75.27 m to 464.7 m.Supported in part by a joint grant with the U.S. National Science Foundation grant # INT 80-19014 and the Brazilian Conselho Nacional de Pesquisas (CNPq).