Ionic Interactions of Calcium Sulfate Dihydrate in Aqueous Sodium Chloride Solutions: Solubilities,Densities, Viscosities,Electrical Conductivities,and Surface Tensions at 35 <Superscript>∘</Superscript>C

The thermodynamic, volumetric, transport, and surface properties, solubilities, densities, viscosities, electrical conductivities, and surface tensions of calcium sulfate dihydrate in aqueous sodium chloride solutions have been measured at 35 C, with a view to determine the ionic interactions that occur in these solutions. The experimental density values have been used to calculate the mean apparent molar volumes of the ternary mixtures. Viscosity values have been analyzed using different empirical equations and the experimental values of the viscosity were combined with conductivity to yield the Walden product. Molar surface energies have been computed using experimental surface tension data. The experimental data have been fitted to polynomial equations by a least-squares analysis to obtain the coefficients and their standard errors. Results have been examined in the light of structure making or structure breaking effects of the various ions present in the solutions.     

Energy transport in the inductively coupled plasma

Time- and space-resolved electron density measurements, made both above the load coil and in the load coil region of a pulsed inductively coupled plasma, are presented. These data, coupled with argon and calcium emission data, give values for the rates of both radial and vertical transport in the plasma. The data indicate that analyte emission behavior is governed primarily by the rate at which the central channel can be heated through radial transport processes. The electron densities measured in the load coil region agree well with electron densities calculated by models assuming local thermodynamic equilibrium, but agree poorly with non-equilibrium models. Some of the timedependent emission behavior observed in previous work with modulated plasmas is explained by non-uniform heating of argon in the load coil region.Presented in part at the 1989 European Winter Conference on Plasma Spectrochemistry, Reutte, Austria     

46.8MeV的 ~(12)C非弹性散射

在Glauber多重散射理论框架下,使用跃迁密度方法和三种N-N湮没势,计算了46·8MeV的反质子在~(12)C上的非弹性散射微分截面.理论曲线与实验数据符合得较好.     

Asymptotic Behavior of the Sum of the Dirichlet Series of Prescribed Growth on Curves

We study the relationship between the growth and decrease of the sum of the entire Dirichlet series of finite order (in the sense of Ritt) on arbitrary curves going to infinity. For a class of exponents having a regular distribution (in a certain sense), we obtain a test for the logarithm of the maximal term to be equivalent to the logarithm of the absolute value of the sum of the Dirichlet series on at least one unbounded sequence of points of the curve.__________Translated from Matematicheskie Zametki, vol. 78, no. 1, 2005, pp. 37–51.Original Russian Text Copyright © 2005 by A. M. Gaisin, I. D. Latypov.     

Storage capacity of a dam with gamma type inputs

Summary Consider mutually independent inputsX ₁,...,X _n onn different occasions into a dam or storage facility. The total input isY=X ₁+...+X _n. This sum is a basic quantity in many types of stochastic process problems. The distribution ofY and other aspects connected withY are studied by different authors when the inputs are independently and identically distributed exponential or gamma random variables. In this article explicit exact expressions for the density ofY are given whenX ₁,...,X _n are independent gamma distributed variables with different parameters. The exact density is written as a finite sum, in terms of zonal polynomials and in terms of confluent hypergeometric functions. Approximations whenn is large and asymptotic results are also given.     

On a completeness property of series expansions of bivariate densities

Random processes passed through zero memory nonlinearities are considered in terms of the preservation of mean square continuity. Then, series expansions of bivariate densities in orthonormal functions are treated, under the assumption that the bivariate density is associated with a first order stationary random process. It is shown that, if the random process is mean square continuous, then the orthonormal functions in the series expansion must be complete.     

Transfer of charge in liquid alloys

Hard sphere diameters of liquid alkali metal alloys (Na-Cs and K-Rb) are calculated at 373 K ensuring the minimum Helmholtz free energy of the system. These diameters are then used to fix the packing density of the alloy. On alloying, the hard sphere diameters of Na in Na-Cs and K in K-Rb alloys expand whereas those of Cs and Rb contract.     

Dilation equations and Markov operators

Using the theory of Markov operators, we give a new proof of the known fact saying that for every positive integers N and k>1, and for every nonnegative reals c₀,…,cN satisfying the first sum rule the dilation equation

     

Nonnull distribution of likelihood ratio criterion for reality of covariance matrix

In this paper the distribution of the likelihood ratio test for testing the reality of the covariance matrix of a complex multivariate normal distribution is investigated. Some simplifications in the noncentral distribution are made and the noncentral distribution is derived for the special case where the rank of the noncentrality matrix is two. In the null case exact expressions for the distribution are given up to p = 6, and percentage points are tabulated. These percentage points were compared with percentage points derived from an asymptotic expansion of the distribution, and the accuracy of the approximation was found to be sufficient for several practical situations.     

Existence of densities of solutions of stochastic differential equations by Malliavin calculus

I considered if solutions of stochastic differential equations have their density or not when the coefficients are not Lipschitz continuous. However, when stochastic differential equations whose coefficients are not Lipschitz continuous, the solutions would not belong to Sobolev space in general. So, I prepared the class Vh which is larger than Sobolev space, and considered the relation between absolute continuity of random variables and the class Vh. The relation is associated to a theorem of N. Bouleau and F. Hirsch. Moreover, I got a sufficient condition for a solution of stochastic differential equation to belong to the class Vh, and showed that solutions of stochastic differential equations have their densities in a special case by using the class Vh.