Bounds and Inequalities for the Perron Root of a Nonnegative Matrix

In this paper, bounds and inequalities for the Perron root of a nonnegative matrix, extending and complementing the classical theorems of Frobenius and Ostrowski in terms of (deleted) row and column sums, are presented. All the results are derived by using the same approach, based on the monotonicity property of the Perron root. Bibliography: 12 titles.     

Recyclization of 2,3-Disubstituted 5-Arylamino-2,5-dihydro-1,2,4-thiadiazoles and Related Salts into Benzothiazole Derivatives

Russian Journal of General Chemistry -     

Norm Series in High-Dimensional Local Fields

In the present paper, the notion of norm series with respect to the norm residue symbol is generalized to high-dimensional local fields. Necessary and sufficient conditions for the existence of norm series are obtained. Bibliography: 12 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 305, 2003, pp. 60–83.     

On the Global Stability of Solutions of Moment Systems in Nonequilibrium Thermodynamics

In this paper, we study the linearization of the Cauchy problem and the mixed problem for the system of Grad--Hermite moments in nonequilibrium thermodynamics in the neighborhood of the equilibrium state. Stability conditions for solutions of the Cauchy problem are proved as a generalization of the classical Hermite--Biller theorem on stable polynomials. For the mixed problem, we prove an analog of the Vishik--Lyusternik theorem on small singular perturbations of general elliptic problems. The last observation allows us to introduce the Shapiro--Lopatinskii condition, which implies the well-posedness of the mixed problem.     

Measurement of the dynamic elastic constants of short isotropic cylinders

A method based on a single test is proposed to characterize the elasticity of an isotropic homogeneous material in the shape of a cylinder of any slenderness (length-diameter) ratio. Firstly, the Rayleigh-Ritz method is used to determine the natural frequencies of the cylinders vibrating axisymmetrically. The study is focused on cylindrical samples with diameter and length of similar magnitude so that the shear modulus and the Poisson ratio can be calculated simultaneously. Subsequently, the theoretical results for cylinders of slenderness ratio between 0.1 and 3 are analyzed in order to obtain the data required to determine the elastic constants from one of the two lowest measured natural frequencies and their quotient. The analysis of the results demonstrates that any slenderness ratio is useful in the calculation of the elastic constants, although in some cases the third natural frequency should be used. Furthermore, the influence of the length-diameter quotient on the sensitivity of the method is analyzed by evaluating the systematic uncertainties for both dynamic elastic constants. Finally, the method is experimentally tested by characterizing two steel cylinders with slenderness ratios 0.1 and 1, respectively. The results demonstrate that uncertainties for both Poisson ratio and the shear modulus are smaller when the slenderness ratio is 1.     

Conditions for confinement and freeze-out

Matter implies the existence of a large-scale connected cluster of a uniform nature. The appearance of such clusters as a function of hadron density is specified by percolation theory. We can therefore formulate the freeze-out of interacting hadronic matter in terms of the percolation of hadronic clusters. The resulting freeze-out condition as a function of temperature and baryo-chemical potential interpolates between resonance gas behavior at low baryon density and repulsive nucleonic matter at low temperature, and it agrees well with the data.Received: 10 September 2003, Published online: 7 November 2003     

Rhythmic pattern formations in gels and Matalon—Packter law: A fresh perspective

The periodic precipitation pattern formation in gelatinous media is interpreted as a moving boundary problem. The time law, spacing law and width law are revisited on the basis of the new scenario. The explicit dependence of the geometric structure on the initial concentrations of the reactants is derived. Matalon—Packter law, which relates the spacing coefficient with the initial concentrations is reformulated removing many ambiguities and impractical parameters. Experimental results are discussed to establish the significance of moving boundary concept in the diffusion controlled pattern forming systems     

Approximation of the basic characteristics of the auditory analyzer

Empirical approximating formulas describing the most important psychophysiological properties of the human auditory analyzer are derived.     

A Variable Neighborhood Search for the Multi Depot Vehicle Routing Problem with Time Windows

The aim of this paper is to propose an algorithm based on the philosophy of the Variable Neighborhood Search (VNS) to solve Multi Depot Vehicle Routing Problems with Time Windows. The paper has two main contributions. First, from a technical point of view, it presents the first application of a VNS for this problem and several design issues of VNS algorithms are discussed. Second, from a problem oriented point of view the computational results show that the approach is competitive with an existing Tabu Search algorithm with respect to both solution quality and computation times.     

Half-width temperature dependence of nitrogen broadened lines in the ν2 band of H2O

Forty-seven N₂ broadened water vapor line-widths have been measured in the 1845-2140 cm⁻¹ spectral range with a Fourier Transform spectrometer in the 258-330 K temperature range at a spectral resolution of 0.005 cm⁻¹ for the lines with upper state rotational quantum number up to 16. The measured exponents of the temperature dependence of the width exhibit a large range of values from 1.60 to −0.86. Theoretical calculations were made using a semi-empirical technique based on the Anderson theory. The calculated broadening coefficients as well as the temperature exponents for the half-width agree satisfactory with measured values.