New algorithms for statistical modeling of inhomogeneous Poisson ensembles

New algorithms for statistical modeling of inhomogeneous Poisson ensembles are proposed. They are based on a special method for modeling discrete random variables. The corresponding modification of the well-known maximum cross section method is developed.     

States of total pure radiation in general relativity

Summary In this paper we investigate and exhibit space-times which admit states of pure radiation in the sense of Lichnerowicz. In § 1 the notion of special total pure radiation is introduced, and in § 2 we derive the canonical line element for this type of radiation. An additional type of spacetime admitting radiation is considered in § 3. A class of singular integrable electromagnetic fields for the space-times of § 2 are constructed in § 4. The final section is concerned with the radiation condition proposed by Zakharov. Work supported by National Science Foundation Grants GP 6876 and GP 7401.     

Scattering of electromagnetic plane waves by a spheroid uniformly moving in free space

We investigate the scattering process, generated by a plane electromagnetic field that is incident upon a moving perfectly conducting spheroid. An accurate treatment of the electromagnetic waves interaction with scatterers in uniform motion is based on the special relativity principle. In the object's frame the incident wave is assumed to have a wavelength which is much larger than the characteristic dimension of the scatterer and thus the low‐frequency approximation method is applicable to the scattering problem. For the near electromagnetic field we obtain the zeroth‐order low‐frequency coefficients, while in the far field we calculate the leading terms for the scattering amplitude and scattering cross‐section. Finally, using the inverse Lorentz transform, we obtain the same approximations in the observer's frame. Copyright © 2006 John Wiley & Sons, Ltd.     

Absolute curvature measures,II

The absolute curvature measures for sets of positive reach in R ^d introduced in [7] satisfy the following kinematic relations: Their integrated values on the intersections with (or on the tangential projections onto) uniformly moved p-planes are constant multiples of the corresponding absolute curvature measures of the primary set. In the special case of convex bodies the first result is the so-called Crofton formula. An analogue for signed curvature measures is well known in the differential geometry of smooth manifolds, but the motion of absolute curvatures used there does not lead to this property. For the special case of smooth compact hypermanifolds our absolute curvature measures agree with those introduced by Santaló [4] with other methods.In the appendix, the section formula is applied to motion invariant random sets.     

Pressure of a plane stamp of nearly circular cross section on an elastic half-space : PMM vol. 40, n 6, 1976, pp. 1143–1145

An approximate method of solving the contact problem of impressing a plane stamp of nearly circular cross section into an elastic half-space is suggested. The friction of the contact surface is neglected. A numerical algorithm for the method is produced. An elliptical and rectangular stamps are considered as examples.There is no general method of solving the problems for stamps of nearly circular cross section. Apart from the classical problem of a plane elliptical stamp, the literature gives solutions for the problems of polygonal stamps, with each problem however requiring a different approach. An approximate solution for the problem of impressing a stamp of nearly circular cross section into an elastic half-space is given in [1]. The method makes it possible to use the same approach to solve the contact problem for an arbitrary region of contact, and to construct an universal numerical algorithm. The program can be adapted to each particular case by making the corresponding changes in the procedure of computing the Fourier coefficients of the equation of the boundary of the area of contact. Below a numerical algorithm for the approximate method in question is given. A more effective formulation of the solution is given for the case of the elliptical stamp.     

Estimating Some Characteristics of the Conditional Distribution in Nonparametric Functional Models

This paper deals with a scalar response conditioned by a functional random variable. The main goal is to estimate nonparametrically some characteristics of this conditional distribution. Kernel type estimators for the conditional cumulative distribution function and the successive derivatives of the conditional density are introduced. Asymptotic properties are stated for each of these estimates, and they are applied to the estimations of the conditional mode and conditional quantiles. Our asymptotic results highlightes the importance of the concentration properties on small balls of the probability measure of the underlying functional variable. So, a special section is devoted to show how our results behave in several situations when the functional variable is a continuous time process, with special attention to diffusion processes and Gaussian processes. Even if the main purpose of our paper is theoretical, an application to some chemiometrical data set coming from food industry is presented in a short final section. This example illustrates the easy implementation of our method as well as its good behaviour for finite sample sizes.     

Some generalizations of the criss-cross method for quadratic programming

Three generalizations of the criss-cross method for quadratic programming are presented here. Tucker’s, Cottle’s and Dantzig’s principal pivoting methods are specialized as diagonal and exchange pivots for the linear complementarity problem obtained from a convex quadratic program

A finite criss-cross method, based on least-index resolution, is constructed for solving the LCP. In proving finiteness, orthogonality properties of pivot tableaus and positive semidefiniteness of quadratic matrices are used

In the last section some special cases and two further variants of the quadratic criss-cross method are discussed. If the matrix of the LCP has full rank, then a surprisingly simple algorithm follows, which coincides with Murty’s ‘Bard type schema’ in the P matrix case     

Harmonic Almost Contact Structures

An almost contact metric structure is parametrized by a section σ of an associated homogeneous fibre bundle, and conditions for σ to be a harmonic section, and a harmonic map, are studied. These involve the characteristic vector field ξ, and the almost complex structure in the contact subbundle. Several examples are given where the harmonic section equations for σ reduce to those for ξ, regarded as a section of the unit tangent bundle. These include trans-Sasakian structures. On the other hand, there are examples where ξ is harmonic but σ is not a harmonic section. Many examples arise by considering hypersurfaces of almost Hermitian manifolds, with the induced almost contact structure, and comparing the harmonic section equations for both structures.      

Modelling of rotating shafts with flexible disks

This paper deals with the methodology of the modelling of rotating shafts with flexible disks. Rotating shafts are modelled as a one dimensional continuum on the basis of the Bernouli-Euler theory, which assumes that the shaft cross section remains a flat plane and is perpendicular to the centerline during vibration. Disks are modelled as a three dimensional continuum by means of the finite element method. The presented approach allows to introduce centrifugal and gyroscopic effects. The special coupling matrix is used for the connecting a rotating shaft and a mounted flexible disk. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Discrete Cost Multicommodity Network Optimization Problems and Exact Solution Methods

We first introduce a generic model for discrete cost multicommodity network optimization, together with several variants relevant to telecommunication networks such as: the case where discrete node cost functions (accounting for switching equipment) have to be included in the objective; the case where survivability constraints with respect to single-link and/or single-node failure have to be taken into account. An overview of existing exact solution methods is presented, both for special cases (such as the so-called single-facility and two-facility network loading problems) and for the general case where arbitrary step-increasing link cost-functions are considered. The basic discrete cost multicommodity flow problem (DCMCF) as well as its variant with survivability constraints (DCSMCF) are addressed. Several possible directions for improvement or future investigations are mentioned in the concluding section.     

Theoretical-Experimental Regressions

We consider a method for the construction of multiple linear regressions with a special basis. In addition to the experimental data, a tabular function is given, approximating the sought regression relationship. This tabular function is used to calculate the special basis. We also consider the case of a mixed basis in which some functions are special and the others are ordinary, e.g., polynomials. An optimal experimental design procedure based on these regressions is proposed.     

The resistive coated sphere in the presence of a point generated wave field

We consider the low‐frequency scattering problem of a point source generated incident field by a small penetrable sphere. The sphere, which is also lossy, contains in its interior a co‐ecentric spherical core on the boundary of which an impedance boundary condition is satisfied. An appropriate modification of the incident wave field allows for the reduction of the solution to the corresponding scattering problem of plane wave incidence, by moving the point source to infinity. For the near field, we obtain the low‐frequency coefficients of the zeroth and the first order. This was done with the help of the corresponding solution for the hard core problem and an appropriate use of linearity with respect to the Robin parameter. In the far field, we derive the leading non‐vanishing terms for the normalized scattering amplitude and the scattering cross‐section, which are both of the second order, as well as for the absorption cross‐section, which is of the zeroth order. The special cases of a lossy or a lossless penetrable sphere, of a resistive sphere, and of a hard sphere are recovered by an appropriate choice of the physical or the geometrical parameters. Copyright © 1999 John Wiley & Sons, Ltd.     

Buckling analysis of a ring under the action of internal pressure in a cylindrical shell

Buckling analysis of a thin cylindrical shell stiffened by rings with T-shaped cross section under the action of uniform internal pressure in the shell is performed. An annular plate stiffened over the outer edge by a circular beam is used as the ring model. The classical ring model, which is a beam with a T-shaped cross section, is inappropriate in this problem, since in the case of the loss of stability, buckling deformations are localized on the ring surface. The beam model does not allow one to find the critical pressure that corresponds to such a loss of stability. In the first approximation, the problem of the loss of stability of the annular plate connected with the shell is reduced to solving the boundary value problem for finding eigenvalues of the annular plate bending equation. Approximate formulas for determining critical pressure are obtained under the assumption that the plate width is much smaller than its inner radius. The results found using the Rayleigh method and the shooting method differ slightly from each other. It has been demonstrated that the critical pressure for rings with rectangular cross section is higher than that for rings with a T-shaped cross section.     

A bilateral asymptotic method of solving the integral equation of the contact problem of the torsion of an elastic half-space inhomogeneous in depth

An approximate semi-analytical method for solving integral equations generated by mixed problems of the theory of elasticity for inhomogeneous media is developed. An effective algorithm for constructing approximations of transforms of the kernels of integral equations by analytical expressions of a special type is proposed, and closed analytical solutions are presented. A comparative analysis of the approximation algorithms is given. The accuracy of the method is analysed using the example of the contact problem of the torsion of a medium with a non-uniform coating by a stiff circular punch. The relation between the error of the approximation of the transform of a kernel by special analytical expressions, constructed using different algorithms and the error of approximate solutions of the corresponding contact problems is investigated using a numerical experiment.     

A method for obtaining approximate solutions for two-dimensional estuaries

An approximate model for the steady flow in a slightly stratified two- dimensional estuary is considered. The method consists of assuming an approximate form of the salinity which satisfies the boundary conditions and which contains two unknown constants. The stream function is calculated from the equation of motion. Two nonlinear equations for the two constants are obtained by applying Galerkin's method to the salt continuity equation and by insisting that there is zero salt flux across some vertical section.     

Differential operators for systems of linear partial differential equations

The aim of this paper is the representation of solutions of systems of formally hyperbolic differential equations of second order. I. N.Vekua gave a representation of the solutions using the Riemann-matrix-function. Here we introduce special differential operators which map holomorphic functions into the set of solutions. An existence theorem for such operators is proved which gives a necessary and sufficient condition on the coefficients of a system. These operators are represented explicitly and several properties of them are investigated. We give different representations of the solutions of such systems and discuss the relation between the integral operator method and the method using differential operators which leads to an explicit representation of the Riemann-matrix-function by means of the differential operators. Two examples of special systems with differential operators are given.     

求矩阵方程AXB+CXD=F的中心对称最小二乘解的迭代算法

该文建立了求矩阵方程AXB+CXD=F的中心对称最小二乘解的迭代算法.使用该算法不仅可以判断该矩阵方程的中心对称解的存在性,而且无论中心对称解是否存在,都能够在有限步迭代计算之后得到中心对称最小二乘解.选取特殊的初始矩阵时,可求得极小范数中心对称最小二乘解.同时,也能给出指定矩阵的最佳逼近中心对称矩阵.     

An interior-point affine-scaling trust-region method for semismooth equations with box constraints

An algorithm for the solution of a semismooth system of equations with box constraints is described. The method is an affine-scaling trust-region method. All iterates generated by this method are strictly feasible. In this way, possible domain violations outside or on the boundary of the box are avoided. The method is shown to have strong global and local convergence properties under suitable assumptions, in particular, when the method is used with a special scaling matrix. Numerical results are presented for a number of problems arising from different areas.     

New numerical methods and some applied aspects of the p-regularity theory

The theory of p-regularity is applied to optimization problems and to singular ordinary differential equations (ODE). The special variant of the method of the modified Lagrangian function proposed by Yu.G. Evtushenko for constrained optimization problems with inequality constraints is justified on the basis of the 2-factor transformation. An implicit function theorem is given for the singular case. This theorem is used to show the existence of solutions to a boundary value problem for a nonlinear differential equation in the resonance case. New numerical methods are proposed including the p-factor method for solving ODEs with a small parameter.