The Polynomial Carathéodory—Fejér Approximation Method for Jordan Regions

We propose a method for the approximation of analytic functions on Jordan regions that is based on a Carathéodory—Fejér type of economization of the Faber series. The method turns out to be very effective if the boundary of the region is analytic. It often still works when the region degenerates to a Jordan arc. We also derive related lower and upper bounds for the error of the best approximatio

The Carathéodory—Fejér Extension of a Finite Geometric Series

It is shown that the Caratheodory—Fejer extension of a finite geometric series can be given explicitly up to a simple polynomial equation in an auxiliary variable. This result allows us to analyse the Caratheodory-Fejer approximation method in the case where the quotients of successive Maclaurin coefficients of the given function tend to a limi

Conformal Mapping on Rough Boundaries II: Applications to bi-harmonic problems

We use a conformal mapping method introduced in a companion paper to study the properties of bi-harmonic fields in the vicinity of rough boundaries. We focus our analysis on two different situations where such bi-harmonic problems are encountered: a Stokes flow near a rough wall and the stress distribution on the rough interface of a material in uni-axial tension. We perform a complete numerical solution of these two-dimensional problems for any univalued rough surfaces. We present results for sinusoidal and self-affine surface whose slope can locally reach 2.5. Beyond the numerical solution we present perturbative solutions of these problems. We show in particular that at first order in roughness amplitude, the surface stress of a material in uni-axial tension can be directly obtained from the Hilbert transform of the local slope. In case of self-affine surfaces, we show that the stress distribution presents, for large stresses, a power law tail whose exponent continuously depends on the roughness amplitude

Germanium Detector with Internal Amplification for Investigation of Rare Processes

Device of new type is suggested - germanium detector with internal amplification. Such detector having effective threshold about 10 eV opens up fresh opportunity for investigation of dark matter, measurement of neutrino magnetic moment, of neutrino coherent scattering at nuclei and for study of solar neutrino problem. Construction of germanium detector with internal amplification and perspectives of its use are described.Comment: 13 pages, latex, 3 figures, report at NANP-99, International Conference on Non-Accelerator Physics, Dubna, Russia, June 29- July 3, 1999. To be published in the Proceeding

Экономическая безопасность функционирования предприятия в условиях сетевой экономики

В наше время возникновение сетевых особенностей в экономике связывают с развитием информационных технологий, что приводит к эволюции современных экономических систем, развитию нерыночных механизмов регулирования и сетевых организационных структур. Другими словами, сетевые экономические отношения играют особую роль в процессе координации экономических взаимодействий. Данные изменения обостряют проблему экономической безопасности предприятия в условиях развития межорганизационных взаимодействий формального и неформального характера с позиции сетевой экономики

Photonic Clusters

We show through rigorous calculations that dielectric microspheres can be organized by an incident electromagnetic plane wave into stable cluster configurations, which we call photonic molecules. The long-range optical binding force arises from multiple scattering between the spheres. A photonic molecule can exhibit a multiplicity of distinct geometries, including quasicrystal-like configurations, with exotic dynamics. Linear stability analysis and dynamical simulations show that the equilibrium configurations can correspond with either stable or a type of quasi-stable states exhibiting periodic particle motion in the presence of frictional dissipation.Comment: 4 pages, 3 figure

Conformal Mapping on Rough Boundaries I: Applications to harmonic problems

The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this boundary. We introduce a conformal mapping technique that is tailored to this problem in two dimensions. An efficient algorithm is introduced to compute the conformal map for arbitrarily chosen boundaries. Harmonic fields can then simply be read from the conformal map. We discuss applications to "equivalent" smooth interfaces. We study the correlations between the topography and the field at the surface. Finally we apply the conformal map to the computation of inhomogeneous harmonic fields such as the derivation of Green function for localized flux on the surface of a rough boundary

A weakly stable algorithm for general Toeplitz systems

We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A. Thus, when the algorithm is used to solve the semi-normal equations R^T.Rx = A^Tb, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear system Ax = b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem.Comment: 17 pages. An old Technical Report with postscript added. For further details, see http://wwwmaths.anu.edu.au/~brent/pub/pub143.htm

Order reduction approaches for the algebraic Riccati equation and the LQR problem

We explore order reduction techniques for solving the algebraic Riccati equation (ARE), and investigating the numerical solution of the linear-quadratic regulator problem (LQR). A classical approach is to build a surrogate low dimensional model of the dynamical system, for instance by means of balanced truncation, and then solve the corresponding ARE. Alternatively, iterative methods can be used to directly solve the ARE and use its approximate solution to estimate quantities associated with the LQR. We propose a class of Petrov-Galerkin strategies that simultaneously reduce the dynamical system while approximately solving the ARE by projection. This methodology significantly generalizes a recently developed Galerkin method by using a pair of projection spaces, as it is often done in model order reduction of dynamical systems. Numerical experiments illustrate the advantages of the new class of methods over classical approaches when dealing with large matrices