Preperfect graphs

We say that a vertexx of a graph is predominant if there exists another vertexy ofG such that either every maximum clique ofG containingy containsx or every maximum stable set containingx containsy. A graph is then called preperfect if every induced subgraph has a predominant vertex. We show that preperfect graphs are perfect, and that several well-known classes of perfect graphs are preperfect. We also derive a new characterization of perfect graphs.     

Existence and Nonlinear Stability of Stationary States of the Schrödinger–Poisson System

We consider the Schrödinger–Poisson system in the repulsive (plasma physics) Coulomb case. Given a stationary state from a certain class we prove its nonlinear stability, using an appropriately defined energy-Casimir functional as Lyapunov function. To obtain such states we start with a given Casimir functional and construct a new functional which is in some sense dual to the corresponding energy-Casimir functional. This dual functional has a unique maximizer which is a stationary state of the Schrödinger–Poisson system and lies in the stability class. The stationary states are parameterized by the equation of state, giving the occupation probabilities of the quantum states as a strictly decreasing function of their energy levels.     

Optimale Quantisierung

Zusammenfassung. Optimale Quantisierungen oder – damit ?quivalent – minimale Summen von Momenten spielen in mehreren Zweigen der Mathematik und ihrer Anwendungen eine Rolle. Ausgehend von der Fejes Tóth'schen Ungleichung für Summen von Momenten in der euklidischen Ebene und einem zugeh?rigen Stabilit?tssatz, werden gewisse Erweiterungen auf normierte R?ume und riemannsche Mannigfaltigkeiten h?herer Dimension besprochen. Die Ergebnisse werden dann auf Probleme aus folgenden Bereichen angewendet: (i) Datenübertragung, (ii) Wahrscheinlichkeitstheorie, (iii) numerische Integration, (iv) Approximation konvexer K?rper und (v) isoperimetrische Probleme. Eingegangen am 29. Mai 2002 / Angenommen am 8. Juli 2002     

Uniform oriented matroids without the isotopy property

We give an easy general construction for uniform oriented matroids with disconnected realization space. This disproves the longstanding isotopy conjecture for simple line arrangements or order types in the plane.The research of Bernd Sturmfels and Neil White was supported in part by the Institute for Mathematics and Its Applications with funds provided by the National Science Foundation.     

Large deviation principle for enhanced Gaussian processes

We study large deviation principles for Gaussian processes lifted to the free nilpotent group of step N. We apply this to a large class of Gaussian processes lifted to geometric rough paths. A large deviation principle for enhanced (fractional) Brownian motion, in Hölder- or modulus topology, appears as special case.     

Asymptotic robustness of standard errors in multilevel structural equation models

Data in social and behavioral sciences are often hierarchically organized. Multilevel statistical methodology was developed to analyze such data. Most of the procedures for analyzing multilevel data are derived from maximum likelihood based on the normal distribution assumption. Standard errors for parameter estimates in these procedures are obtained from the corresponding information matrix. Because practical data typically contain heterogeneous marginal skewnesses and kurtoses, this paper studies how nonnormally distributed data affect the standard errors of parameter estimates in a two-level structural equation model. Specifically, we study how skewness and kurtosis in one level affect standard errors of parameter estimates within its level and outside its level. We also show that, parallel to asymptotic robustness theory in conventional factor analysis, conditions exist for asymptotic robustness of standard errors in a multilevel factor analysis model.     

Non-Achievability of Metal-Insulator Transition in Two-Dimensional Systems

We present a simple demonstration of the nonfeasibility of metal-insulator transition in an exactly two-dimensional （2D） system. The Hartree-Fock potential in the 3D system is suitably modified and presented for the 2D case. The many body effects are included in the screening function, and binding energies of a donor are obtained as a function of impurity concentration so as to find out the possible way leading metal-insulator transition in the 2D system. While solving for the binding energy for a shallow donor in an isolated well of a GaAs/Ga1-x Als As superlattice system within the effective mass approximation, it leads to unphysical results for higher concentrations. It shows that the phase transition, the bound electron entering into the conduction band whereby （H）min=0, is not possible beyond this concentration. The results suggest thai a phase transition is impossible in 213 systems, supporting the scaling theory of localization. The results are compared with the existing data available and discussed in the light of existing literature.