The maximum principle for the Bergman space and the Möbius pseudodistance for the annulus

It is shown that the formula for the Möbius pseudodistance for the annulus yields better estimates than previously known for the constant in the Bergman space maximum principle.

     

具有唯一4度最大度点的图的全色数

一个图Ｇ的全色数χ_T（Ｇ）是使得Ｖ（Ｇ）∪Ｅ（Ｇ）中相邻或相关联元素均染不同颜色的最少颜色数．文中证明了，若图Ｇ只有唯一的一个４度最大度点，则χ_T（Ｇ）＝Δ（Ｇ）＋１．     

Functional Central Limit Theorems for Triangular Arrays of Function-Indexed Processes under Uniformly Integrable Entropy Conditions

Functional central limit theorems for triangular arrays of rowwise independent stochastic processes are established by a method replacing tail probabilities by expectations throughout. The main tool is a maximal inequality based on a preliminary version proved by P. Gaenssler and Th. Schlumprecht. Its essential refinement used here is achieved by an additional inequality due to M. Ledoux and M. Talagrand. The entropy condition emerging in our theorems was introduced by K. S. Alexander, whose functional central limit theorem for so-calledmeasure-like processeswill be also regained. Applications concern, in particular, so-calledrandom measure processeswhich include function-indexed empirical processes and partial-sum processes (with random or fixed locations). In this context, we obtain generalizations of results due to K. S. Alexander, M. A. Arcones, P. Gaenssler, and K. Ziegler. Further examples include nonparametric regression and intensity estimation for spatial Poisson processes.     

A Monte Carlo method for an objective Bayesian procedure

This paper describes a method for an objective selection of the optimal prior distribution, or for adjusting its hyper-parameter, among the competing priors for a variety of Bayesian models. In order to implement this method, the integration of very high dimensional functions is required to get the normalizing constants of the posterior and even of the prior distribution. The logarithm of the high dimensional integral is reduced to the one-dimensional integration of a cerain function with respect to the scalar parameter over the range of the unit interval. Having decided the prior, the Bayes estimate or the posterior mean is used mainly here in addition to the posterior mode. All of these are based on the simulation of Gibbs distributions such as Metropolis' Monte Carlo algorithm. The improvement of the integration's accuracy is substantial in comparison with the conventional crude Monte Carlo integration. In the present method, we have essentially no practical restrictions in modeling the prior and the likelihood. Illustrative artificial data of the lattice system are given to show the practicability of the present procedure.     

Diagrams,orientations, and varieties

One of the central problems in the theory of ordered sets is to describe the orientations of the covering graph of an ordered set. We show that the particular operation called inversion, together with the classical constructions of retraction and product, provide a context for the classification of all such orientations. AMS subject classifications (1980). 06A10, 05C75, 05C20.     

Quadratically constrained minimum cross-entropy analysis

Quadratically constrained minimum cross-entropy problem has recently been studied by Zhang and Brockett through an elaborately constructed dual. In this paper, we take a geometric programming approach to analyze this problem. Unlike Zhang and Brockett, we separate the probability constraint from general quadratic constraints and use two simple geometric inequalities to derive its dual problem. Furthermore, by using the dual perturbation method, we directly prove the strong duality theorem and derive a dual-to-primal conversion formula. As a by-product, the perturbation proof gives us insights to develop a computation procedure that avoids dual non-differentiability and allows us to use a general purpose optimizer to find an-optimal solution for the quadratically constrained minimum cross-entropy analysis.     

Solution of a class of stochastic linear-convex control problems using deterministic equivalents

In this paper, we identify a new class of stochastic linearconvex optimal control problems, whose solution can be obtained by solving appropriate equivalent deterministic optimal control problems. The term linear-convex is meant to imply that the dynamics is linear and the cost function is convex in the state variables, linear in the control variables, and separable. Moreover, some of the coefficients in the dynamics are allowed to be random and the expectations of the control variables are allowed to be constrained. For any stochastic linear-convex problem, the equivalent deterministic problem is obtained. Furthermore, it is shown that the optimal feedback policy of the stochastic problem is affine in its current state, where the affine transformation depends explicitly on the optimal solution of the equivalent deterministic problem in a simple way. The result is illustrated by its application to a simple stochastic inventory control problem.This research was supported in part by NSERC Grant A4617, by SSHRC Grant 410-83-0888, and by an INRIA Post-Doctoral Fellowship.     

Quantitative surface analysis by Auger and x-ray photoelectron spectroscopy

Recent developments in quantitative surface analysis by Auger (AES) and x-ray photoelectron (XPS) spectroscopies are reviewed and problems relating to a more accurate quantitative interpretation of AES/XPS experimental data are discussed. Special attention is paid to consideration of elementary physical processes involved and influence of multiple scattering effects on signal line intensities. In particular, the major features of core-shell ionization by electron impact, Auger transitions and photoionization are considered qualitatively and rigorous approaches used to calculate the respective transition probabilities are analysed. It is shown that, in amorphous and polycrystalline targets, incoherent scattering of primary and signal Auger and photoelectrons can be described by solving analytically a kinetic equation with appropriate boundary conditions. The analytical results for the angular and energy distribution, the mean escape depth, and the escape probability as a function of depth of origin of signal electrons as well as that for the backscattering factor in AES are in good agreement with the corresponding Mote Carlo simulation data. Methods for inelastic background subtraction, surface composition determination and depth-profile reconstructions by angle-resolved AES/XPS are discussed. Examples of novel techniques based on x-ray induced photoemission are considered.     

Global Forcing Number of Benzenoid Graphs

A global forcing set in a simple connected graph G with a perfect matching is any subset S of E(G) such that the restriction of the characteristic function of perfect matchings of G on S is an injection. The number of edges in a global forcing set of the smallest cardinality is called the global forcing number of G. In this paper we prove several results concerning global forcing sets and numbers of benzenoid graphs. In particular, we prove that all catacondensed benzenoids and catafused coronoids with n hexagons have the global forcing number equal to n, and that for pericondensed benzenoids the global forcing number is always strictly smaller than the number of hexagons.     

Unicyclic Graphs with Minimal Energy

If G is a graph and ₁,₂,..., _n are its eigenvalues, then the energy of G is defined as E(G)=|₁|+|₂|++| _n |. Let S _n ³ be the graph obtained from the star graph with n vertices by adding an edge. In this paper we prove that S _n ³ is the unique minimal energy graph among all unicyclic graphs with n vertices (n6).