DATA PREORDERING IN GENERALIZED PAV ALGORITHM FOR MONOTONIC REGRESSION

Monotonic regression （MR） is a least distance problem with monotonicity constraints induced by a partiaily ordered data set of observations. In our recent publication [In Ser. Nonconvex Optimization and Its Applications, Springer-Verlag, （2006） 83, pp. 25-33], the Pool-Adjazent-Violators algorithm （PAV） was generalized from completely to partially ordered data sets （posets）. The new algorithm, called CPAV, is characterized by the very low computational complexity, which is of second order in the number of observations. It treats the observations in a consecutive order, and it can follow any arbitrarily chosen topological order of the poset of observations. The CPAV algorithm produces a sufficiently accurate solution to the MR problem, but the accuracy depends on the chosen topological order. Here we prove that there exists a topological order for which the resulted CPAV solution is optimal. Furthermore, we present results of extensive numerical experiments, from which we draw conclusions about the most and the least preferable topological orders.     

Preparation and Characterization of CuInS2 Thin Films for Solar Cells by Chemical Bath Deposition

Introduction Recent years, chalcopyrite semiconductors have been successfully applied as absorber layers for polycrystalline thin-film solar cells. Among the ternary compound semiconductors, CuInS2 thin films with a direct bandgap of about 1.50 eV and a large absorption coefficient in the range of 104-105cm-1[1] are one kind of the most promising optical absorbers for high efficiency thin film solar cells.To date, CuInS2-based solar cells have shown conversion efficiency of about 12. 5%[2]. They exhibit long-term stability without any signs of degradation.     

竹叶状多孔SnS薄膜的沉积

以硫代乙酰胺、三乙醇胺、氯化亚锡和氨水作反应物,氯化铵作缓冲剂,采用化学浴法在玻璃衬底上沉积SnS薄膜,并用X射线衍射(XRD)、扫描电子显微镜(SEM)等分析手段对样品进行了表征.XRD分析结果表明样品为斜方晶体结构的多晶SnS薄膜.SEM观察结果显示薄膜表面呈竹叶状多孔形貌,此结构有利于增加太阳电池的光吸收.     

The Full Study of Planar Quadratic Differential Systems Possessing a Line of Singularities at Infinity

In this article we make a full study of the class of non-degenerate real planar quadratic differential systems having all points at infinity (in the Poincaré compactification) as singularities. We prove that all such systems have invariant affine lines of total multiplicity 3, give all their configurations of invariant lines and show that all these systems are integrable via the method of Darboux having cubic polynomials as inverse integrating factors. After constructing the topologically distinct phase portraits in this class we give invariant necessary and sufficient conditions in terms of the 12 coefficients of the systems for the realization of each one of them and give representatives of the orbits under the action of the affine group and time rescaling. We construct the moduli space of this class for this action and give the corresponding bifurcation diagram. Dedicated to Professor Zhifen Zhang on the occasion of her 80th birthday     

Quadratic characters in groups of odd order

We prove that in a finite group of odd order, the number of irreducible quadratic characters is the number of quadratic conjugacy classes.     

On the quantum langevin equation

The quantum Langevin equation is the Heisenberg equation of motion for the (operator) coordinate of a Brownian particle coupled to a heat bath. We give an elementary derivation of this equation for a simple coupled-oscillator model of the heat bath.Deceased.     

Semi-invariants in surgery

A semi-invariant in surgery is an invariant of a quadratic Poincaré complex which is defined in terms of a null-cobordism. We define five such gadgets: the semicharacteristic, the semitorsion, the cross semitorsion, the torsion semicharacteristic, and the cross torsion semicharacteristic. We describe applications to the evaluation of surgery obstructions, especially in the odd-dimensional case.     

Behavior of a quantum particle in contact with a classical heat bath

We investigate the behavior of a two-level quantum system in contact with a classical heat bath, e.g., a solute particle with internal degrees of freedom immersed in a solvent of massive particles. Using a combination of analytical and numerical methods, we obtain precise information about localization, time-displaced correlation functions, and the frequency-dependent susceptibility of such solute particles. We find that these quantities can have a strong dependence on the density of the solvent fluid, with the maximum changes from the behavior of the corresponding isolated quantum system occurring in many cases at very low densities. We compare the exact results with those obtained by path integral Monte Carlo. There is good agreement with the imaginary time correlations, but analytic continuation to real time proves elusive: even with the best numerical data on the former, we can only get very gross features of the latter.     

Quadratic convex reformulations for quadratic 0–1 programming

This is a summary of the author’s PhD thesis supervised by A. Billionnet and S. Elloumi and defended on November 2006 at the CNAM, Paris (Conservatoire National des Arts et Métiers). The thesis is written in French and is available from http://www.cedric.cnam.fr/PUBLIS/RC1115. This work deals with exact solution methods based on reformulations for quadratic 0–1 programs under linear constraints. These problems are generally not convex; more precisely, the associated continuous relaxation is not a convex problem. We developed approaches with the aim of making the initial problem convex and of obtaining a good lower bound by continuous relaxation. The main contribution is a general method (called QCR) that we implemented and applied to classical combinatorial optimization problems.      

甘油对白酒中甲醇含量测定的影响

应用水浴控温(<90℃)蒸馏,可消除化学比色法测定白酒中甲醇含量时甘油的干扰,效果良好。