CertainC*-algebras with real rank zero and their corona and multiplier algebras: II

We first determine the homotopy classes of nontrivial projections in a purely infinite simpleC*-algebraA, in the associated multiplier algebraM(A) and the corona algebraM A/A in terms ofK _*(A). Then we describe the generalized Fredholm indices as the group of homotopy classes of non-trivial projections ofA; consequently, we determine theK _*-groups of all hereditaryC*-subalgebras of certain corona algebras. Secondly, we consider a group structure of *-isomorphism classes of hereditaryC*-subalgebras of purely infinite simpleC*-algebras. In addition, we prove that ifA is aC*-algebra of real rank zero, then each unitary ofA, in caseA it unital, each unitary ofM(A) and ofM(A)/A, in caseA is nonunital but -unital, can be factored into a product of a unitary homotopic to the identity and a unitary matrix whose entries are all partial isometries (with respect to a decomposition of the identity).Partially supported by a grant from the National Science Foundation.     

Etude Experimentale et Modelisation des Equilibres Solide—Liquide du Systeme Binaire H2O—UO2(NO3)2

The binary system H₂O—UO₂(NO₃)₂ was studied by solubility measurements and constant heat flow thermal analysis. Temperature and composition of the eutectic transformation between ice and uranyl nitrate hexahydrate were accurately defined. A new hydrate with 24 molecules of water decomposes at –21°C according to the peritectoid reaction<UO₂(NO₃)₂·24H₂O> <UO₂(NO₃)₂·6H₂O> + 18<H₂O>The quasi-ideal model was applied to the solid—liquid equilibria, using the following reaction hypothesis:((UO ₂ ²⁺ )) + 2((NO ₃ ^– ))+ h((H₂O)) ((UO₂OH⁺aq)) + ((H₃O⁺aq + 2((NO ₃ ^– aq))A complete calculation of the binary system was carried out with a global ionic hydration number h equal to 9 in the aqueous solutions. It allowed to the melting enthalpies of uranyl nitrate hydrates.

This revised version was published online in November 2005 with corrections to the Cover Date.     

An investigation of glasses for capillary chromatography

An investigation was conducted of various glasses, other than soda lime or borosilicate, for use in glass capillary gas chromatography. The work has uncovered some unique chromatographic qualities in the use of potash soda lead and fused silica glasses as materials for making glass capillary columns. The fused silica proved to be an ideal material for capillary column construction, being inherently more inert than glass containing metal oxides. It has been shown that through the use of thin wall capillary tubing of high flexibility many of the mechanical problems associated with glass capillary columns, such as fragility and column straightening, can be avoided.     

Three-Way Decision Models Based on Ideal Relations in Multi-Attribute Decision-Making

In recent years, research on applications of three-way decision (e.g., TWD) has attracted the attention of many scholars. In this paper, we combine TWD with multi-attribute decision-making (MADM). First, we utilize the essential idea of TOPSIS in MADM theory to propose a pair of new ideal relation models based on TWD, namely, the three-way ideal superiority model and the three-way ideal inferiority model. Second, in order to reduce errors caused by the subjectivity of decision-makers, we develop two new methods to calculate the state sets for the two proposed ideal relation models. Third, we employ aggregate relative loss functions to calculate the thresholds of each object, divide all objects into three different territories and sort all objects. Then, we use a concrete example of building appearance selection to verify the rationality and feasibility of our proposed models. Furthermore, we apply comparative analysis, Spearman’s rank correlation analysis and experiment analysis to illustrate the consistency and superiority of our methods.     

基于模糊集合论的实物期权定价方法

实物期权的定价在风险投资决策过程中具有重要意义.传统的实物期权定价方法忽略标的资产价值和投资成本的模糊性,从而可能导致错误的投资决策.本文主要研究了具有模糊标的的资产价值和投资成本情形时的实物期权定价模型.文中将这些模糊因素分别视为模糊数和模糊变量,然后运用模糊集合论,结合B-S期权定价理论,对实物期权进行定价,得到了基于模糊集合论的实物期权定价模型.     

节瘤缺陷激光损伤的研究进展

在近红外反射类激光薄膜中,节瘤缺陷是引起薄膜激光损伤的主要因素。为了提高激光薄膜的损伤阈值,对节瘤缺陷及其损伤特性进行研究具有重要意义。从真实节瘤缺陷和人工节瘤缺陷两个方面介绍节瘤缺陷的研究进展。基于真实节瘤缺陷的研究,建立了节瘤缺陷的结构特征,形成了节瘤缺陷损伤特性和损伤机制的初步认识,利用时域有限差分法(FDTD)模拟了电场增强,初步解释了节瘤缺陷的损伤机制,发明了抑制节瘤缺陷种子源的方法和激光预处理技术,减少了节瘤缺陷,提高了薄膜损伤阈值。但是真实节瘤缺陷的性质,如种子源尺寸、吸收性以及位置深度等,都难以控制和预测,难以开展节瘤缺陷损伤特性的系统和量化研究,致使关于节瘤缺陷损伤的科学认识尚有不足。基于人工节瘤缺陷的研究,可以实现节瘤缺陷损伤特性的系统、量化甚至单一因素研究,极大地提高了实验研究的效率和可靠性,获得了一系列定量损伤规律。人工节瘤缺陷的高度受控性使实验研究与理论模拟的可靠对比成为可能,人工节瘤缺陷的损伤形貌和FDTD电场模拟的直接比较实验不仅验证了时域有限差分法(FDTD)模拟电场的正确性,也进一步明确了电场增强是诱导节瘤缺陷损伤的主要机制。对节瘤缺陷的损伤机制有了更为深刻的认识后,人们开始调控节瘤缺陷的电场增强效应提高节瘤缺陷的损伤阈值,发展了宽角度反射薄膜技术和节瘤缺陷平坦化技术,抑制电场增强,提高损伤阈值。这扩展了控制节瘤缺陷的思路和方法,从原来单一的去除节瘤缺陷到调控节瘤缺陷,为进一步提高薄膜的损伤阈值开辟了新的方向和途径。     

A New Entropy Function to Analyze Isentropic Processes of Ideal Gases with Variable Specific Heats

A new entropy function s⁺ is defined in terms of the existing entropy function s° and temperature as s⁺ = s° − R lnT to facilitate the analysis of isentropic processes of ideal gases with variable specific heats. The function s⁺ also makes it possible to calculate the entropy changes of ideal gases during processes when volume information is available instead of pressure information and the variation of specific heats with temperature is to be accounted for. The introduction of the function s⁺ eliminates the need to use the dimensionless isentropic functions relative pressure P_r and relative specific volume v_r of ideal gases and to tabulate their values. The P_r and v_r data are often confused with pressure and specific volume, with an adverse effect on the study of the second law of thermodynamics. The new s⁺ function nicely complements the existing s° function in entropy change calculations: the former is conveniently used when volume information is given while the latter is used when pressure information is available. Therefore, the introduction of the new entropy function s⁺ is expected to make a significant contribution to the thermodynamics education and research by streamlining entropy analysis of ideal gases.     

Jordan operator algebras revisited

Jordan operator algebras are norm‐closed spaces of operators on a Hilbert space with for all . In two recent papers by the authors and Neal, a theory for these spaces was developed. It was shown there that much of the theory of associative operator algebras, in particular, surprisingly much of the associative theory from several recent papers of the first author and coauthors, generalizes to Jordan operator algebras. In the present paper we complete this task, giving several results which generalize the associative case in these papers, relating to unitizations, real positivity, hereditary subalgebras, and a couple of other topics. We also solve one of the three open problems stated at the end of our earlier joint paper on Jordan operator algebras.     

On idempotents of a class of commutative rings

Abstract

In the present work, a procedure for determining idempotents of a commutative ring having a sequence of ideals with certain properties is presented. As an application of this procedure, idempotent elements of various commutative rings are determined. Several examples are included illustrating the main results.