Perturbation analysis of the orthogonal procrustes problem

Given two arbitrary real matricesA andB of the same size, the orthogonal Procrustes problem is to find an orthogonal matrixM such that the Frobenius norm MA – B is minimized. This paper treats the common case when the orthogonal matrixM is required to have a positive determinant. The stability of the problem is studied and supremum results for the perturbation bounds are derived.     

Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant

Summary This work is concerned with the existence and uniqueness of a class of semimartingale reflecting Brownian motions which live in the non-negative orthant of ^d . Loosely speaking, such a process has a semimartingale decomposition such that in the interior of the orthant the process behaves like a Brownian motion with a constant drift and covariance matrix, and at each of the (d-1)-dimensional faces that form the boundary of the orthant, the bounded variation part of the process increases in a given direction (constant for any particular face) so as to confine the process to the orthant. For historical reasons, this pushing at the boundary is called instantaneous reflection. In 1988, Reiman and Williams proved that a necessary condition for the existence of such a semimartingale reflecting Brownian motion (SRBM) is that the reflection matrix formed by the directions of reflection be completely-L. In this work we prove that condition is sufficient for the existence of an SRBM and that the SRBM is unique in law. It follows from the uniqueness that an SRBM defines a strong Markov process. Our results have potential application to the study of diffusions arising as approximations tomulti-class queueing networks.Research supported in part by NSF Grants DMS 8657483, 8722351 and 9023335, and a grant from AT&T Bell Labs. In addition, R.J. Williams was supported in part during the period of this research by an Alfred P. Sloan Research Fellowship     

Preparation of 1,1,1,3,3-pentafluoropropane (HFC-245fa) by using a SbF5-attached catalyst

In this report, a simple process for preparing HFC-245fa through the reaction of 1,1,1,3,3-pentachloropropane (PCP) and anhydrous HF via two-step vapor-phase catalytic fluorination is described. The antimony pentafluoride catalyst was supported on inert porous materials to improve the catalytic activity. The resulting process catalyst not only exhibited high catalytic activity and excellent thermo-stability, but also improved the performance of SbF₅, in terms of hygroscopicity and corrosion.     

Oxine complex of molybdenum

Molybdenum was reported to be precipitated quantitatively by 8-hydroxyquinoline in the pH range 3.3–7.6, the precipitated compound having the composition MoO₂(ox)₂. The pH range reported and the composition of the complex do not seem to be compatible with present knowledge of the pH stability of anionic and cationic molybdenum. It is now shown that under defined conditions, the precipitate is not formed at pH values higher than 2.24. In several estimations of other metals, molybdenum was masked by using a complexone at high pH values. It is now pointed out, that maintaining the solution at high pH value is itself sufficient and no other external complexing agent is necessary for masking molybdenum.     

丁氧基氯化钛载体型催化体系用于乙烯/丁烯-1共聚合的研究

<正> 近十几年来有关载体型高效齐格勒-纳塔催化体系用于乙烯共聚合反应有了不少报道,其中尤以氯化镁为载体的体系居多。本文系统地研究了以氯化镁为载体的一系列正丁氧基氯化钛催化体系,在催化乙烯与丁烯-1共聚合反应的动力学行为,以及催化剂     

用动力学方法研究8,9-苯并-2-亚甲基-1,4,6-三氧螺[4,4]壬烷的聚合反应机理

根据在自由基引发剂存在下,8,9-苯并-2-亚甲基-1,4,6-三氧螺(4,4)壬烷(Ⅰ)可能存在的竞争反应,推导了动力学方程式。用红外光谱法测定了单体的消失速率和苯酞的生成速率。实验结果与推导动力学方程式相符。进一步证明了单体(Ⅰ)的增长反应由加成聚合和开环—异构化—加成这两个反应组成。这两个反应对总速率的相对贡献与单体浓度有关。得到了共聚物的结构。     

First synthesis of α-aminophosphonates from natural porphyrin derivatives by the Kabachnik—Fields reaction

A preparative procedure is proposed for the synthesis of α-aminophosphonates of natural porphyrins by the microwave-assisted Kabachnik—Fields reaction.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 256–259, January, 2005.     

Theoretical Study on the Structures and Electronic Spectra of the Derivatives of C_(60)-P-2,4,6-Triphenyl Borazinc

1 INTRODUCTION The electron-transfer reaction of C60 derivatives, especially light-induced electron-transfer reaction, has been an active research field for a long time. Many researches are focused on the long-live charge- separated state caused by electron-transfer[1]. And several electron-transfers between electron donor and C60 or intramolecular electron-transfer have been confirmed. As an example, TTF-C60 is proved to be a short-live charge-separated compound[2].Due to the excelle…     

Microwave-assisted, solvent-free synthesis of 1-(α- or β-hydroxynaphthyl)-1,2,3,4-tetrahydroisoquinolines by the Mannich reaction

As a new extension of the Mannich reaction of naphthols, 1-(hydroxynaphthyl)-substituted 1,2,3,4-tetrahydroisoquinolines were synthesized by the nucleophilic addition of 1- or 2-naphthol to 3,4-dihydroisoquinolines under solvent-free conditions, using microwave irradiation. The additions to 3-methyl-6,7-dimethoxy-3,4-dihydroisoquinoline proved to be a highly diastereoselective processes, resulting in the cis isomers as the main or the only products.