Hyperbolic-parabolic singular perturbation for quasilinear equations of Kirchhoff type

We consider a hyperbolic-parabolic singular perturbation problem for a quasilinear equation of Kirchhoff type, and obtain parameter-dependent time decay estimates of the difference between the solutions of a quasilinear dissipative hyperbolic equation of Kirchhoff type and the corresponding quasilinear parabolic equation. For this purpose we show time decay estimates for hyperbolic-parabolic singular perturbation problem for linear equations with a time-dependent coefficient.     

A fiberwise analogue of the Borsuk-Ulam theorem for sphere bundles over a 2-cell complex II

We describe a finite complex B as I-trivial if there does not exist a Z₂-map from Si−1 to S(α) for any vector bundle α over B and any integer i with i>dimα. We prove that the m-fold suspension of projective plane FP² is I-trivial if and only if m≠0,2,4 for F=C, m≠0,4 for F=H. In the case where F is the Cayley algebra, the m-fold suspension is shown to be I-trivial for every m>0.     

Equality and inequality constrained optimization algorithms with convergent stepsizes

In this paper, we consider two algorithms for nonlinear equality and inequality constrained optimization. Both algorithms utilize stepsize strategies based on differentiable penalty functions and quadratic programming subproblems. The essential difference between the algorithms is in the stepsize strategies used. The objective function in the quadratic subproblem includes a linear term that is dependent on the penalty functions. The quadratic objective function utilizes an approximate Hessian of the Lagrangian augmented by the penalty functions. In this approximation, it is possible to ignore the second-derivative terms arising from the constraints in the penalty functions.The penalty parameter is determined using a strategy, slightly different for each algorithm, that ensures boundedness as well as a descent property. In particular, the boundedness follows as the strategy is always satisfied for finite values of the parameter.These properties are utilized to establish global convergence and the condition under which unit stepsizes are achieved. There is also a compatibility between the quadratic objective function and the stepsize strategy to ensure the consistency of the properties for unit steps and subsequent convergence rates.This research was funded by SERC and ESRC research contracts. The author is grateful to Professors Laurence Dixon and David Mayne for their comments. The numerical results in the paper were obtained using a program written by Mr. Robin Becker.     

激光对生物分子的共振激发作用

在生物分子的“谐”和“非谐”振子势模型的基础上，用量子力学讨论了激光对生物分子的共振激作用；并用之对激光的生物激活、诱变机理的“共振吸收”定性理论作一解析分析。     

Recent studies on phosphorus-bridging carbonyl derivatives: organophosphorus analogs of aldehydes and ketones

Reactions of disodium tetracarbonylferrate, Na₂Fe(CO)₄, with sterically hindered dialkylaminodichlorophosphines, R₂NPCl₂ (R₂N=diisopropylamino, dicyclohexylamino, and 2,2, 6, 6-tetramethylpiperidino) in diethyl ether lead to the air-stable phosphorus-bridging carbonyl derivatives (R₂NP)₂COFe₂(CO)₆ as the major products. The phosphorus-bridging carbonyl group in (i-Pr₂NP)₂COFe₂(CO)₆ has been found to undergo the following types of reactions: 1)Reduction, 2)Acylation, 3)Extrusion of the carbonyl group. The mechanisms of the reactions have been considered.This work was presented at the Workshop «The Modern Problems of Heteroorganic Chemistry» held on the ship «Nikolai Bauman» during the period May 8–13, 1993.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 1858–1867, November, 1993.     

LB膜中螺吡喃材料的光学性质研究

利用ＬＢ技术制备螺吡喃有序分子膜，研究了气液界面上螺吡喃材料在不同成份和不同ｐＨ值亚相时的成膜行为，着重研究了螺吡喃在ＬＢ膜这个特殊介质环境中不同于溶液的光致变色机理和光学性质     

Electron transfer reactions of nickel(III) and nickel(IV) complexes

This review narrates the electron transfer reactions of various nickel(III) and nickel(IV) complexes reported during the period 1981 until today. The reactions have been categorized mainly with respect to the type of nickel complexes. The reactivity of nickel(III) complexes of macrocycles, 2,2′-bipyridyl and 1,10-phenanthroline, peptides and oxime–imine, and of nickel(IV) complexes derived from oxime–imine, oxime and miscellaneous ligands with various organic and inorganic electron donors have been included. Kinetic and mechanistic features associated with such interactions have been duly analyzed. The relevance of Marcus cross-relation equations in the delineation of the electron transfer paths has also been critically discussed.     

Symmetric form of the Hudson-Parthasarathy stochastic equation

We prove that the Hudson-Parthasarathy equation corresponds, up to unitary equivalence, to the strong resolvent limit of Schrödinger Hamiltonians in Fock space and that the symmetric form of this equation corresponds to the weak limit of the Schrödinger Hamiltonians.Translated fromMatematicheskie Zametki, Vol. 60, No. 5, pp. 726–750, November, 1996.     

The practice for eight-year operation of the cobalt-60 irradiation facility at Beijing Radiation Application Research Center

The radiation facility was made by Sulzer Company in Switzerland. The designed capacity is 3.7 × 10¹⁶Bq( 1MCi) and 12.21 × 10¹⁵Bq(330kCi)of Cobalt -60 source was loaded at the first phase. Current cobalt -60 source-loading is 2.4 × 10¹⁶Bq(650kCi). The equipment assembling and installation regulating and testing were completed at the end of 1988. The facility was put into commissioning in 1989. It operates 7000–8000 hours per year. The facility has been utilized to carry out many research work and irradiate many kinds of items. Lots of economical benefits have been gained since then. Now it is becoming a radiation processing model base in China. This paper summarized the strong and weak points of the design of the facility through in eight years' practice and analysed the economical benefits.