Algorithmic analysis of theMAP/PH/1 retrial queue

In this paper the distribution of the maximum number of customers in a retrial orbit for a single server queue with Markovian arrival process and phase type services is studied. Efficient algorithm for computing the probability distribution and some interesting numerical examples are presented.     

Photon interaction studies using 241Am γ-rays

We have carried out some photon interaction measurements using 59.54 keV γ-rays from a ²⁴¹Am source. These include γ attenuation studies as well as photoelectric absorption studies in various samples. The attenuation studies have been made using leaf and wood samples, samples like sand, sugar etc., which contain particles of varying sizes as well as pellets and aqueous solutions of rare earth compounds. In the case of the leaf and wood samples, we have used the γ-ray attenuation technique for the determination of the water content in fresh and dried samples. The variation of the attenuation coefficient with particle size has been investigated for sand and sugar samples. The attenuation studies as well as the photoelectric studies in the case of rare earth elements have been carried out on samples containing such elements whose K-absorption edge energies lie below and close to the γ-energy used. Suitable compounds of the rare earth elements have been chosen as mixture absorbers in these investigations. A narrow beam good geometry set-up was used for the attenuation measurements. A well-shielded scattering geometry was used for the photoelectric measurements. The mixture rule was invoked to extract the values of the mass attenuation coefficients for the elements from those of the corresponding compounds. The results are consistent with theoretical values derived from the XCOM package.     

次子空间的同构

引入了次子空间同构的概念，并得到次子空间同构的充要条件．     

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.     

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.     

Degeneracy in NLP and the development of results motivated by its presence

We study notions of nondegeneracy and several levels of increasing degeneracy from the perspective of the local behavior of a local solution of a nonlinear program when problem parameters are slightly perturbed. Ideal nondegeneracy at a local minimizer is taken to mean satisfaction of second order sufficient conditions, linear independence and strict complimentary slackness. Following a brief exploration of the relationship of these conditions with the classical definition of nondegeneracy in linear programming, we recall a number of optimality and regularity conditions used to attempt to resolve degeneracy and survey results of Fiacco, McCormick, Robinson, Kojima, Gauvin and Janin, Shapiro, Kyparisis and Liu. This overview may be viewed as a structured survey of sensitivity and stability results: the focus is on progressive levels of degeneracy. We note connections of nondegeneracy with the convergence of algorithms and observe the striking parallel between the effects of nondegeneracy and degeneracy on optimality conditions, stability analysis and algorithmic convergence behavior. Although our orientation here is primarily interpretive and noncritical, we conclude that more effort is needed to unify optimality, stability and convergence theory and more results are needed in all three areas for radically degenerate problems.Research supported by National Science Foundation Grant ECS 90-00560 and Grant N00014-89-J-1537 Office of Naval Research