The convergence properties of direct methods of energy minimization with respect to linear coefficients in the LCAO-MO-SCF approach

It is shown that in the LCAO-MO-SCF problem, if the molecular orbital orthonormality constraints are introduced in the manner first suggested by Fletcher, then the Hessian of the problem is singular. It is suggested that this singularity may well account for the slow convergence observed using direct energy minimization methods to solve the SCF problem. Ways of avoiding the consequences of this singularity are discussed.     

Determination of enthalpies of formation of organic free radicals from bond dissociation energies 2. Halosubstituted radicals

The enthalpies of formation (ΔH _f ^o) for 23 halosubstituted radicals were determined from the published data on bond dissociation energies. The ΔH _f ^o values of the corresponding molecules necessary for the calculation of ΔH _f ^o of the radicals were taken from handbooks or calculated by the additive-group method. The conjugation energies of the radicals are calculated, and the effect of substituents at the π-system on these values was shown. Errors of determination of the ΔH _f ^o values of the radicals were estimated. For Part 1, see Ref. 1. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 643–646, April, 1998.     

原子吸收光谱法测定裂解汽油中铅

报道了用火焰原子吸收光谱法测定裂解汽油中铅的方法。用碘 二甲苯溶液对汽油进行氧化处理,用稀硝酸进行萃取,萃取后浓缩液用原子吸收光谱法进行测定。铅含量在0～7.0μg·ml-1范围内符合比耳定律。对汽油样品进行分析时,相对标准偏差小于3.95%,对样品进行加标回收试验,回收率为97.7%～101.7%,方法的精密度和准确度良好。     

A subjective Bayesian approach to the theory of queues II — Inference and information in M/M/1 queues

This is a sequel to Part I of A Subjective Bayesian Approach to the Theory of Queues. The focus here is on inference and a use of Shannon's measure of information for assessing the amount of information conveyed by the various types of data from queues. The notation and terminology used here is established in Part I.     

The lion and man problem revisited

A pursuerP, whose speed is bounded by 1, wants to get closer to an evaderE, whose speed is bounded by >1.P wants to reduce his distancePE fromE below the capture radius . Both players are confined to a circular arena. This problem is equivalent to a problem discussed by Flynn, who characterized and gave numerical bounds to the least upper boundd* on the values ofPE thatE can maintain. He used direct methods and did not use Isaacs' theory.We solve our problem relying on the theory of singular surfaces in differential games. We construct and investigate barriers of the game of kind, and we replace Flynn's bounds ond* by analytical (exact) values for various speeds .The support of the TW Department of THT, Enschede, Holland, is gratefully acknowledged.     

Consistency of a linear system of inequalities

We show that a consistency check of a linear system of inequalitiesAxb reduces to check whetherQb0 for a certain matrixQ. It is a direct consequence of the Farkas-Minkowski theorem. Thus, when one has to check consistency for different values ofb, one need not run a numerical algorithm for eachb.On leave at the Electronics Research Laboratory of the University of California at Berkeley in a CNRS/NSF Exchange Program.     

Tactical problems involving uncertain actions

The purpose of this paper is to solve anm-silent versusn-silent duel with arbitrary accuracy functionsP andQ which are continuously differentiable in [0, 1] with positive derivatives in (0, 1) and such thatP(0)=Q(0)=0,P(1)(0, 1),Q(1)(0, 1). The game can be interpreted as a game in which the players know only that the numbers of their actions have binomial distribution.Part of this paper was written during the author's stay at the Institute of Statistics and Mathematical Economics, University of Karlsruhe, FRG. The author wishes to thank Prof. S. Trybua, Technical University of Wrocaw, Poland, for helpful discussion in preparing the paper and Prof. D. Pallaschke, University of Karlsruhe, FRG, for help in preparing the numerical example.     

Heat conductivity of three periodic Hard Disks via nonequilibrium molecular dynamics

We use a driving field, of the type first suggested by Evans, to generate a steady heat current in the simplest possible system, a two-dimensional periodic fluid of three hard disks. Hard-disk motion equations can be conveniently derived from repulsive constant-force or linear-force potentials by considering the infinitely repulsive limit of these potentials. We show that the isoenergetic and isokinetic forms of the nonequilibrium equations of motion generate steady-state heat conductivities differing by terms of order 1/N, whereN is the number of particles. The resulting conductivities appear to vary as the logarithm of the driving field strength. Even at low fields, the three-body periodic-system results lie well below Enskog's infinite-system prediction.     

The spherical-model limit in a random field

The spherical-model limitn of then-vector model in a random field, with either a statistically independent distribution or with long-range correlated random fields, is studied to demonstrate the correctness of the replica method in which then and replica limits limits are interchanged, provided the replica and thermodynamic limits are taken in the right order, in the case of long-range correlated random fields. A scaling form for the two-point correlation function relevant to the first-order phase transition below the lower critical dimensionality of the random system is also obtained.     

Conformational energies of cyclenes

An universal function for non-bonded interactions, which takes into account the relative orientation of the bonds is considered in calculating the conformational energies of cycloalkenes and cycloalkadienes. A comparison is made with previous results obtained by using usual 6-exp functions for non-bonded interactions.