Numerical comparison of several variable-metric algorithms

The paper compares the numerical performances of the LDL decomposition of the BFGS variable-metric algorithm, the Dennis-Mei dogleg algorithm on the BFGS update, and Davidon's projections with the BFGS update with the straight BFGS update on a number of standard test problems. Numerical results indicate that the standard BFGS algorithm is superior to all of the more complex strategies.This research was supported by the National Science Foundation under Research Grant No. MCS77-07327.     

On fluctuations in μ-space

A master equation is derived microscopically to describe the fluctuating motion of the particle density in . space. This equation accounts for the drift motion of particles and is valid for any inhomogeneous gas. The Boltzmann equation is obtained from the first moment of this equation by neglecting the second cumulant (the pair correlation function). The successive moments form coarse-grained BBGKY-like hierarchy equations, in which small spatial regions with r_ij < the force range are smeared out. These hierarchy equations are convenient for investigating the nonequilibrium long-range pair correlation function, which arises mainly from sequences of isolated binary collisions and gives rise to the much-discussed long-time tail and the logarithmic term in the density expansion of transport coefficients. It is shown to have a spatial long tail, like the Coulombic potential, in a steady laminar flow. The stochastic nature of the nonlinear Boltzmann-Langevin equation is also investigated; the random source term is found to be expressed as a linear superposition of Poisson random variables and to become Gaussian in special cases.     

Free energies of transfer of alkali halides from water to urea-water mixtures at 25°C from EMF measurements

The standard potentials_s E ^o of M/M⁺ (M=Li, Na, K, Rb, and Cs) electrodes in aqueous urea solutions containing 12, 20, 30 and 37% by weight of urea have been determined at 25°C from emf measurements on the cell M(Hg)/MCl (m), solvent/AgCl–Ag, from the activities of metals in amalgams by use of a similar type of cell in water, and from the values of_s E ^o of the Ag/AgCl electrode determined earlier. The standard free energies of transfer of MCl, G _t ^o (MCl), from water to the mixed solvents, computed by use of these values and those for the Ag–AgCl electrode, rise sharply from Li⁺ to Na⁺ but fall from Na⁺ to K⁺ and rather sharply from K⁺ to Cs⁺ with a maximum at Na⁺ in all the solvent compositions. This has been attributed to the superimposition of soft-soft interactions on the electrostatic interactions between the ions and the negative charge centers of the possible hydrogen-bonded solvent complexes in the mixed solvents. Comparison of G _t ^o (i) values for individual ions, obtained by a simultaneous extrapolation procedure, with those in aqueous mixtures of methanol,t-butanol, and dimethyl sulfoxide leads to the conclusion that the solvation of these ions in all these solvents is chiefly dictated by the acid-base type of ion-solvent interactions.     

Deprotonated and non-deprotonated cobalt(II) complexes of the bis-amide tetradentate ligand N,N′-(dipicolyl)-1,8-naphthylene diamine. Three different modes of coordination by the ligand

The preparation and some properties of the cobalt(II) complexes Co(LH₂)Cl₂·2H₂O, Co(LH₂(NCS)₂ and CoL·H₂O (whereLH₂=N,N-(dipicolyl)-1,8-naphthylenediamine) are reported. On the basis of magnetic moments, visible reflectance and IR data, the structure is proposed to be pseudo-octahedral for Co(LH₂)Cl₂·2 H₂O, pseudo-tetrahedral for Co(LH₂)(NCS)₂ and square planar for CoL·H₂O.

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Deprotonierte und Nicht-deprotonierte Co(II)-Komplexe des vierzähnigen Bisamid-Liganden N,N-(Dipicolyl)-1,8-naphthyldiamin. Drei verschiedene Koordinationstypen

Zusammenfassung Es werden die Darstellung und einige Eigenschaften der Kobalt(II)-Komplexe Co(LH₂)Cl₂·2 H₂O, Co(LH₂)(NCS)₂ und CoL·H₂O [LH₂=N,N-(dipicolyl)-1,8-naphthylendiamin] diskutiert. Auf der Grundlage von magnetischen Momenten, von Daten der sichtbaren Reflektions-und IR-Spektren wird eine pseudooctaedrische Struktur für Co(LH₂)Cl₂·2H₂O, eine pseudotetraedrische für Co(LH₂)(NCS)₂ und eine planar-quadratische für CoL·H₂O vorgeschlagen.

     

Quantum chemical studies on electrophilic addition

The geometries of the 2-aminoethyl cation and the isomeric protonated aziridine have been optimized using ab initio molecular orbital calculations employing the split-valence shell 4-31G basis set. The protonated aziridine is computed to be the more stable ion by 46.5 kcal/mole (4-31G level) and 44.9 kcal/mole (double-zeta basis set). The profile to interconversion is found to have a barrier of less than 15 kcal/mole (relative to the 2-aminoethyl cation) and this profile is compared with those computed for the similar ions XCH₂CH ₂ ⁺ where X=OH, F, SH and Cl.     

Mixed strategy solutions forN-person quadratic games

Mixed strategy -equilibrium points are given forN-person games with cost functions consisting of quadratic, bilinear, and linear terms and strategy spaces consisting of closed balls in Hilbert spaces. The results are applied to linear-quadratic differential games with no information and quadratic integral constraints on the control functions.This work was supported by a Commonwealth of Australia, Postgraduate Research Award.     

About a minimax theorem of Matthies,Strang and Christiansen

We give a new minisup theorem for noncompact strategy sets. Our result is of the type of the Matthies-Strang-Christiansen minimax theorem where the hyperplane should be replaced by any closed convex set. As an application, we derive a slight generalization of the Matthies-Strang-Christiansen minimax theorem.     

Field-theoretic approach to second-order phase transitions in two- and three-dimensional systems

We review the physical principles which are at the basis of recent field-theoretic computations of the critical exponents in two- and three-dimensional systems. We concentrate on those points that do not show up explicitly in the more standard-expansion: they must be discussed with care if one uses a perturbative approach at fixed space dimensions (the loop expansion). We present in detail simple computations of the critical exponents, while we summarize the results of longer and more accurate computations.     

Transformed steroids

A preparative method for 9a-hydroxylation of ⁵-3-hydroxysteroids using the fungi ofCircinella sp. 10Kh-1220 not capable of modifying theA ring has been developed. It is established that the yields of the main and the side products greatly depend on the transformation conditions, mycelium age, and the structure of the steroid substrate. Under the optimal transformation conditions novel 9-hydroxysubstituted derivatives of androstenolone, pregnenolone, 16-dehydro-16,17-epoxy-, and-16-methoxypregnenolone have been obtained in 36–80 % yields.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 737–743, April, 1994.