The electronic spectrum of VCr

The electronic spectrum of VCr has been studied using the complete-active-space self-consistent field complete-active-space second-order perturbation theory approach. Potential-energy curves for 12 electronic states have been computed. Transition energies, with respect to the X² ground state, for some of the calculated electronic states are (with possible experimental values within parentheses) 0.53 eV (0.56) for A²⁺, 1.03 eV (1.14) for A⁴, 1.20 eV (1.14) for B², 1.45 eV (1.51) for B⁴, 1.60 eV (1.51, 1.78) for C², and 1.61 eV (1.63) for A^4–. AcknowledgementsThe research reported in this communication was supported by a grant from the Swedish Natural Science Research Council (NFR). S. Alex and D.G. Leopold are acknowledged for providing results from their negative ion photoelectron spectroscopy on VCr.Contribution to Björn Roos Honorary Issue     

Convexlike and concavelike conditions in alternative,minimax, and minimization theorems

Convexlike and concavelike conditions are of interest for extensions of the Von Neumann minimax theorem. Since the beginning of the 80's, these conditions also play a certain role in deriving generalized alternative theorems of the Gordan, Motzkin, and Farkas type and Lagrange multiplier results for constrained minimization problems.In this paper, we study various known convexlike conditions for vector-valued functions on a set and investigate convexlike and concavelike conditions for real-valued functions on a product setC×D, where we are mainly interested in the relationships between these conditions. At the end of the paper, we point out several conclusions from our results for the above-mentioned mathematical fields.The author is indebted to Dr. R. Reemtsen and Dr. V. Jeyakumar for their helpful comments during the preparations of this paper.     

TRANSIENT TORSIONAL WAVE IN FINITE HOLLOW CYLINDER WITH INITIAL AXIAL STRESS

An analytical solution is obtained for transient torsional vibration of a finite hollow cylinder with initial axial stress. The cylinder is subjected to dynamic shearing stress at the internal surface and is fixed at the external surface. The basic equations are presented and the solution is obtained by means of Fourier series expansion technique and the separation of variables method. The effects of the initial stress on the natural frequencies and transient torsional responses are presented and discussed.     

Multi-State Second-Order Nonlinear Optical Switches Incorporating One to Three Benzazolo-Oxazolidine Units: A Quantum Chemistry Investigation

This contribution employs quantum chemistry methods to describe the variations of the second nonlinear optical responses of molecular switches based on benzazolo-oxazolidine (BOX) units, connected by π-linkers, along their successive opening/closing. Under the fully closed forms, all of them display negligible first hyperpolarizability (β) values. When one BOX is opened, which is sketched as C→O, a push–pull π-conjugated segment is formed, having the potential to enhance β and to set the depolarization ratio (DR) to its one-dimensional-like value (DR = 5). This is observed when only one BOX is open, either for the monoBOX species (C→O) or for the diBOX (CC→CO) and triBOX (CCC→CCO) compounds, i.e., when the remaining BOXs stay closed. The next BOX openings have much different effects. For the diBOXs, the second opening (CO→OO) is associated with a decrease of β, and this decrease is tuned by controlling the conformation of the π-linker, i.e., the centrosymmetry of the whole compound because β vanishes in centrosymmetric compounds. For the triBOXs, the second opening gives rise to a Λ-shape compound, with a negligible change of β, but a decrease of the DR whereas, along the third opening, β remains similar and the DR decreases to the typical value of octupolar systems (DR = 1.5).     

pH值对KDP晶体中散射颗粒的影响

探讨了不同pH值对KDP晶体散射颗粒的影响。结果表明,不同pH值生长条件下生长的KDP晶体中散射颗粒的尺寸、密度呈现明显差异,pH值为5.5条件下KDP晶体中散射颗粒尺寸明显变大,分布稀疏;pH值为2.0时,散射颗粒密度高,尺寸小。其原因在于形成散射的杂质颗粒的存在形式不同。     

On the statistical mechanics of the traveling salesman problem

We consider the statistical mechanics of the traveling salesman problem (TSP) and develop some representations to study it. In one representation the mean field theory has a simple form and brings out some of the essential features of the problem. It shows that the system has spontaneous symmetry breaking at any nonzero temperature. In general the phase progressively changes as one decreases the temperature. At low temperatures the mean field theory solution is very sensitive to any small perturbations, due to the divergence of some local susceptibilities. This critical region extends down to zero temperature. We perform the quenched average for a nonmetric TSP in the second representation and the resulting problem is more complicated than the infinite-range spin-glass problem, suggesting that the free energy landscape may be more complex. The role played by frustration in this problem appears explicitly through the localization property of a random matrix, which resembles the tight binding matrix of an electron in a random lattice.     

On the initial layer solution of the Boltzmann equation with small Knudsen number

We extend our method of systematic removal of secular terms in a singular perturbation treatment of the Boltzmann equation with small Knudsen numbers to the initial layer. The requirement that the solution through the initial layer should connect smoothly to the normal solution removes an ambiguity noted in our previous paper. We show that removal of secular terms improves Grad's solution for the initial layer and reintroduces soundlike modes associated with higher moments, first found by Wang Chang and Uhlenbeck.     

Stationary velocity distribution in an external field: A one-dimensional model

The velocity distribution of a charged hard rod coupled to an external field and moving in a neutral equilibrium hard rod gas is studied on the basis of Boltzmann's equation. The exact stationary solution is found. Above a threshold value the field becomes effective in the high-velocity region slowing down the decay of the velocity distribution. The drift velocity and the mean kinetic energy are discussed as functions of the field.     

系数密集间断边值问题并行计算分析

研究系数密集间断的边值问题，采用降维方法，使得在数值计算上可实现并行计算，并且收敛性的证明变得很简洁．