Relativistic effective potential SCF calculations of AgH and AuH

Relativistic effective potentials (REP) are now widely used in molecular electronic structure calculations. Tests of these REP are needed to assess their accuracy. This can now be done for AgH and AuH since Lee and McLean have published Dirac-Fock calculations for these molecules. Comparative SCF calculations have been performed for two types of effective potential. Satisfactory agreement between the effective potential results and Dirac-Fock values is found for spectroscopic constants and dipole moments, which supports the use of these potentials for heavy atom containing molecules.     

Oxygen effects on the EPR signals from wood charcoals: experimental results and the development of a model

Charcoals prepared from certain tropical woods contain stable paramagnetic centers, and these have been characterized by EPR spectroscopy in the absence and presence of oxygen. The EPR-detectable spin density has been determined, as has been the temperature- and frequency-dependence of the oxygen broadening of the EPR signal, which is orders of magnitude larger than that observed with other materials, such as lithium phthalocyanine. Three Lorentzian components are required to fit the char EPR spectrum in the presence of oxygen, and the oxygen-dependence of the line width, intensity, and resonance position of the three components have been quantified. These results and the properties of porous carbonaceous materials are used to develop a model to explain the effect of oxygen on the char EPR spectral properties. The model is based on oxygen adsorption on the char surface according to a Langmuir isotherm and a dipolar interaction between the paramagnetic adsorbed gas and the charcoal spins. The three EPR components are correlated with the three known classes (sizes) of pores in charcoal, with the largest line broadening attributed to dipolar relaxation of spins in micropores, which have a larger specific surface area and a higher concentration of adsorbed oxygen. An attenuated, but similar, EPR response to oxygen by chars when they are immersed in aqueous solution is attributed to water competition with oxygen for adsorption on the char surface.     

Some remarks on complete simply connected minimal surfaces meeting the planes x3 = Constant Transversally

The helicoid and plane are the only known complete embedded minimal surfaces inR ³ that are simply connected. We prove the helicoid and plane are the only surfaces of this type that have bounded curvature and meet each plane x₃ = constant in (at most) one smooth connected curve.     

Analytical examples of diffusive waves generated by a traveling wave

We construct analytical solutions for a system composed of a reaction–diffusion equation coupled with a purely diffusive equation. The question is to know if the traveling wave solutions of the reaction–diffusion equation can generate a traveling wave for the diffusion equation. Our motivation comes from the calcic wave, generated after fertilization within the egg cell endoplasmic reticulum, and propagating within the egg cell. We consider both the monostable (Fisher–KPP type) and bistable cases. We use a piecewise linear reaction term so as to build explicit solutions, which leads us to compute exponential tails whose exponents are roots of second-, third-, or fourth-order polynomials. These raise conditions on the coefficients for existence of a traveling wave of the diffusion equation. The question of positivity and monotonicity is only partially answered.     

Statistical energy analysis by finite elements for middle frequency vibration

Statistical energy analysis (SEA) is commonly used in industry to predict high-frequency vibrational response of structures. Since only local modes are used in SEA, only high-frequency responses can be predicted. This study extends SEA to the middle-frequency region by additionally using global modes. Methods using impedance matrices that can be found by NASTRAN are developed. Then the results are post processed to determine coupling loss factors.     

A better step-off algorithm for the knapsack problem

The knapsack problem, maximize Σ^m_{i = 1}c_ix_i when Σ^m_{i = 1}a_ix_i?b for integers x_i?0, can be solved by the classical step-off algorithm. The algorithm develops a series of feasible solutions with ever-increasing objective values. We make a change in the problem so that the step-off algorithm produces a series of solutions of not necessarily increasing objective values. A point is reached when no better solutions can be found and the calculation is stopped.