Exact solutions to linear programming problems

The use of floating-point calculations limits the accuracy of solutions obtained by standard LP software. We present a simplex-based algorithm that returns exact rational solutions, taking advantage of the speed of floating-point calculations and attempting to minimize the operations performed in rational arithmetic. Extensive computational results are presented.     

Another independent self-dual basis for the trivial variety

We give a new independent self-dual 3-basis for the trivial variety with two binary operations. Received October 24, 2006; accepted in final form January 25, 2007.     

Theoretical insight of adsorption thermodynamics of multifunctional molecules on metal surfaces

Adsorption thermodynamics based on density functional theory (DFT) calculations are exposed for the interaction of several multifunctional molecules with Pt and Au(1 1 0)-(1 × 2) surfaces. The Gibbs free adsorption energy explicitly depends on the adsorption internal energy, which is derived from DFT adsorption energy, and the vibrational entropy change during the chemisorption process. Zero-point energy (ZPE) corrections have been systematically applied to the adsorption energy. Moreover the vibrational entropy change has been computed on the basis of DFT harmonic frequencies (gas and adsorbed phases, clean surfaces), which have been extended to all the adsorbate vibrations and the metallic surface phonons. The phase diagrams plotted in realistic conditions of temperature (from 100 to 400 K) and pressure (0.15 atm) show that the ZPE corrected adsorption energy is the main contribution. When strong chemisorption is considered on the Pt surface, the multifunctional molecules are adsorbed on the surface in the considered temperature range. In contrast for weak chemisorption on the Au surface, the thermodynamic results should be held cautiously. The systematic errors of the model (choice of the functional, configurational entropy and vibrational entropy) make difficult the prediction of the adsorption-desorption phase boundaries.     

General Quantization

In the Darwinian evolution of physical theories, stability (genericity) has survival value. To convert a singular physical theory based on Lie algebras of several levels into a generic quantum theory with the same levels and nearly the same predictions and symmetries in a limited correspondence domain, it suffices to simplify the algebra of each level by a small homotopy (general quantization). This extends and unifies special relativization, general relativization, and canonical quantization. For exercise I general-quantize the scalar meson field in Minkowski space-time. The predictions of the resulting theory are finite, including its zero-point energy.This updates part of a talk given at Glafka 2005, Athens. quant-ph/0601002     

Aberrations theory of a time dependent magnetic field lens

We analyze new forms of aberrations affecting a time dependent magnetic field lens recently proposed. The lens consist of an axially symmetric ellipsoidal solenoid producing a spatially uniform but time pulsating homogeneous field. The dynamics of electrons emitted by some object and injected into this coil shows that this system is capable of focusing a parallel beam or produce images free of geometrical aberrations. The cardinal elements of this lens change periodically in positions and therefore to obtain a stationary image it is necessary to employ a chopped electron beam. Two forms of aberrations originate from the finite duration of the electron pulse and the energy dispersion of the incoming beam (chromatic aberration). Their image degradation effects are quite similar and result from recording different axially displaced images at some fixed stationary plane. We show how, by adjusting the parameters characterizing the magnetic pulse and introducing small apertures that increase the depth of focus, their effects can be reduced or in some cases eliminated. Other forms of instrumental aberrations characteristic of this time dependent magnetic field lens are briefly discussed.     

SRB States and Nonequilibrium Statistical Mechanics Close to Equilibrium

Nonequilibrium statistical mechanics close to equilibrium is studied using SRB states and a formula [10] for their derivatives with respect to parameters. We write general expressions for the thermodynamic fluxes (or currents) and the transport coefficients, generalizing the results of [4, 5]. In this framework we give a general proof of the Onsager reciprocity relations. Received: 2 December 1996 / Accepted: 13 March 1997