Primal cutting plane algorithms revisited

Dual fractional cutting plane algorithms, in which cutting planes are used to iteratively tighten a linear relaxation of an integer program, are well-known and form the basis of the highly successful branch-and-cut method. It is rather less well-known that various primal cutting plane algorithms were developed in the 1960s, for example by Young. In a primal algorithm, the main role of the cutting planes is to enable a feasible solution to the original problem to be improved. Research on these algorithms has been almost non-existent.  In this paper we argue for a re-examination of these primal methods. We describe a new primal algorithm for pure 0-1 problems based on strong valid inequalities and give some encouraging computational results. Possible extensions to the case of general mixed-integer programs are also discussed.     

Some Estimates for the Derivative of a Quasiconformal Reflection Spiral-Shaped Domains

Some estimates of derivatives are sharpened for quasiconformal reflections of a special class of simply connected plane domains. Bibliography: 2 titles.     

Rank-perfect and" weakly rank-perfect graphs

An edge e of a perfect graph G is critical if G−e is imperfect. We would like to decide whether G−e is still “almost perfect” or already “very imperfect”. Via relaxations of the stable set polytope of a graph, we define two superclasses of perfect graphs: rank-perfect and weakly rank-perfect graphs. Membership in those two classes indicates how far an imperfect graph is away from being perfect. We study the cases, when a critical edge is removed from the line graph of a bipartite graph or from the complement of such a graph.     

Continuation theorem of fractional order evolutionary integral equations

The fractional order evolutionary integral equations have been considered by the first author in [6], the existence, uniqueness and some other properties of the solution have been proved. Here we study the continuation of the solution and its fractional order derivative. Also we study the generality of this problem and prove that the fractional order diffusion problem, the fractional order wave problem and the initial value problem of the equation of evolution are special cases of it. The abstract diffusion-wave problem will be given also as an application.     

Possible Loss and Recovery of Gibbsianness¶During the Stochastic Evolution of Gibbs Measures

We consider Ising-spin systems starting from an initial Gibbs measure ν and evolving under a spin-flip dynamics towards a reversible Gibbs measure μ≠ν. Both ν and μ are assumed to have a translation-invariant finite-range interaction. We study the Gibbsian character of the measure νS(t) at time t and show the following: (1) For all ν and μ, νS(t) is Gibbs for small t. (2) If both ν and μ have a high or infinite temperature, then νS(t) is Gibbs for all t > 0. (3) If ν has a low non-zero temperature and a zero magnetic field and μ has a high or infinite temperature, then νS(t) is Gibbs for small t and non-Gibbs for large t. (4) If ν has a low non-zero temperature and a non-zero magnetic field and μ has a high or infinite temperature, then νS(t) is Gibbs for small t, non-Gibbs for intermediate t, and Gibbs for large t. The regime where μ has a low or zero temperature and t is not small remains open. This regime presumably allows for many different scenarios. Received: 26 April 2001 / Accepted: 10 October 2001     

Electrical conduction and dielectric properties of vanadium phosphate glasses doped with lithium

AC conductivity and dielectric studies on vanadium phosphate glasses doped with lithium have been carried out in the frequency range 0.2-100 kHz and temperature range 290-493 K. The frequency dependence of the conductivity at higher frequencies in glasses obeys a power relationship, σ_ac=Aω^s. The obtained values of the power s lie in the range 0.5≤s≤1 for both undoped and doped with low lithium content which confirms the electron hopping between V⁴⁺ and V⁵⁺ ions. For doped glasses with high lithium content, the values of s≤0.5 which confirm the domination of ionic conductivity. The study of frequency dependence of both dielectric constant and dielectric loss showed a decrease with increasing frequency while they increase with increasing temperature. The results have been explained on the basis of frequency assistance of electron hopping besides the ionic polarization of the glasses. The bulk conductivity increases with increasing temperature whereas decreases with increasing lithium content which means a reduction of the V⁵⁺.     

Field Theory Methods in Classical Dynamics

A Dirac picture perturbation theory is developed for the time evolution operator in classical dynamics in the spirit of the Schwinger–Feynman–Dyson perturbation expansion and detailed rules are derived for computations. Complexification formalisms are given for the time evolution operator suitable for phase space analyses, and then extended to a two-dimensional setting for a study of the geometrical Berry phase as an example. Finally a direct integration of Hamilton's equations is shown to lead naturally to a path integral expression, as a resolution of the identity, as applied to arbitrary functions of generalized coordinates and momenta.     

Monte Carlo study of interfacial silicon suboxide layers and oxidation kinetics

A simple simulation scheme that simultaneously describes the growth kinetics of SiO₂ films at the nanometer scale and the SiO_x/Si interface dynamics (its extent, and spatial/temporal evolution) is presented. The simulation successfully applies to experimental data in the region above and below 10 nm, reproduces the Deal and Grove linear-parabolic law and the oxide growth rate enhancement in the very thin film regime (the so-called anomalous region). According to the simulation, the oxidation is governed mainly by two processes: (a) the formation of a transition suboxide layer and (b) its subsequent drift towards the silicon bulk. We found that it is the superposition of these two processes that produces the crossover from the anomalous oxidation region behavior to the linear-parabolic law.     

Lasing in the far IR spectral range under femtosecond optical excitation of the InAs semiconductor in a magnetic field

Generation of a coherent electromagnetic radiation in the far IR (THz) spectral range upon excitation of a semiconductor InAs crystal by 70-fs Ti: sapphire laser pulses is studied. The effect of a magnetic field of different orientation on generation in the submillimeter-wavelength range is analyzed. Placing the crystal into the magnetic field of an optimized permanent magnet with a strength of 5 kOe aligned along the surface of the semiconductor increased the power of generated radiation by a factor of six compared with that in the absence of the field. For the average pump-laser output power of 150 mW and repetition rate of 80 MHz, the average power of the THz radiation reached 100 nW. For detection of ultrashort pulses of the THz radiation, we used, for the first time, a highly sensitive uncooled optoacoustic detector, which detected signals with a power lower than 1 nW.