Investigation of anode and cathode jets influence on electric arc properties with current up to 500 kA

A number of phenomena connected with the formation of electrode jets in discharges in hydrogen at a current of 10/sup 5/-10/sup 6/ A, a current growth rate of 10/sup 10/ A/s, an initial pressure 0.1-4.0 MPa, and a discharge gap length of 5-40 mm were studied. After the secondary breakdown, the jets are observed through a discharge semitransparent channel, widening with velocity (4-7) /spl middot/ 10/sup 2/ m/s. Shockwave formation was detected at the interaction of jets with the surrounding gas and the opposite electrode. Plasma vapor pressure of metal near the end of the tungsten cathode 70 /spl mu/s after initiation of a discharge was 180 MPa. Thus, magnitude of brightness temperature was 59 /spl middot/ 10/sup 3/ K, with an average charge of ions-m~=3.1, and a concentration of metal vapors n=5.3/spl middot/10/sup 19/ cm/sup -3/. While those at the end of the anode 90 /spl mu/s after initiation of discharge: m~=2.6, n=7.4/spl middot/10/sup 19/ cm/sup -3/. Probable reasons of high-voltage drops near the electrodes (the summarized magnitude of which is /spl sim/1 kV) are discussed on the basis of experimental data. For the first time, the shadow method registered symmetric ejection of material from the all-cathode surface the maximum discharge current was observed.     

A column generation approach for the timetabling problem of Greek high schools

A column generation (CG) approach for the solution of timetabling problems is presented. This methodology could be used for various instances of the timetabling problem, although in this paper the solution of the high-school situation in Greece is presented. The results obtained show clearly that the CG approach that has been extremely successful in recent years in the solution of airline crew scheduling problems could also be very efficient and robust for the solution of timetabling problems. Several large timetabling problems corresponding to real problems have been successfully solved, with the solutions obtained feasible and of very high quality in accordance with the problem definition. In addition, none of the solutions contained any idle hour for any of the teachers, which was one of the main goals of this optimization effort.     

Use of anion-exchange high-performance liquid chromatography for the study of smooth muscle myosin light-chain kinase and its catalytic domain

Avian myosin light-chain kinase from smooth muscle of the gizzard and its catalytic domain, derived from the intact enzyme by trypsin digestion, was purified within 30-40 min by both analytical and preparative anion-exchange high-performance liquid chromatography. The proteins obtained were more than 95% pure and retained their biological activity. The high-performance anion-exchange chromatography protocols represent a significant decrease in purification time when compared with conventional ion-exchange chromatography.     

Asymptotics of Dirichlet Spectrum on Some Class of Noncompact Domains

We investigate the asymptotic behaviour of the counting function of Dirichlet eigenvalues on some class of noncompact manifolds. We prove that in cases when the volume or the perimeter (the volume of the boundary) of the manifold is infinite, some additional (nonclassical) terms appear in the precise asymptotics. The coefficients at the classical terms in those are regularized in some special way volume (resp. perimeter) of the manifold.     

On some periodic solutions of singularly perturbed parabolic equations

We present results from the theory of singular perturbations and, in particular, from a new branch of this theory (contrast alternating-type structures). __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 3, pp. 359–369, March, 2007.     

New methods for proving the existence and stability of periodic solutions in singularly perturbed delay systems

We carry out a detailed analysis of the existence, asymptotics, and stability problems for periodic solutions that bifurcate from the zero equilibrium state in systems with large delay. The account is based on a specific meaningful example given by a certain scalar nonlinear second-order differential-difference equation that is a mathematical model of a single-circuit RCL oscillator with delay in a feedback loop.     

A second order numerical scheme for the solution of the one-dimensional Boussinesq equation

A predictor–corrector (P-C) scheme is applied successfully to a nonlinear method arising from the use of rational approximants to the matrix-exponential term in a three-time level recurrence relation. The resulting nonlinear finite-difference scheme, which is analyzed for local truncation error and stability, is solved using a P-C scheme, in which the predictor and the corrector are explicit schemes of order 2. This scheme is accelerated by using a modification (MPC) in which the already evaluated values are used for the corrector. The behaviour of the P-C/MPC schemes is tested numerically on the Boussinesq equation already known from the bibliography free of boundary conditions. The numerical results are derived for both the bad and the good Boussinesq equation and conclusions from the relevant known results are derived.      

Smooth Frame-Path Termination for Higher Order Sigma-Delta Quantization

We study the performance of finite frames for the encoding of vectors by applying standard higher-order sigma-delta quantization to the frame coefficients. Our results are valid for any quantizer with accuracy ε > 0 operating in the no-overload regime. The frames under consideration are obtained from regular sampling of a path in a Hilbert space. In order to achieve error bounds that are comparable to results on higher-order sigma-delta for the quantization of oversampled bandlimited functions, we construct frame paths that terminate smoothly in the zero vector, that is, with an appropriate number of vanishing derivatives at the endpoint.     

Embedding and wavelet decomposition of spaces of minimal splines

On a sequence of embedded nonuniform grids, chains of embedded spaces of minimal splines (not necessarily polynomial) are constructed. The wavelet decomposition is given. The basis wavelets are compactly supported and admit simple analytic representation. The corresponding decomposition and reconstruction formulas are derived. The variety of spaces under consideration is identified with the variety of complete sequences of points of the direct product of an interval and a projective plane. Bibliography: 20 titles. __________ Translated from Problemy Matematicheskogo Analiza, No. 35, 2007, pp. 15–31