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.     

20-relative neighborhood graphs are hamiltonian

For any two points p and q in the Euclidean plane, define LUN_pq = { v | v ∈ R², d_pv < d_pq and d_qv < d_pq}, where d_uv is the Euclidean distance between two points u and v . Given a set of points V in the plane, let LUN_pq(V) = V ∩ LUN_pq. Toussaint defined the relative neighborhood graph of V, denoted by RNG(V) or simply RNG, to be the undirected graph with vertices V such that for each pair p,q ∈ V, (p,q) is an edge of RNG(V) if and only if LUN_pq (V) = ?. The relative neighborhood graph has several applications in pattern recognition that have been studied by Toussaint. We shall generalize the idea of RNG to define the k-relative neighborhood graph of V, denoted by kRNG(V) or simply kRNG, to be the undirected graph with vertices V such that for each pair p,q ∈ V, (p,q) is an edge of kRNG(V) if and only if | LUN_pq(V) | < k, for some fixed positive number k. It can be shown that the number of edges of a kRNG is less than O(kn). Also, a kRNG can be constructed in O(kn₂) time. Let E_c = {e_pq| p ∈ V and q ∈ V}. Then G_c = (V,E_c) is a complete graph. For any subset F of E_c, define the maximum distance of F as max_epq∈Fd_pq. A Euclidean bottleneck Hamiltonian cycle is a Hamiltonian cycle in graph G_c whose maximum distance is the minimum among all Hamiltonian cycles in graph G_c. We shall prove that there exists a Euclidean bottleneck Hamiltonian cycle which is a subgraph of 20RNG(V). Hence, 20RNGs are Hamiltonian.     

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.     

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.     

Diffraction in a cylindrically orthotropic elastic solid containing a stress free crack

A cylindrically orthotropic elastic solid is excited by a point impulsive body force. The solid contains a semi-infinite stress free crack. The resulting anti-plane wave motion problem has been solved in the form of a finite series representing the incident and reflected pulses plus an integral representing the diffraction pulse. The series part of the solution has been previously treated. In the present investigation the diffraction integral is integrated when λ (which measures the anisotropy of the solid) is an odd integer number. The diffraction integral is also integrated when λ is half an odd integer, for the special case in which the source lies in the plane of the crack and parallel to the crack edge. The displacement jump across the circular diffraction wave front is given for unrestricted (positive) values of λ.     

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.