Romanovski polynomials in selected physics problems

We briefly review the five possible real polynomial solutions of hypergeometric differential equations. Three of them are the well known classical orthogonal polynomials, but the other two are different with respect to their orthogonality properties. We then focus on the family of polynomials which exhibits a finite orthogonality. This family, to be referred to as the Romanovski polynomials, is required in exact solutions of several physics problems ranging from quantum mechanics and quark physics to random matrix theory. It appears timely to draw attention to it by the present study. Our survey also includes several new observations on the orthogonality properties of the Romanovski polynomials and new developments from their Rodrigues formula.     

Generation of slanted gas-filled icicles

A procedure for the generation of slanted gas-filled icicles by freezing, using a domestic refrigerator, is described. The freezing vessel was a plastic ice-cube tray, which was filled both with tap and deionized water and was frozen successively from the outer to the inner compartments of the tray. Icicles having slanted elevations grew out of the surface of the deionized water of the innermost compartments. The erection angle of the icicles to the horizontal lay between 30° and 60°, for the three longest and thinnest specimens it was almost exactly 30°. All icicles have gas inclusions. Their shape varies between an irregular distribution of circular bubbles and a nearly uninterrupted axial gas channel together with dendrite-like, radially distorted bubbles. If a cold (-18°C) specimen comes into contact with warm and humid room-air, then hoarfrost is observed at the bottom and the top of the icicle, while the area in between remains transparent.     

Achievement of laser fusion of biological cells using UV pulsed dye laser beams

This paper reports a successful achievement of laser-induced biological cell fusion using an excimer laser excited dye laser. To our knowledge, we examined for the first time the dependence of fusion rate on laser pulse energy, number of laser pulses, and laser wavelength. Maximum fusion rate of approximately 50% was obtained by this laser fusion technology.     

Quantum wire heterostructure for optoelectronic applications

Quantum wire (QWR) heterostructures suitable for optoelectronic applications should meet a number of requirements, including defect free interfaces, large subband separation, long carrier lifetime, efficient carrier capture. The structural and opticl properties of GaAs/AlGaAs and InGaAs/GaAs quantum wire (QWR) heterostructures grown by organometallic chemical vapor deposition on nonplanr substrates, which satisfy many of these criteria, are described. These crescent-shaped QWRs are formed in situ during epitaxial growth resulting in virtually defect free interfaces. Effective wire widths as small as 10nm have been achieved, corresponding to electron subband separations greater than K_BT at room temperature. The enhanced density of states at the QWR subbands manifests itself in higher optical absorption and emission as visualized in photoluminescence (PL), PL excitation, amplified spontaneous emission and lasing spectra of these structures. Effective carrier capture into the wires via connected quantum well regions, which is important for enhancing the otherwise extremely small capture cross section of these wires, has also been observed. Room temperature operation of GaAs/AlGaAs and strained InGaAs/GaAs QWR lasers with threshold currents as low as 0.6mA has been demonstrated.     

Synchronization of Distributed Electron–Wave Self-Oscillatory Systems with a Backward Wave

We present the results of studying the phenomenon of synchronization in distributed electron–wave self-oscillatory systems with a counterpropagating wave. General laws governing the appearance of the classical synchronization in distributed systems are revealed. We propose methods for increasing the synchronization bandwidth by using the distributed input of a signal to the interaction space by means of coupled waveguide structures. Transient processes in nonautonomous self-oscillation regimes are studied. In particular, the effect of ultrafast synchronization is found. The possibility of chaotic synchronization in a gyro-oscillator with a counterpropagating wave under the action of a deterministic chaotic signal is shown. Mutual oscillation regimes in a system of two distributed oscillators with coupled waveguide systems are studied.     

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.     

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.     

Bodies of constant width in arbitrary dimension

We give a number of characterizations of bodies of constant width in arbitrary dimension. As an application, we describe a way to construct a body of constant width in dimension n, one of its (n – 1)‐dimensional projection being given. We give a number of examples, like a four‐dimensional body of constant width whose 3D‐projection is the classical Meissner's body. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)