Generalized slant Toeplitz operators on H2

For an integer k ≥ 2, k^th‐order slant Toeplitz operator U_φ [1] with symbol φ in L^∞(??), where ?? is the unit circle in the complex plane, is an operator whose representing matrixM = (α_ij ) is given by α_ij = 〈φ, z^ki–j〉, where 〈. , .〉 is the usual inner product in L²(??). The operator V_φ denotes the compression of U_φ to H²(??) (Hardy space). Algebraic and spectral properties of the operator V_φ are discussed. It is proved that spectral radius of V_φ equals the spectral radius of U_φ, if φ is analytic or co‐analytic, and if T_φ is invertible then the spectrum of V_φ contains a closed disc and the interior of the disc consists of eigenvalues of infinite multiplicities. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the production of slow particles in high energy heavy ion collisions

The mechanism for producing slow, target associated particles in high energy heavy ion collisions is investigated. It is shown that the same mechanism which was proposed for hadron induced interactions is likely to appear also for heavy-ion reactions. The results indicate however a much weaker correlation between impact parameter and yield of slow particles.     

Regioselective synthesis of symmetrical pyridyl selenium compounds by bromine–magnesium exchange of bromopyridines using isopropyl magnesium chloride: X‐ray crystal structure of 2,2′,5,5′‐tetrabromo‐3,3′‐dipyridyldiselenide

2,2′‐Dipyridyl‐3,3′‐dipyridyl,5,5′‐dipyridyl‐diselenides have been synthesized by a convenient method employing non‐cryogenic conditions. Various bromopyridines (2‐Bromopyridine, 2,5‐dibromopyridines and 2,3,5‐Tribromopyridines) undergo selective monobromine–magnesium exchange to yield the corresponding pyridyl magnesium chlorides at room temperature upon treatment with ⁱPrMgCl. The resulting pyridyl magnesium chloride is quenched with elemental selenium, which upon further oxidation affords the above diselenides in good yields. The compounds prepared using this methodology have been characterized by elemental analysis, IR, NMR (¹H, ¹³C, ⁷⁷Se) and mass spectral analysis. The molecular structure of 2,2′,5,5′‐Tetrabromo‐3,3′‐dipyridyldiselenide has been established by single‐crystal X‐ray diffraction analysis. It exists as a dimeric form due to the non‐bonding interactions between the selenium of one pyridine moiety and the hydrogen of the other. Copyright © 2004 John Wiley & Sons, Ltd.     

Performance of YBaCuO thick film rf SQUIDs at 77 K

RF SQUID behaviour has been observed at 77 K in YBaCuO thick films prepared by screen printing technique. A hole shunted with a microbridge type of geometry is patterned manually for observing rf SQUID behaviour. Flux noise spectrum is also studied and it is found to depend on the quality of the film. The spectral density of the flux noise in the white noise region is 1.7×10⁻³ Φ₀/√Hz at 77 K.     

First passage time for a class of one-dimensional stochastic systems

We consider the time evolution of a class of stochastic systems of finite size with polynomial nearest neighbor transition rates. We obtain analytical expressions for the first passage time (FPT) and its moments. We show that the mean FPT, averaged over a uniform initial distribution, shows a simple asymptotoc behavior with the system size and the parameters of the transition rates.     

Some stability results in the theory of whirling

The whirling motion of a fixed-free viscoelastic shaft, whose model is based on the spring and dashpot (Kelvin element), is considered. We develop a precise determination of the system's stability by first obtaining its eigenvalues. It is shown that asymptotic stability exists as long as the angular speed of the shaft is below a certain critical value. On the other hand, the degree of stability first increases as the speed is increased but eventually decreases again.

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Zusammenfassung Es wird die Wirbelbewegung einer einseitig eingespannten Welle untersucht, deren Modell dem Kelvin-Element entspricht. Zur Beurteilung der Stabilität werden zunächst die Eigenwerte ermittelt. Dann wird gezeigt, dass asymptotische Stabilität besteht, solange die Winkelgeschwindigkeit unter einem kritischen Wert liegt. Der Stabilitätsgrad nimmt zuerst mit der Winkelgeschwindigkeit zu und schliesslich wieder ab.

     

An O(k2 + kh2 + h4) arithmetic average discretization for the solution of 1‐D nonlinear parabolic equations

This article develops a new two‐level three‐point implicit finite difference scheme of order 2 in time and 4 in space based on arithmetic average discretization for the solution of nonlinear parabolic equation ε u_xx = f(x, t, u, u_x, u_t), 0 < x < 1, t > 0 subject to appropriate initial and Dirichlet boundary conditions, where ε > 0 is a small positive constant. We also propose a new explicit difference scheme of order 2 in time and 4 in space for the estimates of (?u/?x). The main objective is the proposed formulas are directly applicable to both singular and nonsingular problems. We do not require any fictitious points outside the solution region and any special technique to handle the singular problems. Stability analysis of a model problem is discussed. Numerical results are provided to validate the usefulness of the proposed formulas. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Study of precipitation in NaCl:Pb2+ by light scattering and ultramicroscopy

The formation and dissolution behaviour of precipitates in NaCl : Pb²⁺ single crystals is studied by light scattering and ultramicroscopy. Measurements of Rayleigh ratio together with ultramicroscopic observations during isochronal annealing indicate the presence of two types of precipitates in as-grown crystals. Isochronal annealing after suitable thermal and thermomechanical treatments shows that precipitates of first type (I) which form and dissolve at lower temperatures, are due to homogeneous nucleation. Precipitates of the second category (II) which form and dissolve at higher temperatures are aligned along crystallographic directions and have their origin in stress-assisted processes. Isothermal annealing has been used to study the dissolution kinetics of the precipitated fraction, and it is found that the kinetics is of first order. The enthalpy of solution is determined from a study of the temperature dependence of the kinetic rate constant, in conjunction with available information on the migration energy of Pb²⁺ in NaCl. The enthalpy so deduced is in good agreement with the value as usually obtained from the concentration dependence of the dissolution temperature.