Elliptic bundle and generating operators

A hierarchy of Poisson Hamiltonian structures connected with an elliptic spectral problem is constructed. Generating operators connected with the Landau-Lifshits equations and asymmetric chiral 0(3)-field are found.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 161, pp. 76–87, 1987.The author is profoundly grateful to P. P. Kulish, A. G. Reiman, and M. A. Semenov-Tyan-Shanskii for interest in the present paper and helpful comments.     

Spectrum of the algebra of pseudodifferential operators in a halfspace

One considers C*-algebras, generated by pseudodifferential operators in a halfspace. The operators act in functional spaces with weighted norms. One describes the set of all classes of equivalent irreducible representations of algebras and reveals the topology on the spectrum. One investigates, in particular, the dependence of the spectrum on the choice of the weighted functional space.Translated from Problemy Matematicheskogo Analiza, No. 10, pp. 160–180, 1986.     

Index formulas for generalized Wiener-Hopf operators and boson-fermion correspondence in 2N dimensions

The kernels of operators associated with special chiral gauge transformations (kinks) in the 2N-dimensional Dirac theory are explicitly determined. The result is used to obtain index formulas for Fredholm operators corresponding to continuous chiral gauge transformations. Moreover, the Fock space quadratic forms corresponding to the kinks are proved to converge to the Dirac field as the kink size goes to zero. It is also shown that forN 1, 2(mod 4) the Majorana field can be reached in a similar fashion.Work supported by the Netherlands Organisation for the Advancement of Research (NWO)     

Disorder arising from the location of enantiomers in a twist-boat structure: 2,6-trans-2,4,6-tris(trichloromethyl)-1-oxa-3,5-dithian

Crystals of the title compound are orthorhombic, Pca2₁;a=27.586(4),b=10.509(3),c=11.080(2) Å,V=3212(1) ų,Z=8. The structure was solved by direct methods, from data collected at room temperature on an Enraf-Nonius CAD4 diffractometer, and refined by full-matrix least squares to a finalR value of 0.055 using 2043 reflections. One of the two independent molecules in the asymmetric unit is disordered. The disorder is manifested mainly between the oxygen atom and one sulfur atom and is caused by opposite enantiomers occupying corresponding positions in different unit cells. The endocyclic torsion angles in both independent molecules are very similar but the disposition of the heteroatoms on the twist-boat framework is different in the two molecules. Site occupancy of the two models on this framework in the disordered molecule is in the ratio 2179 with the smaller proportion being very similar to the ordered molecule and the remainder similar to that found in the normal molecule oftrans-4-chloro-2,4,6-tris(trichloromethyl)-1-oxa-3,5-dithian (Irving and Irving, 1988).     

On characterizing the bivariate exponential and geometric distributions

In this note, a characterization of the Gumbel's bivariate exponential distribution based on the properities of the conditional moments is discussed. The result forms a sort of bivariate analogue of the characterization of the univariate exponential distribution given by Sahobov and Geshev (1974) (cited in Lau and Rao ((1982), Sankhy Ser. A, 44, 87)). A discrete version of the property provides a similar conclusion relating to a bivariate geometric distribution.     

Nonlinear void-fraction waves in two-phase bubbly flow

It is shown that nonlinear void-fraction waves constitute exact solutions of the two-fluid equations for bubbly flow, if and only if the virtual-mass coefficientm() is a definite function of the void fraction. In the case of spherical bubbles the functional dependence is given bym()=(1/2)(1–a)(1–3). A similar expression was obtained recently by means of an elaborate linear stability analysis of a uniform two-phase flow. It is remarkable that the greater part of the physical quantities of a nonlinear void-fraction wave depends linearly on. The virtual-mass coefficient may be derived directly from a special form of Hamilton's variational principle.

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Zusammenfassung Es wird gezeigt daß nichtlineare Konzentrationswellen exakte Lösungen der Zweifluiden Gleichungen einer Blasenströmung darstellen dann und nur dann, wenn der Koeffizientm() der virtuellen Masse eine bestimmte Funktion der Volumenkonzentration der Blasen ist. Die funktionelle Abhängigkeit ist im Falle kugelförmiger Blasen gegeben durchm()= (1/2)(1–) (1–3). Ein gleicher Ausdruck wurde neulich mittels einer umständlichen linearen Stabilitätsanalysis einer uniformen Zweiphasen-Strömung erhalten. Es ist bemerkenswert daß der größere Teil der physikalischen Größen einer nichtlinearen Konzentrationswelle in linearer Weise von abhängt. Der Koeffizient der virtuellen Masse kann in direkter Weise von einer speziellen Form des Hamiltonschen Variationsprinzips hergeleitet werden.

     

Drag on an elliptic cylinder in a fluid particle suspension

An elliptic cylinder is performing oscillations parallel to either of the principal axes of the cross-sectional ellipse in a fluid particle suspension. The stream function governing the flow and the velocity components are determined in terms of Mathieu functions. The drag on the cylinder is evaluated and expressed in terms of two parametersK andK. The effects of the variation of the frequency parameter, eccentricity parameter and relaxation time parameter on the drag parametersK, K is studied numerically.     

A finitely convergent “row-action” method for the convex feasibility problem

We present a modification of the Cyclic Subgradient Projection (CSP) method by Censor and Lent, which solves the convex feasibility problem in a finite number of steps when a Slater type condition holds, while preserving its row-action properties. A linear rate of convergence for the CSP method is established assuming the same hypothesis.Research partially supported by CNPq, under Grant No. 301699/81.     

Wide-angle one-way wave equations

A one-way wave equation, also known as a paraxial or parabolic wave equation, is a differential equation that permits wave propagation in certain directions only. Such equations are used regularly in underwater acoustics, in geophysics, and as energy-absorbing numerical boundary conditions. The design of a one-way wave equation is connected with the approximation of (1-s2)1/2 on [-1,1] by a rational function, which has usually been carried out by Padé approximation. This article presents coefficients for L2, L infinity, and other alternative classes of approximants that have better wide-angle behavior. For theoretical results establishing the well posedness of these wide-angle equations, see the work of Trefethen and Halpern ["Well-posedness of one-way wave equations and absorbing boundary conditions," Math. Comput. 47, 421-435 (1986)].     

Every 8-uniform 8-regular hypergraph is 2-colorable

As is well known, Lovász Local Lemma implies that everyd-uniformd-regular hypergraph is 2-colorable, providedd 9. We present a different proof of a slightly stronger result; everyd-uniformd-regular hypergraph is 2-colorable, providedd 8.Research supported in part by Allon Fellowship and by a grant from the United States Israel Binational Science Foundation.