Quantum field theories of vortices and anyons

We develop the quantization of topological solitons (vortices) in three-dimensional quantum field theory, in terms of the Euclidean region functional integral. We analyze in some detail the vortices of the abelian Higgs model. If a Chern-Simons term is added to the action, the vortices turn out to be anyons, i.e. particles with arbitrary real spin and intermediate () statistics. Localization properties of the interpolating field, scattering theory and spin-statistics connection of anyons are discussed. Such analysis might be relevant in connection with the fractional quantum Hall effect and two-dimensional models of HighT _csuperconductors.     

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).     

Effect of the flow regime in an underexpanded jet issuing into a subsonic counterstream on the pressure distribution on a body

The pressure distribution on a cone with a half-angle =75°, from which a single central underexpanded jet issues into a subsonic counterstream, has been experimentally investigated. The effect of the flow regime in the jet on the pressure distribution is demonstrated. Generalized relations for the pressure on the body are obtained for various jet-flow momentum ratios J and flow Mach numbers M = 0.35–0.9; the Mach number M_a at the exit of the conical nozzle with half-angle _a=10° was equal to 2.9. The working medium of the jet and the flow was air with stagnation temperatures T_0a = T₀ 260–265°K. The ratio of the nozzle outlet radius to the radius of the maximum cross section of the cone _a/R_M=0.1.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 182–185, January-February, 1988.     

Messung der Gewebetemperatur mit infrarotem Thermometer in einer Trockenanlage

Zusammenfassung Es wurde eine theoretische Analyse der kontaktlosen Temperaturmessung des an der Spann-, Trocken- und Fixiermaschine bearbeiteten Gewebes vorgenommen. Der Einfluß der Trocknerwand ist durch die Korrektive Funktion ausgedrückt, zu deren Festlegung ein allgemein anwendbares Diagramm zusammengestellt wurde. Dabei wird die Tatsache berücksichtigt, daß die Messung in einem beschränkten Teil des Spektrums durchgeführt wird, welcher außerhalb der Wasserdampfabsorptionsbänder liegt.

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Measuring temperature of textiles in driers with infrared thermometer

The paper undertakes a theoretical analysis of contactless temperature measurement of textiles processed on a stretching, drying and fixation machine. The effect of the drier wall is expressed through a corrective function for whose determination a universal diagram has been established. The measurements have been performed in a narrow part of the spectrum lying outside the water vapour absorption bands.

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Formelzeichen B W· m^–2 Effektive Wärmestromdichte durch Strahlung - K _i Radiationskoeffizient für Oberflächei - q W · m^–2 Wärmestromdichte durch Strahlung - T K Temperatur - t °C Temperatur - dtj Kroneckersches Symbol - Emissionsgrad der Oberfläche - m Wellenlänge - _ij Radiationskoeffizient - _T W·m ^–2 ·K ^–4 Koeffizient in der Gleichung (2) - Winkelkoeffizient für Strahlung zwischen Oberflächen 1, 2 - – Korrektionsfunktion - W·m ^–2 Wärmestromdichte des schwarzen Körpers Indizes c Gewebe - M Meßwert - w Trocknerwand     

Intra- versus intermolecular hydrogen bonds in salicylamide derivatives

The crystal structures, solid-state infrared patterns, and thermal properties of two polymorphs of 4-nitrosalicylanilide are presented. In both polymorphs, intramolecular hydrogen bonds are found between the phenol oxygen and the amide proton, and intermolecular hydrogen bonds are found between the amide carbonyl oxygen and the phenol proton. These hydrogen bond patterns are compared to those found in other known salicylamide derivatives and an analysis is given of the factors contributing to preferences for intra- or intermolecular hydrogen bonds in these structures. Crystal data: polymorph, orthorhombic,Pbca,a=11.003(4),b=27.959(7),c=7.622(5) Å,Z=4,V=2345(3) ų, andR=0.038 (1351 reflections); polymorph, monoclinic,P2₁/a,a=28.36(1),b=11.64(1),c=7.293(8) Å,=90.68(6)°,Z=8,V=2408 ų, andR=0.043 (2425 reflections).     

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.

     

On a characteristic of random matrices connected with unconditional convergence almost everywhere

В статье рассматрива ются множестваM _N , 1≦N<∞ всех систем функций Φ={?(x)} _j ^=1/N , заданных на [0,1] с где (ε _{i, j} ) _{i, j} ^=1/N — матрица с э лементами ± 1. Изучаетс я поведение наМ _N функц ии $$\alpha _N (\Phi ) = \mathop {\sup }\limits_\sigma \mathop {\sup }\limits_{\sum a_j^2 = 1} (\int\limits_0^1 {\mathop {\sup }\limits_{1 \leqq k \leqq N} (\sum\limits_{j = 1}^k {a_j \varphi _{\sigma (j)} (x)} } )^2 dx)^{1/2} $$ гдеσ: {1, ...,N}?{1, ...,N}. Дока зьгаается, что сущест вуют абсолютные постоянн ыеc ₃,c ₄>0,y ₀>1, такие, что для любог оN=1,2, ... иy>y ₀ $$\mu _N (\{ \Phi \in {\rm M}_{\rm N} :\alpha _N (\Phi )/\left\| \Phi \right\| > y\} ) \leqq c_3 \exp [ - \exp (c_4 y)N]$$ гдеμ _N — мера наM _N с µ _N ({Ф}) = 2^?N2 дл я любой системыΦ∈M     

Distribution density of the norm of a stable vector

Let B be a Banach space,X be a stable B -valued random vector with exponentd(0,2), and P(·) be the distribution density of the norm of X. In this paper we study the question of the boundedness of P. In particular, we construct examples of a space B with a symmetric stable vector X with exponentd(1,2) with unbounded P and prove that if X is a nondegenerate strictly stable vector with exponentd(0,1), then P is bounded.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 105–114, 1987.The author is grateful to Yu. A. Davydov, V. I. Paulauskas, V. Yu. Bentkus, and D. Pap for stimulating discussions of the subject of this paper. When the paper was finished the author learned that similar results are found in [9].     

Superbranching processes and projections of random Cantor sets

We study sequences (X ₀, X ₁, ...) of random variables, taking values in the positive integers, which grow faster than branching processes in the sense that , for m, n0, where the X _n (m, i) are distributed as X _n and have certain properties of independence. We prove that, under appropriate conditions, X _n ^1/n almost surely and in L ¹, where =sup E(X _n )^1/n . Our principal application of this result is to study the Lebesgue measure and (Hausdorff) dimension of certain projections of sets in a class of random Cantor sets, being those obtained by repeated random subdivisions of the M-adic subcubes of [0, 1] ^d . We establish a necessary and sufficient condition for the Lebesgue measure of a projection of such a random set to be non-zero, and determine the box dimension of this projection.Work done partly whilst visiting Cornell University with the aid of a Fulbright travel grant