Gelfand Pairs with Coherent States

The notion of solvable Gelfand pairs (K,N) (K is a compact Lie group acting on N, a solvable connected and simply connected Lie group) is due to Benson, Jenkins and Ratcliff. Thanks to the localization lemma, they came back to the case where K is a connected subgroup of U(n) acting on N = Hn, the 2n + 1-dimensional Heisenberg group. They gave a geometrical condition for such a pair: (K,Hn) is a Gelfand pair if and only if the intersection of each coadjoint orbit of G = K Hn with (Lie K) contains at most one integral K-orbit. Using coherent states, we define here a generating function of multiplicity m for each in K^. m is holomorphic on D(0,1), m (r) = n = 0 an rn, an and limr 1 m (r) = mtp (, W) (W is the generic representation of Hn naturally extended to K). (K,Hn) is thus a Gelfand pair if and only if limr 1 m 1. We prove here that if m is a non homogeneous function, then there is at least two K-orbits in the intersection of the generic coadjoint orbit associated to with (Lie K).     

УСТАНОВИВШЕЕСЯ ТЕМП ЕРАТУРНОЕ ПОЛЕ В БЕСКОНЕЧНОЙ ПЛОСКО Й ПЛАСТИНКЕ ИЗ ДВУХ СЛОЕВ С ОБЫЧНЫМ РАСПР ЕДЕЛЕНИЕМ ТЕМПЕРАТУ РЫ НА ГРАНИЧНЫХ СТЕНАХ

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Double quantum transitions in paramagnetic resonance

The theory of double quantum transitions of the M=±2 type, with regard to inhomogeneously broadened spin systems is studied in this paper with the approximation ²T₂T₃ 1. We suppose that the inhomogeneous broadening is formed by an inhomogeneous crystal field. The obtained results describe the magnitude of absorption as a function of the h.f. power and also describe the shape of the absorption curve. It is demonstrated that in inhomogeneously broadened spin systems the absorption curve of double quantum transitions has the form of the difference of two different Lorentz's curves and that at the saturation ( ²T₂T₁ 1) the absorption increases with the cube of the h.f. field intensity. The shape of the curves is expressed by means of phenomenological relaxation constants of the system.

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M=±2 ²T₂T₃ 1. , - . . , ( ²T₂T₁ 1) . .

     

Representations of state space transformations by Markov kernels

Every convex subset of a locally convex Hausdorff space (X, ) is equipped with the (-algebra generated by its-relatively open subsets. Within the set () of probability measures on two particular convex subsets are considered: (a) the set ^s () of probability measures with a separable support, and (b) the set ^c () of probability measures with a compact convex support. If is the base of a cone inX, then there exists an affine barycenter map from ^c () onto whose composition with the natural embedding of in ^c () yields the identity map on , and every-continuous affine transformation of can be represented by an affine transformation of ^c () that is induced by a Markov kernel. If (X, ) is a Banach space and is a closed, bounded, generating cone base inX that is contained in a hyperplane, then analogous results are obtained with respect to ^s (). Since the state spaces considered in noncommutative measure theory are cone bases and every change in time of an empirical system can be thought of as an affine transformation of the associated state space (Schrödinger picture), the existence of these representation theorems implies that the time evolution of general empirical systems can be described by dynamical concepts borrowed from classical probability theory.     

РАДИАЦИОННЫЙ ЗАХВАТ НЕЙТРОНА ЯДРАМИ Sc,Fe, Cu,Mo, Cd и La

, . 20–1000 keV Sc, Fe, Cu, Mo, Cd La.

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The radiative capture of a neutron on Sc, Fe, Cu, Mo, Cd and La nuclei

The energies and intensities of the transitions of a compound nucleus, produced by the capture of a neutron, were measured by means of a single-crystal scintillation spectrometer. The region of energies 20–1000 keV was measured on Sc, Fe, Cu, Mo, Cd and L a nuclei.

     

The thickness dependence of the permittivity of barium titanate single crystals

A thickness dependence of the permittivity ofc-domain barium titanate single crystals was found. The experimental results were explained by means of a model of a dielectric with surface layers. The thickness of the layer and the permittivity of the surface layer and bulk of the crystal were determined.

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iO₃

iO₃, -. . , .

     

Основные соотношени я длн построения механических селект оров нейтронов

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Спектралъный метод о пределения изотонно го состава свинца. Частъ I

, . , . - . PbI4058 Å . , . 1000000. , , . - , .     

Two-quantum annihilation of polarized positrons

The cross-section for the two-quantum annihilation-in-flight of partially polarized beams of particles, obtained by using the polarization density matrix, is given. The formula includes the special results of L. A. Page [1]. The annihilation of a longitudinally polarized positron with a transversally polarized electron is discussed. Computations are made in a centre-of-mass system with summing over photon polarizations.

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Abbreviated version of a diploma-thesis for the degree graduate physicist.

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The author wishes to express his sincere gratitude to Professor V. Votruba and Dr. L. Valenta for suggesting this work and for many helpful discussions and criticisms.     

Das Verteilungsgesetz der Ferromagnetischen Bereiche vom Standpunkt des Aktivierungsfeldes aus Betrachtet

Zusammenfassung Unter der Voraussetzung, daß das Ahtivierungsfeld für die reversible Bewegung der Blochschen Wände dem Maxwellschen Verteilungsgesetz unterliegt, wird die Entstehung des Maximums der inneren Reibung im Wechselfeld theoretisch erläutert. Weiter wird die Lösung der Differenzialgleichung für die Bewegung einer Blochschen Wand bei gleichzeitiger Wirkung des Wechselfeldes und der Torsionsbeanspruchung gegeben. Die Messung bei einigen Torsionsfrequenzen ermöglicht die Bestimmung gewisser mikroskopischer Konstanten.

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Millimeter wave propagation through a chiral medium model of human trunk

That millimeter wave propagation through a chiral medium of human trunk has been discussed by obtaining the electromagnetic filed, absorbent power, specific absorption rate, temperature field and their distribution in a human trunk model with plane strati calate homogeneous tissues under a normal incidence plane wave. The chiral medium is described electromagnetically by the constitutive relationsD=E+B andB=H+E. The constants, and ate real and have values that are fixed by the size, the shape, and the spatial distribution of the elements that collectively compose the medium. Also, the principle of thermal therapeutics for millimeter wave is discussed preliminaryly.     

Wavelength distribution of X-rays in the focus of a monochromator and an estimate of the influence of this distribution on precision measurements of lattice constants

Wavelength distribution in the focus of a Johansson type monochromator is computed assuming the tube focus emissivityG(), reflection curveR() and wavelength distribution of the incident radiationJ(-₀) are known. It is shown e.g. that the centre of gravity may be shifted in accordance with the position of the crystal on the focal circle which may considerably influence precision measurements of lattice parameters.

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, G(,) R() J(-₀) . , , , .

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The author is grateful to Z. Hemanová for carrying out all the computations very carefully.     

Theory of moving striations in plasma of D-C discharge I. Basic equation and its general solution

As a base for the theory of moving striations a partial integro-differential equation (26) is derived from the equations of continuity (1), (2), the Laplace-Poisson equation (3) and relation (4) between the electric field and the temperature of the electrons. Apart from the processes necessary for the actual formation of striations according to [1] and for the amplification of the wave of stratification according to [2], the equation also includes the processes defining the Debye length of the electrons, the influence of the axial electric field and of its local deflections on the motion of current carriers and the direct influence of the deviations in concentration of the electrons on the rate of production of current carriers. In deriving the equation the main attention is paid to the physical sense of the mathematical operations applied. The general solution is found by the method of the two-sided Laplace transformation and is described by triple integral convolution (42).

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I.

(1), (2), - (3) (4) (26). , , [1], , [2], , , . . (42).

     

АНТИПРОТОННАЯ СХЕМА β-РАСПАДА

, .     

Sewing Polyakov amplitudes I: Sewing at a fixed conformal structure

We consider the problem of reconstructing the correlation functions of a conformal field theory on a surface from the correlation functions on a surface obtained from by cutting along a closed curve. We show that under quite general conditions, the correlation functions on the cut surface can be sewn by integrating over appropriate boundary valuess of the field.Supported in part by DOE grant DE-AC02-76ERO2220Supported in part by DOE grant DE-AS06-88ER40423     

КРУЧЕНИЕ ПРИЗМАТИЧЕ СКИХ СТЕРЖНЕЙ ШВЕЛЛЕ РНОГО ПОПЕРЕЧНОГО СЕЧЕНИЯ

- [3], [4], U(x, y) . - U(x, y) -, . B § 10 - . , - , - D, . - .     

Two-barrier detector

The paper describes the principle of a detector with two opposite surface barriers and the experimental verification of its functioning. The detector permits double the effective depth to be attained on the material with a given bias voltage. The principle of opposite barriers also permits a reduction in the system of dE/dx andE detectors to one detector.

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. . dE/dx E .

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The authors thank A. Irra for carefully preparing the plates, K. Putz and J. imková for very effective help in measuring on the cyclotron and the members of of the cyclotron staff for their cooperation.     

On Borchers' Theorem

We give a simplified proof of the following important theorem,which is due to Borchers. Let be a von Neumann algebra with cyclic and separating vector and let U(t), t R, be a group with positive generator, which leaves fixed and induces for positive arguments endomorphisms of . The modular group of (, ) acts then as dilatations on this group. Our proof can also be applied to half-sided modular inclusions.     

Mikrophy'sikalische Vorgänge,die die Entstehung der Schnellen Schichtungswellen in der Neonglimmentladung bedingen

Zusammenfassung Im nachstehenden Artikel werden mikrophysikalische Vorgänge behandelt, die das Auftreten schneller Schichtungswellen in Neonglimmentladungen veranlassen können. Es werden sowohl die qualitativen Abhängigkeiten, als auch die ziffernmäigen Werte der Parameter der Schichtungswellen mit den charakteristischen Gröenwerten der in diesem Entladungstypus vor sich gehenden Vorgänge verglichen. Auf Grund der vorgenommenen Vergleiche kann gesagt werden, da die Relaxationszeiten der schnellen Wellen durch die Diffusionslebensdauer der atomaren, bzw. molekularen Ionen gegeben sind.

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Zum Schlu danken wir F. Kroupa und V. Krejí für die aufmerksame Lesung der Arbeit und wertvolle Hinweise.