Unbounded derivations and invariant states

Let be a von Neumann algebra with a cyclic and separating vector . Let =i[H, ·] be the spatial derivation implemented by a selfadjoint operatorH, such thatH=0. Let be the modular operator associated with the pair (, ). We prove the equivalence of the following three conditions:1)H is essential selfadjoint onD(), andH commutes strongly with .2) The restriction ofH toD() is essential selfadjoint onD(^1/2) equipped with the inner product(|)_#=(|)+(^1/2|^1/2), , D(^1/2).3) exp (itH) exp (–itH)= for anyt.We show by an example, that the first part of 1),H is essential selfadjoint onD(), does not imply 3). This disproves a conjecture due to Bratteli and Robinson [3].Part of this work was done while O.B. was a member of Zentrum für interdisziplinäre Forschung der Universität Bielefeld     

ИЗМЕРЕНИЕ УПРУГОСТИ ПАРОВ НЕКОТОРЫХ ВЫСОКОМОЛ ЕКУЛЯРНЫХ ВЕЩЕСТВ РАДИОМЕТРИЧЕСКИМ МА НОМЕТРОМ С БОЛБШОЙ ЧУВСТВИТЕЛ ЬНОСТЬЮ

- — — - ; napc. - , - , , 9 . - . - 3. 10^–6–1. 10^–6 mmpm. cm.     

КРУЧЕНИЕ СТЕРЖНЕЙ С С ЕЧЕНИЕМ ФОРМЫ ПРЯМОУГОЛЬНИКА С ВЫР ЕЗОМ

[1] , 1) . [2].

---

Twisting of notched rectangularly-shaped bars

It was pointed out in paper [1] that special cases of this solution are the problems of the torsion of a notched and unnotched rectangularly-shaped bar. Here, some results obtained earlier are generalized and in one concrete case very good agreement is obtained with the results of Sapondjan [2].

     

Short distance scale invariance and high-energy processes in field theory

The dynamics of short distance interaction is considered from viewpoint of the quark field theory. If the effective coupling of quarks (the invariant charge(p ²)) decreases with distance (with increasingp ²) the field picture unifies different phenomenological models: reggeology in the region of smallp and partonology in the region of highp but(p ² ) lnp ² 1 and predict deviations with a subsequent increase ofp . A character of the deviations depends on the behaviour of whenp ². The variants of the asymptotic freedom (0) and scale invariance (g ₂ ⁰ ) are discussed. The strong suppression of—3 decay is considered as a support for the latter.Presented at the Symposium on Hadron-Hadron Scattering at High Energies, Liblice, Czechoslovakia, June 16–21, 1975.     

Logically independent von Neumann lattices

Three definitions of logical independence of two von Neumann latticesP₁,P₂ of two sub-von Neumann algebras ₁, ₂ of a von Neumann algebra are given and the relations of the definitions clarified. It is shown that under weak assumptions the following notion, called logical independence is the strongest:A B 0 for any 0 A P₁, 0 B P₂. Propositions relating logical independence ofP₁,P₂ toC ^*-independence,W ^* independence, and strict locality of ₁, ₂ are presented.     

ПЛОТНОСТЬ ТОКА В КАТО ДНЫХ ПЯТНАХ В КОНДЕНСИРОВАННОМ Р АЗРЯДЕ

- . , .     

Interacting spinor and scalar fields: Exact self-consistent solutions in Bianci I space

Exact self-consistent solutions of the equations that describe a system of interacting spinor and massless scalar fields with the interaction Lagrangian L_int=_,^,(S), where (S) is an arbitrary function of the invariant S=, are obtained in Bianci I space. The possibility of excluding the initial singularity is studied for the case of a power-law function (S), and isotropic expansion of the space as t is established.Russian University of International Amity. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 53–58, July, 1995.     

Production of lepton pairs in processes with hadronic jets

We propose a model for the production of extra (additional) lepton pairs in deep inelastic lepton-hadron scattering, e⁺e^– annihilation and large p_T processes. Extra lepton pairs are supposed to be originated by annihilations of quarks and antiquarks created during the space-time evolution of quark initiated jets. This mechanism yields predominantly dileptons with rather low masses. Predictions following from the model are compared with the recent data on trimuon production in neutrino-nucleon interactions. It is also suggested that internal hard processes can lead to dileptons with both small and large masses. The latter mechanism has rather small cross section but it is particularly interesting from the point of view of the simple quark-parton model.Dedicated to Academician Václav Votruba on the occasion of his seventieth birthday.     

О взаимодействии экс итонов с колебаниями кристаллической реш етки

, - . : - . - .     

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.

---

,

, . , . , , .

---

---

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

ИспОльжОВАНИЕ ФлУОР ЕсцЕНтНОгО РЕНтгЕНО ВскОгО ИжлУЧЕНИь Дль кОНтАк тНОИ МИкРОРАДИОгРАФ ИИ

( )K- Fe, Ti Ca . , , , . , , , K- , .

---

The use of fluorescent X-rays for contact microradiography

The possibilities of using fluorescentK-radiation of the elements Fe, Ti and Ca for contact microradiography of thin, little absorbing samples were studied and a simple set-up for carrying out this method, which uses a common type of microstructural X-ray tube as a source of the exciting radiation, was proposed. The experiments performed showed that if large magnifications are not required secondary-excitedK-radiation of the above-mentioned elements can be advantageously used for contact microradiography without the exposure times becoming impracticably long.

     

Evidence of Hg-chain formation in Hg x TiS2: a199mHg-TDPAC study

We determined the^199mHg nuclear quadrupole interaction in the misfit or superstoichiometric compound Hg _x TiS₂ by time differential perturbed angular correlation. A unique Hg-site withv _Q =511(1) MHz and =0.410(4) was observed, irrespective of the Hg-uptake (2/3x4/3). We propose a model of Hg-Hg zig-zag chains which accounts for these observations as well as for the X-ray diffraction data.     

The formation of dislocations by a spark discharge

The arrangement of dislocations formed in a single crystal of the alloy Fe-4·2% Si by a spark discharge in air is studied. The dislocations are made visible by etching on the surfaces perpendicular and parallel to the axis of the crater. The results of the observations are explained on the basis of microphysical conceptions of plastic deformation.

---

, Fe— 4,2% Si . , . .

     

A new procedure for thin-film deposition by solution spraying

The major reasons for the low photovoltaic efficiency of Cu₂S/CdS cells, in which the CdS film is deposited by spraying, are due to small film thicknesses which do not exceed 4 m and the small average grain size which ranges from 0.1 to 0.5 m.A new experimental solution spraying procedure is described that prevents both restrictions by controlling the substrate temperature. Average grain sizes of more than 1 m are obtained.Work supported by Ministere Pubblica Istruzione and Centro Regionale Ricerche Nucleari e di Struttura della Materia     

Der Einfluss von Beimengungen auf die Fasersubstruktur von Zink-Einkristallen

Zusammenfassung An Einkristallen von Zn mit Beimengungen von Cd oder Cu wurde experimentell die Abhä agigkeit der Größe des Durchmessers der Fasersubstruktur vom Gehalt der Beimengungen untersucht, die aus der Theorie von Rutter und Chalmers [1] hervorgeht. Es wird die Möglichkeit gezeigt, die Größe des Verteilungskoeffizientenk aus den erzielten Ergebnissen abzuschätzen.

---

, . , k.

     

The inelastic reactions πp→λ(⌆) K with allowance for the contribution of branch cuts

The method of complex angular moments is used to analyze the experimental data on the inelastic reactions p ()K, taking into account branch cuts in the j-plane in the eikonal approximation. An optical model for the backward scattering is considered. Agreement with experiment is obtained in the region of small angles for the reactions (⁰)K⁰. In the case of ^–P K⁰(^–K⁺) processes, agreement is obtained with the experimental results for large (180) scattering angles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 26–30, August, 1972.     

ПОГЛОЩЕНИЕ И РАССЕЯНИЕ МОНОКРИСТАЛЛОВ NaCl ∶ Ni

NaCl Cd [10]. , NaCl Ni , .

---

Absorption and dispersion on NaCl Ni crystals

The results of measuring the absorption and dispersion of light on NaCl Cd crystals were compared with the X-ray diffraction measurements by Toman [10]. The comparison showed that under certain conditions micro-regions of segregated impurities are produced in NaCl Ni crystals, apparent in an increased dispersion of light in the ultra-violet region.

     

On the geometric structure underlying the eikonal equation

Given the eikonal equation _i=1 ³ (/x ⁱ ) ² =n ², we investigate the geometric structure that underlies the law of propagation of the wavefronts (x ¹,x ²,x ³) —ct=0. It turns out that Huygens' principle for the propagation of wavefronts is given in terms of a contact structure. Wavefronts are carried into wavefronts by contact transformations. As regards the wave-particle duality principle that arises in quantum mechanics, there is a natural geometric structure, a symplectic manifold (M ²ⁿ , ), which unifies Fermat's principle and the eikonal equation (Huygens' principle).On leave of absence from Institut für Angewandte Mathematik, Fachbereich Mathematik der Universität Mainz, Mainz, German Federal Republic.     

Diffusion in a one-dimensional gas of hard point particles

We simulate the classical diffusion of a particle of massM in an infinite one-dimensional system of hard point particles of massm in equilibrium. Each computer run corresponds to about 10⁸ collisions of the diffusive particle. We find that (t) 1/t fort large enough, and a crossover from an M m regime where=2 to=3 forM=m. The diffusion constant has a sharp maximum atM=m. We study moments x(t)² and x(t)⁴, and examine the behavior ofq ² (t)=x(t)⁴/3x(t)²². We find thatq(t)1 (consistent with a normal distribution) in theM limit (for all timest) and in the t limit for allM. On sabbatical leave from IVIC-Instituto Venezolano de Investigaciones Cientificas.     

The perminvar effect and magnetic after-effect in magnesium manganese ferrite

An unstable perminvar effect was found in magnesium manganese ferrite at a temperature of –195°C and its connection with the magnetic after-effect was investigated. The analysis carried out on the basis of Néel's theory showed that both effects are a result of the same diffusion process. The experimental results also show that 180° Bloch walls are displaced when the sample is magnetized.

---

-

- – 195° C qe, , . , - . , 180- .