Observables on hypergraphs

Observables on hypergraphs are described by event-valued measures. We first distinguish between finitely additive observables and countably additive ones. We then study the spectrum, compatibility, and functions of observables. Next a relationship between observables and certain functionals on the set of measures M(H) of a hypergraph H is established. We characterize hypergraphs for which every linear functional on M(H) is determined by an observable. We define the concept of an effect and show that observables are related to effect-valued measures. Finally, we define operational transformations from M(H) to itself and show that they can be described as a certain combination of effects.On leave from University of Berne, Institute of Mathematical Statistics, Sidlerstrasse 5, CH-3012 Berne, Switzerland.     

Complete integrability of the supersymmetric model (cos φ)2

Complete integrability of the supersymmetric, two-dimensional sine-Gordon model of field theory within the framework of the Hamiltonian interpretation of the method of the inverse problem is proved. The classical r-matrix of the model is computed, and its equivalence to the r-matrix the Grassmann Thirring model is established. Variables of creation-annihilation type are constructed, and the spectrum of elementary excitations of the system is obtained.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 120, pp. 122–135, 1982.     

Distribution of a nonstationary electron beam in a dense gas

The problem of the temporal and spatial dependences of the parameters of the action of a modulated fast-electron beam on a dense gas is posed on the basis of the transport equation. The problem is simplified by making it nondimensional and by transforming to the Fokker-Planck approximation. A Green's function formalism is developed for this problem and is used to express the solution of the general nonstationary problem in the form of a convolution of a nonstationary boundary flow with a stationary Green's function. The use of the derived equation is illustrated using as an example the solution of a problem with the simplest stationary Green's function corresponding to the straight-ahead approximation. This approximation is used to consider a general relativistic case with model scattering cross sections. The methods and results of a numerical computer solution of the nonstationary problem of electron retardation in the upper layer of the atmosphere are surveyed.Translated from Trudy Ordena Lenina Fizicheskogo Instituta im. P. N. Lebedeva AN SSSR, Vol. 145, pp. 172–188, 1984.     

Gallium arsenide avalanche-type S-diode based on a n+-π-ν-n structure

The results are presented of an investigation of the electrical characteristics of avalanche S-diodes based on a new type of structure (⁺---n), which is obtained by diffusing iron in GaAs with n = 1.10¹⁷ cm^–3. The diodes have regions of S-type negative differential resistance (NDR), for both bias polarities and have a number of other features by comparison with diodes based on the --n structures with fused contacts. We discuss the mechanism for the formation of the NDR region of the voltage-current characteristics of the diode.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 54–58, April, 1986.     

Vacuum polarization by a Coulomb center and strong magnetic field. modification of Coulomb's law

The proper time method is used to examine the effect of polarization of the electron-positron vacuum on the nature of the interaction of a charged particle with the field of a nucleus and a magnetic field. It is shown that the interaction of an electron with a nucleus becomes anisotropic in the presence of a magnetic field. The dielectric constants of the vacuum and the effective charge of the Coulomb center are calculated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 38–45, November, 1986.     

Site-specific core level spectroscopy of CO and NO adsorption on Pt(110)(1×2) and (1×1) surfaces

The adsorption of CO and NO on the (1×2) and (1×1) modifications of the Pt(110) surface was studied by x-ray photoemission spectroscopy, LEED and work-function change measurements. The O(1s) binding energy of adsorbed CO is site-specific and differentiates between on-top and bridge adsorbed species. CO adsorption on Pt(110)(1×2) at 120 K occurred sequentially into on-top and bridge sites yielding an orderedc(8×4) layer at the maximum coverage. At 300 K only on-top bonded CO was present after CO adsorption on the (1×2) surface. CO adsorption on the (1×1) surface at 120 K showed a transient bridge adsorbed CO and on-top CO at saturation, with an ordered (2×1)p1g1 LEED pattern. Heating the (2×1)p1g1 CO layer to 400 K also showed this transient bridge CO species. Work function changes generally correlated with the appearance of different CO species but were complex in detail. The findings for CO adsorption are consistent with the missing row model of the (1×2) surface.Parallel data for NO adsorption on (1×2) and (1×1) surfaces at 120 K were less informative than those for CO because O(1s) spectra showed single broad peaks. Peak contributions due to bridge and on-top bonded NO could be estimated.     

Simple functional-differential equations for the bound-state wave-function components

We present a new method of a direct derivation of differential equations for the wave-function components of identical-pariticles systems. The method generates in a simple manner all the possible variants of these equations. In some cases they are the differential equations of Faddeev of Yakubovskii. It is shown that the case of the bound states allows to formulate very simple equations for the components which are equivalent to the Schrödinger equation for the complete wave function. The components with a minimal antisymmetry are defined and the corresponding equations are derived.