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.     

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.     

Crystal and molecular structure of 1R,3S,5S,7R,10R-3,6,6,10,14-Pentamethyltricyclo[10.3.0.05,7]pentadeca-11,14-diene-1, 10-dihydroxy-2,13-dione (Japodagrol), C20H28O4

A new cytotoxic macrocyclic diterpenoid named Japodagrol, C₂₀H₂₈O₄, has been isolated from the ornamental plantJatropha podagrica, family Euphorbiaceae, grown in Nigeria. The structure of the title compound, C₂₀H₂₈O₄, was solved by X-ray analysis.M _r =332.44, monoclinic space groupC2,a=23.285(4),b=6.5105(12),c=12.505(3) Å,=98.504(17),V=1874.8 ų,Z=4,D _c =1.178 Mg/m³. CuK radiation (graphite crystal monochromator, =1.54184 A), (CuK)=6.13 cm^–1,F(000)=720,T=290 K. Final conventionalR factor=0.035,R _w =0.038 for 3349 observed reflections. The structure was solved with the programDirdif. The 5-membered ring is closed to a half-chair form. The compound contains inter- and intramolecular hydrogen bonds.     

Homogeneous spaces and invariant tensors

In the present survey a method is presented for the construction of invariant tensors (with respect to a given representation) called the inclusion principle and the possibility of applying the cited method to various problems of algebra, topology, geometry, and analysis.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 18, pp. 105–142, 1986.     

Ultra'soft X-ray diagnostics of short-living plasmas

Ultrasoft X-ray plasma diagnostics in IPP is realized by using X-ray diodes with Al photocathodes and submicrometer nitrocellulose filters. The X-ray detections system is suitable for measurements in a relatively broad range of radiation intensities in the spectral interval of (10–1000) eV with the time resolution of (1–10) ns under various plasma conditions. Construction, calibration and characteristic properties of the measuring apparatus are described. To illustrate its use, some results of the diagnostics of REB-heated plasma are presented.We would like to acknowledge Dr. P. unka for many helpful discussions and Dr. J. Ullschmied for cooperation in REB-heated plasma diagnostics interpretation.     

Three-body Coulomb effects in neutral-particle-exchange singularity

In a three-body model with Coulomb interactions the Faddeev equations for the Alt-Grassberger-Sandhas transition operators are used to find the leading term of the neutron-transfer amplitude near the exchange singularity in the cos plane. We derive formulae containing three-body Coulomb effects for the renormalization of the second-order exchange pole in the calculation of observables, such as the cross section and polarizations.     

Production of light superpartners in π0 radiative decays

The production rate of light photinos in radiative pion decay \(\pi ^0 \to \gamma \tilde \gamma \tilde \gamma\) is calculated. Experimental constraints on masses and mass splittings of scalar quarks imply the following upper bound on the decay rate \(BR(\pi ^0 \to \gamma \tilde \gamma \tilde \gamma ) \lesssim 10^{ - 16}\) .