On the dynamics of cosmological particle production

The time evolution of the particle number density and spectrum of massive scalar particles, coupled conformally to a classical Friedman-Robertson-Walker gravitational field is followed numerically. Not only for a pure radiation cosmos, but also for one with an inflationary interlude, the density of particles produced remains constant in time. This results in a constant equivalent temperature scale up to the Compton time of the massive particles, and opens the possibility that during a sufficiently long inflation the energy density of the particles produced can exceed that of the radiation background.     

Quantum field-theory models on fractal spacetime

Continuing the analysis of a previous paper, the present work applies rigorous renormalization group methods to the hierarchical models to establish the existence of field theories with non-Gaussian ultraviolet renormalization group fixed points in 4- dimensions.     

The van der Waerden Theorem and the Burnside Problem for semigroups

Ohne Zusammenfassung     

Crystal structures of dimethylsuccinate and dimethyloxalate: Carbonyl group orientation for C13 chemical shielding tensor studies

The crystal structures of dimethylsuccinate (DMS) and dimethyloxalate (DMO) have been determined to facilitate the determination of the C-13 chemical shielding tensors of the carbonyl carbon in esters. Crystals of DMS are monoclinic, space groupC2/c,Z=4,a=13.154(4),b=6.156(1),c=9.363(4)Å,=98.53(3)°. The structure was solved by direct methods and refined by leastsquares procedures to giveR=0.071 for 932 observed data. Crystals of DMO are monoclinic space group,P2₁/n,Z=2, witha=3.891(1),b=11.879(2),c=6.213(2) Å,=103.32(2)°. The structure is the same (within experimental error) as that reported by Dougill and Jeffrey (1953) and refined to giveR=0.074 for 395 observed data.     

Variation of the instability index on stationary curves of elliptic equations depending on a parameter

The set of solutions of the equation A(u, )=0 in the case of general position consists of smooth curves. Solutions of a quasilinear elliptic equation with large instability index are constructed and an estimate obtained for the number of turning points of the solution curves.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 12, pp. 47–58, 1987.     

Spectral asymptotics for the Schrödinger operator with potential which steadies at infinity

We consider the discrete spectrum of the selfadjoint Schrödinger operatorA _h =–h ² +V defined inL ²(^m) with potentialV which steadies at infinity, i.e.V(x)=g+|x|^– f(1+o(1)) as |x| for>0 and some homogeneous functionsg andf of order zero. Let _h (),0, be the total multiplicity of the eigenvalues ofA _h smaller thanM–, M being the minimum value ofg over the unit sphereS ^m–1 (hence,M coincides with the lower bound of the essential spectrum ofA _h ). We study the asymptotic behaviour of ₁() as0, or of _h () ash0, the number0 being fixed. We find that these asymptotics depend essentially on the structure of the submanifold ofS ^m–1, where the functiong takes the valueM, and generically are nonclassical, i.e. even as a first approximation (2) ^m _h () differs from the volume of the set {(x, )^2m:h ²||²+V(x)<M–}.Partially supported by Contract No. 52 with the Ministry of Culture, Science and Education     

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.