A renormalization group proof of perturbative renormalizability

This paper presents a proof of bounds on the renormalized perturbation expansion of the euclidean ₄ ⁴ theory. Its aim is partly pedagogical: by combining the insights and techniques of numerous authors it is now possible to define the perturbation expansion and bound it in a very few pages. The present version is based on the renormalized tree expansion adapted to the continuous renormalization group: all detailed results are proved by induction on the size of the tree. The continuous RG version presented here has one big advantage over the discrete RG version discussed elsewhere. In the continuous version, a tree has a more restrictive structure: there is a one-to-one correspondence between forks of the tree and lines of Feynman graphs. This extra structure eliminates the need to introduce Feynman graphs in the first place. It also reduces the number of cases to be analyzed at a given inductive step and simplifies the combinatorical estimates.Research supported by the Natural Sciences and Engineering Research Council     

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.     

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.     

Asymptotic behavior of the spectrum of certain problems,connected with the oscillation of fluids

One obtains the principal term of the asymptotics of the spectrum in a series of problems of the theory of small oscillations of fluids, filling partially a container. First one discusses a certain problem of general character, the nonlocal Steklov type problem. The considered problems are connected with the oscillations of a capillary ideal (or capillary stratified) fluid, of a heavy viscous fluid, of a capillary viscous fluid, and with the oscillations of a fluid in container with an elastic bottom.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 152, pp. 158–164, 1986.The author is deeply grateful to her scientific advisor M. Sh. Birman. The author is grateful also to N. D. Kopachevskii for his interest in the paper.     

Laser-pulse fluctuations due to thermal self-action in a turbulent atmosphere

Conclusions Refractive-index fluctuations caused by heating alter the intensity and phase fluctuation spectra arising from the turbulence. The large-scale part of the spectra is weakened, whereas the small-scale part is strengthened, and the spatial-frequency range in which the fluctuations are attenuated becomes narrower as the beam energy increases. Correspondingly, the fluctuation structure functions alter. For values of the arguments in those functions less than the radius of the first Fresnel zone , the thermal nonlinearity causes increases in the structural functions D_, with the energy. For , the dependence of D_, on energy is nonmonotone, with the fluctuations at first weakened but then strengthened. The reduction in fluctuation variance and the improvement in coherence is less pronounced over long lines than on short ones. The range in which geometrical optics can be used to derive the fluctuations is independent of the nonlinearity and is defined by k₂z/2k /4. The trend to the diffraction asymptote becomes slower as the nonlinearity increases.Atmospheric Physics Institute, Academy of Sciences of the USSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 9, pp. 1063–1071, September, 1989.     

Dynamical scattering of X-rays by dislocations in the Bragg and Laue case

The interbranch scattering of X-rays at dislocations is studied experimentally and with the aid of numerical simulations. Narrow beam of a small divergence is used for the study which is made both in the Laue and Bragg case of diffraction. The role of interbranch scattering in the formation of defect contrast in X-ray topography is discussed.     

Investigation of the character of the exchange interaction in the system Hg1−xMnxSe

A new method is proposed for determining the magnetic characteristics (magnitude and sign of the exchange interaction energy and the average size of clusters of magnetic ions) of dilute solid solutions of semimagnetic semiconductors at low temperatures based on oscillation measurements. The method makes it possible to find the magnetic characteristics of the indicated systems at temperatures between the point of the transition into the spin glass state and the temperature corresponding to the characteristic binding energy of magnetic atoms in clusters, for which standard methods based on the measurement of the magnetic susceptibility are not effective. The method is used to study the character of the exchange interaction in the system of solid solutions Hg_1–xMn_xSe as a function of their composition as well as under conditions of hydrostatic compression. To this end the oscillations of the magnetoresistance (Shubnikov-de Haas (SH) effect) in single-crystalline samples of Hg_1–xMn_xSe in the region of compositions 0.001 x 0.23 in magnetic fields H up to 65 kOe at temperatures T = (0.4–20) K and pressures up to 16 kbar were studied.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 29–39, November, 1989.     

Possible mechanism of metal ion extraction from aqueous solutions by fibrous polypropylene

Peculiarities of the extraction of metal ions from aqueous solutions by fibrous polypropylene have been investigated. It has been found that metal ion adsorption proceeds owing to the existence of a gas-liquid-hydrophobic polymer boundary line. The process mechanism has been discussed.     

Effect of methanol dilution on H-ZSM-5 zeolite deactivation in the process of light olefin formation

Conversion of methanol in the presence of H₂O, O₂, H₂, CO, CO₂ and He was studied at 733 K on H-ZSM-5 zeolite. The effect of diluent on the selectivity to light olefins and resistance to coking of H-ZSM-5 were observed. Among the diluents studied only water exerts a promoting effect on prolonged activity of the catalyst. Some explanations of the deactivation process are given.

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H₂O, O₂, H₂, CO, CO₂ He H-ZSM-5 733K. H-ZSM-5. . .