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.     

Structure of a nonequilibrium high-frequency discharge

The problem for a one-temperature plasma is considered with allowance for the finite ionization rate. It is shown that in the developed nonequilibrium case the leading effect of ambipolar electron diffusion and ionization lag lead to a qualitatively different picture as compared with the equilibrium case. In particular, the heat release zone covers only a relatively small leading part of the ionization zone with a relatively low (n_e n_ef) electron concentration.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 161–169, May–June, 1989.The authors thank A. A. Barmin and A. G. Kulikovskii for useful discussions.     

Impossibility of centrally symmetric shock waves in vacuum in the relativistic theory of gravitation

Burevestnik Scientific-Industrial Union, Leningrad. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 79, No. 3, pp. 473–480, June, 1989.     

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.     

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.     

Quantum field theories of vortices and anyons

We develop the quantization of topological solitons (vortices) in three-dimensional quantum field theory, in terms of the Euclidean region functional integral. We analyze in some detail the vortices of the abelian Higgs model. If a Chern-Simons term is added to the action, the vortices turn out to be anyons, i.e. particles with arbitrary real spin and intermediate () statistics. Localization properties of the interpolating field, scattering theory and spin-statistics connection of anyons are discussed. Such analysis might be relevant in connection with the fractional quantum Hall effect and two-dimensional models of HighT _csuperconductors.     

On the longitudinal range of a dual jet

The paper describes experiments in which one of the major properties of the dual jet — the longitudinal range — has been addressed. Hot film anemometry has been employed to determine the development of the plane turbulent dual jet for the different geometries and flow rates. It has been found that the separation distance of the discharging nozzles influences significantly the centre-line mean velocity decay. The method of calculating of the axial velocity distribution in the combined region of the dual jet, based on the correlation of the experimental results for the separation distance tillB ⁺=10 is shown. The other important feature of the dual jet is the substantially reduced local flow rate.

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Über den Längsbereich eines Zweistrahls

Zusammenfassung Diese Untersuchung beschreibt Experimente über die Haupteigenschaften eines Zweistrahls-den Längsbereich. Es wurde eine Heiß-Film-Anemometrie durchgeführt, um die Entwicklung des ebenen turbulenten Zweistrahls für verschiedene Geometrien und Strömungssorten bestimmen zu können. Es wurde herausgefunden, daß der Abstand der Ausströmdüsen signifikant den mittleren Geschwindigkeitsabfall beeinflußt. Dargestellt wird die Methode, die axiale Geschwindigkeitsverteilung in dem kombinierten Bereich des Zweistrahls, basierend auf den experimentellen Ergebnissen für Abstände bis zuB ⁺=10 zu berechnen. Das andere wichtige Merkmal des Zweistrahls ist die wesentliche Reduzierung der lokalen Strömungsgeschwindigkeit.

     

Nonlinear void-fraction waves in two-phase bubbly flow

It is shown that nonlinear void-fraction waves constitute exact solutions of the two-fluid equations for bubbly flow, if and only if the virtual-mass coefficientm() is a definite function of the void fraction. In the case of spherical bubbles the functional dependence is given bym()=(1/2)(1–a)(1–3). A similar expression was obtained recently by means of an elaborate linear stability analysis of a uniform two-phase flow. It is remarkable that the greater part of the physical quantities of a nonlinear void-fraction wave depends linearly on. The virtual-mass coefficient may be derived directly from a special form of Hamilton's variational principle.

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Zusammenfassung Es wird gezeigt daß nichtlineare Konzentrationswellen exakte Lösungen der Zweifluiden Gleichungen einer Blasenströmung darstellen dann und nur dann, wenn der Koeffizientm() der virtuellen Masse eine bestimmte Funktion der Volumenkonzentration der Blasen ist. Die funktionelle Abhängigkeit ist im Falle kugelförmiger Blasen gegeben durchm()= (1/2)(1–) (1–3). Ein gleicher Ausdruck wurde neulich mittels einer umständlichen linearen Stabilitätsanalysis einer uniformen Zweiphasen-Strömung erhalten. Es ist bemerkenswert daß der größere Teil der physikalischen Größen einer nichtlinearen Konzentrationswelle in linearer Weise von abhängt. Der Koeffizient der virtuellen Masse kann in direkter Weise von einer speziellen Form des Hamiltonschen Variationsprinzips hergeleitet werden.

     

Supplement to the paper “the averaging operator with respect to a countable partition on a minimal symmetric ideal of the space L1(0, 1)”

Let A be a partition of the segment [0, 1] into a countable number of disjoint subsets of positive measure, let tL₁(0,1), let N_t be the smallest rearrangement-invariant order ideal vector lattice in L₁(0,1), containing t. In the paper one investigates the properties of the image E(N_t¦A) of the averaging operator with respect to A. In particular, one elucidates under what conditions there exists a function g, gL₁(0,1), such that E(N_t¦A)N_g. One formulates a generalization of the known Hardy-Littlewood inequality, namely Theorem E(tA)QE(t*A*), where is the Hardy-Littlewood preorder, t* and A* are the decreasing rearrangements of the function ¦t¦ and (in a special sense) of the partition A, while Q is an absolute constant, 1Q2⁵. One formulates the problem of the smallest value of Q.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 149, pp. 137–141, 1986.     

Singular series of genus 2 for sums of squares

Let f₁, ..., f_h be representatives of classes in the genus of a positive quadratic form f, r_i(k) the number of representations of k by the form f_i, (k) the value of the singular Hardy-Littlewood series, E_i the number of integer automorphisms of f_i. We derive an expression for in terms of the values of singular series of genus 1 and 2. This expression is evaluated for the simplest model f(x)=x ₁ ² +...+x _m ² , m1 (mod 8), k is a prime in-integer, k=1(mod 8).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 151, pp. 26–39, 1986.