Temperature-dependent chemical shift and relaxation times of (23)Na in Na(4)HTm[DOTP

We describe the characterization of a (23)Na temperature-dependent chemical shift and relaxation rates in the complex, Na(4)HTm[DOTP]. This is the first characterization of a (23)Na temperature-dependent chemical shift in a nonmetallic sample. The (23)Na temperature-dependent chemical shift coefficient is approximately -0. 5 PPM/ degrees C for both an aqueous solution and a 6% agarose gel of this compound. This is 50 times the magnitude of the temperature-dependent chemical shift coefficient of water protons. The relaxation times, T(1), T(2f), and T(2s) increased by 0.1, 0.01, and 0.05 ms/ degrees C, respectively. Applications of these unique properties for designing an MRI technique for monitoring heat deposition in tissue and tissue phantoms are discussed.     

Artificial compressibility, characteristics-based schemes for variable density, incompressible, multi-species flows. Part I. Derivation of different formulations and constant density limit

The paper presents various formulations of characteristics-based schemes in the framework of the artificial-compressibility method for variable-density incompressible flows. In contrast to constant-density incompressible flows, where the characteristics-based variables reconstruction leads to a single formulation, in the case of variable density flows three different schemes can be obtained henceforth labeled as: transport, conservative and hybrid schemes. The conservative scheme results in pseudo-compressibility terms in the (multi-species) density reconstruction. It is shown that in the limit of constant density, the transport scheme becomes the (original) characteristics-based scheme for incompressible flows, but the conservative and hybrid schemes lead to a new characteristics-based variant for constant density flows. The characteristics-based schemes are combined with second and third-order interpolation for increasing the computational accuracy locally at the cell faces of the control volume. Numerical experiments for constant density flows reveal that all the characteristics-based schemes result in the same flow solution, but they exhibit different convergence behavior. The multigrid implementation and numerical studies for variable density flows are presented in Part II of this study.     

Group-renormalization approach in quantum field theory in curved spacetime with torsion

The nature of the interaction of the gauge models SU(N) and O(N) with an external torsion field is studied from the group-renormalization point of view. Consideration of the radiation corrections to the nonminimal interaction gives a possible explanation for the absence of a torsion field in observational data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 34–38, October, 1990.The authors thank I. L. Buchbinder for discussion of the work.     

Vinylcyclopropanation of norbornadiene,norbornene, and dispiroheptadiene by methyl esters of 1-alkylcyclopropene-3-carboxylic acids

Methyl esters of 1-alkylcyclopropene-3-carboxylic acids (I) in the presence of CuCl·P(OPh)₃ cyclopropanate the intracyclic norbornene double bonds of norbornene, norbornadiene, and dispiroheptadiene to give the corresponding vinylcyclopropane adducts in yields up to 80%. 3,5-Dioxo-4-oxatricyclo[5.2.1. 0^2,6]dec-8-ene and 5-acetyl-7-oxabicyclo[2.2.1]hept-2-ene, which are heteroanalogs of dicyclopentadiene and norbornene, are inert relative to (I).Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 1, pp. 214–216, January, 1990.     

Stochastic Programming with Equilibrium Constraints

In this paper, we discuss here-and-now type stochastic programs with equilibrium constraints. We give a general formulation of such problems and study their basic properties such as measurability and continuity of the corresponding integrand functions. We discuss also the consistency and rate of convergence of sample average approximations of such stochastic problems     

The Regular Truncation Scheme of the BBGKY Hierarchy Equations for the Multi-Component Weakly Non-Ideal Plasma

A regular truncation scheme in which the divergencies characteristic of the Debye truncation are removed by taking into account the shall-range correlations. As a result, the two radii of screening the Debye radius D and √2 D appear in plasma which is not symmetrical as to its particle charges. The criterion of the applicability of this approach relates the plasma parameter to the potential depth of unlike-charged particles interaction.     

Chamber behavior of double Hurwitz numbers in genus 0

We study double Hurwitz numbers in genus zero counting the number of covers CP¹→CP¹ with two branching points with a given branching behavior. By the recent result due to Goulden, Jackson and Vakil, these numbers are piecewise polynomials in the multiplicities of the preimages of the branching points. We describe the partition of the parameter space into polynomiality domains, called chambers, and provide an expression for the difference of two such polynomials for two neighboring chambers. Besides, we provide an explicit formula for the polynomial in a certain chamber called totally negative, which enables us to calculate double Hurwitz numbers in any given chamber as the polynomial for the totally negative chamber plus the sum of the differences between the neighboring polynomials along a path connecting the totally negative chamber with the given one.