Affine gravity,Palatini formalism and charges

Affine gravity and the Palatini formalism contribute both to produce a simple and unique formula for calculating charges at spatial and null infinity for Lovelock type Lagrangians whose variational derivatives do not depend on second-order derivatives of the field components. The method is based on the covariant generalization due to Julia and Silva of the Regge–Teitelboim procedure that was used to define properly the mass in the classical formulation of Einstein’s theory of gravity. Numerous applications reproduce standard results obtained by other secure but mostly specialized method like in ADM energy for asymptotically flat spacetimes and in Abbot and Deser for asymptotically de Sitter and anti-de Sitter spacetimes, both at spatial infinity. As a novel application we calculate the Bondi energy loss in five dimensional gravity, based on the asymptotic solution given by Tanabe et al. and obtain, as expected, the same result. We also give the for Einstein–Gauss–Bonnet gravity and find the superpotential for Lovelock theories of gravity when the number of dimensions tends to infinity with maximally symmetrical boundaries. The paper is written in standard component formalism.     

Probability of ruin of an insurance company for the poisson model

The probability of ruin of an insurance company over an infinite interval and the conditional average time before the ruin of the insurance company for the Poisson flows of insurance premiums and payments are found. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 28–33, April, 1999.     

Influence of Advertising Expenses on the Characteristics of Functioning of an Insurance Company

The basic characteristics of the functioning of an insurance company, including the average capital, ruin and survival probabilities, and the conditional time before ruin, are examined with allowance for advertising expenses.     

微积分的再思考

基于代数和显式一致估计的微积分思想可以追溯到前牛顿时代,或者欧拉和拉格朗日.由于所涉及的数学非常简单,新的方法可以从一些简单的例子出发,直接、自然却严格地建立微分和积分的流线型理论,并不需要连续性、极限和紧性的概念.     

On n-term approximation with positive coefficients

In this paper, we consider algorithms for constructing n-terms approximations with nonnegative coefficients. The convergence theorem is proved for a “positive” analog of the Pure Greedy Algorithm. We establish a condition on the sequence of weakness coefficients which is sufficient for the convergence of the Positive Weak Greedy Algorithm. This condition is also necessary for the class of monotone sequences.     

Structure and Dynamics of Ternary Complexes of Cucurbit[8]uril with Spin-Labeled Indicators and Biologically Active Analytes

Ternary host–guest complexes have been first obtained from cucurbituril CB[8] as a host molecule and two guest molecules: nitroxyl probes of different structures and biologically important amino acids (AA) and aromatic compounds. To characterize the binding of the guests, parameters of the polarity of the environment and the rotational mobility of the spin probes have been used. These parameters have been shown to depend on the nature of the analytes. For the ternary complexes, in addition to the usual triplet ESR spectra from nitroxyl probes (S3), supramolecular ensembles consisting of three equivalent ternary complexes (“triads”) have been found, whose ESR spectra have a seven-component hyperfine structure (S7) due to delocalization of the unpaired electron over three nitrogen nuclei. The relative intensity of the S7 spectra increases with increasing NaCl concentration in the solution, and also depends significantly on the nature of the analyte and the spin probe. Quantum chemical calculations have shown that (1) to determine the stability of the complexes, it is necessary to allow for the van der Waals interaction, and (2) the complexes involving the zwitterionic form of AA are much more stable than those with the neutral form of AA.     

Synthesis and biological activity of RS-abscisic acid and its analogs

Chemistry of Natural Compounds - RS-Abscisic acid and some of its analogs have been obtained. The biological activity of these compounds has been studied in dependence on their structure. It was...