On Bohr-Sommerfeld bases

This paper combines algebraic and Lagrangian geometry to construct a special basis in every space of conformal blocks, the Bohr-Sommerfeld (BS) basis. We use the method of [D. Borthwick, T. Paul and A. Uribe, Legendrian distributions with applications to the non-vanishing of Poincar\'e series of large weight, Invent. math, 122 (1995), 359-402, preprint hep-th/9406036], whereby every vector of a BS basis is defined by some half-weighted Legendrian distribution coming from a Bohr-Sommerfeld fibre of a real polarization of the underlying symplectic manifold. The advantage of BS bases (compared to bases of theta functions in [A. Tyurin, Quantization and ``theta functions'', Jussieu preprint 216 (Apr 1999), e-print math.AG/9904046, 32pp.]) is that we can use information from the skillful analysis of the asymptotics of quantum states. This gives that Bohr-Sommerfeld bases are unitary quasi-classically. Thus we can apply these bases to compare the Hitchin connection with the KZ connection defined by the monodromy of the Knizhnik-Zamolodchikov equation in combinatorial theory (see, for example, [T. Kohno, Topological invariants for 3-manifolds using representations of mapping class group I, Topology 31 (1992), 203-230; II, Contemp. math 175} (1994), 193-217]).Comment: 43 pages, uses: latex2e with amsmath,amsfonts,theore

Radiation-induced hydrogen transfer in metals

The paper presents processes of hydrogen (deuterium) diffusion and release from hydrogen-saturated condensed matters in atomic, molecular and ionized states under the influence of the electron beam and X-ray radiation in the pre-threshold region. The dependence is described between the hydrogen isotope release intensity and the current density and the electron beam energy affecting sample, hydrogen concentration in the material volume and time of radiation exposure to the sample. The energy distribution of the emitted positive ions of hydrogen isotopes is investigated herein. Mechanisms of radiation-induced hydrogen transfer in condensed matters are suggested

Methods of verification of compliance with an asymptotically power law

© Published under licence by IOP Publishing Ltd. This paper describes methods of the power law verification using different empirical data. We do not analyse the value of deviations from the model but try to found out whether these deviations are regular or random. The suggested approach is based on the idea of finding local power approximation of the considered series for each range of ranks, after which one or another trend criterion is applied to the obtained series of local exponents. Application of the runs test is also discussed. The suggested methods were tested using 10 sets of empirical data, which are available for free. It was shown that compliance with the power law is satisfactory only in one case

Spectroscopic characterization of the complex of vinyl radical and carbon dioxide : Matrix isolation and ab initio study

We report on the preparation and vibrational characterization of the C2H3 center dot center dot center dot CO2 complex, the first example of a stable intermolecular complex involving vinyl radicals. This complex was prepared in Ar and Kr matrices using UV photolysis of propiolic acid (HC3OOH) and subsequent thermal mobilization of H atoms. This preparation procedure provides vinyl radicals formed exclusively as a complex with CO2, without the presence of either CO2 or C2H3 monomers. The absorption bands corresponding to the nu(5)(C2H3), nu(7)(C2H3), nu(8)(C2H3), nu(2)(CO2), and nu(3)(CO2) modes of the C2H3 center dot center dot center dot CO2 complex were detected experimentally. The calculations at the UCCSD(T)/L2a level of theory predict two structures of the C2H3 center dot center dot center dot CO2 complex with C-s and C-1 symmetries and interaction energies of -1.92 and -5.19 kJ mol(-1). The harmonic vibrational frequencies of these structures were calculated at the same level of theory. The structural assignment of the experimental species is not straightforward because of rather small complexation-induced shifts and matrix-site splitting of the bands (for both complex and monomers). We conclude that the C-1 structure is the most probable candidate for the experimental C2H3 center dot center dot center dot O-2 complex based on the significant splitting of the bending vibration of CO2 and on the energetic and structural considerations. Published by AIP Publishing.Peer reviewe

The Economic Foundations of the Rule of Law in the Russian Federation

This study, based on the economic and legal metrics of the Russian Federation, considers the possibility of implementing the concept of the rule of law in the modern world. The study emphasises the issue of the rule of law in any country being directly related to the problem of redistribution of public goods. In many ways, this can be considered an example of how economic stability ensures legal stability. The research methodology includes a dialectical method, which allowed to ensure compliance with the principles of scientific knowledge. The study shows the dynamics of ensuring human rights, the distribution of income and expenses in society over different periods in the history of the Russian Federation. In this regard, the authors come to the conclusion that the perception and functions of the concept of the rule of law will soon deviate from classical liberal values towards the basic ideas of social equality and justice

Study of internal structures of 9,10Be and 10B in scattering of 4He from 9Be

A study of inelastic scattering and single-particle transfer reactions was performed by an alpha beam at 63 MeV on a 9$Be target. Angular distributions of the differential cross sections for the 9Be(4He,4He')9Be*, 9Be(4He,3He)10Be and 9Be(4He,t)10B reactions were measured. Experimental angular distributions of the differential cross sections for the ground state and a few low-lying states were analyzed in the framework of the optical model, coupled channels and distorted-wave Born approximation. An analysis of the obtained spectroscopic factors was performed.Comment: 16 pages, 7 figures, 3 tables, regular paper, mispritns are corrected in new versio

An improvement of the Berry--Esseen inequality with applications to Poisson and mixed Poisson random sums

By a modification of the method that was applied in (Korolev and Shevtsova, 2009), here the inequalities $$\rho(F_n,\Phi)\le\frac{0.335789(\beta^3+0.425)}{\sqrt{n}}$$ and $$\rho(F_n,\Phi)\le \frac{0.3051(\beta^3+1)}{\sqrt{n}}$$ are proved for the uniform distance $\rho(F_n,\Phi)$ between the standard normal distribution function $\Phi$ and the distribution function $F_n$ of the normalized sum of an arbitrary number $n\ge1$ of independent identically distributed random variables with zero mean, unit variance and finite third absolute moment $\beta^3$. The first of these inequalities sharpens the best known version of the classical Berry--Esseen inequality since $0.335789(\beta^3+0.425)\le0.335789(1+0.425)\beta^3<0.4785\beta^3$ by virtue of the condition $\beta^3\ge1$, and 0.4785 is the best known upper estimate of the absolute constant in the classical Berry--Esseen inequality. The second inequality is applied to lowering the upper estimate of the absolute constant in the analog of the Berry--Esseen inequality for Poisson random sums to 0.3051 which is strictly less than the least possible value of the absolute constant in the classical Berry--Esseen inequality. As a corollary, the estimates of the rate of convergence in limit theorems for compound mixed Poisson distributions are refined.Comment: 33 page