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

Sum rules for spin asymmetries

Starting from rotational invariance we derive sum rules for the single-spin asymmetries in inclusive production and binary processes. We also get sum rules for spin correlation parameters in elastic pp-scattering.Comment: 4 page

Monitoring vibrations and microdisplacement for "pin on disc" tribology studies

The paper studies the example of applying accelerometers to evaluate tribocoupling vibration characteristics and verification methods in the testing system "pin on disc". Microelectromechanical systems (MEMS) intended for operation over a wide static and spectral ranges were applied. Accelerator spatial track recovery was implemented through the double integration algorithm. In the course of the work, the vibrations occurring through the friction between fluorocarbon and brass alloy LS59-1 under the conditions of dry friction were studied

Temperature Diffusivity Measurement and Nondestructive Testing Requiring No Extensive Sample Preparation and Using Stepwise Point Heating and IR Thermography

This chapter describes a modification to the laser flash method that allows determining temperature diffusivity and nondestructive testing of materials and constructions without cutting samples of predefined geometry. Stepwise local heating of the studied object surface at a small spot around 0.1 mm radius with simultaneous high temporary-spatial resolution infrared (IR) filming of the transient temperature distribution evolution with a thermal camera provides a wide range of possibilities for material characterization and sample testing. In case of isotropic and macroscopic homogeneous materials, the resulting transient temperature distribution is radially symmetric that renders possible to improve temperature measurement accuracy by averaging many pixels of the IR images located at the same distance from the heating spot center. The temperature diffusivity measurement can be conducted either on thin plates or on massive samples. The developed emissivity independent in plain IR thermographic method and mathematical algorithms enable thermal diffusivity measurement for both cases with accuracy around a few per cent for a wide range of materials starting from refractory ceramics to well-conducting metals. To detect defects, the differential algorithm was used. Subtracting averaged radial symmetric temperature distribution from the original one for each frame makes local inhomogeneities in the sample under study clearly discernible. When applied to crack detection in plates, the technique demonstrates good sensitivity to part-through cracks located both at the visible and invisible sides of the studied object

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

Stable bundles on hypercomplex surfaces

A hypercomplex manifold is a manifold equipped with three complex structures I, J, K satisfying the quaternionic relations. Let M be a 4-dimensional compact smooth manifold equipped with a hypercomplex structure, and E be a vector bundle on M. We show that the moduli space of anti-self-dual connections on E is also hypercomplex, and admits a strong HKT metric. We also study manifolds with (4,4)-supersymmetry, that is, Riemannian manifolds equipped with a pair of strong HKT-structures that have opposite torsion. In the language of Hitchin's and Gualtieri's generalized complex geometry, (4,4)-manifolds are called ``generalized hyperkaehler manifolds''. We show that the moduli space of anti-self-dual connections on M is a (4,4)-manifold if M is equipped with a (4,4)-structure.Comment: 17 pages. Version 3.0: reference adde

Supersymmetric Quantum Corrections and Poisson-Lie T-Duality

The quantum actions of the (4,4) supersymmetric non-linear sigma model and its dual in the Abelian case are constructed by using the background superfield method. The propagators of the quantum superfield and its dual and the gauge fixing actions of the original and dual (4,4) supersymmetric sigma models are determined. On the other hand, the BRST transformations are used to obtain the quantum dual action of the (4,4) supersymmetric non-linear sigma model in the sense of Poisson-Lie T-dualityComment: 18 page