Random membrane model for lattice gluodynamics

odel for studying coupling dependence on lattice spacing a in gluodynamics is suggested. The model predicts $g-> g_{0}>0 with a->0. Free energy density in the model does not depend on temperature

Asymptotic transition from Fourier series to integrals in LGT

It is shown that in asymptotic transition from Fourier series to integrals an error and ambiguity may arise. Ambiguity reduces to a possibility of addition of some distribution to the result. Properties of such distributions are studied and conditions are established under which ambiguity doesn't arise. Method for correction computation is suggested and conditions for correction turning to zero are specified

Analytical study of fermion determinant and chiral condensate behavior at finite temperatures in toy model approximation

Fermion determinant is computed analytically on extremely large lattices $N_\tau \to \infty$ in the toy model approximation in which action is truncated so that in the Hamiltonian limit of $a_\tau \to 0$ all terms of order $a_\tau /a_\sigma$ are discarded$.$ Chiral condensate is studied in the area of small ($m<<T$) quark masses

Spatial string tension in gluodynamics at finite temperature in a spherical model approximation

Spatial string tension is computed in finite temperature gluodynamics on asymmetric lattices in a spherical model approximation. Conditions of scaling behavior are specified. Discrepancies with a standard renormalisation procedure are discussed.Comment: 13 pages, revte

Asymmetry Parameter Role in Description of Phase Structure of Lattice Gluodynamics at Finite Temperature

The role of lattice asymmetry parameter in description of the SU(2) gluodynamics phase structure at finite temperature is studied analytically. The fact that renormalization group relations which permit to remove the lattice asymmetry parameter from the thermodynamical quantities in the "naive" limit don't do the same in the approximation SU(N) = Z(N) keeping the "naive" limit results at the same time was point out. An additional condition which would fix asymmetry parameter is needed for this dependence removal.Comment: 20 pages, 6 LaTex figure

A Probabilistic Model of Machine Translation

A probabilistic model for computer-based generation of a machine translation system on the basis of English-Russian parallel text corpora is suggested. The model is trained using parallel text corpora with pre-aligned source and target sentences. The training of the model results in a bilingual dictionary of words and "word blocks" with relevant translation probability

q-Conformal Invariant Equations and q-Plane Wave Solutions

We give new solutions of the quantum conformal deformations of the full Maxwell equations in terms of deformations of the plane wave. We study the compatibility of these solutions with the conservation of the current. We also start the study of quantum linear conformal (Weyl) gravity by writing the corresponding q-deformed equations.Comment: 18 pages, Latex2e; v2: corrected misprints; v3: small text improvement; v4: misprints in f-la (3.14) correcte

Zero-cycles on a twisted Cayley plane

This is an essentially extended version of the preprint dated by August 2005 (this includes now the varieties of types F_4, E_6 and E_7). Let k be a field of characteristic not 2 and 3. Let G be an exceptional simple algebraic group of type F_4, inner type E_6 or E_7 with trivial Tits algebras. Let X be a projective G-homogeneous variety. If G is of type E_7 we assume in addition that the respective parabolic subgroup is of type P_7. The main result of the paper says that the degree map on the group of zero cycles of X is injective.Comment: 15 page

Chow motives of twisted flag varieties

Let G be an adjoint simple algebraic group of inner type. We express the Chow motive (with integral coefficients) of some anisotropic projective G-homogeneous varieties in terms of motives of simpler G-homogeneous varieties, namely, those that correspond to maximal parabolic subgroups of G. We decompose the motive of a generalized Severi-Brauer variety SB_2(A), where A is a division algebra of degree 5, into a direct sum of two indecomposable motives. As an application we provide another counter-example to the uniqueness of a direct sum decomposition in the category of motives with integral coefficients.Comment: 28 page

Heavy quark thermodynamics in full QCD

We analyze the large-distance behaviour of static quark-anti-quark pair correlations in QCD. The singlet free energy is calculated and the entropy contribution to it is identified allowing us to calculate the excess internal energy. The free energy has a sharp drop in the critical region, leading to sharp peaks in both excess entropy and internal energy