Quasi-exactly solvable problems and the dual (q-)Hahn polynomials

A second-order differential (q-difference) eigenvalue equation is constructed whose solutions are generating functions of the dual (q-)Hahn polynomials. The fact is noticed that these generating functions are reduced to the (little q-)Jacobi polynomials, and implications of this for quasi-exactly solvable problems are studied. A connection with the Azbel-Hofstadter problem is indicated.Comment: 15 pages, LaTex; final version, presentation improved, title changed, to appear in J.Math.Phy

The Determinant Representation for a Correlation Function in Scaling Lee-Yang Model

We consider the scaling Lee-Yang model. It corresponds to the unique perturbation of the minimal CFT model M(2,5). This is not a unitary model. We used known expression for form factors in order to obtain a closed expression for a correlation function of a trace of energy-momentum tensor. This expression is a determinant of an integral operator. Similar determinant representation were proven to be useful not only for quantum correlation functions but also in matrix models.Comment: 14 pages, LaTeX, no figure

Synthesis and tribological properties of new fluoro-containing oligomers

Oligomers based on (polyfluoroalkyl)methyl oxiranes and thiiranes was first synthesized by the cationic polymerization in the presence of boron trifluoride etherate. Molecular weights of the products were defined by cryoscopic method. It was found that synthesized oligomers can be used as additives to industrial lubricants and sulfur oligomers are of the greatest positive tribological effect. © Pleiades Publishing, Ltd., 2013

Estimation of coupling between oscillators from short time series via phase dynamics modeling: limitations and application to EEG data

We demonstrate in numerical experiments that estimators of strength and directionality of coupling between oscillators based on modeling of their phase dynamics [D.A. Smirnov and B.P. Bezruchko, Phys. Rev. E 68, 046209 (2003)] are widely applicable. Namely, although the expressions for the estimators and their confidence bands are derived for linear uncoupled oscillators under the influence of independent sources of Gaussian white noise, they turn out to allow reliable characterization of coupling from relatively short time series for different properties of noise, significant phase nonlinearity of the oscillators, and non-vanishing coupling between them. We apply the estimators to analyze a two-channel human intracranial epileptic electroencephalogram (EEG) recording with the purpose of epileptic focus localization.Comment: 22 pages, 7 figures, the paper is to be published in Chaos, 2005, vol.15, issue 2, see http://chaos.aip.org

Sine-Gordon breather form factors and quantum field equations

Using the results of previous investigations on sine-Gordon form factors exact expressions of all breather matrix elements are obtained for several operators: all powers of the fundamental bose field, general exponentials of it, the energy momentum tensor and all higher currents. Formulae for the asymptotic behavior of bosonic form factors are presented which are motivated by Weinberg's power counting theorem in perturbation theory. It is found that the quantum sine-Gordon field equation holds and an exact relation between the ``bare'' mass and the renormalized mass is obtained. Also a quantum version of a classical relation for the trace of the energy momentum is proven. The eigenvalue problem for all higher conserved charges is solved. All results are compared with perturbative Feynman graph expansions and full agreement is found.Comment: LaTeX, 31 page

The determinant representation for quantum correlation functions of the sinh-Gordon model

We consider the quantum sinh-Gordon model in this paper. Using known formulae for form factors we sum up all their contributions and obtain a closed expression for a correlation function. This expression is a determinant of an integral operator. Similar determinant representations were proven to be useful not only in the theory of correlation functions, but also in the matrix models.Comment: 21 pages, Latex, no figure

The quasiclassical theory of the Dirac equation with a scalar-vector interaction and its applications in the theory of heavy-light mesons

We construct a relativistic potential quark model of $D$, $D_s$, $B$, and $B_s$ mesons in which the light quark motion is described by the Dirac equation with a scalar-vector interaction and the heavy quark is considered a local source of the gluon field. The effective interquark interaction is described by a combination of the perturbative one-gluon exchange potential $V_{\mathrm{Coul}}(r)=-\xi/r$ and the long-range Lorentz-scalar and Lorentz-vector linear potentials $S_{\mathrm{l.r.}}(r)=(1-\lambda)(\sigma r+V_0)$ and $V_{\mathrm{l.r.}}(r)=\lambda(\sigma r+V_0)$, where $0\leqslant\lambda<1/2$. Within the quasiclassical approximation, we obtain simple asymptotic formulas for the energy and mass spectra and for the mean radii of $D$, $D_s$, $B$, and $B_s$ mesons, which ensure a high accuracy of calculations even for states with the radial quantum number $n_r\sim 1$. We show that the fine structure of P-wave states in heavy-light mesons is primarily sensitive to the choice of two parameters: the strong-coupling constant $\alpha_s$ and the coefficient $\lambda$ of mixing of the long-range scalar and vector potentials $S_{\mathrm{l.r.}}(r)$ and $V_{\mathrm{l.r.}}(r)$. The quasiclassical formulas for asymptotic coefficients of wave function at zero and infinity are obtained.Comment: 22 pages, 6 figure

p-Adic Mathematical Physics

A brief review of some selected topics in p-adic mathematical physics is presented.Comment: 36 page

Paramagnetic and antiferromagnetic resonances in the diamagnetically diluted Haldane magnet PbNi2V2O8

The impurity-induced antiferromagnetic ordering of the doped Haldane magnet Pb(Ni{1-x}Mg{x})2V2O8 (0 < x <0.06) was studied by electron spin resonance (ESR) on ceramic samples in the frequency range 9-110 GHz. Below the N\'{e}el temperature a transformation of the ESR spectrum was found, indicating an antiferromagnetic resonance mode of spin precession. The excitation gap of the spin-wave spectrum increases with increasing Mg-concentration $x$ in the same manner as the N\'{e}el temperature, reaching its maximum value of 80 GHz at x > 0.04. At small concentrations x < 0.02 the signals of antiferromagnetic resonance were found to coexist with the signal of the paramagnetic resonance indicating a microscopic separation of the magnetic phases.Comment: 10 pages, 9 figure