Essential Variational Poisson Cohomology

In our recent paper “The variational Poisson cohomology” (2011) we computed the dimension of the variational Poisson cohomology for any quasiconstant coefficient ℓ × ℓ matrix differential operator K of order N with invertible leading coefficient, provided that is a normal algebra of differential functions over a linearly closed differential field. In the present paper we show that, for K skewadjoint, the -graded Lie superalgebra is isomorphic to the finite dimensional Lie superalgebra . We also prove that the subalgebra of “essential” variational Poisson cohomology, consisting of classes vanishing on the Casimirs of K, is zero. This vanishing result has applications to the theory of bi-Hamiltonian structures and their deformations. At the end of the paper we consider also the translation invariant case.     

Thermal expansion of thin C60 films

The thermal expansion coefficient a and structure of C₆₀ films with thickness t∼3–10 nm were investigated in the temperature interval from room to liquid-nitrogen temperature by electron-optical methods. The thermal expansion coefficient was determined from the temperature shift of the diffraction maxima in the electron diffraction patterns. The objects of investigation were epitaxial C₆₀ films condensed in vacuum on a (100) NaCl cleavage surface and oriented in the (111) plane. A surface-induced size effect in the thermal expansion coefficient was observed. It was established that as t decreases α _f increases and is described well by the relation α _f=17·10⁻⁶ K⁻¹+8.3·10⁻⁵ nm K⁻¹ t ⁻¹. This relation was used to estimate the linear expansion coefficient α _s of the C₆₀ surface in the (111) plane as α _s=60·10⁻⁶K⁻¹, which is several times larger than the bulk value. The experimental results agree satisfactorily with the theoretical calculations of the mean-square displacements of molecules located in a region near the surface. Zh. éksp. Teor. Fiz. 114, 1868–1875 (November 1998)     

Quantum Invariant Measures

We derive an explicit expression for the Haar integral on the quantized algebra of regular functions ℂ _q [K] on the compact real form K of an arbitrary simply connected complex simple algebraic group G. This is done in terms of the irreducible ✶-representations of the Hopf ✶-algebra ℂ _q [K]. Quantum analogs of the measures on the symplectic leaves of the standard Poisson structure on K which are (almost) invariant under the dressing action of the dual Poisson algebraic group K ^✶ are also obtained. They are related to the notion of quantum traces for representations of Hopf algebras. As an application we define and compute explicitly quantum analogs of Harish-Chandra c-functions associated to the elements of the Weyl group of G. Received: 26 January 2001 / Accepted: 31 May 2001     

Implications of time-reversal symmetry for the band structure of single-wall carbon nanotubes

When electron states in carbon nanotubes are characterized by two-dimensional wave vectors with the components K ₁ and K ₂ along the nanotube circumference and cylindrical axis, respectively, then two such vectors symmetric about a M-point in the reciprocal space of graphene are shown to be related by the time-reversal operation. To each carbon nanotube there correspond five relevant M-points with the following coordinates: K ₁⁽¹⁾ = N/2R, K ₂⁽¹⁾= 0; K ₁⁽²⁾ = M/2R, K ₂⁽²⁾= −π/T; K ₁⁽³⁾= (2N −M)/2R, K ₂⁽³⁾= π/T; K ₁⁽⁴⁾= (M + N)/2R, K ₂⁽⁴⁾= -π/T, and K ₁⁽⁵⁾= (N − M)/2R, K ₂⁽⁵⁾= π/T, where M and N are the integers relating the chiral, C _h , symmetry, R, and translational, T, vectors of the nanotube by N R = C _h + M T, T = |T|, and R is the nanotube radius. The states at the edges of the one-dimensional Brillouin zone, which are symmetric about the M-points with K ₂ = ±π/T, are shown to be degenerate due to the time-reversal symmetry.     

Superdiffusion and stable laws

The superdiffusion equation with a fractional Laplacian Δ ^α/2 in _N-dimensional space describes the asymptotic (t→∞) behavior of a generalized Poisson process with the range (discontinuity) distribution density ∼|x|−α−1. The solutions of this equation belong to a class of spherically symmetric stable distributions. The main properties of these solutions are given together with their representations in the form of integrals and series and the results of numerical calculations. It is shown that allowance for the finite velocity of free particle motion for α>1 merely amounts to a reduction in the diffusion coefficient with the form of the distribution remaining stable. For α<1 the situation changes radically: the expansion velocity of the diffusion packet exceeds the velocity of free particle motion and the superdiffusion equation becomes physically meaningless. Zh. éksp. Teor. Fiz. 115, 1411–1425 (April 1999)     

Classical Dynamical r-Matrices¶and Homogeneous Poisson Structures on G/H and K/T

Let G be a finite dimensional simple complex group equipped with the standard Poisson Lie group structure. We show that all G-homogeneous (holomorphic) Poisson structures on G/H, where H⊂G is a Cartan subgroup, come from solutions to the Classical Dynamical Yang–Baxter equations which are classified by Etingof and Varchenko. A similar result holds for a maximal compact subgroup K, and we get a family of K-homogeneous Poisson structures on K/T, where T=K∩H is a maximal torus of K. This family exhausts all K-homogeneous Poisson structures on K/T up to isomorphisms. We study some Poisson geometrical properties of members of this family such as their symplectic leaves, their modular classes, and the moment maps for the T-action. Received: 4 September 1999 / Accepted: 25 January 2000     

Discovery of a narrow resonance state of the system K S K S at mass 1520 MeV

Data are presented which indicate the existence of a previously unknown narrow resonance near mass 1520 MeV, discovered while analyzing the system K _S K _S . The data were obtained at ITEP using the 6-m magnetic spectrometer in a beam of 40-GeV negative particles. The resonance is observed in π⁻ p and K ⁻ p interactions with a total statistical confidence of not less than 5 standard deviations. The width of this state is comparable to the mass resolution of the spectrometer (∼5 MeV). The mass is 1521.5±2.5 MeV. Estimates of the product σ·BR (K _S K _S ) give ∼5.0 nb in π⁻ p interactions and ∼250 nb in K ⁻ p interactions. From the fact that the production cross section of this resonance in the K ⁻ beam is approximately 50 times greater than the production cross section in the π⁻ beam, it can be concluded that this new state belongs to a system of mesons with hidden strangeness. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 4, 242–246 (25 August 1999)     

Elementary muon, pion, and kaon particles as resonators for neutrino quanta. Calculations of mass ratios for e, μ, π0, π±, K 0, K ±, and ν e

Masses of a number of elementary particles are calculated on the basis of the model suggested in [1] with the use of one parameter. In this model, an electron is considered as an electric cloud enclosed inside an elastic lepton shell, electron neutrino ν _е is considered as an elastic lepton shell contracted to a minimal size, and muon, pion and kaon are considered as resonators for quanta of virtual neutrinos excited inside the elastic lepton shell. The number and type of these quanta are determined from the decay scheme for μ, π, and K: 2 for the muon (ν _е and ), 3 for the pion (ν _е , ν _μ, and ), and at least 21 for the kaon. The model allows mass ratios approximating the experimental data for these particles to be obtained for the first time, with the ratio of μ and е masses equal to (6πℏс/е ²)^2/3 ≅ 188, the ratio of π ⁰ and μ masses equal to (3/2)^2/3, and the ratio of K ⁰ and π ⁰ equal masses to 7^2/3. The calculated e, μ , π ⁰, and K ⁰ masses are in the 0.547:105.707:134.963:493.87 (MeV) ratios (normalized by the neutral pion mass). This is in good agreement with the available experimental data. The mass ν _е (≅ 0.02 eV) is also estimated in this model, and the variety of K-meson decay schemes is naturally explained as a result of the variety of excited intrinsic neutrino field structures with the same energy. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 23–29, January, 2009.     

Study of fission track registration efficiency of γ-irradiated polyester track detector in solution medium

The fission track registration efficiency (K _wet) of the Garware polyester track (GPF) detector in solution has been determined with respect to the Lexan detector whose K _wet is very well known in the literature. The K _wet is found to be (1.2 ± 0.1) 10⁻³ cm. The track registration efficiency of the GPF detector in solution is better than the efficiencies of other nuclear track detectors reported in the literature. This implies that the threshold energies for track registration are different for different detectors and that GPF detector has a lower threshold-energy value. The effects of gamma irradiation in the dose range of 5–51 Mrad on the fission track registration efficiency (K _wet) of this track detector from the solution medium are also investigated. The results show that the K _wet values for the gamma-irradiated detectors in the above dose range in 2M HNO₃ solution medium decreases by ∼7–15%. The changes induced in the gamma-irradiated detectors as a function of gamma dose have also been studied by bulk-etch rate measurements.     

Resonance behavior of a K S K S system near the mass 1775 MeV

The preliminary results of an investigation of a system of two K _S mesons in the mass interval 1600–1950 MeV are reported. The events were obtained on a 6-m magnetic spark spectrometer at ITEP in π ⁻ p interactions at 40 GeV, using a neutral trigger which suppressed both charged particles and γ rays. A peak of width ≃30 MeV with statistical significance not lower than six standard deviations is observed with momentum transfer selection |tu|0.23 GeV² near the mass 1775 MeV of the K _S K _S system. The observed phenomena can be interpreted as the existence of one resonance with the indicated parameters, or two narrower resonances. In the latter case, their masses are 1768±1.5 and 1787±1.5 MeV. The widths of these states are comparable to the mass resolution of the spectrometer (∼5 MeV). Estimates of the product σ ⋅BR(K _S K _S ) give ∼1.5 and 2.5 nb, respectively, for the first and second states. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 10, 727–731 (25 November 1998)     

Thermodynamic parameters of diffuse phase transitions in Ag2Te

A differential thermal analysis in vacuum and studies of the coefficients of electrical conductivity and thermal conductivity, and of the thermal emf are made in Ag₂Te in the neighborhood of the structural phase transition. It is shown that these data can be used to calculate the switching factor L(T), determine the region in which the phases coexist within the transition, and calculate the thermodynamic parameters. Prior to and after the main phase transition, additional displacement transitions are observed. It is found that the phase transition takes place roughly according to the scheme α _{385 K}→α′_{405 K}→β′_{420 K}→β _{440 K}. The specific heat C _p, changes in entropy ΔS and transition enthalpy ΔH, as well as the minimum phase fluctuation volume V, and the heat Q of the phase transition are determined. It is shown that excesses of Te and Ag have almost no effect on the transition temperatures T ₀, but have a substantial effect on the thermodynamic parameters. Fiz. Tverd. Tela (St. Petersburg) 40, 1693–1697 (September 1998)     

Influence of anisotropy on the dispersion of surface plasmon-phonon polaritons in silicon carbide

Surface plasmon-phonon polaritons (SPPP’s) of types 3 and 4 are investigated in doped anisotropic single crystals of hexagonal silicon carbide (6H-SiC) in the orientation corresponding to K⊥C and xy⊥C. It is shown that a dispersion dependence of the type-3 SPPP’s bounded by K appears in 6H-SiC when the plasmon frequency increases to ν _p⊥⩾350 cm⁻¹. At ν _p⊥⩾400 cm⁻¹, ν _s(K) exists for type-4 SPPP’s in the frequency range Ω _∥ ⁺ <ν< _⊥ ⁺ . When the concentration of free charge carriers is increased, the dispersion curves are displaced toward higher frequencies. The conditions for the existence of type-3 and type-4 SPPP’s in 6H-SiC are determined. Fiz. Tverd. Tela (St. Petersburg) 40, 636–639 (April 1998)     

A Fe<Superscript>3+</Superscript>/Hg<Superscript>2+</Superscript>-Selective Anthracene-Based Fluorescent PET Sensor with Tridentate Ionophore of Amide/β-Amino Alcohol

A new anthracene-based fluorescent PET sensor 1 with a tridentate ionophore of amide/β-amino alcohol displays very good selectivity and sensitivity for Fe³⁺ (K _a = 1.6 × 10³ M⁻¹) and Hg²⁺ (K _a = 2.1 × 10³ M⁻¹) in CH₃CN–H₂O (3:7, v/v) with detection limit of 1 μM. More fluorescence enhancement was observed when 1 selectively detected Fe³⁺ or Hg²⁺ in CH₃CN and its detection limit was up to 0.03 μM.     

A convergent star product for linear Poisson structures

An explicit star product ⋆ _α ^Γ on the dual of a general Lie algebra equipped with the linear Poisson bracket is constructed. An equivalence operator between this star product and the Kontsevich star product in [K₁] is given and diverse properties of the star product ⋆ _α ^Γ are studied. It is also proved that the star product ⋆ _α ^Γ provides a convergent deformation quantization in the sense of Rieffel [R₁].     

Construction of Fredholm representations and a modification of the Higson-Roe corona

The Fredholm representation theory is well adapted to the construction of homotopy invariants of non-simply-connected manifolds by means of the generalized Hirzebruch formula [σ(M)] = 〈L(M)ch _A f*ξ, [M]〉 ∈ K _A ⁰(pt) ⊗ Q, where A = C*[π] is the C*-algebra of the group π, π = π ₁(M). The bundle ξ ∈ K _A ⁰(Bπ) is the canonical A-bundle generated by the natural representation π → A. Recently, the first author constructed a natural family of Fredholm representations that lead to a symmetric vector bundle on the completion of the fundamental group with a modification of the Higson-Roe corona, provided that the completion is a closed manifold.     

Recent Result of Muon Catalyzed t–t Fusion at RIKEN-RAL

We have measured X-rays and neutrons associated with the muon catalyzed t–t fusion process at the RIKEN-RAL Muon facility. In the X-ray measurement, we observed K_α and K_β X-rays originating from the muon sticking process in muon catalyzed t–t fusion, and obtained the K_α X-ray yield and the K_β/K_α intensity ratio. An average recoil energy of the (μ⁻α) atoms in a solid T₂ medium was determined from the observed Doppler broadening width of the K_α X-ray line. The obtained t–t fusion neutron has shown an exponential time spectrum with a single component and a continuous energy spectrum with a maximum energy of 9 MeV. We have determined the t–t fusion neutron yield, the t–t fusion cycling rate and the muon sticking probability from the neutron data. The obtained maximum neutron energy is a very peculiar value from the view point of the reaction Q value (11.33 MeV) with the three-particle decay mode at the exit channel: t + t → α + n + n + Q. The obtained neutron energy distribution was analyzed by a simple model with two neutron energy components; reasonable agreement has been obtained, suggesting a strong (n–α) correlation in the exit channel of the t–t muon catalyzed fusion reaction. This revised version was published online in August 2006 with corrections to the Cover Date.     

Titanium K-edge absorption structure in Ti1−x NbxO2

The fine structure in the titanium x-ray K-edge absorption has been measured in Ti_1−x Nb_xO₂ mixed dioxides (x=0–0.1) with rutile structure in a laboratory-type spectrometer by total electron quantum-yield measurement. The position of the XANES lines is shown to be in good agreement with classical x-ray absorption spectra obtained in transmission. The structure and main features of the XANES spectra, including the effects of impurities and manyelectron excitations, are discussed. It is suggested that the intensity of the B peak characteristic of the titanium K edge depends on the Nb concentration and correlates with the charge state of titanium ions. Fiz. Tverd. Tela (St. Petersburg) 41, 894–896 (May 1999)     

On the Poisson Limit Theorems of Sinai and Major

Let f(ϕ) be a positive continuous function on 0 ≤ϕ≤Θ, where Θ≤ 2 π, and let ξ be the number of two-dimensional lattice points in the domain Π _R (f) between the curves r=(R+c ₁/R)f(ϕ) and r=(R+c ₂/R)f(ϕ), where c ₁<c ₂ are fixed. Randomizing the function f according to a probability law P, and the parameter R according to the uniform distribution μ _L on the interval [a ₁ L,a ₂ L], Sinai showed that the distribution of ξ under P×μ _L converges to a mixture of the Poisson distributions as L→∞. Later Major showed that for P-almost all f, the distribution of ξ under μ _L converges to a Poisson distribution as L→∞. In this note, we shall give shorter and more transparent proofs to these interesting theorems, at the same time extending the class of P and strengthening the statement of Sinai. Received: 15 June 1999 / Accepted: 11 February 2000     

Intrinsic <Emphasis Type="Italic">g</Emphasis><Subscript><Emphasis Type="Italic">K</Emphasis></Subscript> factors of odd-mass <Superscript>167–179</Superscript>Lu isotopes

In this paper, g _K -factors of the intrinsic magnetic moments and effective spin gyromagnetic factors (g _s^eff) of the ^167–179Lu isotopes have been studied within the Tamm-Dancoff approximation (TDA) (Kuliev et al, Sov. J. Nucl. Phys. 9, 185 (1969)) by using a realistic potential such as Woods-Saxon potential for the first time. The effects of the spin-spin and spin-isospin interactions on magnetic moments were investigated. The results of the theoretical calculations are compared with the experimental data for related nuclei. The experimental values of g _K and g _s^eff were computed from the observed magnetic moments (Georg et al, Eur. Phys. J. A3, 225 (1998)) using the spin matrix elements. The theoretical predictions for the g _K factors exhibit good agreement with the experimental g _K factors with increasing mass number A of the lutetium isotopes. The strongest influence of the neutron-proton spin interaction occurs at q = −1. Sufficient agreement between the calculated and the experimental values of g _K is obtained for κ = (45/A) MeV and q = −1.     

Anomalous absorption of ultrasound in gadolinium in a magnetic field

The absorption coefficient α _k for longitudinal ultrasonic (15 MHz) waves propagating transverse to the direction of a magnetic field H is measured in single crystal gadolinium. It is found that in fields H⩽600 Oe, the peak in α _k is shifted toward lower temperatures, while the absolute magnitude of the absorption rises with increasing H. It is shown on the basis of dynamic scaling that the anomalous behavior of α _k in fields H⩽600 Oe can be explained by introducing a magnetic field analog of the Landau-Khalatnikov relaxation mechanism. Fiz. Tverd. Tela (St. Petersburg) 39, 339–340 (February 1997)