The dual (p,q)-Alexander-Conway Hopf algebras and the associated universal ℐ-matrix

The dually conjugate Hopf algebrasFun _p,q (R) andU _p,q (R) associated with the two-parametric (p,q)-Alexander-Conway solution (R) of the Yang-Baxter equation are studied. Using the Hopf duality construction, the full Hopf structure of the quasitriangular enveloping algebraU _p,q (R) is extracted. The universal ?-matrix forsFun _p,q (R) is derived. While expressing an arbitrary group element of the quantum group characterized by the noncommuting parameters in a representation independent way, the ?-matrix generalizes the familiar exponential relation between a Lie group and its Lie algebra. The universal ?-matrix and the FRT matrix generators,L ^(±), forU _p,q (R) are derived from the ?-matrix.     

Quantum deformation of compactified Minkowski space

The quantum GrassmanianG(2|0; ? _q ^4|0 ) of “quantum 2-planes ? _q ^2|0 in the quantum 4-plane ? _q ^4|0 ”, which provides aq-deformation of compactified complexified Minkowski space, is proposed. A quantum analogue of classical Plücker embedding of the usual GrassmanianG(2; ?²) into a non-degenerate quadric in ??⁵ is found.     

The far-infrared spectrum of tetrahydrothiophene: The bend/twist vibrations and associated barriers

The far-infrared spectrum of tetrahydrothiophene is reinvestigated with a resolution of 0.12 cm^?1 in the region of 50–350 cm^?1. In addition to the bend transitions (ν_b) below 120 cm^?1 reported previously, a number of sequences revealed by the improved resolution are observed for the first time and assigned to transitions of 2ν_b, of the twist (ν_t), and of difference combinations (ν_t - ν_b). Simple one-dimensional modeling of the twist sequence, which is derived from a self-consistent bend-twist energy level diagram, with a quadratic-quartic Hamiltonian suggests a barrier to planarity on the order of 4250 cm^?1. A two-dimensional potential function in the dimensionless coordinates is found to be V(q_b, q_t) = ?249.6q_b² + 4.48q_b⁴ ? 215.5q_t² + 2.73q_t⁴ + 7.00q_b²q_t².     

u q(2,1) noncompact quantum algebra: Intermediate discrete series of unitary irreducible representations

The unitary irreducible representations of the u _q(2,1) quantum algebra that belong to the intermediate discrete series are considered. The q analog of the Mickelsson-Zhelobenko algebra is developed. Use is made of the U basis corresponding to the reduction u _q(2,1) ? u _q(2). Explicit formulas for the matrix elements of the generators are obtained in this basis. The projection operator that projects an arbitrary vector onto the extremal vector of the intermediate-series representation is found.     

Fluctuations and defects in the spiral state of magnetic superconductors

We want to point out three properties of a magnetic superconductor: (i) The absence of true long-range order in the spiral state leads to the structure functions behaving like (q₆ ? q₀)^η?2 and (q²_⊥)^η?2 for q_⊥=0 and q₆=0, respectively, where q₀ is the preferred momentum. The indices η are measured via Bragg-like neutron scattering. (ii) The state is perforated by line-like defects. (iii) Above some critical temperature the defect lines proliferate, thereby destroying the spiral quasi-order.     

Some identities on the q-Euler polynomials of higher order and q-stirling numbers by the fermionic p-adic integral on ℤ p

A systemic study of some families of q-Euler numbers and families of polynomials of Nörlund type is presented by using the multivariate fermionic p-adic integral on ? _p . The study of these higher-order q-Euler numbers and polynomials yields an interesting q-analog of identities for Stirling numbers.     

Sensitivity of polarization observables in elastic ed scattering to the neutron form factors

The deuteron elastic form factors are calculated within the Bethe-Salpeter approach with separable interaction. The charge, quadrupole, and magnetic form factors [F _C(q ²), F _Q(q ²), and F _M(q ²), respectively]; the structure functions A(q ²) and B(q ²); and the tensor polarization components T ₂₀(q ², T ₂₁(q ²), and T ₂₂(q ²) are investigated up to ?q ²=50 fm^?2. The role of relativistic effects is discussed, and a comparison with nonrelativistic calculations is performed. The effect of the neutron form factors on the deuteron form factors and especially on tensor polarization components is discussed too.     

Secondary ion emission under the bombardment of Si by multiply charged Si q+ ions

The spectra of secondary ion emission under the bombardment of a B-doped Si target by multiply charged Si ^q+ ions (q = 1?C5) have been studied in the energy range of 1 to 10 keV per unit of charge. A multifold increase in the yield of secondary cluster Sk _n ⁺ ions, multiply charged Si ^q/+ ion (q = 1?C3), and H⁺, C⁺, B⁺, Si₂N⁺, Si₂O⁺ is observed as the charge of the multiply charged ions increases. The increase in the yield of secondary ions with increasing charge of the multiply charged-ion charge is most significant for ions with relatively high ionization potentials.     

Analytical properties of the forward elastic scattering amplitudes following from microcausality

The forward elastic scattering amplitudes T_i(v,q²), (i = 1,2), of the virtual photon with the mass q² are considered in variables σ and ? where σ and ? are related to q² and v by the formulae q² = exp (2σ) and v = exp (σ) ch?. It has been proved that microcausality requirement implies the analyticity of amplitudes in the tube region [Im σ + π/2] + |Im?| < π/2 as a function of both complex variables σ and ?. Formulae are obtained expressing amplitudes T_l(v,q²) at arbitrary v and q² through functions W_l^(?)(v, q²) describing the electroproduction process ?2v < q² < 0.     

A multi-channel scattering theory for some time dependent Hamiltonians,charge transfer problem

Scattering theory for time dependent HamiltonianH(t)=?(1/2) Δ+ΣV _j (x?q _j (t)) is discussed. The existence, asymptotic orthogonality and the asymptotic completeness of the multi-channel wave operators are obtained under the conditions that the potentials are short range: |V _j (x)|≦C _j (1+|x|)^?2?ε, roughly spoken; and the trajectoriesq _j (t) are straight lines at remote past and far future, and |q _j (t)?q _k (t)| → ∞ ast → ± ∞ (j≠k).     

The pair distributions and the osmotic coefficient in anomalous electrolytes up to concentrations c≈ 1 mol/1

The osmotic coefficient of anomalous electrolytes up to concentrations c ≈ 1 mol/l is explained by the pair distributions $\text{n(r) =}\text{exp}\text{[-β(}\text{V}{}_{\mathrm{c}}\text{(r) + V(}{}^{\mathrm{hs}}\text{)(r) + V}{}_1\text{(r))]}$. Here $\text{V}$_c(r) is a screened Coulomb potential, V(^hs)(r) a hard sphere potential and V₁(r) = ?A/r⁶ a short range attractive potential. For the contact distances R₊₊, R_?? and R_+? of the hard sphere potentials between ions with the same sign of their charges (++,??) and ions of opposite charges (+?) the relations R₊₊ = R_?? = R and R_+? = q₁R with 0 < q₁ < 1 are assumed. In contrast to a previous paper the parameter q₁ takes a fixed value q₁ ≈ 0,8. The constant A is determined by the fraction q₂ defined by A/R⁶ = q₂(Z²e²/DR) where the positive integer Z is the charge number of the ions and D the dielectric constant of the solvent. The numerical calculation of the osmotic coefficient of 1-1-valent hydrous electrolytes in the range of temperature 273 K ? T ? 293 K shows that the anomalous electrolytes are described by fractions q₂ in the range 0,25 ? q₂ ? 0,5 if the contact distances R are in the range $\text{3}\text{A}\text{?}\text{? R ? 7}\text{A}\text{?}$.     

Spin correlations in YBa2(Cu1−x Fx)3O7+y ceramic

To detect scattering by magnetic correlations and to estimate their characteristic space scale, YBa₂(Cu_1?x Fe_x)₃O_7+y ceramic with x=0.13 and y=0.4 is investigated by the small-angle scattering of polarized neutrons. The measurements are carried out in the range of temperatures 15 K?T?315 K and magnetic fields 0<H?4500 Oe. Anomalies in the temperature curves of the intensity I(T,q) (where q is the momentum transfer) and the polarization P(T,q) are observed in the temperature range T<40 K. Interference between nuclear and magnetic scattering is also observed in this temperature range. The observed phenomena are interpreted as scattering by magnetic correlations having a scale 70 Å<R<370 Å. Irreversible effects and the type of magnetic ordering are discussed.     

Creation of fermion pairs near the cosmological singularity

The energy density ? and the pressure P of fermion pairs near the homogeneous isotropic singularity are obtained. In general case the contributions of the real pairs and the virtual ones to the ? and the P are approximately equal. The contribution of the real pairs is leading when the law of the expansion is a(t) = a₁t^q, q ? 1 ? 1. In this case all the matter in the Friedman's cosmological model can be created by a quantum explosion.     

The elastic constants of solid CD4—I from neutron measurements

The dispersion law ω (q)-for molecular motions in phase I of solid CD₄ (89.7°K ? T ? 27.0°K) is investigated by coherent inelastic neutron scattering from single crystals. No optical branches are found. By extrapolation of observed acoustic branches to q → 0 the elastic constants are determined.     

An analytic calculation of the weak field limit of the static color dielectric constant

We analyze the Dyson equation/Ward identity system for the axial gauge n · A = 0 gluon propagator Δ_μν(q)whenn · q = 0. The solution behaves like (q^?4 + (q²)^ν?1) for small q₂, and we are able to calculate the power ν analytically. It turns out to be 0.1737. This analytic calculation verifies our earlier numerical solutions to these equations. For static problems, n · q = 0 is the temporal gauge, and in this gauge the gluon propagator is directly related to the color dielectric constant. We can thus calculate the dielectric constant in the infrared limit.     

Two-dimensional neutral Coulomb gas

Accurate bounds for the classical canonical partition function of the two-dimensional Coulomb gas interacting through the Coulomb potential ?q _i q _j logr _ij are calculated (valid for allT>T _c ). The existence of the thermodynamic limit is proved.     

Electroproduction of π+ mesons in the resonance region

Results on the reaction ep→e′nπ⁺ are presented in the mass range 1.355 ?W ?1.775 GeV at q₂=1GeV² and in the range 1.415 ? W ? 1.595 GeV at q²=0.6 GeV². From the angular distribution of the π⁺ meson the polarization terms σ_u + ?σ_L, σ_p and σ_I have been determined in the range of production angles 0 <θ_π⁺ ?63°     

SU(3) ⊗ SU(2) ⊗ U(1) from D = 11 supergravity

In this paper we show that D = 11 supergravity admits an infinite discrete class of solutions having the phenomenological group SU(3) ? SU(2) ? U(1) as a symmetry of the internal space M₇. These solutions lead, in dimensional reduction, to SU(3) ? SU(2) ? U(1) gauge fields.In general all these spaces produce a complete breaking of supersymmetry except in one case where N = 2 supersymmetry survives. The parameter which classifies the solutions is a rational number q/p which describes the embedding of the stability subgroup SU(2) ? U(1) ? U(1) of M₇ in SU(3) ? SU(2) ? U(1). For all q/p ≠ 1 the holonomy group is SO(7) and all supersymmetries are broken. For q/p = 1 the holonomy group is SU(3) and two supersymmetries survive. In this last case we can also find a solution with internal photon curl $\text{F}{}_{\mathrm{\alpha \beta \gamma \delta }}\text{≠ 0}$. It breaks all sypersymmetries.     

Intermittency in branching processes

We study the intermittency properties of two branching processes, one with a uniform and another with a singular splitting kernel. The asymptotic intermittency indices, as well as the leading corrections to the asymptotic linear regime are explicitly computed in an analytic framework. Both models are found to possess a monofractal spectrum with ? _q =q ? 1 and inverse logarithmic corrections. Relations with previous results are discussed.     

A simple theory of spin-wave relaxation in ferromagnetic metals

The anisotropic exchange interaction between localized spins and conduction electrons is described by an appropriate spin hamiltonian. This is used to calculate the lifetime of magnons for arbitrary values of Λ_eq, where Λ_e is the electron mean free path and q the magnon wavevector. At Λ_eq ? 1, this lifetime depends on the angle between q and the saturation magnetization. The antisymmetric part of anisotropic exchange (Dzialoshinsky-Moriya interaction) may dominate the relaxation of spin-waves of large q. The complicated band structure of transition metals gives rise to a magnon lifetime independent of Λ_e. The contribution of isotropic exchange is also considered.