Constrained KP models as integrable matrix hierarchies

We formulate the constrained KP hierarchy (denoted by cKP K+1,M) as an affine sl(M + K+ 1) matrix integrable hierarchy generalizing the Drinfeld-Sokolov hierarchy. Using an algebraic approach, including the graded structure of the generalized Drinfeld-Sokolov hierarchy, we are able to find several new universal results valid for the cKP hierarchy. In particular, our method yields a closed expression for the second bracket obtained through Dirac reduction of any untwisted affine Kac-Moody current algebra. An explicit example is given for the case sl(M + K + 1), for which a closed expression for the general recursion operator is also obtained. We show how isospectral flows are characterized and grouped according to the semisimple non-regular element E of sl(M + K+ 1) and the content of the center of the kernel of E. © 1997 American Institute of Physics.

Insulator-to-metal transition driven by clustering of solitons in polyacetylene

It's believed that the simple Su-Schrieffer-Heeger Hamiltonian can not predict the insulator to metal transition of transpolyacetylene (t-PA). The soliton lattice configuration at a doping level y=6% still has a semiconductor gap. Disordered distributions of solitons close the gap, but the electronic states around the Fermi energy are localized. However, within the same framework, it is possible to show that a cluster of solitons can produce dramatic changes in the electronic structure, allowing an insulator-to-metal transition.

Synthesis, characterization and spectroscopy of the europium doped lanthanum trimetaphosphate

Orthorhombic modification of europium doped lanthanum trimetaphosphate has been prepared. The compound was obtained by precipitation of rare earth chloride solution with trimetaphosphoric acid. The characterizations were made using X-ray diffractometry, chemical analysis and infrared spectroscopy. Excitation and emission spectra were recorded at liquid nitrogen and room temperatures. Assignments of the 5D0→7FJ (J=0, 1, 2, 3, 4, 5) transitions were made and an unusual high 5D0→7F4 transition intensity with six split lines has been observed. Structural distortion of the crystal lattice may be caused by the Eu3+ ion inclusion. The simple overlap model was applied for the calculation of the total splitting of the 5D0→7F1 transition, the 5D0→7F0/5D 0→7F2 transition intensity ratio and the Ωλ (λ=2.4) intensity parameters. Theoretical predictions showed to be in good accordance with the experimental data. © 1988 Elsevier Science S.A.

The substitution of cations by magnesium in the structure K3Ho(VO4)2

The cation substitutions in the crystal lattice of binary potassium-holmium vanadate (V) K3Ho(VO4)2 by magnesium have been studied using various types of chemical solid state reactions. It was shown that in the presence of the quasi-ternary system K3VO4-Mg3(VO4)2-HoVO 4 at 700°C there a compound defined as K3Ho(VO4)2 with a narrow homogeneity range where K and Ho are partially substituted by Mg in accordance with various schemes. © 1998 Published by Elsevier Science S.A.

Probing negative-dimensional integration: Two-loop covariant vertex and one-loop light-cone integrals

The negative-dimensional integration method (NDIM) seems to be a very promising technique for evaluating massless and/or massive Feynman diagrams. It is unique in the sense that the method gives solutions in different regions of external momenta simultaneously. Moreover, it is a technique whereby the difficulties associated with performing parametric integrals in the standard approach are transferred to a simpler solving of a system of linear algebraic equations, thanks to the polynomial character of the relevant integrands. We employ this method to evaluate a scalar integral for a massless two-loop three-point vertex with all the external legs off-shell, and consider several special cases for it, yielding results, even for distinct simpler diagrams. We also consider the possibility of NDIM in non-covariant gauges such as the light-cone gauge and do some illustrative calculations, showing that for one-degree violation of covariance (i.e. one external, gauge-breaking, light-like vector n μ) the ensuing results are concordant with the ones obtained via either the usual dimensional regularization technique, or the use of the principal value prescription for the gauge-dependent pole, while for two-degree violation of covariance - i.e. two external, light-like vectors n μ, the gauge-breaking one, and (its dual) n * μ - the ensuing results are concordant with the ones obtained via causal constraints or the use of the so-called generalized Mandelstam-Leibbrandt prescription. © 1999 Elsevier Science B.V.

Some constraints on the modelling using the uranium isotopes 238U and 234U for dating groundwaters from Guarany aquifer, South America

Groundwaters from the Guarany aquifer located at the South American continent and sampled at four wells with described geological sections in São Paulo State, Brazil, were chemically and isotopically analysed with two aims: to evaluate the quality of this important hydrological resource and to investigate the possibility of using the natural uranium isotopes 234U and 238U as a chronological tool, since the 234U/238U activity ratio and dissolved U content data in groundwater systems have generated models for dating purposes.

Gaussian extended cubature formulae for polyharmonic functions

The purpose of this paper is to show certain links between univariate interpolation by algebraic polynomials and the representation of polyharmonic functions. This allows us to construct cubature formulae for multivariate functions having highest order of precision with respect to the class of polyharmonic functions. We obtain a Gauss type cubature formula that uses ℳ values of linear functional (integrals over hyperspheres) and is exact for all 2ℳ-harmonic functions, and consequently, for all algebraic polynomials of n variables of degree 4ℳ - 1.

Influence of barium and strontium addition on the ratio c/a of PZT obtained by the polymeric precursor method

Lead zirconate titanate powder, with Zr/Ti ratio of 50/50 was prepared by Pechini method after adding up to 10,0 mol% of Ba +2 and Sr +2 ions. Tetragonal phase is favored by the increase of barium and strontium concentration in the LiNbO 3 crystal lattice. The ratio c/a for tetragonal phase increases with the content of Ba +2 and Sr +2.

The two-impurity Anderson model: An effective medium approach

The two-impurity Anderson model is solved within a effective medium approach. All impurity parameters are modelled via Slater atomic orbitals. Impurity spectral densities and spin correlation functions are readily computed. Results are presented for the zero temperature, half-filled case. © 2002 Elsevier Science B.V. All rights reserved.

An analytical solution to the optimal power flow

This letter presents an approach for a geometrical solution of an optimal power flow (OPF) problem for a two-bus system (slack and PV busses). The algebraic equations for the calculation of the Lagrange multipliers and for the minimum losses value are obtained. These equations are used to validate the results obtained using an OPF program.

Specific and nonspecific collapse in protein folding funnels

Experiments with fast folding proteins are beginning to address the relationship between collapse and folding. We investigate how different scenarios for folding can arise depending on whether the folding and collapse transitions are concurrent or whether a nonspecific collapse precedes folding. Many earlier studies have focused on the limit in which collapse is fast compared to the folding time; in this work we focus on the opposite limit where, at the folding temperature, collapse and folding occur simultaneously. Real proteins exist in both of these limits. The folding mechanism varies substantially in these two regimes. In the regime of concurrent folding and collapse, nonspecific collapse now occurs at a temperature below the folding temperature (but slightly above the glass transition temperature).

Array of Bose-Einstein condensates under time-periodic Feshbach-resonance management

The investigation of the dynamics of a discrete soliton in an array of Bose-Einstein condensates under the action of a periodically time-modulated atomic scattering length [Feshbach-resonance management (FRM)] was discussed. The slow and rapid modulations, in comparison with the tunneling frequency were considered. An averaged equation, which was a generalized discrete nonlinear Schrödinger equation, including higher-order effective nonlinearities and intersite nonlinear interactions was derived in the case of the rapid modulation. It was demonstrated that the modulations of sufficient strength results in splitting of the soliton by direct simulations.

Stable two-dimensional dispersion-managed soliton

The existence of a dispersion-managed soliton in two-dimensional nonlinear Schrodinger equation with periodically varying dispersion has been explored. The averaged equations for the soliton width and chirp are obtained which successfully describe the long time evolution of the soliton. The slow dynamics of the soliton around the fixed points for the width and chirp are investigated and the corresponding frequencies are calculated. Analytical predictions are confirmed by direct partial differential equation (PDE) and ordinary differential equation (ODE) simulations. Application to a Bose-Einstein condensate in optical lattice is discussed. The existence of a dispersion-managed matter-wave soliton in such system is shown.

Landau and Kolmogoroff type polynomial inequalities II

Let 0 < j < m ≤ n. Kolmogoroff type inequalities of the form ∥f(j)∥2 ≤ A∥f(m)∥ 2 + B∥f∥2 which hold for algebraic polynomials of degree n are established. Here the norm is defined by ∫ f2(x)dμ(x), where dμ(x) is any distribution associated with the Jacobi, Laguerre or Bessel orthogonal polynomials. In particular we characterize completely the positive constants A and B, for which the Landau weighted polynomial inequalities ∥f′∥ 2 ≤ A∥f″∥2 + B∥f∥ 2 hold. © Dynamic Publishers, Inc.

WZW-like action for heterotic string field theory

We complete the construction of the Neveu-Schwarz sector of heterotic string field theory begun in [9] by giving a closed-form expression for the action and gauge transformations. Just as the Wess-Zumino-Witten (WZW) action for open superstring field theory can be constructed from pure-gauge fields in bosonic open string field theory, our heterotic string field theory action is constructed from pure-gauge fields in bosonic closed string field theory. The construction involves a simple alternative form of the WZW action which is consistent with the algebraic structures of closed string field theory. © SISSA/ISAS 2004.