Kinematics of a spacetime with an infinite cosmological constant

A solution of the sourceless Einstein's equation with an infinite value for the cosmological constant L is discussed by using Inonu-Wigner contractions of the de Sitter groups and spaces. When Lambda --> infinity, spacetime becomes a four-dimensional cone, dual to Minkowski space by a spacetime inversion. This inversion relates the four-cone vertex to the infinity of Minkowski space, and the four-cone infinity to the Minkowski light-cone. The non-relativistic limit c --> infinity. is further considered, the kinematical group in this case being a modified Galilei group in which the space and time translations are replaced by the non-relativistic limits of the corresponding proper conformal transformations. This group presents the same abstract Lie algebra as the Galilei group and can be named the conformal Galilei group. The results may be of interest to the early Universe Cosmology.

The complex sine-Gordon equation as a symmetry flow of the AKNS hierarchy

It is shown how the complex sine-Gordon equation arises as a symmetry flow of the AKNS hierarchy. The AKNS hierarchy is extended by the 'negative' symmetry flows forming the Borel loop algebra. The complex sine-Gordon and the vector nonlinear Schrodinger equations appear as lowest-negative and second-positive flows within the extended hierarchy. This is fully analogous to the well known connection between the sine-Gordon and mKdV equations within the extended mKdV hierarchy. A general formalism for a Toda-like symmetry occupying the 'negative' sector of the sl(N) constrained KP hierarchy and giving rise to the negative Borel sl(N) loop algebra is indicated.

Classical integrable super sinh-Gordon equation with defects

The introduction of defects is discussed under the Lagrangian formalism and Backlund transformations for the N = 1 super sinh-Gordon model. Modified conserved momentum and energy are constructed for this case. Some explicit examples of different Backlund soliton solutions are discussed. The Lax formulation within the space split by the defect leads to the integrability of the model and henceforth to the existence of an infinite number of constants of motion.

Modified Korteweg-de Vries hierarchy with hodograph transformation: Camassa-Holm and Harry-Dym hierarchies

In this paper, we present relations between Camassa-Holm (CH), Harry-Dym (HD) and modified Korteweg-de Vries (mKdV) hierarchies, which are given by the hodograph type transformation. (C) 2001 IMACS. Published by Elsevier B.V. B.V. All rights reserved.

q-Analog of the gap equation for cuprates

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Description of Heavy Quark Mass by Lippmann-Schwinger Equation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Adsorption of MX2 (M = Mn, Ni, Cu, Zn, and Cd; X = Cl, Br, and I) and FeCl3 by modified silica surface with imidazolylpropyl group

Silica gel surface modified with imidazolylpropyl group was used to adsorb MX2 (M = Mn, Ni, Cu, Zn, and Cd; X = Cl, Br, and I) and FeCl3 from ethanol and acetone solution. The adsorption capacity and the intensity of the adsorption were determined by using the Langmuir equation. The influences of the solvent, temperature, and degree of functionalization on the adsorption were also studied. The infrared spectra of the functionalized silica were recorded between 1700-1300 cm-1. The bands of the imidazole skeletal vibrations are shifted to higher frequencies upon metal-to-base nitrogen interaction. © 1985.

Two-matrix string model as constrained (2+1)-dimensional integrable system

We show that the 2-matrix string model corresponds to a coupled system of 2 + 1-dimensional KP and modified KP ((m)KP2+1) integrable equations subject to a specific symmetry constraint. The latter together with the Miura-Konopelchenko map for (m)KP2+1 are the continuum incarnation of the matrix string equation. The (m)KP2+1 Miura and Backhand transformations are natural consequences of the underlying lattice structure. The constrained (m)KP2+1 system is equivalent to a 1 + 1-dimensional generalized KP-KdV hierarchy related to graded SL(3,1). We provide an explicit representation of this hierarchy, including the associated W(2,1)-algebra of the second Hamiltonian structure, in terms of free currents.

Structure of cobalt (II) perchlorate adsorbed on silica gel surface chemically modified with benzimidazole molecule

Covalently attached benzimidazole molecules on silica gel surface, ≡SiL (where L = N-propyl-benzimidazole), adsorbs Co(ClO4)2 from non-aqueous solvent by forming a surface complex according to the reaction: m ≡SiL + Co(ClO4)2 → (≡SiL)mCo(ClO4)2. The equilibrium constant and the adsorption capacity, determined by applying the Langmuir equation were b = 3.0 × 103 L mol-1 and Ns= 0.098 × 10-3 mol g-1, respectively. The metal is bonded through the nitrogen atom and the perchlorate ion is not coordinated. The ESR study indicated that the complex has essentially an octahedral geometry with tetragonal distortion, with the electrons of the four nitrogen atoms interacting with the cobalt central metal ion in the equatorial plane. Only one complex species was detected on the surface.

Geometrical wave equation and the cauchy-like theorem for octonions

Riemann surfaces, cohomology and homology groups, Cartan's spinors and triality, octonionic projective geometry, are all well supported by Complex Structures [1], [2], [3], [4]. Furthermore, in Theoretical Physics, mainly in General Relativity, Supersymmetry and Particle Physics, Complex Theory Plays a Key Role [5], [6], [7], [8]. In this context it is expected that generalizations of concepts and main results from the Classical Complex Theory, like conformal and quasiconformal mappings [9], [10] in both quaternionic and octonionic algebra, may be useful for other fields of research, as for graphical computing enviromment [11]. In this Note, following recent works by the autors [12], [13], the Cauchy Theorem will be extended for Octonions in an analogous way that it has recentely been made for quaternions [14]. Finally, will be given an octonionic treatment of the wave equation, which means a wave produced by a hyper-string with initial conditions similar to the one-dimensional case.

A cubic silsesquioxane modified with purpald®: Preparation, characterization and a voltammetric application for determination of sulfite

A novel composite formed by interaction of a octa(3-chloropropyl)octasilsesquioxane modified with Purpald®, and its subsequent reaction with silver and hexacyanoferrate (III) (AgHSP), was synthesized and initially characterized by Fourier transform infrared spectra (FTIR) and cyclic voltammetry. The cyclic voltammogram of the modified graphite paste electrode with AgHSP, showed one redox couple with formal potential Eθ'=0.64V (vs Ag/AgCl, KNO3, 1.0 mol L-1; v = 20 mV s-1), attributed to the Fe2+(CN)6/ Fe3+(CN)6 process. The redox couple presents an electrocatalytic response for determination of sulfite. The modified electrode showed a linear response from 7.0×10-5 to 1.0×10-3 mol L-1 with the corresponding equation Y(μA) = 18.05 + 29.983×103 [sulfite], and a correlation coefficient of r=0.999. The method showed a detection limit of 0.115×10-4 mol L-1 with a relative standard deviation of ± 4% (n = 3) and amperometric sensitivity of 29.983×10-3A mol L-1. The modified electrode showed a excellent stability and good reproducibility during experiments. © 2013 by ESG.

The algebraic structure behind the derivative nonlinear Schrödinger equation

The Kaup-Newell (KN) hierarchy contains the derivative nonlinear Schrödinger equation (DNLSE) amongst others interesting and important nonlinear integrable equations. In this paper, a general higher grading affine algebraic construction of integrable hierarchies is proposed and the KN hierarchy is established in terms of an Ŝℓ2Kac-Moody algebra and principal gradation. In this form, our spectral problem is linear in the spectral parameter. The positive and negative flows are derived, showing that some interesting physical models arise from the same algebraic structure. For instance, the DNLSE is obtained as the second positive, while the Mikhailov model as the first negative flows. The equivalence between the latter and the massive Thirring model is also explicitly demonstrated. The algebraic dressing method is employed to construct soliton solutions in a systematic manner for all members of the hierarchy. Finally, the equivalence of the spectral problem introduced in this paper with the usual one, which is quadratic in the spectral parameter, is achieved by setting a particular automorphism of the affine algebra, which maps the homogeneous into principal gradation. © 2013 IOP Publishing Ltd.

A proposal for a modified Human Development Index

Includes bibliography.

A cubic silsesquioxane modified with purpald (r) : preparation, characterization and a voltammetric application for determination of sulfite

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)