Discrete approximations for strict convex continuous time problems and duality

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

ON DISCRETE SYSMMETRIES OF THE MULTI-BOSON KP HIERARCHIES

We show that the multi-boson KP hierarchies possess a class of discrete symmetries linking them to discrete Toda systems. These discrete symmetries are generated by the similarity transformation of the corresponding Lax operator. This establishes a canonical nature of the discrete transformations. The spectral equation, which defines both the lattice system and the corresponding Lax operator, plays a key role in determining pertinent symmetry structure. We also introduce the concept of the square root lattice leading to a family of new pseudo-differential operators with covariance under additional Backlund transformations.

Doxorubicin as an antioxidant: Maintenance of myocardial levels of lycopene under doxorubicin treatment

The mechanism of doxorubicin-induced cardiotoxicity remains controversial. Wistar rats (n=96) were randomly assigned to a control (C), lycopene (L), doxorubicin (D), or doxorubicin+lycopene (DL) group. The L and DL groups received lycopene (5 mg/kg body wt/day by gavage) for 7 weeks. The D and DL groups received doxombicin (4 mg/kg body wt intraperitoneally) at 3, 4, 5, and 6 weeks and were killed at 7 weeks for analyses. Myocardial tissue lycopene levels and total antioxidant performance (TAP) were analyzed by HPLC and fluorometry, respectively. Lycopene metabolism was determined by incubating H-2(10)-lycopene with intestinal mucosa postmitochondrial fraction and lipoxygenase and analyzed with HPLC and APCI mass spectroscopy. Myocardial tissue lycopene levels in DL and L were similar. TAP adjusted for tissue protein were higher in myocardium of D than those of C (P=0.002). Lycopene metabolism study identified a lower oxidative cleavage of lycopene in D as compared to those of C. Our results showed that lycopene was not depleted in myocardium of lycopene-supplemented rats treated with doxorubicin and that higher antioxidant capacity in myocardium and less oxidative cleavage of lycopene in intestinal mucosa of doxorubicin-treated rats suggest an antioxidant role of doxombicin rather than acting as a prooxidant. (c) 2007 Elsevier B.V. All rights reserved.

Fluctuating dimension in a discrete model for quantum gravity based on the spectral principle

The spectral principle of Connes and Chamseddine is used as a starting point to define a discrete model for Euclidean quantum gravity. Instead of summing over ordinary geometries, we consider the sum over generalized geometries where topology, metric, and dimension can fluctuate. The model describes the geometry of spaces with a countable number n of points, and is related to the Gaussian unitary ensemble of Hermitian matrices. We show that this simple model has two phases. The expectation value , the average number of points in the Universe, is finite in one phase and diverges in the other. We compute the critical point as well as the critical exponent of . Moreover, the space-time dimension delta is a dynamical observable in our model, and plays the role of an order parameter. The computation of is discussed and an upper bound is found, < 2.

The relationship between differential equations with piecewise constant argument and the associated discrete equations, via dichotomic maps

Dichotomic maps are considered by means of the stability and asymptotic stability of the null solution of a class of differential equations with argument [t] via associated discrete equations, where [.] designates the greatest integer function.

Discrete coherent states and probability distributions in finite-dimensional spaces

Operator bases are discussed in connection with the construction of phase space representatives of operators in finite-dimensional spaces, and their properties are presented. It is also shown how these operator bases allow for the construction of a finite harmonic oscillator-like coherent state. Creation and annihilation operators for the Fock finite-dimensional space are discussed and their expressions in terms of the operator bases are explicitly written. The relevant finite-dimensional probability distributions are obtained and their limiting behavior for an infinite-dimensional space are calculated which agree with the well known results. (C) 1996 Academic Press, Inc.

Dynamics in discrete phase spaces and time interval operators

The von Neumann-Liouville time evolution equation is represented in a discrete quantum phase space. The mapped Liouville operator and the corresponding Wigner function are explicitly written for the problem of a magnetic moment interacting with a magnetic field and the precessing solution is found. The propagator is also discussed and a time interval operator, associated to a unitary operator which shifts the energy levels in the Zeeman spectrum, is introduced. This operator is associated to the particular dynamical process and is not the continuous parameter describing the time evolution. The pair of unitary operators which shifts the time and energy is shown to obey the Weyl-Schwinger algebra. (C) 1999 Elsevier B.V. B.V. All rights reserved.