Geometric singular perturbartion theory for non-smooth dynamical systems

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

H-infinity control design for time-delay linear systems: a rational transfer function based approach

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

Generic Bifurcations of Planar Filippov Systems via Geometric Singular Perturbations

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

Extension of PT-symmetric quantum mechanics to the Dirac theory with position-dependent mass

We present a new method to construct the exactly solvable PT-symmetric potentials within the framework of the position-dependent effective mass Dirac equation with the vector potential coupling scheme in 1 + 1 dimensions. In order to illustrate the procedure, we produce three PT-symmetric potentials as examples, which are PT-symmetric harmonic oscillator-like potential, PT-symmetric potential with the form of a linear potential plus an inversely linear potential, and PT-symmetric kink-like potential, respectively. The real relativistic energy levels and corresponding spinor components for the bound states are obtained by using the basic concepts of the supersymmetric quantum mechanics formalism and function analysis method. (C) 2007 Elsevier B.V. All rights reserved.

Colombeau's theory and shock wave solutions for systems of PDEs

In this article we study the existence of shock wave solutions for systems of partial differential equations of hydrodynamics with viscosity in one space dimension in the context of Colombeau's theory of generalized functions. This study uses the equality in the strict sense and the association of generalized functions (that is the weak equality). The shock wave solutions are given in terms of generalized functions that have the classical Heaviside step function as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function that have to satisfy part of the equations in the strict sense and part of the equations in the sense of association.

An existence theorem for an analytic first order PDE in the framework of Colombeau's theory

We study the existence of a holomorphic generalized solution u of the PDE[GRAPHICS]where f is a given holomorphic generalized function and (alpha (1),...alpha (m)) is an element of C-m\{0}.

Composition and invertibility for a class of generalized functions in the Colombeau's theory

In this work we define the composite function for a special class of generalized mappings and we study the invertibility for a certain class of generalized functions with real values.

Relationship between global structural parameters and Enzyme Commission hierarchy: Implications for function prediction

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

Stochastic quantization of real-time thermal field theory

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Linking the hydrodynamic and kinetic description of a dissipative relativistic conformal theory

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

Applications of Subleading-Color Amplitudes in N=4 SYM Theory

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Pure spinor partition function and the massive superstring spectrum

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

THE PARTITION-FUNCTION FOR AN ANYON-LIKE OSCILLATOR

We compute the partition function of an anyon-like harmonic oscillator. The well known results for both the bosonic and fermionic oscillators are then re-obtained as particular cases of our function. The technique we employ is a non-relativistic version of the Green function method used in the computation of one-loop effective actions of quantum field theory.

EXPANSION OF THE DISTURBING FUNCTION FOR HIGH ECCENTRICITY AND LARGE-AMPLITUDE OF LIBRATION

Following some ideas, developed by Woltjer (1928), Message (1989), Yokoyama (1988, 1989) and Duriez (1990) an expansion of the disturbing function is given for high values of the eccentricity and large amplitude of libration. The classical expansion can be obtained as a particular case of the present model. Several asteroids with high eccentricity and large amplitude of libration are tested and the results are much better than those obtained from the classical theory.

Disturbances in beta-cell function in impaired fasting glycemia

In a cross-sectional study, we assessed beta-cell function and insulin sensitivity index (ISI) with hyperglycemic clamps (10 mmol/l) in 24 subjects with impaired fasting glycemia (IFG, fasting plasma glucose [FPG] between 6.1 and 7.0 mmol/l), 15 type 2 diabetic subjects (FPG >7.0 mmol/l), and 280 subjects with normal fasting glycemia (NFG, FPG <6.1 mmol/l). First-phase insulin release (0-10 min) was lower in IFG (geometric mean 541 pmol/l (.) 10 min; 95% confidence interval [CI] 416-702 pmol/l (.) 10 min) and in type 2 diabetes (geometric mean 376 pmol/l (.) 10 min; 95% CI 247-572 pmol/l (.) 10 min) than NFG (geometric mean 814 pmol/l (.) 10 min; 95% CI 759-873 pmol/l (.) 10 min) (P < 0.001). Second-phase insulin secretion (140-180 min) was also lower in IFG (geometric mean 251 pmol/l; 95% CI 198-318 pmol/l; P = 0.026) and type 2 diabetes (geometric mean 157 pmol/l; 95% CI 105-235 pmol/l; P < 0.001) than NFG (geometric mean 295 pmol/l; 95% CI 276-315 pmol/l): IFG and type 2 diabetic subjects had a lower ISI (0.15 +/- 0.02 and 0.16 +/- 0.02 mumol/kg fat-free mass [FFM]/min/ pmol/l, respectively) than NFG (0.24 +/- 0.01 mumol/kg FFM/min/pmol/l, P < 0.05). We found a stepwise decline in first-phase (and second-phase) secretion in NFG subjects with progressive decline in oral glucose tolerance (P < 0.05). IFG subjects with impaired glucose tolerance (IGT) had lower first-phase secretion than NFG subjects with IGT (P < 0.02), with comparable second-phase secretion and ISI. NFG and IFG subjects with a diabetic glucose tolerance (2-h glucose >11.1 mmol/l) had a lower ISI than their respective IGT counterparts (P < 0.05). We conclude that the early stages of glucose intolerance are associated with disturbances in beta-cell function, while insulin resistance is seen more markedly in later stages.