Birkhoff normal forms for Fourier integral operators II

Iantchenko, A.; Sj?strand, J., (2001) 'Birkhoff normal forms for Fourier integral operators II', American Journal of Mathematics 124(4) pp.817-850 RAE2008

Development of a structured program for conversion to prenex normal form

The method of structured programming or program development using a top-down, stepwise refinement technique provides a systematic approach for the development of programs of considerable complexity. The aim of this paper is to present the philosophy of structured programming through a case study of a nonnumeric programming task. The problem of converting a well-formed formula in first-order logic into prenex normal form is considered. The program has been coded in the programming language PASCAL and implemented on a DEC-10 system. The program has about 500 lines of code and comprises 11 procedures.

The Supercore for Normal Form Games

We study the supercore of a system derived from a normal form game. For the case of a finite game with pure strategies, we define a sequence of games and show that the supercore of that system coincides with the set of Nash equilibrium strategy profiles of the last game in the sequence. This result is illustrated with the characterization of the supercore for the n-person prisoners’ dilemma. With regard to the mixed extension of a normal form game, we show that the set of Nash equilibrium profiles coincides with the supercore for games with a finite number of Nash equilibria. For games with an infinite number of Nash equilibria this need not be no longer the case. Yet, it is not difficult to find a binary relation which guarantees the coincidence of these two sets.

Birkhoff normal forms in semi-classical inverse problems

Iantchenko, A.; Sj?strand, J.; Zworski, M., (2002) 'Birkhoff normal forms in semi-classical inverse problems', Mathematical Research Letters 9(3) pp.337-362 RAE2008

Diagonalization and Jordan Normal Form – motivation through Maple

Following an introduction to the diagonalization of matrices, one of the more difficult topics for students to grasp in linear algebra is the concept of Jordan normal form. In this note, we show how the important notions of diagonalization and Jordan normal form can be introduced and developed through the use of the computer algebra package Maple®.

Scattering poles near the real axis for two strictly convex obstacles

Iantchenko, A., (2007) 'Scattering poles near the real axis for two strictly convex obstacles', Annales of the Institute Henri Poincar? 8 pp.513-568 RAE2008

Teoria de singularidades e classificação de problemas de bifurcação Z2-equivariantes de Corank 2

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Propriedades genéricas de sistemas hamiltonianos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Classical and quantal aspects of resonant normal forms

The Birkhoff-Gustavson normal form is employed to study separately chaos and resonances in a system with two degrees of freedom. In the integrable regime, tunnelling effects are appreciable when the nearest level spacings show oscillations. Tunnelling among states in the libration and rotation tori regions is also observed. The regularity of avoided crossings due to tunnelling indicates a collective effect and is associated with an isolated resonance. The spectral fluctuations also show a strong level correlation. The Husimi distribution, on the other hand, is insensitive to avoided crossings. An integrable approximation to the overlap of resonances is obtained and a theoretical description is given for an isolated cubic resonance plus a complex orbit. In the non-integrable regime chaos is stronger after overlapping and preferentially at low energies.

Splittings of free groups, normal forms and partitions of ends

Splittings of a free group correspond to embedded spheres in the 3-manifold M = # (k) S (2) x S (1). These can be represented in a normal form due to Hatcher. In this paper, we determine the normal form in terms of crossings of partitions of ends corresponding to normal spheres, using a graph of trees representation for normal forms. In particular, we give a constructive proof of a criterion determining when a conjugacy class in pi (2)(M) can be represented by an embedded sphere.

L'Escola Normal de Mestres en els seus origens i el reformisme liberal. 'La Escuela Normal de Maestros en sus orígenes y el reformismo liberal'.

Presenta un apéndice documental que recoge documentación oficial de la época analizada

Normal Forms for Codimension One Planar Piecewise Smooth Vector Fields

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

Mice deficient for prion protein exhibit normal neuronal excitability and synaptic transmission in the hippocampus.

We recorded in the CA1 region from hippocampal slices of prion protein (PrP) gene knockout mice to investigate whether the loss of the normal form of prion protein (PrPC) affects neuronal excitability as well as synaptic transmission in the central nervous system. No deficit in synaptic inhibition was found using field potential recordings because (i) responses induced by stimulation in stratum radiatum consisted of a single population spike in PrP gene knockout mice similar to that recorded from control mice and (ii) the plot of field excitatory postsynaptic potential slope versus the population spike amplitude showed no difference between the two groups of mice. Intracellular recordings also failed to detect any difference in cell excitability and the reversal potential for inhibitory postsynaptic potentials. Analysis of the kinetics of inhibitory postsynaptic current revealed no modification. Finally, we examined whether synaptic plasticity was altered and found no difference in long-term potentiation between control and PrP gene knockout mice. On the basis of our findings, we propose that the loss of the normal form of prion protein does not alter the physiology of the CA1 region of the hippocampus.