A partial solution for Feynman's problem – a new derivation of the Weyl equation.
A stochastic scheme for constructing solutions of the Schrödinger equations
Approximation par la diffusion et automorphismes hyperboliques du tore
Equivariance, variational principles, and the Feynman integral.
Erratum : «Approximation par la diffusion et automorphismes hyperboliques du tore»
Feynman path integrals on phase space and the metaplectiv representation.
Generic properties of von Kármán equations
Hysteresis memory preserving operators
The recent development of mathematical methods of investigation of problems with hysteresis has shown that the structure of the hysteresis memory plays a substantial role. In this paper we characterize the hysteresis operators which exhibit a memory effect of the Preisach type (memory preserving operators). We investigate their properties (continuity, invertibility) and we establish some relations between special classes of such operators (Preisach, Ishlinskii and Nemytskii operators). For a general...
L'oscillateur relativiste et les fonctions de Mathieu
Moduli spaces of anti-self-dual connections on ALE gravitational instantons.
Non linear evolution equations Cauchy problem and scattering theory
On space-time, reference frames and the structure of relativity groups
Opérateurs elliptiques et mesures sur l'espace des lacets invariants par le groupe des difféomorphismes du cercle
Path integrals in finite sets
Quantum Mechanics of Guiding Center Motion in Strong Magnetic Field (Coherent State Path Integral Approach)
A new approach is proposed for the quantum mechanics of guiding center motion in strong magnetic field. This is achieved by use of the coherent state path integral for the coupled systems of the cyclotron and the guiding center motion. We are specifically concerned with the effective action for the guiding center degree, which can be used to get the Bohr- Sommerfeld quantization scheme. The quantization rule is similar to the one for the vortex motion as a dynamics of point particles.
Stochastic methods and differential geometry
The Feynman path integral as an improper integral over the Sobolev space
The topology of the Yang-Mills theory over torus
Thermo-viscous fluid flow in porous slab bounded between two impermeable parallel plates in relative motion: Four stage algorithm approach
The problem of an approximate solution of thermo-viscous fluid flow in a porous slab bounded between two impermeable parallel plates in relative motion is examined in this paper. The two plates are kept at two different temperatures and the flow is generated by a constant pressure gradient together with the motion of one of the plates relative to the other. The velocity and temperature distributions have been obtained by a four-stage algorithm approach. It is worth mentioning that reverse effects...
Well-posedness of the Euler and Navier-Stokes equations in the Lebesque spaces Lsp(R2).
In this paper we show that the Euler equation for incompressible fluids in R2 is well posed in the (vector-valued) Lebesgue spacesLsp = (1 - ∆)-s/2 Lp(R2) with s > 1 + 2/p, 1 < p < ∞and that the same is true of the Navier-Stokes equation uniformly in the viscosity ν.