Factorisation des polynômes de Poncelet

La condition pour qu’il existe des n-gones de Poncelet, inscrits dans un cercle, et circonscrits à un autre cercle, est polynomiale en les paramètres définissant ces deux cercles. Nous décomposons ces polynômes “de Poncelet” en facteurs irréductibles que nous interprétons géométriquement.     

Nash Equilibria in Noncooperative Predator-Prey Games

A noncooperative game governed by a distributed-parameter predator-prey system is considered, assuming that two players control initial conditions for predator and prey, respectively. Existence of a Nash equilibrium is shown under the condition that the desired population profiles and the environmental carrying capacity for the prey are sufficiently small. A conceptual approximation algorithm is proposed and analyzed. Finally, numerical simulations are performed, too.     

Visions: The coming revolutions in particle physics

We study the branching ratio, CP-violating asymmetry, forward-backward asymmetry and the CP-violating asymmetry in the forward-backward asymmetry for the exclusive decay B → Kτ⁺τ⁻ in the two Higgs doublet model with tree level flavor changing neutral currents (model III). We analyse the dependencies of these quantities on the neutral Higgs boson contributions and the CP parameter sinθ in the model III. We observe that to determine the neutral Higgs boson effects, the measurements of the forward-backward asymmetry and the CP-violating asymmetry in the forward-backward asymmetry for the decay B → Kτ⁺τ⁻ are promising.     

New classes of 2-weight cyclic codes

We introduce new classes of 2-weight cyclic codes which are direct sums of 1-weight irreducible cyclic codes      

Supersymmetry search via gauge boson fusion

We propose a novel method for the search of supersymmetry, especially for the electroweak gauginos at the large hadron collider (LHC). Gauge boson fusion technique was shown to be useful for heavy and intermediate mass Higgs bosons. In this article, we have shown that this method can also be applied to find the signals of EW gauginos in supersymmetric theories where the canonical search strategies for these particles fail.     

On acoustic and electric waves diffraction in piezoelectric medium by a permeable half-plane crack

The problem of electric and acoustic waves diffraction by a half-plane crack in a transversal isotropic piezoelectric medium is investigated. The crack is assumed to be electric permeable and free of tractions. The so-called “quasi-hyperbolic approximation” [15] is adopted. Applying Laplace transformations and Wiener–Hopf technique a closed form solution is obtained. By the means of Cagniard–de Hoop method a detailed dynamic full electroacoustic wavefield’s investigation is conducted. Mode conversion between electric and acoustic waves, effect of electroacoustic head wave, Bleustein–Gulyaev surface wave and the wavefield structure depending on the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in details. The dynamic field intensity factors at the crack tip depending on the angle of incidence and on time are derived explicitly. Numerical analysis is presented.     

Essentially optimal explicit Runge–Kutta methods with application to hyperbolic–parabolic equations

Optimal explicit Runge–Kutta methods consider more stages in order to include a particular spectrum in their stability domain and thus reduce time-step restrictions. This idea, so far used mostly for real-line spectra, is generalized to more general spectra in the form of a thin region. In thin regions the eigenvalues may extend away from the real axis into the imaginary plane. We give a direct characterization of optimal stability polynomials containing a maximal thin region and calculate these polynomials for various cases. Semi-discretizations of hyperbolic–parabolic equations are a relevant application which exhibit a thin region spectrum. As a model, linear, scalar advection–diffusion is investigated. The second-order-stabilized explicit Runge–Kutta methods derived from the stability polynomials are applied to advection–diffusion and compressible, viscous fluid dynamics in numerical experiments. Due to the stabilization the time step can be controlled solely from the hyperbolic CFL condition even in the presence of viscous fluxes.     

An algorithm for decomposing a polynomial system into normal ascending sets

We present an algorithm to decompose a polynomial system into a finite set of normal ascending sets such that the set of the zeros of the polynomial system is the union of the sets of the regular zeros of the normal ascending sets.If the polynomial system is zero dimensional,the set of the zeros of the polynomials is the union of the sets of the zeros of the normal ascending sets.