We demonstrate that the symmetric elliptic polynomials $E_\lambda(x)$ originally discovered in study of generalized Noumi-Shiraishi functions are eigenfunctions Ruijsenaars-Schneider (eRS) Hamiltonians act on mother function variable $y_i$ (substitute Young-diagram $\lambda$). This means they dual eRS system. At same time, their orthogonal complements Schur scalar product, $P_R(x)$ reduction Ko...

this work deals with effects of asymmetric stiffness on the dynamic behaviour of the rotor system. the analysis is presented through an extended lagrangian hamiltonian mechanics on the asymmetric rotor system, where symmetries are broken in terms of the rotor stiffness. the complete dynamics of asymmetries of rotor system is investigated with a case study. in this work, a mathematical model is ...

this paper is concerned with the existence of multiple positive‎ ‎solutions for a quasilinear elliptic system involving concave-convex‎ ‎nonlinearities‎ ‎and sign-changing weight functions‎. ‎with the help of the nehari manifold and palais-smale condition‎, ‎we prove that the system has at least two nontrivial positive‎ ‎solutions‎, ‎when the pair of parameters $(lambda,mu)$ belongs to a certai...

Selection Algorithm and Generation Algorithm of elliptic curves have been the focus of research and hotspot of the Elliptic Curve Cryptosystem. This paper discusses a random elliptic curve realization method of Embedded Mobile Equipment, the SEA algorithm and its improved algorithm from Elliptic Curve's selection, Elliptic Curve's structure and Elliptic Curve's generation. Ensuring that the emb...

We study 1+1 field-generalizations of the rational and elliptic Gaudin models. For sl(N) case we introduce equations of motion and L-A pair with spectral parameter on the Riemann sphere and elliptic curve. In sl(2) case we study the equations in detail and find the corresponding Hamiltonian densities. The n-site model describes n interacting Landau– Lifshitz models of magnets. The interaction d...

We consider the infinite horizon risk-sensitive problem for nondegenerate diffusions with a compact action space, and controlled through the drift. We only impose a structural assumption on the running cost function, namely near-monotonicity, and show that there always exists a solution to the risk-sensitive Hamilton–Jacobi–Bellman (HJB) equation, and that any minimizer in the Hamiltonian is op...

The time-dependent motion of water waves with a parametrically-defined free surface is mapped to a fixed time-independent rectangle by an arbitrary transformation. The emphasis is on the general properties of transformations. Special cases are algebraic transformations based on transfinite interpolation, conformal mappings, and transformations generated by nonlinear elliptic PDEs. The aim is to...

It is proved that periodic and homoclinic trajectories which are tangent to the boundary of any scattering (ergodic) billiard produce elliptic islands in the ‘nearby’ Hamiltonian flows i.e. in a family of two-degrees-of-freedom smooth Hamiltonian flows which converge to the singular billiard flow smoothly where the billiard flow is smooth and continuously where it is continuous. Such Hamiltonia...

Scattering theory is a subset of spectral theory that seeks to parametrize the absolutely continuous spectrum of an elliptic operator H on a complete manifold M with uniform structure at infinity. In the simplest case where M is compact, the spectrum of H is discrete, and scattering theory is trivial. On R, scattering theory is already non-trivial, and the techniques used in studying scattering...