We discuss the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips S-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exact...

We introduce partial (co)actions of a Hopf algebra H on an algebra. To this end, we introduce first the notion of lax coring, generalizing Wisbauer's notion of weak coring. We also have the dual notion of lax ring. Several duality results are given, and we develop Galois theory for partial H-comodule algebras.

Based on the Gerstenhaber Theory it is clarified how operadic dynamics may be introduced. Operadic observables satisfy the Gerstenhaber algebra identities and their time evolution is governed by the Gerstenhaber-Lax or Gerstenhaber-Heisenberg equation. In this way one can describe classical and quantum time evolution of operations. The notion of an operadic Lax pair is introduced as well.

In this paper, we construct a new Lax operator for the elliptic An−1 Calogero-Moser model with general n(2 ≤ n) from the classical dynamical twisting, in which the corresponding r-matrix is purely numeric (nondynamical one). The nondynamical r-matrix structure of this Lax operator is obtained, which is elliptic Zn-symmetric r-matrix. Mathematics Subject Classification : 70F10 , 70H33 , 81U10.

In this paper a new discrete isospectral problem is constructed, from which a new Lax integrable discrete equation is generated and obtain its hierarchy structure. The Hamiltonian structures for the hierarchy of the Lax integrable discrete equation is established by using the trace identity which was proposed by Tu.

We study the C2 Ruijsenaars-Schneider(RS) model with interaction potential of trigonometric type. The Lax pairs for the model with and without spectral parameter are constructed. Also given are the involutive Hamiltonians for the system. Taking nonrelativistic limit, we obtain the Lax pair of C2 Calogero-Moser model.

In this paper we study a metric Hopf-Lax formula looking in particular at the Carnot-Carathéodory case. We generalize many properties of the classical euclidean Hopf-Lax formula and we use it in order to get existence results for Hamilton-Jacobi-Cauchy problems satisfying a suitable Hörmander condition.

We present a (partial) historical summary of the mathematical analysis finite difference and volume methods, paying special attention to Lax–Richtmyer Lax–Wendroff theorems. then state consistency result for convection operators on staggered grids (often used in fluid flow simulations), which illustrates recent generalization flux notion designed cope with general discrete functions.

BACKGROUND The purpose of the study was to compare the accuracy and evaluation time of quantifying left ventricular (LV), left atrial (LA) volume and LV mass using short axis (SAX) and long axis (LAX) methods when using cardiovascular magnetic resonance (CMR). MATERIALS AND METHODS We studied 12 explanted canine hearts and 46 patients referred for CMR (29 male, age 47 ± 18 years) in a clinica...