Related papers: On characterization of integrable sesquilinear for…
The possibility of defining sesquilinear forms starting from one or two sequences of elements of a Hilbert space is investigated. One can associate operators to these forms and in particular look for conditions to apply representation…
We prove an abstract Birkhoff normal form theorem for Hamiltonian partial differential equations on torus. The normal form is complete up to arbitrary finite order. The proof is based on a valid non-resonant condition and a suitable norm of…
Let S be a compact, connected surface and H in C^2(T^* S) a Tonelli Hamiltonian. This note extends V. V. Kozlov's result on the Euler characteristic of S when H is real-analytically integrable, using a definition of topologically-tame…
We present a necessary and sufficient condition for a root greater than unity of a monic reciprocal polynomial of an even degree at least four, with integer coefficients, to be a Salem number. We determine the probability of fulfillment the…
Great progress has been made recently in establishing conditions for separability of a particular class of Werner densities on the tensor product space of $n$ $d$--level systems (qudits). In this brief note we complete the process of…
We construct an integral form for the universal enveloping algebra of the Onsager algebra and an explicit integral basis for this integral form. We also formulate straightening identities among some products of basis elements.
We consider bosonized $QCD_2$, and prove that after rewritting the theory in terms of gauge invariant fields, there exists an integrability condition valid for the quantum theory as well. Furthermore, performing a duality type…
This paper provides an overview of the necessary and sufficient conditions for guaranteeing the unique solvability of absolute value equations. In addition to discussing the basic form of these equations, we also address several…
Von Neumann established that discretized algebraic equations must be consistent with the differential equations, and must be stable in order to obtain convergent numerical solutions for the given differential equations. The "stability" is…
We determine a precise necessary and sufficient condition for completeness of the Hamiltonian vector field associated to a homogeneous cubic polynomial on a symplectic plane.
We study a family of Li\'enard--type equations. Such equations are used for the description of various processes in physics, mechanics and biology and also appear as traveling--wave reductions of some nonlinear partial differential…
We study the structure of the generator of a symmetric, conservative quantum dynamical semigroup with norm-bounded generator on a von Neumann algebra equipped with a faithful semifinite trace. For von Neumann algebras with abelian commutant…
Suppose $M$ is a tracial von Neumann algebra embeddable into $\mathcal R^{\omega}$ (the ultraproduct of the hyperfinite $II_1$-factor) and $X$ is an $n$-tuple of selfadjoint generators for $M$. Denote by $\Gamma(X;m,k,\gamma)$ the…
We present stability conditions for the category of coherent systems on an integral curve. We define a three-parameter family of pre-stability conditions in its derived category using tilting, and we then investigate when these conditions…
We discuss the main features of quantum integrable models taking the classes of universality of the Ising model and the repulsive Lieb-Liniger model as paradigmatic examples. We address the breaking of integrability by means of two…
We consider a semilinear Neumann problem with exponential nonlinearity in a smooth bounded domain $\Omega \subset \mathbb{R}^2$. We prove that there exists a threshold $\bar{\varepsilon}>0$ such that for all $\varepsilon>\bar{\varepsilon}$,…
We show that the class of representable substitution algebras is characterized by a set of universal first order sentences. In addition, it is shown that a necessary and sufficient condition for a substitution algebra to be representable is…
Let $\Lambda$ be a 1-Auslander-Gorenstein Algebra. We give a necessary and sufficient condition for $\Lambda$ to be a tilted algebra.
We suggest the notion of perfect integrability for quantum spin chains and conjecture that quantum spin chains are perfectly integrable. We show the perfect integrability for Gaudin models associated to simple Lie algebras of all finite…
Generalized coherent states for shape invariant potentials are constructed using an algebraic approach based on supersymmetric quantum mechanics. We show this generalized formalism is able to: a) supply the essential requirements necessary…