We completely determine necessary and suucient conditions for the nor-malizability of the wave functions giving the algebraic part of the spectrum of a quasi-exactly solvable Schrr odinger operator on the line. Methods from classical invariant theory are employed to provide a complete list of canonical forms for normalizable quasi-exactly solvable Hamiltonians and explicit normalizability condi...

Recently proposed quasi-classical ∂̄-dressing method provides a systematic approach to study the weakly dispersive limit of integrable systems. We apply the quasi-classical ∂̄-dressing method to describe dispersive corrections of any order. We show how calculate the ∂̄ problems at any order for a rather general class of integrable systems, presenting explicit results for the KP hierarchy case. We ...

Multiple valued logic (abbreviated MVL and also known as ‘many-valued’ or ‘multi-valued’ logic) has a long tradition [17, 15, 7] and needs no presentation. In this paper we lift the concept of quasi-variety of first-order models from classical (two valued) logic to MVL and study some of its important properties. Our results can be seen as MVL extensions or generalizations of corresponding class...

We study the relationship between general dynamical Poisson groupoids and Lie quasi-bialgebras. For a class of Lie quasi-bialgebras G naturally compatible with a reductive decomposition , we extend the description of the moduli space of classical dynamical r-matrices of Etingof and Schiffmann. We construct, in each gauge orbit, an explicit analytic representative l can. We translate the notion ...

This paper compares quasi Monte Carlo methods, in particular so– called (t,m, s)–nets, with classical Monte Carlo approaches for simulating econometric time–series models. Quasi Monte Carlo methods have found successful application in many fields, such as physics, image processing, and the evaluation of finance derivatives. However, they are rarely used in econometrics. Here, we apply both trad...

We introduce the notion of t-quasi-spanners as an alternative to classical t-spanners. Our motivation for quasi-spanners comes from the problem of computing a sparse backbone for ad hoc wireless networks with fixed transmission ranges. We study the computational complexity of the problem of computing the sparsest quasi-spanner. Then we concentrate on the case t = 2 and give a distributed algori...

In this paper we derive a formula for the expectation of random Hermite polynomials in Skorohod integrals, extending classical results in the adapted case. As an application we recover, under simple conditions and with short proofs, the anticipative Girsanov identity and quasi-invariance results obtained in [6] for quasi-nilpotent shifts on the Wiener space.

We consider the Schrödinger operator H(V ) on L(R) or L(R), with constant magnetic field and electric potential V which typically decays at infinity exponentially fast or has a compact support. We investigate the asymptotic behaviour of the discrete spectrum of H(V ) near the boundary points of its essential spectrum. If the decay of V is Gaussian or faster, this behaviour is non-classical in t...

We study the connection between the BCS pairing model and the inhomogeneous vertex model. The two spectral problems coincide in the quasi– classical limit of the off–shell Bethe Ansatz of the disordered six vertex model. The latter problem is transformed into an auxiliary spectral problem which corresponds to the diagonalization of the integrals of motion of the BCS model. A generating function...