Recent interest in discrete, classical integrable systems has focused on their connection to quantum integrable systems via the Bethe equations. In this note, solutions to the rational nested Bethe ansatz (RNBA) equations are constructed using the “completed Calogero-Moser phase space” of matrices which satisfy a finite dimensional analogue of the canonical commutation relationship. A key featu...

In this paper we develop a canonical state space representation for rational stochastic processes containing unit roots with integer integration orders at arbitrary points on the unit circle. It is shown that the state space framework, which is – in a certain sense made precise in the paper – equivalent to the ARMA framework, is very suitable for the analysis of unit roots and cointegration iss...

| In this paper, we consider combined M/G/1-G/M/1 type Markov chains with block-structured transition. It is assumed that all the blocks are generated with rational generating matrices. We provide an algorithmic approach to nd the stationary probability distribution based on well-known concepts in linear system theory. These chains arise in the (correlated) G/G/1 queueing systems and known stru...

Given a minimal surface S equipped with a generically finite map to an Abelian variety and C ⊂ S a rational or an elliptic curve, we show that the canonical degree of C is bounded by four times the self-intersection of the canonical divisor of S. As a corollary, we obtain the finiteness of rational and elliptic curves with an optimal uniform bound on their canonical degrees on any surface of ge...

Let X be a K3 surface with an involution σ which has non-empty fixed locus X σ and acts non-trivially on a non-zero holomorphic 2-form. We shall construct all such pairs (X, σ) in a canonical way, from some better known double coverings of log del Pezzo surfaces of index ≤ 2 or rational elliptic surfaces, and construct the only family of each of the three extremal case where X σ contains 10 (ma...

Defeasible Description Logics (DDLs) can state defeasible concept inclusions and often use rational closure according to the KLM postulates for reasoning. If in DDLs with quantification a defeasible subsumption relationship holds between concepts, it can also hold if these concepts appear nested in existential restrictions. Earlier reasoning algorithms did not detect this kind of relationships....

Let K be a function field in one variable over an arbitrary field F. Given a rational function φ ∈ K(z) of degree at least two, the associated canonical height on the projective line was defined by Call and Silverman. The preperiodic points of φ all have canonical height zero; conversely, if F is a finite field, then every point of canonical height zero is preperiodic. However, if F is an infin...