We construct a symplectic realization of the KM-system and obtain the higher order Poisson tensors and commuting flows via the use of a recursion operator. This is achieved by doubling the number of variables through Volterra’s coordinate transformation. An application of Oevel’s theorem yields master symmetries, invariants and deformation relations. MSC 37J35, 70H06 keywords: Volterra system, ...

A general interpolation problem for operator–valued Stieltjes functions is studied using V. P. Potapov’s method of fundamental matrix inequalities and the method of operator identities. The solvability criterion is established and under certain restrictions the set of all solutions is parametrized in terms of a linear fractional transformation. As applications of a general theory, a number of c...

In model management, the Merge operator takes as input a pair of schemas, together with a set of mappings between their objects, and returns an integrated schema. In this paper we present a new approach to implementing the Merge operator based on semantic mappings between objects. Our approach improves upon previous work by (1) using formal low-level transformation rules that can be translated ...

Many inductive logic programming systems have operators reorganizing the program so far inferred, such as the intra-construction operator of CIGOL. At the same time, there is a similar reorganizing operator, called the “folding rule,” developed in program transformation. We argue that there are advantages in using an extended folding rule as a reorganizing operator for inductive-inference syste...

Operator cutoff regularization based on the original Schwinger's proper-time formalism is examined. By constructing a regulating smearing function for the proper-time integration, we show how this regularization scheme simulates the usual momentum cutoff prescription yet preserves gauge symmetry even in the presence of the cutoff scales. Similarity between the operator cutoff regularization and...

In functional programming, fold is a standard operator that encapsulates a simple pattern of recursion for processing lists. This article is a tutorial on two key aspects of the fold operator for lists. First of all, we emphasize the use of the universal property of fold both as a proof principle that avoids the need for inductive proofs, and as a definition principle that guides the transforma...

Necessary and sufficient geometric conditions for the equivalence of a nonlinear time– delay system with one output, under bicausal change of coordinates and output transformation, to a linear weakly observable time–delay system up to output injection are given. These conditions are derived through the use of the Extended Lie Bracket operator recently introduced in the literature for dealing wi...

By using the Deift–Trubowitz transformations for adding or removing bound states to the spectrum of the Schrödinger operator on the line we construct a simple algorithm allowing one to reduce the problem of deriving symplectic expansions to its simplest case when the spectrum is purely continuous, and vice versa. We also obtain the transformation formulas for the correponding recursion operator...

We present a method for the calculation of the a3/2 heat kernel coefficient of the heat operator trace for a partial differential operator of Laplace type on a compact Riemannian manifold with oblique boundary conditions. Using special case evaluations, restrictions are put on the general form of the coefficients, which, supplemented by conformal transformation techniques, allows the entire sme...

2 Exercise. Prove it. ◦ In fact, as sophisticates can show you, on a complex space a linear operator which preserves all norms will also preserve all inner products. But the key thing is to remember is that a unitary operator preserves all inner products (and therefore all norms). • This is analogous to the fact that translations and rotations in ordinary three-dimensional space preserve distan...