This paper tries to analyse, from the mathematical point of view, the system of equations proposed by P.J. Armstrong and C.O. Frederick and used in the theory of inelastic deformations of metals. We present global in time existence result for so called "weak-type admissible solutions" for the...

Diagnosis based on medical image data is common in clinical research and clinical routine. We discuss a strategy to derive a classifier with good performance on clinical image data and to justify the properties of the classifier by an adapted simulation model of image data. As learning set we...

Based on the three-parameter solution in natural numbers of the four squares equation by Sierpinski(1962) and an identity by Catalan(1885), we determine in two different ways the set of all primitive solutions to this equation. The obtained algorithms are illustrated with lists of the first...

Strict positive realness (SPR) is an important concept in absolute stability theory, adaptive control, system identification, etc. This paper characterizes the strictly positive real (SPR) regions in coefficient space and presents a robust design method for SPR transfer functions. We first...

Some Kharitonov-like robust Hurwitz stability criteria are established for a class of complex polynomial families with nonlinearly correlated perturbations. These results are extended to the polynomial matrix case and non-interval D-stability case. Applications of these results in testing of...

For the left-sector stability of interval polynomials, it suffices to check a subset of its vertex polynomials. This paper provides a recipe for construction of these critical vertices. Illustrative examples are presented

Let be a hypergraph. For a -edge coloring let (, ) be the number of components in the subhypergraph induced by the color class with the least number of components. Let () be the maximum possible value of (, ) ranging over all k-edge colorings of . If is the complete graph then, trivially, . In...

Let be a k-uniform hypergraph with vertices. A is a partition of the vertices into parts, such that each edge of intersects each part. A strong r-coloring is called if the size of each part is or . We prove that for all ≥ 1, if the maximum degree of satisfies then has an equitable coloring...

Let tree automaton over Σ be arbitrary. We construct a deterministic tree automaton over Σ such that . We show that the following two statements are equivalent, (i) The ground tree transformation () induced by is equal to the ground tree transformation () induced by . (ii) There is a...

We present a model that allows for a relatively simple analytical valuation of a full requirements contract in terms of power spot prices and load in the case when power spot prices follow a geometric mean-reverting process and load follows a mean-reverting process. This model represents a...