We investigate the defining ideal IX of a set of points X in P n1 × · · · × Pk with a special emphasis on the case that X is in generic position, that is, X has the maximal Hilbert function. When X is in generic position, we determine the degrees of the generators of the associated ideal IX. Letting ν(IX) denote the minimal number of generators of IX, we use this description of the degrees to c...

The paper refers to problems of modeling and computer simulation of generic memristors caused by the so-called window functions, namely the stick effect, nonconvergence, and finding fundamentally incorrect solutions. A profoundly different modeling approach is proposed, which is mathematically equivalent to windowbased modeling. However, due to its numerical stability, it definitely smoothes th...

Extending results for space curves we establish bounds for the cohomology of a non-degenerate curve in projective n-space. As a consequence, for any given n we determine all possible pairs (d, g) where d is the degree and g is the (arithmetic) genus of the curve. Furthermore, we show that curves attaining our bounds always exist and describe properties of these extremal curves. In particular, w...

The holonomic rank of an A-hypergeometric system HA(β) is conjectured to be independent of the parameter vector β if and only if the toric ideal IA is Cohen Macaulay. We attack this conjecture by explicitly constructing more than vol (A) many linearly independent hypergeometric functions for parameters β coming from embedded primes of certain initial ideals of IA. As a consequence, we prove the...

We present a generic treatment of wave-packet revivals for quantum-mechanical systems. This treatment permits a classification of certain ideal revival types. For example, wave packets for a particle in a one-dimensional box are shown to exhibit perfect revivals. We also examine the revival structure of wave packets for quantum systems with energies that depend on two quantum numbers. Wave pack...

A natural generalization of Cohen's set of forcing conditions (the t w ~ valued functions with domain a finite subset of w) is the set of twovalued functions with domain an element of an ideal J on ~. The I~roblem treated in this paper is to determine when such forcing yields a generic real of minimal degree of constructibility. A :;imple decomposition argument shows that the non-maximality of ...

Although different satisfiability decision procedures can be combined by algorithms such as those of Nelson-Oppen or Shostak, current tools typically can only support a finite number of theories to use in such combinations. To make SMT solving more widely applicable one needs theory-generic satisfiability algorithms allowing a potentially infinite number of decidable theories to be user-definab...