Abstract The total positivity of collocation, Wronskian and Gram matrices corresponding to bases the form ( e λ t , ,…, n ) is analyzed. A bidiagonal decomposition providing accurate numerical resolution algebraic linear problems with these derived. experimentation confirms accuracy proposed methods.

The automorphism group of a curve is studied from the viewpoint canonical embedding and Petri’s theorem. A criterion for identifying as an algebraic subgroup general linear given. Furthermore, action extended to on generators minimal free resolution ring X.

The theorem is the best possible in the sense that the components of nonsingular algebraic subsets in the conclusion cannot be replaced by nonsingular algebraic subsets (see Remark 14). It is well known that the topology of the singularities of 7/2-homology cycles is closely related to real algebraic structures on V [AK 2, AK3]. Therefore it is natural to study to what extent general homology c...

We present size-space trade-offs for the polynomial calculus (PC) and polynomial calculus resolution (PCR) proof systems. These are the first true size-space trade-offs in any algebraic proof system, showing that size and space cannot be simultaneously optimized in these models. We achieve this by extending essentially all known size-space trade-offs for resolution to PC and PCR. As such, our r...

Given a three-dimensional complex algebraic variety with isolated singular point and a sufficiently fine complete resolution of the singularity, we can make a careful choice of hyperplane that allows us to construct an exact sequence of weighted Nash complexes.

This paper presents an algebra for conflict resolution in nonlinear planning. A set of conflicts in a plan is considered as a constraint network. Each node in the network represents a conflict, and is associated with a set of alternative ways for resolving it. Thus, resolving conflicts in a plan corresponds to selecting a set of consistent resolution methods so that, after they are applied to t...

We relate two formerly independent areas: Formal concept analysis and logic of domains. We will establish a correspondene between contextual attribute logic on formal contexts resp. concept lattices and a clausal logic on coherent algebraic cpos. We show how to identify the notion of formal concept in the domain theoretic setting. In particular, we show that a special instance of the resolution...

We relate two formerly independent areas: Formal concept analysis and logic of domains. We will establish a correspondene between contextual attribute logic on formal contexts resp. concept lattices and a clausal logic on coherent algebraic cpos. We show how to identify the notion of formal concept in the domain theoretic setting. In particular, we show that a special instance of the resolution...

Integrating an SMT solver in a certified environment such as an LF-style proof assistant requires the solver to output proofs. Unfortunately, those proofs may be quite large, and the overhead of rechecking the proof may account for a significant fraction of the proof time. In this paper we explore techniques for reducing the sizes of propositional proofs, which are at the core of SMT proofs. Ou...

W.C. Rounds and G.-Q. Zhang have recently proposed to study a form of disjunctive logic programming generalized to algebraic domains [RZ01]. This system allows reasoning with information which is hierarchically structured and forms a (suitable) domain. We extend this framework to include reasoning with negative information, i.e. the implicit or explicit absence of bits of information. These inv...