This article describes the method of construction the Gröbner basis based on the information in the Anick’s resolution.

Let M (f) denote the midpoint rule and T (f) the trapezoidal rule for estimating ∫ b a f(x) dx. Then Simpson’s rule = M (f) + (1 − )T (f), where = 3 . We generalize Simpson’s rule to multiple integrals as follows. Let Dn be some polygonal region in R; let P0; : : : ; Pm denote the vertices of Dn, and let Pm+1 equal the center of mass of Dn. De4ne the linear functionals M (f) =Vol(Dn)f(Pn+1), wh...

The determination of a set of geometric entities that satisfy a series of geometric relations (constraints) constitutes the Geometric Constraint Satisfaction or Scene Feasibility (GCS/SF) problem. This problem appears in diierent forms in Assembly Planning, Constraint Driven Design, Computer Vision, etc. Its solution is related to the existence of roots to systems of polynomial equations. Previ...

p. 1 Redundancy Criteria for Constrained Completion p. 2 Bi-rewriting, a Term Rewriting Technique for Monotonic Order Relations p. 17 A Case Study of Completion Modulo Distributivity and Abelian Groups p. 32 A Semantic Approach to Order-Sorted Rewriting p. 47 Distributing Equational Theorem Proving p. 62 On the Correctness of a Distributed Memory Grobner Basis Algorithm p. 77 Improving Transfor...

Quadratization is a transform of system ODEs with polynomial right-hand side into at most quadratic via the introduction new variables. It has been recently used as pre-processing step for model order reduction methods, so it important to keep number variables small. Several algorithms have designed search quadratization being monomials in original To understand limitations and potential ways i...

Nephrogenic systemic fibrosis (NSF), first described in 2000 in a 15-patient case series, is an extremely debilitating, multisystemic fibrosing disorder. Since that initial report, more than 300 cases have been recognized, and their histopathologic features have been categorized. Two known associations with NSF are renal dysfunction and exposure to gadolinium (Gd)– containing magnetic resonance...

In the thesis we have investigated the complexity of proofs in several propositional proof systems. Our main motivation has been to contribute to the line of research started by Cook and Reckhow to obtain how much knowledge as possible about the complexity of di erent proof systems to show that there is no super proof system. We also have been motivated by more applied questions concerning the ...

In a previous article [35] an algebraicity result for the central critical value for L-functions for GLn × GLn−1 over Q was proved assuming the validity of a nonvanishing hypothesis involving archimedean integrals. The purpose of this article is to generalize [35, Thm. 1.1] for all critical values for L-functions for GLn×GLn−1 over any number field F while using the period relations of [37] and...