In [R. Cluckers, Classification of semi-algebraic sets up to semi-algebraic bijection, J. Reine Angew. Math. 540 (2001) 105–114], it is shown that a p-adic semi-algebraic set can be partitioned in such a way that each part is semi-algebraically isomorphic to a Cartesian product ∏l i=1 R(k) where the sets R(k) are very basic subsets of Qp . It is suggested in [R. Cluckers, Classification of semi...

We study the MaxSAT Resolution (MaxRes) rule in context of certifying unsatisfiability. show that it can be exponentially more powerful than tree-like resolution, and when augmented with weakening (the system MaxResW), p -simulates resolution. In devising a lower bound technique specific to MaxRes (and not merely inheriting bounds from Res), we define new proof called SubCubeSums system. This s...

We consider two well-known algebraic proof systems: Polynomial Calculus (PC) and Polynomial Calculus with Resolution (PCR), a system introduced in [2] which combines together PC and Resolution. Moreover we introduce an algebraic proof system PCRk , which combines together Polynomial Calculus (PC) and k-DNF Resolution (RESk). This is a natural generalization to RESk of PCR. In the paper we study...

We synthesize a refutationally complete tableau calculus for propositional logic by a new method, using ordered resolution as a procedural framework at the meta level. Algebraically, the calculus solves the word problem for free distributive lattices. Goal-directedness of the construction is enforced by a ne-tuned well-founded ordering on terms, atoms and clauses. The synthesis is performed in ...

Let G ⊂ SL(n, C) be a finite subgroup and φ:Y → X = C/G any resolution of singularities of the quotient space. We prove that crepant exceptional prime divisors of Y correspond one-to-one with “junior” conjugacy classes of G. When n = 2 this is a version of the McKay correspondence (with irreducible representations of G replaced by conjugacy classes). In the case n = 3, a resolution with KY = 0 ...

Introduction. The embedded resolution of singular algebraic varieties of dimension > 3 defined over fields of characteristic p > 0 is still an open problem. The inductive argument which works in characteristic zero fails for positive characteristic. The main obstruction is the failure of maximal contact, which, in turn, manifests in the occurence of wild singularities and kangaroo points at cer...

In this article, we study the jumping numbers of an ideal in the local ring at rational singularity on a complex algebraic surface. By understanding the contributions of reduced divisors on a fixed resolution, we are able to present an algorithm for finding of the jumping numbers of the ideal. This shows, in particular, how to compute the jumping numbers of a plane curve from the numerical data...

For finite detector and focal spot sizes, here we propose a projection model for high spatial resolution. First, for a given x-ray source point, a projection datum is modeled as an area integral over a narrow fan-beam connecting the detector elemental borders and the x-ray source point. Then, the final projection value is expressed as the integral obtained in the first step over the whole focal...

This article will be devoted to generalisations of Fermat’s equation x + y = z. Very soon after the Wiles and Taylor proof of Fermat’s Last Theorem, it was wondered what would happen if the exponents in the three term equation would be chosen differently. Or if coefficients other than 1 would be chosen. We discuss the reduction of the resolution of such equations to the determination of rationa...