The book contains a collection of articles by participants of the Working Week on Resolution of Singularities held at Obergurgl in Tirol, September 7-14, 1997. It is dedicated to Oscar Zariski, the founder of the school of algebraic geometry in the United States. During his long career as a mathematician he obtained ground-breaking results in algebra and algebraic geometry. Many years of his ca...

Overview. My work is in the area of commutative algebra, and is motivated by the connections between algebra and geometry. Commutative algebra is the study of commutative rings (e.g. polynomial rings over fields and their quotients) and modules over these rings, while algebraic geometry is the study of finitely many polynomial equations in finitely many unknowns. The set of all solutions to suc...

Electron tomography is currently the highest resolution imaging modality available to study the 3D structures of pleomorphic macromolecular assemblies, viruses, organelles and cells. Unfortunately, the resolution is currently limited to 3-5nm by several factors including the dose tolerance of biological specimens and the inaccessibility of certain tilt angles. Here we report the first experimen...

This paper describes an 8 kbit/s ACELP speech coder with high performance for both speech and non-speech signals such as background noise. While the traditional waveform matching LPAS structure employed in many existing speech coders provides high quality for speech signals, it has significant performance limitations for e.g. background noise. The coder presented here employs a novel adaptive g...

A generalised Thurston-Bennequin invariant for a Q-singularity of a real algebraic variety is defined as a linking form on the homologies of the real link of the singularity. The main goal of this paper is to present a method to calculate the linking form in terms of the very good resolution graph of a real normal unibranch singularity of a real algebraic surface. For such singularities, the va...

The Jacobian Conjecture is a long-standing open problem in algebraic geometry. Though the problem is inherently algebraic, it crops up in fields throughout mathematics including perturbation theory, quantum field theory and combinatorics. This thesis is a unified treatment of the combinatorial approaches toward resolving the conjecture, particularly investigating the work done by Wright and Sin...

This paper presents an approach for decision making under security risks in a computer network environment. The proposed method relies on a many sorted algebraic signature and on a rewriting system. This latter is shown to be terminating and yielding a normal form, called the risk analysis equation, that models the cost-benefit balance. Furthermore, a gradual algebraic resolution of the risk an...

An algebraic approach to finding all edge-weighted-colored paths within a weighted colored multidigraph is developed. Generally, the adjacency matrix represents a simple digraph and determines all paths between any two vertices, and is not readily extendable to colored multidigraphs. To bridge the gap, a conversion function is proposed to transform the original problem of searching edge-colored...

Two space-time variational formulations of linear parabolic evolution equations are considered, one is symmetric and elliptic on the trial space while the other is not. In each case, a space-time Petrov–Galerkin discretization using suitable tensor product trial and test functions leads to a large linear system of equations. The well-posedness of this system with respect to parabolic norms indu...

This work focuses on the management of safety constraints for control cyber-physical manufacturing systems. A methodology constructing a set to ensure an existing law is proposed. The resolution this constraint performed using algebraic synthesis. tool facilitates implementation logic filter in way that complies with IEC 61131-3.