Multidimensional minimax single facility location problems with Chebyshev distance are examined within the framework of idempotent algebra. A new algebraic solution based on an extremal property of the eigenvalues of irreducible matrices is given. The solution reduces both unconstrained and constrained location problems to evaluation of the eigenvalue and eigenvectors of an appropriate matrix. ...

Recently D. Buchholz and R. Verch have proposed a method for implementing in algebraic quantum field theory ideas from renormalization group analysis of short-distance (high energy) behavior by passing to certain scaling limit theories. Buchholz and Verch distinguish between different types of theories where the limit is unique, degenerate, or classical, and the method allows in principle to ex...

In this article, the minimum distance of the dual C⊥ of a functional code C on an arbitrary–dimensional variety X over a finite field Fq is studied. The approach is based on problems à la Cayley–Bacharach and consists in describing the minimal configurations of points on X which fail to impose independent conditions on forms of some fixed degree m. If X is a curve, the result improves in some s...

Within the framework of algebraic quantum field theory a general method is presented which allows one to compute and classify the short distance (scaling) limit of any algebra of local observables. The results can be used to determine the particle and symmetry content of a theory at very small scales and thereby give an intrinsic meaning to notions such as “parton” and “confinement”. The method...

The concept of an error-correcting array gives a new bound on the minimum distance of linear codes and a decoding algorithm which decodes up to half this bound. This gives a unified point of view which explains several improvements on the minimum distance of algebraic-geometric codes. Moreover it is explained in terms of linear algebra and the theory of semigroups only.

Network sparsification methods play an important role in modern network analysis when fast estimation of computationally expensive properties (such as the diameter, centrality indices, and paths) is required. We propose a method of network sparsification that preserves a wide range of structural properties. Depending on the analysis goals, the method allows to distinguish between local and glob...

Høholdt, van Lint and Pellikaan proposed a generalization of one-point AG codes called the evaluation codes, and enabled us to construct linear codes from arbitrary algebraic varieties [5], [6]. To construct an evaluation code, we find an appropriate K-algebra R with an order function w and an epimorphism φ : R → Kn of K-algebras, where K is a finite field and n is the code length. Then we defi...

Our purpose is to present some computations and estimates for the minimum distance of some families of evaluation codes. We introduce the Feng-Rao distance of an algebraic-geometry code and its extension to codes from order domains. Finally we give an algorithm to compute the Feng-Rao distance of a code from an order domain and we show its implementation in the computer algebra system SINGULAR.

Distance constraints are an emerging formulation that offers intuitive geometrical interpretation of otherwise complex problems. It has applications in problems such as position and singularity analysis and path planning of mechanisms and structures. This paper reviews the recent advances in Distance Geometry providing a unified view of these apparently disparate problems. This survey reviews a...

Distance-regular graphs are a key concept in Algebraic Combinatorics and have given rise to several generalizations, such as association schemes. Motivated by spectral and other algebraic characterizations of distance-regular graphs, we study ‘almost distance-regular graphs’. We use this name informally for graphs that share some regularity properties that are related to distance in the graph. ...