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We describe and classify countable Boolean rings (which may or may not have a multiplicative identity) with finitely many distinguished ideals whose elementary theory is countably categorical. This extends the description by Macintyre and…
We propose an effective algorithm that decides if a prime ideal in a polynomial ring over the complex numbers can be transformed into a toric ideal by a linear automorphism of the ambient space. If this is the case, the algorithm computes…
In this paper, we define the concepts of semi-canonical and canonical binary matrix. Strictly mathematical, we prove the correctness of these definitions. We describe and we implement an algorithm for finding all semi-canonical binary…
The aim of this work is to study duality of fractional ideals with respect to a fixed ideal and to investigate the relationship between value sets of pairs of dual ideals in admissible rings, a class of rings that contains the local rings…
The notion of a k-automatic set of integers is well-studied. We develop a new notion - the k-automatic set of rational numbers - and prove basic properties of these sets, including closure properties and decidability.
In this paper we generalize the canonical positive scaling of rows and columns of a matrix to the scaling of selected-rank subtensors of an arbitrary tensor. We expect our results and framework will prove useful for sparse-tensor completion…
In this paper, binomial difference ideals are studied. Three canonical representations for Laurent binomial difference ideals are given in terms of the reduced Groebner basis of Z[x]-lattices, regular and coherent difference ascending…
A practical version of the polynomial canonical formalism is developed for normal mesoscopic systems consisting of N independent electrons. Drastic simplification of calculations is attained by means of proper ordering excited states of the…
In this paper, a new kind of soft sets related with some common decision making problems in real life called central soft sets is introduced. Properties of some basic operations on central soft sets are shown. It is investigated that some…
A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…
In this work we consider the task of relaxing the i.i.d assumption in pattern recognition (or classification), aiming to make existing learning algorithms applicable to a wider range of tasks. Pattern recognition is guessing a discrete…
Given a graded sequence of ideals (a_m) on a smooth variety $X$ having finite log canonical threshold, suppose that for every m we have a divisor E_m over X that computes the log canonical threshold of a_m, and such that the log…
We study a pair consisting of a smooth variety over a field of positive characteristic and a multi-ideal with a real exponent. We prove the finiteness of the set of minimal log discrepancies for a fixed exponent if the dimension is less…
Let P be the direct product of countably many copies of the additive group Z of integers. We study, from a set-theoretic point of view, those subgroups of P for which all homomorphisms to Z annihilate all but finitely many of the standard…
We demonstrate the possibility of classifying causal systems into kinds that share a common structure without first constructing an explicit dynamical model or using prior knowledge of the system dynamics. The algorithmic ability to…
We consider the Rosenfeld-Groebner algorithm for computing a regular decomposition of a radical differential ideal generated by a set of ordinary differential polynomials in n indeterminates. For a set of ordinary differential polynomials…
The purpose of this paper is to introduce a set of four test images containing features and structures that can facilitate effective examination and comparison of image processing algorithms. More specifically, the images are designed to…
We mainly investigate model of set theory with restricted choice, e.g., ZF + DC + "the family of countable subsets of lambda is well ordered for every lambda" (really local version for a given lambda). In this frame much of pcf theory can…
This is the continuation of Montes' paper "On the canonical discussion of polynomial systems with parameters". In this paper we define the Minimal Canonical Comprehensive Groebner System (MCCGS) of a parametric ideal and fix under which…
We describe arithmetic algorithms on a canonical number representation based on the Catalan family of combinatorial objects specified as a Haskell type class. Our algorithms work on a {\em generic} representation that we illustrate on…