Related papers: An algebraic approach to the set of intervals
We define a notion of an arithmetic set in an arbitrary countable group and study properties of these sets in the cases of Abelian groups and non-abelian free groups.
This paper generalizes the traditional statistical concept of prediction intervals for arbitrary probability density functions in high-dimensional feature spaces by introducing significance level distributions, which provides…
Many statistical models are algebraic in that they are defined in terms of polynomial constraints, or in terms of polynomial or rational parametrizations. The parameter spaces of such models are typically semi-algebraic subsets of the…
We introduce a notion of integration defined from filters over families of finite sets. This procedure corresponds to determining the average value of functions whose range lies in any algebraic structure in which finite averages make…
In this article we consider partial abelianization of associative algebra with respect to a subalgebra. This notion is a generalization of usual abelianization of associative algebra and has an application in Quantum Mechanics and Quantum…
With each piecewise monotonic map of the unit interval, a dimension triple is associated. The dimension triple, viewed as a Z[t, t^{-1}] module, is finitely generated, and generators are identified. Dimension groups are computed for Markov…
We enumerate the intervals in the Tamari lattices. For this, we introduce an inductive description of the intervals. Then a notion of "new interval" is defined and these are also enumerated. A a side result, the inverse of two special…
For any finite totally ordered set, the multisets of intervals form an abelian category. Various classes of subcategories admit natural combinatorial descriptions, and counting them yields familiar integer sequences. Surprisingly, in some…
A unitary (Euclidean) representation of a quiver is given by assigning to each vertex a unitary (Euclidean) vector space and to each arrow a linear mapping of the corresponding vector spaces. We recall an algorithm for reducing the matrices…
There are many complementary approaches to the construction of solutions to the field equations of general relativity. Among these, numerical approximation offers the only possibility to compute a variety of dynamical spacetimes, and so has…
We produce and study a family of representations of relative graph algebras on Hilbert spaces that arise from the orbits of points of one dimensional dynamical systems, where the underlying Markov interval maps $f$ have escape sets. We…
In this paper, we shall establish a rather general asymptotic formula in short intervals for a classe of arithmetic functions and announce two applications about the distribution of divisors of square-full numbers and integers representable…
We investigate the representation of lattices as sublattices of the lattice of all convex subsets (intervals) of a linearly ordered set $(X,\le)$. We introduce the purely lattice-theoretic notion of a \textit{loc-lattice} and prove that…
The paper provides an introduction to the field of Algebraic Set Theory (AST). AST is a flexible categorical framework for studying different kinds of set theories: both classical and constructive, predicative and impredicative. We discuss…
A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
Interval Pairwise Comparison Matrices have been widely used to account for uncertain statements concerning the preferences of decision makers. Several approaches have been proposed in the literature, such as multiplicative and fuzzy…
Symbolic Data Analysis works with variables for which each unit or class of units takes a finite set of values/categories, an interval or a distribution (an histogram, for instance). When to each observation corresponds an empirical…
A semi-algebraic set is a subset of the real space defined by polynomial equations and inequalities having real coefficients and is a union of finitely many maximally connected components. We consider the problem of deciding whether two…
New notions are introduced in algebra in order to better study the congruences in number theory. For example, the <special semigroups> makes an important such contribution.