Related papers: Levels of uniformity
We classify the unimodular equivalence classes of inclusion-minimal polygons with a certain fixed lattice width. As a corollary, we find a sharp upper bound on the number of lattice points of these minimal polygons.
We are going to introduce a new algebraic, analytic structure that is a kind of generalization of the Hausdorff dimension and measure. We give many examples and study the basic properties and relations of such systems.
Matrix properties are a type of property of categories which includes the ones of being Mal'tsev, arithmetical, majority, unital, strongly unital and subtractive. Recently, an algorithm has been developed to determine implications…
In this paper we introduce a new kind of topological space, called 'structured space', which locally resembles various kinds of algebraic structures. This can be useful, for instance, to locally study a space that cannot be globally endowed…
We study analytic Zariski structures from the point of view of non-elementary model theory. We show how to associate an abstract elementary class with a one-dimensional analytic Zariski structure and prove that the class is stable,…
We analyze the degree-structure induced by large reducibilities under the Axiom of Determinacy. This generalizes the analysis of Borel reducibilities given in references [1], [6] and [5] e.g. to the projective levels.
We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite…
The Univalence Principle is the statement that equivalent mathematical structures are indistinguishable. We prove a general version of this principle that applies to all set-based, categorical, and higher-categorical structures defined in a…
Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones. The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of…
We consider how the problem of determining normal forms for a specific class of nonholonomic systems leads to various interesting and concrete bridges between two apparently unrelated themes. Various ideas that traditionally pertain to the…
We study associative multiplications in semi-simple associative algebras over C compatible with the usual one or, in other words, linear deformations of semi-simple associative algebras over C. It turns out that these deformations are in…
In this article, we introduce a notion of reducibility for partial functions on the natural numbers, which we call subTuring reducibility. One important aspect is that the subTuring degrees correspond to the structure of the realizability…
We present a logic for reasoning about graded inequalities which generalizes the ordinary inequational logic used in universal algebra. The logic deals with atomic predicate formulas of the form of inequalities between terms and formalizes…
Inspired by multigrid methods for linear systems of equations, multilevel optimization methods have been proposed to solve structured optimization problems. Multilevel methods make more assumptions regarding the structure of the…
We give lower bounds on the largest singular value of arbitrary matrices, some of which are asymptotically tight for almost all matrices. To study when these bounds are exact, we introduce several combinatorial concepts. In particular, we…
We introduce a new class of symmetric algebras, which we call hybrid algebras. This class contains on one extreme Brauer graph algebras, and on the other extreme general weighted surface algebras. We show that hybrid algebras are precisely…
We compare three notions of genericity of separable metric structures. Our analysis provides a general model theoretic technique of showing that structures are generic in descriptive set theoretic (topological) sense and in measure…
Polynomial reduction is one of the main tools in computational algebra with innumerable applications in many areas, both pure and applied. Since many years both the theory and an efficient design of the related algorithm have been solidly…
Recently Jenei introduced a new structure called equality algebras which is inspired by ideas of BCK-algebras with meet. These algebras were generalized by Jenei and K\'or\'odi to pseudo equality algebras which are aimed to find a…
We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…