Related papers: Exact Unification
We present a new method for characterizing the interpretive possibilities generated by elliptical constructions in natural language. Unlike previous analyses, which postulate ambiguity of interpretation or derivation in the full clause…
We relate proper isometry classes of maximal lattices in a totally definite quaternary quadratic space (V,q) with trivial discriminant to certain equivalence classes of ideals in the quaternion algebra representing the Clifford invariant of…
We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.
We obtain a complete classification of minimal simple unitary $W$-algebras.
In this paper, we introduce the notion of unit reducibility for number fields, that is, number fields in which all positive unary forms attain their nonzero minimum at a unit. Furthermore, we investigate the link between unit reducibility…
We show pro-definability of spaces of definable types in various classical complete first order theories, including complete o-minimal theories, Presburger arithmetic, $p$-adically closed fields, real closed and algebraically closed valued…
The concept of differential uniformity was recently extended to the $c$-differential uniformity. An interesting problem in this area is the construction of functions with low $c$-differential uniformity and a lot of research has been done…
We define a numerical quasi-isometry invariant of a finitely generated group, whose values parametrize the difference between the group being uniformly embeddable in a Hilbert space and the reduced C*-algebra of the group being exact.
A new set of exact scattering matrices in 1+1 dimensions is proposed by solving the bootstrap equations. Extending earlier constructions of colour valued scattering matrices this new set has its colour structure associated to non…
Exactly integrable systems connected to semisimple algebras of second rank with an arbitrary choice of grading are presented in explicit form. General solutions of these systems are expressed in terms of matrix elements of two fundamental…
We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof…
We prove matching direct and inverse theorems for uniform polynomial approximation with $A^*$ weights (a subclass of doubling weights suitable for approximation in the $L_\infty$ norm) having finitely many zeros and not too "rapidly…
Recently, a geometrical characterization of vector spaces served to generalize them into a new class of algebras. Instead of the algebraic properties of the underlying fields, we generalized the recently discovered property of such spaces…
Metric algebras are metric variants of $\Sigma$-algebras. They are first introduced in the field of universal algebra to deal with algebras equipped with metric structures such as normed vector spaces. Recently a similar notion of…
We introduce invertible subalgebras of local operator algebras on lattices. An invertible subalgebra is defined to be one such that every local operator can be locally expressed by elements of the inveritible subalgebra and those of the…
Classical algebraic structures require exact satisfaction of their defining axioms. We propose similarity algebra, a framework extending algebraic and Lie structures to settings where operations satisfy quantitative bounds up to a tolerance…
We give a unified treatment of the model theory of various enrichments of infinite atomic Boolean algebras, with special attention to quantifier-eliminations, complete axiomatizations and decidability. A classical example is the enrichment…
Some completely positive maps on reduced amalgamated free products of C*-algebras are constructed; these allow a proof that the class of exact unital C*-algebras is closed under taking reduced amalgamated free products. Consequently, the…
We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner…
In this article we show that hybrid type-logical grammars are a fragment of first-order linear logic. This embedding result has several important consequences: it not only provides a simple new proof theory for the calculus, thereby…