In [5] Lenz and Stollmann proved the existence of the integrated density of states in the sense of uniform convergence of the distributions for certain operators with aperiodic order. The goal of this paper is to establish a relation between aperiodic order, uniform spectral convergence and the continuous algebras invented by John von Neumann. We illustrate the technique by proving the uniform ...

using the hyers-ulam-rassias stability method, weinvestigate isomorphisms in banach algebras and derivations onbanach algebras associated with the following generalized additivefunctional inequalitybegin{eqnarray}|af(x)+bf(y)+cf(z)|  le  |f(alpha x+ beta y+gamma z)| .end{eqnarray}moreover, we prove the hyers-ulam-rassias stability of homomorphismsin banach algebras and of derivations on banach ...

We propose a generalization of differentiable algebras, where the underlying differential structure is replaced by a uniform idempotent right quasigroup (irq). Then a emergent algebra is a algebra A over the uniform irq X such that all operations and algebraic relations from A can be constructed or deduced from combinations of operations in the uniform irq, possibly by taking limits which are u...

We use Macaulay's inverse system to study the Hilbert series for almost complete intersections generated by uniform powers of general linear forms. This allows us give a classification Weak Lefschetz property these algebras, settling conjecture Migliore, Mir\'o-Roig, and Nagel.

Recent years have seen much effort put into attempts to develop an "abstract" function theory. In the complex domain, this has led to the study of the structure of uniform algebras. A uniform algebra 31 is a family of continuous complex-valued functions on a compact Hausdorff space X, which contains the function 1, which is closed with respect to the algebraic operations of addition and multipl...

We prove that the factorization homologies of a scheme with coefficients in truncated polynomial algebras compute cohomologies its generalized configuration spaces. Using Koszul duality between commutative and Lie algebras, we obtain new expressions for latter. As consequence, uniform conceptual approach treating homological stability, densities, arithmetic densities Our results categorify, gen...

In this paper we study the structure of finitely presented Heyting algebras. Using algebraic techniques (as opposed to techniques from proof-theory) we show that every such Heyting algebra is in fact coHeyting, improving on a result of Ghilardi who showed that Heyting algebras free on a finite set of generators are co-Heyting. Along the way we give a new and simple proof of the finite model pro...

The problem of nding sound and complete semantics for the logic underlying the lambda-Prolog programming language: Higher Order Hereditarily Harrop formulas with resolution (uniform) proofs has been open for over a decade. It is settled in this paper. Church's Simple Theory of Types introduced in 1940, is a classical theory: all instances of the excluded middle are derivable in it. A suitable i...