A theory of quasi modules at infinity for (weak) quantum vertex algebras including vertex algebras was previously developed in [Li6]. In this current paper, we develop this theory of quasi modules at infinity for vertex algebras further. Among the main results, we obtain a commutator formula for general quasi modules at infinity and we establish a category equivalence between the category of qu...

In this paper, we introduce the notions of L-fuzzy quasi-uniformities and Lfuzzy interior operators in complete residuated lattices. We investigate the L-fuzzy quasiuniformities induced by L-fuzzy interior operators. We study the relationships between Lfuzzy interior operators and L-fuzzy quasi-uniformities. We give their examples. AMS Subject Classification: 03E72, 06A15, 06F07, 54F05

For a class C of finite lattices, the question arises whether any lattice in C can be embedded into some atomistic, biatomic lattice in C. We provide answers to the question above for C being, respectively, — The class of all finite lattices; — The class of all finite lower bounded lattices (solved by the first author's earlier work). — The class of all finite join-semidistributive lattices (th...

In this paper, sufficient conditions have been obtained so that all oscillatory solutions of the n-th order differential equations with quasi derivatives tend to zero as t tends to infinity.

A bstract . Graph transformations tha.t ma.y be reduced to the form x(l +l) = x(I)+vu(Ax(I)), with x(I),x(I+1 ) E R , u convex function and A symmet ric mat rix, are studied. In par t icular , a reduction to t he class is exhibited for some graph t ransformations recentl y introduced by Odlyzko and Randall. Fur ther result s on periods, quasi-periods, and pre-periods are presented. A class of m...

The purpose of this short article is to announce, and briefly describe, a Maple package, PARTITIONS, that (inter alia) completely automatically discovers, and then proves, explicit expressions (as sums of quasi-polynomials) for pm(n) for any desired m. We do this to demonstrate the power of “rigorous guessing” as facilitated by the quasi-polynomial ansatz.

If P ⊂ Rd is a rational polytope, then iP (t) := #(tP ∩Zd) is a quasi-polynomial in t, called the Ehrhart quasi-polynomial of P . A period of iP (t) is D(P ), the smallest D ∈ Z+ such that D ·P has integral vertices. Often, D(P ) is the minimum period of iP (t), but, in several interesting examples, the minimum period is smaller. We prove that, for fixed d, there is a polynomial time algorithm ...

We study the interplay between the properties of the germ of a singular variety N ⊂ Rn given in the title and the algebra of vector fields tangent to N . The Poincare lemma property means that any closed differential (p+1)-form vanishing at any point ofN is a differential of a p-form which also vanishes at any point of N . In particular, we show that the classical quasi-homogeneity is not a nec...

We show that secure homomorphic evaluation of any non-trivial functionality of sufficiently many inputs with respect to any CPA secure encryption scheme cannot be implemented by constant depth, polynomial size circuits, i.e. in the class AC. In contrast, we observe that certain previously studied encryption schemes (with quasipolynomial security) can be implemented in AC. We view this as eviden...

In reverse mathematics, one formalizes theorems of ordinary mathematics in second order arithmetic and attempts to discover which set theoretic axioms are required to prove these theorems. Often, this project involves making choices between classically equivalent definitions for the relevant mathematical concepts. In this paper, we consider a number of equivalent definitions for the notions of ...