In this paper we carry out an algebraic investigation of the Weak Nilpotent Minimum logic (WNM) and its t-norm based axiomatic extensions. We consider the algebraic counterpart of this logic, the variety of WNM-algebras (WNM) and we prove that it is locally finite, so all its subvarieties are generated by finite chains. We give criteria to compare varieties generated by finite families of WNM-c...

A research proposal on the algebraic structure, the representations and the possible applications of paraparticle algebras is structured in three modules: The first part stems from an attempt to classify the inequivalent gradings and braided group structures present in the various parastatistical algebraic models. The second part of the proposal aims at refining and utilizing a previously publi...

This contribution presents a comprehensive analysis of Colombeau (-type) algebras in the range between the diffeomorphism invariant algebra G = E M / N d introduced in Part I (see [Gro01]) and Colombeau’s original algebra G introduced in [Col85]. Along the way, it provides several classification results (again see [Gro01]) which are indispensable for obtaining an intrinsic description of a (ful...

Defining the WBCn algebras as the commutant of certain screening charges a special form for the classical generators is obtained which does not change under quantisation. This enables us to give explicitly the first few generators in a compact form for arbitrary WBCn algebras.

We study positively-graded Hopf algebras and obtain (dual) Gabriel-type results on graded Hopf algebras. Using it, we get certain (non-degenerate) graded Hopf pairings between quantum symmetric algebras.

An incidence algebra of a nonlocally finite partially ordered set Q is a very rare concept, perhaps nonexistent. In this note, we will attempt to construct such an algebra. 1. Introduction. Let P be a partially ordered set (poset) and K a field of characteristic 0. The functions f : P × P → K, such that x y implies f (x,y) = 0, are called the incidence functions of P over K. The set of such fun...

In the present article, a new class of solutions of Einstein field equations is investigated for a spherically symmetric space-time when the source of gravitation is a perfect fluid. All the solutions have been derived by making some suitable arrangements in the field equations. The solutions so obtained have been seen to describe Schwarzschild interior solutions. Most of the solutions are subj...

Since 1999 it became obvious that the would be 'isomorphism' between the affinê sl(2) algebra and the N=2 superconformal algebras, proposed by some authors, simply does not work. However, this issue was never properly discussed in the literature and, as a result, some confusion still remains. In this article we finally settle down, clearly and unambiguously, the true facts: there is no isomorph...

We study that the n−graphs defining by smooth map f : Ω ⊂ R n → R m , m ≥ 2, in R m+n of the prescribed mean curvature and the Gauss image. We derive the interior curvature estimates sup DR(x)

Using the fact that the class of representable cylindric algebras of infinite dimension fails to have the amalgamation property, we solve an open problem in the monograph “Cylindric Algebras, Part I” by Henkin, Monk and Tarski. Our result applies to other algebras of logic, namely Pinter’s substitution algebras and Halmo’s quasi-polyadic algebras.