In [1] a recursive warrant semantics for Defeasible Logic Programming extended with levels of possibilistic uncertainty for defeasible rules was introduced. The resulting argumentation framework, called RP-DeLP, is based on a general notion of collective (non-binary) conflict among arguments allowing to ensure direct and indirect consistency properties with respect to the strict knowledge. An o...

Let X be a compact set in the z-plane. We are interested in two function spaces associated with X: C(X) — space of all continuous complex-valued functions on X. P(X) =space of all uniform limits of polynomials on X. Thus a function ƒ on X lies in P{X) if there exists a sequence {Pn} of polynomials converging to ƒ uniformly on X. Clearly P(X) is part of C(X). QUESTION I. When is P(X) = C(X)t i.e...

We investigated maximal Prym varieties on finite fields by attaining their upper bounds on the number of rational points. This concept gave us a motivation for defining a generalized definition of maximal curves i.e. maximal morphisms. By MAGMA, we give some non-trivial examples of maximal morphisms that results in non-trivial examples of maximal Prym varieties.

Can there be a structure space-type theory for an arbitrary class of ideals ring? The ideal spaces introduced in this paper allows such study and our includes (but not restricted to) prime, maximal, minimal strongly irreducible, completely proper, minimal, primary, nil, nilpotent, regular, radical, principal, finitely generated ideals. We characterise that are sober. introduce the notion discon...

Suppose that R is an analytically irreducible or excellent local domain with maximal ideal m . We consider multiplicities and mixed of by filtrations -primary ideals. show the theorem Teissier, Rees Sharp, Katz, characterizing equality in Minkowski inequality for ideals, true divisorial filtrations, larger category bounded filtrations. This not arbitrary

It is proved that if R is a valuation domain with maximal ideal P and if RL is countably generated for each prime ideal L, then R R is separable if and only RJ is maximal, where J = ∩n∈NP . When R is a valuation domain satisfying one of the following two conditions: (1) R is almost maximal and its quotient field Q is countably generated (2) R is archimedean Franzen proved in [2] that R is separ...

If R is a valuation domain of maximal ideal P with a maximal immediate extension of finite rank it is proven that there exists a finite sequence of prime ideals P = L0 ⊃ L1 ⊃ · · · ⊃ Lm ⊇ 0 such that RLj /Lj+1 is almost maximal for each j, 0 ≤ j ≤ m − 1 and RLm is maximal if Lm 6= 0. Then we suppose that there is an integer n ≥ 1 such that each torsion-free R-module of finite rank is a direct s...