J. Reine Angew. Math 436 (1993), pp. 209– 219. Stony Brook IMS Preprint #1991/23 December 1991 Let G ⊂ PSL(2,C) be a geometrically finite Kleinian group, with region of discontinuity Ω(G). By Ahlfors’ finiteness theorem, the quotient, Ω(G)/G, is a finite union of Riemann surfaces of finite type. Thus on it, there are only finitely many mutually disjoint free homotopy classes of simple closed cu...

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...

The writer recently* gave a new conception of integral elements of a rational associative algebra A having a modulus 1, which avoids the serious objections against all earlier conceptions. The integral elements of A are defined to be the elements which belong to a set 5 of elements having the following four properties: C (closure) : The sum, difference and product of any two elements of 5 are a...

Maximal monotonicity is explored as a generalization of the linear theory passivity, aiming at an algorithmic input/output analysis physical models. The developed for maximal monotone one-port circuits, formed by series and parallel interconnection basic elements. These circuits generalize passive LTI transfer functions. Periodic input signals are shown to be mapped periodic output signals, the...

Let W be a Coxeter group. We generalise the Knuth plactic relations to W and we show that their equivalence classes decompose the Kazhdan-Lusztig cells. In the case of symmetric groups, we show that the set of elements of minimal length in a double sided cell is the set of elements of maximal length in conjugated parabolic (i.e. Young) subgroups. We also give an interpretation of this set with ...

To assist Java programming educations, we have developed a Web-based Java Programming Learning Assistant System (JPLAS). JPLAS provides fill-in-blank problems for novice students to learn Java by filling blank elements composed of reserved words, identifiers, and control symbols. In this paper, we propose a graph-based blank element selection algorithm to select as many blanks as possible such ...

Let g be a simple Lie algebra over C. Fix a Borel subalgebra b and a Cartan subalgebra t ⊂ b. The corresponding set of positive (resp. simple) roots is ∆ (resp. Π). Write θ for the highest root in∆. An ideal of b is called ad-nilpotent, if it is contained in [b, b]. Consequently, such a subspace is fully determined by the corresponding set of positive roots, and this set is called an ideal (in ...

The aim of this paper is to study semigroups possessing $E$-regular elements, where an element $a$ of a semigroup $S$ is {em $E$-regular} if $a$ has an inverse $a^circ$ such that $aa^circ,a^circ a$ lie in $ Esubseteq E(S)$. Where $S$ possesses `enough' (in a precisely defined way) $E$-regular elements, analogues of Green's lemmas and even of Green's theorem hold, where Green's relations ${mathc...

We consider sets of positive integers containing no sum of two elements in the set and also no product of two elements. We show that the upper density of such a set is strictly smaller than 2 and that this is best possible. Further, we also find the maximal order for the density of such sets that are also periodic modulo some positive integer.

In 3] a probabilistic space PCSP of processes is constructed uniformly from the standard CSP failures-divergences model. Here we identify the deterministic (probabilistic) elements of PCSP as the maximal elements in the reenement ordering. We extend the standard characterisation of deterministic processes in terms of of properties of their nite approximations, and formulate some analogues of th...