We consider the problem of nding and classifying representations in algebraic logic. This is approached by letting two players build a representation using a game. Homogeneous and universal representations are characterised according to the outcome of certain games. The Lyndon conditions deening representable relation algebras (for the nite case) and a similar schema for cylindric algebras are ...

We confirm a conjecture, about neat embeddings of cylindric algebras, made in 1969 by J. D. Monk, and a later conjecture by Maddux about relation algebras obtained from cylindric algebras. These results in algebraic logic have the following consequence for predicate logic: for every finite cardinal α ≥ 3 there is a logically valid sentence X, in a first-order language L with equality and exactl...

Boolean contact algebras are the abstract counterpart of region–based theories of space, which date back to the early 1920s. In this paper, we survey the development of these algebras and relevant construction and representation theorems.

Recently it has been discovered that the W-algebras (orbifold of) WDn can be defined even for negative integers n by an analytic continuation of their coupling constants. In this letter we shall argue that also the algebras WA−n−1 can be defined and are finitely generated. In addition, we show that a surprising connection exists between already known W-algebras, for example between the CP(k)-mo...

Modes are idempotent and entropic algebras. More precisely, an algebra (A,Ω) of type τ : Ω −→ Z is called a mode if it is idempotent and entropic, i.e. each singleton in A is a subalgebra and each operation ω ∈ Ω is actually a homomorphism from an appropriate power of the algebra. Both properties can also be expressed by the following identities: (I) ∀ω ∈ Ω, x . . . xω = x (E) ∀ω, φ ∈ Ω, with m...

We find a smooth solution of the 2D Euler equation on a bounded domain which exists and is unique in a natural class locally in time, but blows up in finite time in the sense of its vorticity losing continuity. The domain’s boundary is smooth except at two points, which are interior cusps.

The classical detection theorem for finite groups (due to D. Quillen [Q] and B. Venkov [Q-V]) tells that if π is a finite group and Λ is a Z/p[π]-algebra then a cohomology class z ∈ H(π,Λ) is nilpotent iff for every elementary abelian psubgroup i : π0 →֒ π the restriction i (z) ∈ H(π0,Λ) of z to π0 is nilpotent. This theorem is very useful for the identification of the support variety of the gro...

This contribution describes the automatic creation of highly realistic flexible 3D models of participants for distributed 3D videoconferencing systems. The proposed technique uses a flexible mesh template surrounding an interior skeleton structure, which is based on a simplified human skeleton. The vertices of this template are arranged in rigid rings along the bones of the skeleton. Using 3D d...