Let G=(V,E) be a graph, a subset X of V is an interval of G whenever for a, b E X and xE V X , (a,x)EE (resp. (x,a)EE) if and only if (b,x)EE (resp. (x,b)EE). For instance, 0, {x}, where x E V, and V are intervals of G, called trivial intervals. A graph G is then said to be indecomposable when all of its intervals are trivial. In the opposite case, we will say that G is decomposable. We now int...

The decomposition of an arbitrary axiomatic topological quantum field theory or TQFT into indecomposable theories is given. In particular, unitary TQFT’s in arbitrary dimensions are shown to decompose into a sum of theories in which the Hilbert space of the sphere is one-dimensional, and indecomposable two-dimensional theories are classified.

It is stated in Montpetit (1987) that cyclic codes are indecomposable, but it is not true in general. In fhis paper we will give a necessary and sufficient condition for a cyclic code to be indecomposable, using its generator polynomial. @ 1999 Elsevier Science B.V. All rights reserved

In the twenties Brouwer established the well-known continuity theorem “every real function is locally uniformly continuous”, [Brouwer 1924, Brouwer 1924a, Brouwer 1927]. From this theorem one immediately concludes that the continuum is indecomposable (unzerlegbar), i.e. if R = A∪B and A∩B = ∅ (denoted by R = A+B), then R = A or R = B. Brouwer deduced the indecomposability directly from the fan ...

Being motivated by some methods for construction of homothetically indecomposable polytopes, we obtain new methods for construction of families of integrally indecomposable polytopes. As a result, we find new infinite families of absolutely irreducible multivariate polynomials over any field F . Moreover, we provide different proofs of some of the main results of Gao [2].

We introduce a new family of indecomposable positive linear maps based on entangled quantum states. Central to our construction is the notion of an unextendible product basis. The construction lets us create indecomposable positive linear maps in matrix algebras of arbitrary high dimension. Typeset using REVTEX 1

Precis: We discuss the behaviour of prices in an n-sector, circulating capital model with no joint production, of the type considered by Sraffa in Part I of his book. Instead of following Sraffa's approach, which uses the notion of proportions of labour to means of production in the various "layers" of means of production, we base our analysis directly on the characteristic roots and vectors of...

A useful method of proving the nite decidability of an equationally de nable class V of algebras (i.e., variety) is to prove the decidability of the class of nite directly indecomposable members of V. The validity of this method relies on the well-known result of Feferman-Vaught: if a class K of rst-order structures is decidable, then so is the class f Q i<n Ai Ai 2 K (i < n); n 2 !g. In this p...