We establish the relationship between regularity of a Hausdorff (LB)tv -space and its properties like (K), M.c.c., sequential completeness, local completeness. We give a sufficient and necessary condition for a Hausdorff (LB)tv-space to be an (LS)tv-space. A factorization theorem for (LN)tv-spaces with property (K) is also obtained.

In image processing, textures are generally represented as homogeneous random fields, homogeneous meaning stationary or second-order stationary. This paper presents a generalization of the second-order stationarity to the second-order invariance under a group of transforms. Some examples of interesting groups are given. The Cholesky factorization is applied for the synthesis of random fields sh...

We study the Maurer-Cartan equation of the pre-Lie algebra of graphs controling the deformation theory of associative algebras and prove that there is a canonical solution within the class of graphs without circuits, without assuming the Jacobi identity. The proof is based on the unique factorization property of graph insertions.

In the work, we rebuild the masks of well-known interpolatory symmetric subdivision schemes-binary 2n-point interpolatory schemes, the ternary 4-point interpolatory scheme using only the symmetry and the necessary condition for smoothness and the butterfly scheme, and the modified butterfly scheme using the factorization property. 2006 Elsevier Inc. All rights reserved.

A hereditary property R of graphs is said to be reducible if there exist hereditary properties P1,P2 such that G ∈ R if and only if the set of vertices of G can be partitioned into V (G) = V1 ∪ V2 so that 〈V1〉 ∈ P1 and 〈V2〉 ∈ P2. The problem of the factorization of reducible properties into irreducible factors is investigated.

This paper presents a stochastic subspace identification algorithm to compute stable, minimum phase models from a stationary time-series data. The algorithm is based on spectral factorization techniques and a stochastic subspace identification method via a block LQ decomposition (Tanaka and Katayama, 2003c). Two Riccati equations are solved to ensure both stability and minimum phase property of...

Let C be a category with strong monomorphic strong coimages, that is, every morphism ƒ of C factors as ƒ = u ° g so that g is a strong epimorphism and u is a strong monomorphism and this factorization is universal. We define the notion of strong Mittag-Leffler property in pro-C. We show that if ƒ : X → Y is a level morphism in pro-C such that ( ) p Y ! " is a strong epimorphism for all β > α, t...

Equivalence relations on the edge set of a hypergraph that satisfy the “grid-property” (a certain restrictive condition on diagonal-free grids that can be seen as a generalization of the more familiar “square property” on graphs) play a crucial role in the theory of Cartesian hypergraph products. In particular, every convex relation with the grid property induces a factorization w.r.t. the Cart...

In this paper, we propose a structured bisection method with adaptive randomized sampling for finding selected or all of the eigenvalues of certain real symmetric matrices A. For A with a low-rank property, we construct a hierarchically semiseparable (HSS) approximation and show how to quickly evaluate and update its inertia in the bisection method. Unlike some existing randomized HSS construct...

We consider the problem of structure prediction for sparse LU factorization with partial pivoting. In this context, it is well known that the column elimination tree plays an important role for matrices satisfying an irreducibility condition, called the strong Hall property. Our primary goal in this paper is to address the structure prediction problem for matrices satisfying a weaker assumption...