S U M M A R Y Using a classical averaging approach, we derive a two-phase theory to describe the deformation of a porous material made of a matrix containing voids. The presence and evolution of surface energy at the interface between the solid matrix and voids is taken into account with non-equilibrium thermodynamic considerations that allow storage of deformational work as surface energy on g...

In the Hilbert space ?2 ?(Z; E) (Z := {0,? 1, ? 2, ...}, dim E = N < ?), maximal dissipative singular second-order matrix difference operators that extensions of a minimal symmetric operator with deficiency indices (2N, 2N) (in limit-circle cases at ?) are considered. The general boundary conditions investigated. For operator, self-adjoint dilation and is its incoming outgoing spectral repre...

We study multivariate trigonometric polynomials satisfying the “sum-rule” conditions of a certain order. Based on the polyphase representation of these polynomials relative to a general dilation matrix, we develop a simple constructive method for a special type of decomposition of such polynomials. These decompositions are of interest in the analysis of convergence and smoothness of multivariat...

We continue the study of projective module wavelet frames corresponding to diagonal dilation matrices on Rn with integer entries, focusing on the construction of a projective multi-resolution analysis corresponding to dilations whose domains are finitely generated projective modules over continuous complex-valued functions on ntori, n ≥ 3. We are able to generalize some of these results to dila...

Abstract. A composite dilation wavelet is a collection of functions generating an orthonormal basis for L2(Rn) under the actions of translations from a full rank lattice and dilations by products of elements of non-commuting groups A and B. A minimally supported frequency composite dilation wavelet has generating functions whose Fourier transforms are characteristic functions of a lattice tilin...

We provide a method for constructing regular sampling lattices in arbitrary dimensions together with an integer dilation matrix. Subsampling using this dilation matrix leads to a similarity-transformed version of the lattice with a chosen density reduction. These lattices are interesting candidates for multidimensional wavelet constructions with a limited number of subbands. 1. Primer on sampli...

Varicose veins are a common venous disease of the lower extremity. Although the mechanisms and determinants in the development of varicosities are not clearly defined, recent clinical studies and basic science research have cast some light on possible mechanisms of the disease. In varicose veins, there are reflux and incompetent valves as well as vein wall dilation. Primary structural changes i...