The Reproducing Kernel Particle Method (RKPM) has many attractive properties that make it ideal for treating a broad class of physical problems. RKPM may be implemented in a \mesh-full" or a \mesh-free" manner and provides the ability to tune the method, via the selection of a window function and its associated dilation parameter, in order to achieve the requisite numerical performance. RKPM al...

The effect of polystyrene (PS) matrix relaxation on interdiffusion at a PS and poly(viny1 methyl ether) (PVME) interface was investigated with attenuated total internal reflectance infrared spectroscopy (ATR-FTIR) at 105 and 85 "C, corresponding to 5 "C above and 15 "C below the Tg of PS, respectively. Monodisperse PS samples with M, of 3.0 x lo6 and 1.05 x lo5 were used to simulate relaxation ...

An analysis is given of ∗-representations of rank 2 single vertex graphs. We develop dilation theory for the nonselfadjoint algebras Aθ and Au which are associated with the commutation relation permutation θ of a 2 graph and, more generally, with commutation relations determined by a unitary matrix u in Mm(C)⊗Mn(C). We show that a defect free row contractive representation has a unique minimal ...

A refinable spline in R is a compactly supported refinable function whose support can be decomposed into simplices such that the function is a polynomial on each simplex. The best known refinable splines in R are the box splines. Refinable splines play a key role in many applications, such as numerical computation, approximation theory and computer aided geometric design. Such functions have be...

This paper gives a practical method of extending an nr matrix P (z), r n, with Laurent polynomial entries in one complex variable z, to a square matrix also with Laurent polynomial entries. If P (z) has orthonormal columns when z is restricted to the torus T, it can be extended to a paraunitary matrix. If P (z) has rank r for each z 2 T, it can be extended to a matrix with nonvanishing determin...

The cascade algorithm with mask a and dilation M generates a sequence φ n , n = 1, 2,. .. , by the iterative process φ n (x) = α∈Z s a(α)φ n−1 (Mx − α) x ∈ R s , from a starting function φ 0 , where M is a dilation matrix. A complete characterization is given for the strong convergence of cascade algorithms in Sobolev spaces for the case in which M is isotropic. The results on the convergence o...

RATIONALE Diabetes mellitus is associated with cardiac fibrosis. Matricellular proteins are induced in fibrotic conditions and modulate fibrogenic and angiogenic responses by regulating growth factor signaling. OBJECTIVE Our aim was to test the hypothesis that the prototypical matricellular protein thrombospondin (TSP)-1, a potent angiostatic molecule and crucial activator of transforming gro...