Sparse block-Jacobi matrices with arbitrarily accurate Hausdorff dimension

We show that the Hausdorff dimension of the spectral measure of a class of deterministic, i.e. nonrandom, block-Jacobi matrices may be determined with any degree of precision, improving a result of Zlatos [Andrej Zlatos,. Sparse potentials with fractional Hausdorff dimension, J. Funct. Anal. 207 (2004) 216-252]. (C) 2010 Elsevier Inc. All rights reserved.

Polymorphism, crystallinity and hydrophilic-lipophilic balance of stearic acid and stearic acid-capric/caprylic triglyceride matrices for production of stable nanoparticles

There is an increasing interest in lipid nanoparticles because of their suitability for several administration routes. Thus, it becomes even more relevant the physicochemical characterization of lipid materials with respect to their polymorphism, lipid miscibility and stability, as well as the assessment of the effect of surfactant on the type and structure of these nanoparticles. This work focuses on the physicochemical characterization of lipid matrices composed of pure stearic acid or of mixtures of stearic acid-capric/caprylic triglycerides, for drug delivery. The lipids were analyzed by Differential Scanning Calorimetry (DSC), Wide Angle X-ray Diffraction (WAXD), Polarized Light Microscopy (PLM) and hydrophilic-lipophilic balance (HLB) in combination with selected surfactants to determine the best solid-to-liquid ratio. Based on the results obtained by DSC and WAXD, the selected qualitative and quantitative composition contributed for the production of stable nanoparticles, since the melting and the tempering processes provided important information on the thermodynamic stability of solid lipid matrices. The best HLB value obtained for stearic acid-capric/caprylic triglycerides was 13.8, achieved after combining these lipids with accepted surfactants (trioleate sorbitan and polysorbate 80 in the ratio of 10:90). The proposed combinations were shown useful to obtain a stable emulsion to be used as intermediate form for the production of lipid nanoparticles. (C) 2011 Elsevier B.V. All rights reserved.

A note on the eigenvalues of a special class of matrices

In the analysis of stability of a variant of the Crank-Nicolson (C-N) method for the heat equation on a staggered grid a class of non-symmetric matrices appear that have an interesting property: their eigenvalues are all real and lie within the unit circle. In this note we shall show how this class of matrices is derived from the C-N method and prove that their eigenvalues are inside [-1, 1] for all values of m (the order of the matrix) and all values of a positive parameter a, the stability parameter sigma. As the order of the matrix is general, and the parameter sigma lies on the positive real line this class of matrices turns out to be quite general and could be of interest as a test set for eigenvalue solvers, especially as examples of very large matrices. (C) 2010 Elsevier B.V. All rights reserved.

Enzyme activity of horseradish peroxidase immobilized in chitosan matrices in alternated layers

The successful immobilization of enzymes such as horseradish peroxidase (HRP) in solid films is essential for applications in sensors and for fundamental studies aimed at identifying possible biotechnological devices. In this study we show that HRP can be immobilized in alternated layers with chitosan as the template material. The activity of HRP in HRP/chitosan films was preserved for several weeks, and could be detected optically upon monitoring the reaction with pyrogallol. The morphology of the film displayed stripes that disappeared after reaction with pyrogallol. Though the activity in the HRP/chitosan film was lower than in a homogeneous solution or in an LB film investigated earlier, the response was linear for a considerable period of time, which may be advantageous for sensing hydrogen peroxide. (C) 2009 Elsevier B.V. All rights reserved.

On the efficiency of data representation on the modeling and characterization of complex networks

Specific choices about how to represent complex networks can have a substantial impact on the execution time required for the respective construction and analysis of those structures. In this work we report a comparison of the effects of representing complex networks statically by adjacency matrices or dynamically by adjacency lists. Three theoretical models of complex networks are considered: two types of Erdos-Renyi as well as the Barabasi-Albert model. We investigated the effect of the different representations with respect to the construction and measurement of several topological properties (i.e. degree, clustering coefficient, shortest path length, and betweenness centrality). We found that different forms of representation generally have a substantial effect on the execution time, with the sparse representation frequently resulting in remarkably superior performance. (C) 2011 Elsevier B.V. All rights reserved.

Automatic camera control in virtual environments augmented using multiple sparse videos

Automated virtual camera control has been widely used in animation and interactive virtual environments. We have developed a multiple sparse camera based free view video system prototype that allows users to control the position and orientation of a virtual camera, enabling the observation of a real scene in three dimensions (3D) from any desired viewpoint. Automatic camera control can be activated to follow selected objects by the user. Our method combines a simple geometric model of the scene composed of planes (virtual environment), augmented with visual information from the cameras and pre-computed tracking information of moving targets to generate novel perspective corrected 3D views of the virtual camera and moving objects. To achieve real-time rendering performance, view-dependent textured mapped billboards are used to render the moving objects at their correct locations and foreground masks are used to remove the moving objects from the projected video streams. The current prototype runs on a PC with a common graphics card and can generate virtual 2D views from three cameras of resolution 768 x 576 with several moving objects at about 11 fps. (C)2011 Elsevier Ltd. All rights reserved.

Sparse partition universal graphs for graphs of bounded degree

In 1983, Chvatal, Trotter and the two senior authors proved that for any Delta there exists a constant B such that, for any n, any 2-colouring of the edges of the complete graph K(N) with N >= Bn vertices yields a monochromatic copy of any graph H that has n vertices and maximum degree Delta. We prove that the complete graph may be replaced by a sparser graph G that has N vertices and O(N(2-1/Delta)log(1/Delta)N) edges, with N = [B`n] for some constant B` that depends only on Delta. Consequently, the so-called size-Ramsey number of any H with n vertices and maximum degree Delta is O(n(2-1/Delta)log(1/Delta)n) Our approach is based on random graphs; in fact, we show that the classical Erdos-Renyi random graph with the numerical parameters above satisfies a stronger partition property with high probability, namely, that any 2-colouring of its edges contains a monochromatic universal graph for the class of graphs on n vertices and maximum degree Delta. The main tool in our proof is the regularity method, adapted to a suitable sparse setting. The novel ingredient developed here is an embedding strategy that allows one to embed bounded degree graphs of linear order in certain pseudorandom graphs. Crucial to our proof is the fact that regularity is typically inherited at a scale that is much finer than the scale at which it is assumed. (C) 2011 Elsevier Inc. All rights reserved.

A criterion for unitary similarity of upper triangular matrices in general position

Each square complex matrix is unitarily similar to an upper triangular matrix with diagonal entries in any prescribed order. Let A = [a(ij)] and B = [b(ij)] be upper triangular n x n matrices that are not similar to direct sums of square matrices of smaller sizes, or are in general position and have the same main diagonal. We prove that A and B are unitarily similar if and only if parallel to h(A(k))parallel to = parallel to h(B(k))parallel to for all h is an element of C vertical bar x vertical bar and k = 1, ..., n, where A(k) := [a(ij)](i.j=1)(k) and B(k) := [b(ij)](i.j=1)(k) are the leading principal k x k submatrices of A and B, and parallel to . parallel to is the Frobenius norm. (C) 2011 Elsevier Inc. All rights reserved.

A canonical form for nonderogatory matrices under unitary similarity

A square matrix is nonderogatory if its Jordan blocks have distinct eigenvalues. We give canonical forms for (1) nonderogatory complex matrices up to unitary similarity, and (2) pairs of complex matrices up to similarity, in which one matrix has distinct eigenvalues. The types of these canonical forms are given by undirected and, respectively, directed graphs with no undirected cycles. (C) 2011 Elsevier Inc. All rights reserved.

Tridiagonal canonical matrices of bilinear or sesquilinear forms and of pairs of symmetric, skew-symmetric, or Hermitian forms

Tridiagonal canonical forms of square matrices under congruence or *congruence, pairs of symmetric or skew-symmetric matrices under congruence, and pairs of Hermitian matrices under *congruence are given over an algebraically closed field of characteristic different from 2. (C) 2008 Elsevier Inc. All rights reserved.

Effects of gamma radiation on the photoluminescence properties of polycarbonate matrices doped with terbium complex

Luminescent films containing terbium complex [Tb(acac)(3)(H(2)O)(3)] (acac = acetylacetonate) doped into a polycarbonate (PC) matrix were prepared and irradiated at low-dose gamma radiation with ratio of 5 and 10 kGy. The PC polymer was doped with 5% (w/w) of the Tb(3+) complex. The thermal behavior was investigated by utilization of differential scanning calorimetry (DSC) and thermogravimetry analysis (TGA). Changes in thermal stability due to the addition of doping agent into the polycarbonate matrix. Based on the emission spectra of PC:5% Tb(acac)(3) film were observed the characteristic bands arising from the (5)D(4) -> (7)F(J) transitions of Tb(3+) ion (J = 0-6), indicating the ability to obtain the luminescent films. Doped samples irradiated at low dose of gamma irradiation showed a decrease in luminescence intensity with increasing of the dose. (C) 2009 Elsevier Ltd. All rights reserved.

Ionized-air-treated curaua fibers as reinforcement for phenolic matrices

Curaua fibers were treated with ionized air to improve the fiber/phenolic matrix adhesion.The treatment with ionized air did not change the thermal stability of the fibers. The impact strength increased with increase in the fiber treatment time. SEM micrographs of the fibers showed that the ionized air treatment led to separation of the fiber bundles. Treatment for 12 h also caused a partial degradation of the fibers, which prompted the matrix to transfer the load to a poorer reinforcing agent during impact, thereby decreasing the impact strength of the related composite. The composites reinforced with fibers treated with ionized air absorbed less water than those reinforced with untreated fibers.

Phenolic matrices and sisal fibers modified with hydroxy terminated polybutadiene rubber: Impact strength, water absorption, and morphological aspects of thermosets and composites

The aim of the present work was to investigate the toughening of phenolic thermoset and its composites reinforced with sisal fibers, using hydroxyl-terminated polybutadiene rubber (HTPB) as both impact modifier and coupling agent. Substantial increase in the impact strength of the thermoset was achieved by the addition 10% of HTPB. Scanning electron microscopy (SEM) images of the material with 15% HTPB content revealed the formation of some rubber aggregates that reduced the efficiency of the toughening mechanism. In composites, the toughening effect was observed only when 2.5% of HTPB was added. The rubber aggregates were found located mainly at the matrix-fiber interface suggesting that HTPB could be used as coupling agent between the sisal fibers and the phenolic matrix. A composite reinforced with sisal fibers pre-impregnated with HTPB was then prepared; its SEM images showed the formation of a thin coating of HTPB on the surface of the fibers. The ability of HTBP as coupling agent between sisal fibers and phenolic matrix was then investigated by preparing a composite reinforced with sisal fibers pre-treated with HTPB. As revealed by its SEM images, the HTPB pre-treatment of the fibers resulted on the formation of a thin coating of HTPB on the surface of the fibers, which provided better compatibility between the fibers and the matrix at their interface, resulting in a material with low water absorption capacity and no loss of impact strength. (C) 2009 Elsevier B.V. All rights reserved.

THERMAL BEHAVIOR OF IN VITRO MINERALIZED ANIONIC COLLAGEN MATRICES

In the present study porcine skin and bovine pericardium were used as a source of type I collagen. Both were submitted to an alkaline treatment and mineralized by the alternate soaking method. Thermal stability and extent of mineralization have been investigated using DSC and TG. After alkaline hydrolysis there is a decrease in thermal stability but mineralization stabilizes collagen structure. Thermogravimetric data have shown that the amount of hydroxyapatite present in bovine pericardium matrix (45%) was greater than on porcine skin matrix (20%). Presence of hydroxyapatite was confirmed by EDX.