A solution of the trigonometric moment problem via Tagamlitzki's "Theorem of the Cones"

In 1952 Y. Tagamlitzki gave an elegant proof of the classical Bochner’s theorem on the positively definite functions. Unfortunately, he never published his proof. In this paper we consider a related but simpler problem, the trigonometric moment problem, by using Tagamlitzki’s approach.

Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

Solution of the Least Squares Method problem of pairwise comparison matrices

The aim of the paper is to present a new global optimization method for determining all the optima of the Least Squares Method (LSM) problem of pairwise comparison matrices. Such matrices are used, e.g., in the Analytic Hierarchy Process (AHP). Unlike some other distance minimizing methods, LSM is usually hard to solve because of the corresponding nonlinear and non-convex objective function. It is found that the optimization problem can be reduced to solve a system of polynomial equations. Homotopy method is applied which is an efficient technique for solving nonlinear systems. The paper ends by two numerical example having multiple global and local minima.

Fully Anisotropic Solution of the Three Dimensional Boltzmann Transport Equation

The development of accurate modeling techniques for nanoscale thermal transport is an active area of research. Modern day nanoscale devices have length scales of tens of nanometers and are prone to overheating, which reduces device performance and lifetime. Therefore, accurate temperature profiles are needed to predict the reliability of nanoscale devices. The majority of models that appear in the literature obtain temperature profiles through the solution of the Boltzmann transport equation (BTE). These models often make simplifying assumptions about the nature of the quantized energy carriers (phonons). Additionally, most previous work has focused on simulation of planar two dimensional structures. This thesis presents a method which captures the full anisotropy of the Brillouin zone within a three dimensional solution to the BTE. The anisotropy of the Brillouin zone is captured by solving the BTE for all vibrational modes allowed by the Born Von-Karman boundary conditions.

Influence of the network modifier on the characteristics of MSnO 3 (M=Sr and Ca) thin films synthesized by chemical solution deposition

CaSnO3 and SrSnO3 alkaline earth stannate thin films were prepared by chemical solution deposition using the polymeric precursor method on various single crystal substrates (R- and C-sapphire and 100-SrTiO3) at different temperatures. The films were characterized by X-ray diffraction (θ-2θ, ω- and φ-scans), field emission scanning electron microscopy, atomic force microscopy, micro-Raman spectroscopy and photoluminescence. Epitaxial SrSnO3 and CaSnO 3 thin films were obtained on SrTiO3 with a high crystalline quality. The long-range symmetry promoted a short-range disorder which led to photoluminescence in the epitaxial films. In contrast, the films deposited on sapphire exhibited a random polycrystalline growth with no meaningful emission regardless of the substrate orientation. The network modifier (Ca or Sr) and the substrate (sapphire or SrTiO3) influenced the crystallization process and/or the microstructure. Higher is the tilts of the SnO6 octahedra, as in CaSnO3, higher is the crystallization temperature, which changed also the nucleation/grain growth process. © 2012 Elsevier Inc. All rights reserved.

Influence of the network modifier on the characteristics of MSnO3 (M=Sr and,Ca) thin films synthesized by chemical solution deposition

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Influence of the network modifier on the characteristics of MSnO3 (M=Sr and Ca) thin films synthesized by chemical solution deposition

CaSnO3 and SrSnO3 alkaline earth stannate thin films were prepared by chemical solution deposition using the polymeric precursor method on various single crystal substrates (R- and C-sapphire and 100-SrTiO3) at different temperatures. The films were characterized by X-ray diffraction (θ-2θ, ω- and φ-scans), field emission scanning electron microscopy, atomic force microscopy, micro-Raman spectroscopy and photoluminescence. Epitaxial SrSnO3 and CaSnO3 thin films were obtained on SrTiO3 with a high crystalline quality. The long-range symmetry promoted a short-range disorder which led to photoluminescence in the epitaxial films. In contrast, the films deposited on sapphire exhibited a random polycrystalline growth with no meaningful emission regardless of the substrate orientation. The network modifier (Ca or Sr) and the substrate (sapphire or SrTiO3) influenced the crystallization process and/or the microstructure. Higher is the tilts of the SnO6 octahedra, as in CaSnO3, higher is the crystallization temperature, which changed also the nucleation/grain growth process.

Characterization of the interdependency between residues that bind the substrate in a β-glycosidase

The manner by which effects of simultaneous mutations combine to change enzymatic activity is not easily predictable because these effects are not always additive in a linear manner. Hence, the characterization of the effects of simultaneous mutations of amino acid residues that bind the substrate can make a significant contribution to the understanding of the substrate specificity of enzymes. In the β-glycosidase from Spodoptera frugiperda (Sfβgly), both residues Q39 and E451 interact with the substrate and this is essential for defining substrate specificity. Double mutants of Sfβgly (A451E39, S451E39 and S451N39) were prepared by site-directed mutagenesis, expressed in bacteria and purified using affinity chromatography. These enzymes were characterized using p-nitrophenyl β-galactoside and p-nitrophenyl β-fucoside as substrates. The k cat/Km ratio for single and double mutants of Sfβgly containing site-directed mutations at positions Q39 and E451 was used to demonstrate that the effect on the free energy of ES‡ (enzyme-transition state complex) of the double mutations (∆∆G‡xy) is not the sum of the effects resulting from the single mutations (∆∆G‡x and ∆∆G‡y). This difference in ∆∆G‡ indicates that the effects of the single mutations partially overlap. Hence, this common effect counts only once in ∆∆G‡xy. Crystallographic data on β-glycosidases reveal the presence of a bidentate hydrogen bond involving residues Q39 and E451 and the same hydroxyl group of the substrate. Therefore, both thermodynamic and crystallographic data suggest that residues Q39 and E451 exert a mutual influence on their respective interactions with the substrate.

Scaling of the elastic contribution to the surface free energy of a nematic liquid crystal on a sawtoothed substrate

We characterize the elastic contribution to the surface free energy of a nematic liquid crystal in the presence of a sawtooth substrate. Our findings are based on numerical minimization of the Landau-de Gennes model and analytical calculations on the Frank-Oseen theory. The nucleation of disclination lines (characterized by non-half-integer winding numbers) in the wedges and apexes of the substrate induces a leading order proportional to q ln q to the elastic contribution to the surface free-energy density, with q being the wave number associated with the substrate periodicity.

Numerical solution of a PDE system with non-linear steady state conditions that translates the air stripping pollutants removal

This work deals with the numerical simulation of air stripping process for the pre-treatment of groundwater used in human consumption. The model established in steady state presents an exponential solution that is used, together with the Tau Method, to get a spectral approach of the solution of the system of partial differential equations associated to the model in transient state.

The development of a stable oral solution of captopril for paediatric patients

Study objectives: Many major drugs are not available in paediatric form. The aim of this study was to develop a stable liquid solution of captopril for oral paediatric use allowing individualised dosage and easy administration to newborn and young patients. Methods: A specific HPLC-UV method was developed. In a pilot study, a number of formulations described in the literature as affording one-month stability were examined. In the proper long-term study, the formulation that gave the best results was then prepared in large batches and its stability monitored for two years at 5°C and room temperature, and for one year at 40°C. Results: Most formulations described in the literature were found wanting in our pilot study. A simple solution of the drug (1 mg/mL) in purified water (European Pharmacopeia) containing 0.1% disodium edetate (EDTA-Na) as preservative proved chemically and microbiologically stable at 5°C and room temperature for two years. Conclusion: The proposed in-house formulation fulfils stringent criteria of purity and stability and is fully acceptable for oral administration to newborn and young patients.

Characterization of the interdependency between residues that bind the substrate in a β-glycosidase

The manner by which effects of simultaneous mutations combine to change enzymatic activity is not easily predictable because these effects are not always additive in a linear manner. Hence, the characterization of the effects of simultaneous mutations of amino acid residues that bind the substrate can make a significant contribution to the understanding of the substrate specificity of enzymes. In the β-glycosidase from Spodoptera frugiperda (Sfβgly), both residues Q39 and E451 interact with the substrate and this is essential for defining substrate specificity. Double mutants of Sfβgly (A451E39, S451E39 and S451N39) were prepared by site-directed mutagenesis, expressed in bacteria and purified using affinity chromatography. These enzymes were characterized using p-nitrophenyl β-galactoside and p-nitrophenyl β-fucoside as substrates. The k cat/Km ratio for single and double mutants of Sfβgly containing site-directed mutations at positions Q39 and E451 was used to demonstrate that the effect on the free energy of ES‡ (enzyme-transition state complex) of the double mutations (∆∆G‡xy) is not the sum of the effects resulting from the single mutations (∆∆G‡x and ∆∆G‡y). This difference in ∆∆G‡ indicates that the effects of the single mutations partially overlap. Hence, this common effect counts only once in ∆∆G‡xy. Crystallographic data on β-glycosidases reveal the presence of a bidentate hydrogen bond involving residues Q39 and E451 and the same hydroxyl group of the substrate. Therefore, both thermodynamic and crystallographic data suggest that residues Q39 and E451 exert a mutual influence on their respective interactions with the substrate.

Mesh adaptation on the sphere using optimal transport and the numerical solution of a Monge-Ampère type equation

An equation of Monge-Ampère type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistributed with respect to a monitor function. Optimal transport generates meshes that keep the same connectivity as the original mesh, making them suitable for r-adaptive simulations, in which the equations of motion can be solved in a moving frame of reference in order to avoid mapping the solution between old and new meshes and to avoid load balancing problems on parallel computers. The semi-implicit solution of the Monge-Ampère type equation involves a new linearisation of the Hessian term, and exponential maps are used to map from old to new meshes on the sphere. The determinant of the Hessian is evaluated as the change in volume between old and new mesh cells, rather than using numerical approximations to the gradients. OT meshes are generated to compare with centroidal Voronoi tesselations on the sphere and are found to have advantages and disadvantages; OT equidistribution is more accurate, the number of iterations to convergence is independent of the mesh size, face skewness is reduced and the connectivity does not change. However anisotropy is higher and the OT meshes are non-orthogonal. It is shown that optimal transport on the sphere leads to meshes that do not tangle. However, tangling can be introduced by numerical errors in calculating the gradient of the mesh potential. Methods for alleviating this problem are explored. Finally, OT meshes are generated using observed precipitation as a monitor function, in order to demonstrate the potential power of the technique.