Non-covalent hydrogels of cyclodextrins and poloxamines for the controlled release of proteins

Different types of gels were prepared by combining poloxamines (Tetronic), i.e. poly(ethylene oxide)/poly(propylene oxide) (PEO/PPO) octablock star copolymers, and cyclodextrins (CD). Two different poloxamines with the same molecular weight (ca. 7000) but different molecular architectures were used. For each of their four diblock arms, direct Tetronic 904 presents PEO outer blocks while in reverse Tetronic 90R4 the hydrophilic PEO blocks are the inner ones. These gels were prepared by combining alpha-CD and poloxamine aqueous solutions. The physicochemical properties of these systems depend on several factors such as the structure of the block copolymers and the Tetronic/alpha-CD ratio. These gels were characterized using differential scanning calorimetry (DSC), viscometry and X-ray diffraction measurements. The 90R4 gels present a consistency that makes them suitable for sustained drug delivery. The resulting gels were easily eroded: these complexes were dismantled when placed in a large amount of water, so controlled release of entrapped large molecules such as proteins (Bovine Serum Albumin, BSA) is feasible and can be tuned by varying the copolymer/CD ratio. 

Solutions of fourth-order parabolic equation modeling thin film growth

In this paper we study the well-posedness for a fourth-order parabolic equation modeling epitaxial thin film growth. Using Kato's Method [1], [2] and [3] we establish existence, uniqueness and regularity of the solution to the model, in suitable spaces, namelyC⁰([0,T];L^p(Ω)) where  with 1<α<2, n∈N and n≥2. We also show the global existence solution to the nonlinear parabolic equations for small initial data. Our main tools are L_p–L_q-estimates, regularization property of the linear part of e^−tΔ2 and successive approximations. Furthermore, we illustrate the qualitative behavior of the approximate solution through some numerical simulations. The approximate solutions exhibit some favorable absorption properties of the model, which highlight the stabilizing effect of our specific formulation of the source term associated with the upward hopping of atoms. Consequently, the solutions describe well some experimentally observed phenomena, which characterize the growth of thin film such as grain coarsening, island formation and thickness growth.

Exact and numerical solutions for diffusio-reaction equations with convection term

Esta dissertação estuda essencialmente dois problemas: (A) uma classe de equações unidimensionais de reacção-difusão-convecção em meios não uniformes (dependentes do espaço), e (B) um problema elíptico não-linear e paramétrico ligado a fenómenos de capilaridade. A Análise de Perturbação Singular e a dinâmica de Hamilton-Jacobi são utilizadas na obtenção de expressões assimptóticas para a solução (com comportamento de frente) e para a sua velocidade de propagação. Os seguintes três métodos de decomposição, Adomian Decomposition Method (ADM), Decomposition Method based on Infinite Products (DIP), e New Iterative Method (NIM), são apresentados e brevemente comparados. Adicionalmente, condições suficientes para a convergência da solução em série, obtida pelo ADM, e uma aplicação a um problema da Telecomunicações por Fibras Ópticas, envolvendo EDOs não-lineares designadas equações de Raman, são discutidas. Um ponto de vista mais abrangente que unifica os métodos de decomposição referidos é também apresentado. Para subclasses desta EDP são obtidas soluções numa forma explícita, para diferentes tipos de dados e usando uma variante do método de simetrias de Bluman-Cole. Usando Teoria de Pontos Críticos (o teorema usualmente designado mountain pass) e técnicas de truncatura, prova-se a existência de duas soluções não triviais (uma positiva e uma negativa) para o problema elíptico não-linear e paramétrico (B). A existência de uma terceira solução não trivial é demonstrada usando Grupos Críticos e Teoria de Morse.

Non-linear analysis of composite structures with integrated piezoelectric sensors and actuators

This paper deals with the geometrically non linear analysis of thin plate/shell laminated structures with embedded integrated piezoelectric actuors or sensors layers and/or patches.The model is based on the Kirchhoff classical laminated theory and can be applied to plate and shell adaptive structures with arbitrary shape, general mechanical and electrical loadings. the finite element model is a nonconforming single layer triangular plate/shell element with 18 degrees of fredom for the generalized displacements and one eçlectrical potential degree of freedom for each piezoelectric layer or patch. An updated Lagrangian formulation associated to Newton-Raphson technique is used to solve incrementally and iteratively the equilibrium equation.The model is applied in the solution of four illustrative cases, and the results are compared and discussedwith alternative solutions when available.

Positive radial solutions of the Dirichlet problem for the Minkowski-Curvature equation in a ball

We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation { -div(del upsilon/root 1-vertical bar del upsilon vertical bar(2)) in B-R, upsilon=0 on partial derivative B-R,B- where B-R is a ball in R-N (N >= 2). According to the behaviour off = f (r, s) near s = 0, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.

On the system of rational difference equations x(n) = A+(1)over-bar y(n-p), y(n) = A+(gamma(n-1))over-bar x(n-r)y(n-5)

In this paper, we study the behavior of the positive solutions of the system of two difference equations [GRAPHICS] where p >= 1, r >= 1, s >= 1, A >= 0, and x(1-r), x(2-r),..., x(0), y(1-max) {p.s},..., y(0) are positive real numbers. (c) 2005 Elsevier Inc. All rights reserved.

Solutions of a two-dimensional dam-break problem

Solutions of a two-dimensional dam break problem are presented for two tailwater/reservoir height ratios. The numerical scheme used is an extension of one previously given by the author [J. Hyd. Res. 26(3), 293–306 (1988)], and is based on numerical characteristic decomposition. Thus approximate solutions are obtained via linearised problems, and the method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids non-physical, spurious oscillations.

On wave action and phase in the non-canonical Hamiltonian formulation

The long time–evolution of disturbances to slowly–varying solutions of partial differential equations is subject to the adiabatic invariance of the wave action. Generally, this approximate conservation law is obtained under the assumption that the partial differential equations are derived from a variational principle or have a canonical Hamiltonian structure. Here, the wave action conservation is examined for equations that possess a non–canonical (Poisson) Hamiltonian structure. The linear evolution of disturbances in the form of slowly varying wavetrains is studied using a WKB expansion. The properties of the original Hamiltonian system strongly constrain the linear equations that are derived, and this is shown to lead to the adiabatic invariance of a wave action. The connection between this (approximate) invariance and the (exact) conservation laws of pseudo–energy and pseudomomentum that exist when the basic solution is exactly time and space independent is discussed. An evolution equation for the slowly varying phase of the wavetrain is also derived and related to Berry's phase.

Solutions of the fully compressible semi-geostrophic system

The fully compressible semi-geostrophic system is widely used in the modelling of large-scale atmospheric flows. In this paper, we prove rigorously the existence of weak Lagrangian solutions of this system, formulated in the original physical coordinates. In addition, we provide an alternative proof of the earlier result on the existence of weak solutions of this system expressed in the so-called geostrophic, or dual, coordinates. The proofs are based on the optimal transport formulation of the problem and on recent general results concerning transport problems posed in the Wasserstein space of probability measures.

Numerical analyses of Runge–Kutta implicit–explicit schemes for horizontally explicit, vertically implicit solutions of atmospheric models

With the prospect of exascale computing, computational methods requiring only local data become especially attractive. Consequently, the typical domain decomposition of atmospheric models means horizontally-explicit vertically-implicit (HEVI) time-stepping schemes warrant further attention. In this analysis, Runge-Kutta implicit-explicit schemes from the literature are analysed for their stability and accuracy using a von Neumann stability analysis of two linear systems. Attention is paid to the numerical phase to indicate the behaviour of phase and group velocities. Where the analysis is tractable, analytically derived expressions are considered. For more complicated cases, amplification factors have been numerically generated and the associated amplitudes and phase diagnosed. Analysis of a system describing acoustic waves has necessitated attributing the three resultant eigenvalues to the three physical modes of the system. To do so, a series of algorithms has been devised to track the eigenvalues across the frequency space. The result enables analysis of whether the schemes exactly preserve the non-divergent mode; and whether there is evidence of spurious reversal in the direction of group velocities or asymmetry in the damping for the pair of acoustic modes. Frequency ranges that span next-generation high-resolution weather models to coarse-resolution climate models are considered; and a comparison is made of errors accumulated from multiple stability-constrained shorter time-steps from the HEVI scheme with a single integration from a fully implicit scheme over the same time interval. Two schemes, “Trap2(2,3,2)” and “UJ3(1,3,2)”, both already used in atmospheric models, are identified as offering consistently good stability and representation of phase across all the analyses. Furthermore, according to a simple measure of computational cost, “Trap2(2,3,2)” is the least expensive.

Antimicrobial Photodynamic Therapy in the Non-Surgical Treatment of Aggressive Periodontitis: Cytokine Profile in Gingival Crevicular Fluid, Preliminary Results

Background: Aggressive periodontitis is a specific form of periodontal disease that is characterized by rapid attachment loss and bone destruction. Cytokine profiles are of considerable value when studying disease course during treatment. The aim of this trial was to investigate cytokine levels in the gingival crevicular fluid (GCF) of patients with aggressive periodontitis, after treatment with photodynamic therapy (PDT) or scaling and root planing (SRP), in a split-mouth design on -7, 0, +1, +7, +30, and +90 days. Methods: Ten patients were randomly treated with PDT using a laser source associated with a photosensitizer or SRP with hand instruments. GCF samples were collected, and the concentrations of tumor necrosis factor-alpha (TNF-alpha) and receptor activator of nuclear factor-kappa B ligand (RANKL) were determined by enzyme-linked immunosorbent assays. The data were analyzed using generalized estimating equations to test the associations among treatments, evaluated parameters, and experimental times (alpha = 0.05). Results: Non-surgical periodontal treatment with PDT or SRP led to statistically significant reductions in TNF-alpha level 30 days following treatment. There were similar levels of TNF-alpha and RANKL at the different time points in both groups, with no statistically significant differences. Conclusion: SRP and PDT had similar effects on crevicular TNF-alpha and RANKL levels in patients with aggressive periodontitis. J Periodontol 2009;80:98-105.

Soliton solutions for quasilinear Schrodinger equations with critical growth

In this paper we establish the existence of standing wave solutions for quasilinear Schrodinger equations involving critical growth. By using a change of variables, the quasilinear equations are reduced to semilinear one. whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration-compactness principle due to P.L. Lions together with some classical arguments used by H. Brezis and L. Nirenberg (1983) in [9]. (C) 2009 Elsevier Inc. All rights reserved.

Some exact solutions of the Dirac equation

Exact analytic solutions are found to the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic potentials, with the scalar part dominating, can be chosen to give exact analytic Dirac wave functions.

Non-relativistic spacetimes with cosmological constant

Recent data on supernovae favour high values of the cosmological constant. Spacetimes with a cosmological constant have non-relativistic kinematics quite different from Galilean kinematics. de Sitter spacetimes, vacuum solutions of Einstein's equations with a cosmological constant, reduce in the non-relativistic limit to Newton-Hooke spacetimes, which are non-metric homogeneous spacetimes with non-vanishing curvature. The whole non-relativistic kinematics would then be modified, with possible consequences to cosmology, and in particular to the missing-mass problem.

Vertex operators and soliton solutions of affine Toda model with U(2) symmetry

The symmetry structure of the non-Abelian affine Toda model based on the coset SL(3)/SL(2) circle times U(1) is studied. It is shown that the model possess non-Abelian Noether symmetry closing into a q-deformed SL(2) circle times U(1) algebra. Specific two-vertex soliton solutions are constructed.