Unified Approach to Stabilization of Waves on Compact Surfaces by Simultaneous Interior and Boundary Feedbacks of Unrestricted Growth

Let $\mathcal{M}\subset\mathbb{R}^{3}$ be an oriented compact surface on which we consider the system: $$\left \{ \begin{array}{l@{\quad}l} u_{tt} - \Delta_{\mathcal{M}} u + a(x)g_{0}(u_{t})=0 & \text{in } \mathcal{M}\times\mathopen{]} 0,\infty[ ,\\ \partial_{\nu_{co}}u +u + b(x)g(u_t)=0 & \text{on } \partial \mathcal {M}\times\mathopen{]}0,+\infty[. \end{array} \right . $$ If $\mathcal{M}$ along with the localizers a, b and the nonlinear feedbacks g,g ₀ satisfy certain conditions then uniform (but not necessarily exponential) decay rates of the finite energy of solutions can be established. We present a unified approach that bridges and extends a number of earlier results on stabilization of 2nd-order hyperbolic equations on manifolds. The methodology captures geometric requirements for damping acting simultaneously on subsets of the interior and of the boundary, and shows how placements of these feedbacks can complement each other depending on the underlying surface. In addition, the results conveniently incorporate the existing theory that allows elimination of geometric conditions from the controlled boundary (in absence of nearby interior damping), and elimination of damping entirely from certain boundary neighborhoods. The model also admits feedbacks that grow sub- or super-linearly not only at the origin, but also at infinity and demonstrates an interplay between the regularity of solutions and asymptotic energy decay rates.     

Analysis of ibuprofen enantiomers in rat plasma by liquid chromatography with tandem mass spectrometry

A sensitive and selective method for the analysis of ibuprofen enantiomers by LC–MS/MS was developed and validated for the purpose of application in pharmacokinetic studies in small experimental animals. Aliquots of 200 μL plasma were submitted to liquid–liquid extraction with hexane/diisopropylether (50:50 v/v) in acid pH. Separation was accomplished in a Chirex® 3005 (250 × 4.6 mm, 5 μm) column at 25°C with a mobile phase that consisted of 0.01 M ammonium acetate in methanol at a flow rate of 1.1 mL/min. The mass spectrometer consisted of an ESI interface operating at negative ionization mode and multiple reaction monitoring. The transitions 205 > 161 and 240 > 197 were monitored for ibuprofen enantiomers and fenoprofen (internal standard), respectively. Method validation included the evaluation of the matrix effect, stability, linearity, lower LOQ, within‐run and between‐run precision, and accuracy. The lower LOQ was 25 ng/mL for each ibuprofen enantiomer, and the calibration curves showed good linearity in the range 0.025–50 μg/mL. The method was successfully applied in the investigation of pharmacokinetic disposition of ibuprofen enantiomers in rats treated orally with 25 mg/kg of the racemate. Enantioselective kinetic disposition was observed with accumulation of (+)‐(S)‐ibuprofen in rats following single oral administration.     

Isolation ofTrypanosoma cruzi from blood by histopaque and continuous percoll gradient centrifugations

Separation of the blood forms of trypanosomes from the blood of infected animals is difficult, especially in the case of Trypanosoma cruzi Y strain. Two procedures to isolate the Y strain blood forms of T. cruzi using polyvinyl pyrrolidone-coated silica (percoll) and histopaque are reported in this study. The recovery rates of parasites were 16 +/- 5 and 68 +/- 16%, respectively. The parasites isolated by these methods presented normal motility and morphology and were infective to albino mice with prepatent periods, parasitemia curves, and polymorphism patterns during the infection that were similar to those of control parasites. In addition, the preservation of surface antigens was confirmed by immunocytochemical studies.     

Existence and uniform decay of the wave equation with nonlinear boundary damping and boundary memory source term

We consider the nonlinear model of the wave equation subject to the following nonlinear boundary conditions We show existence of solutions by means of Faedo-Galerkin method and the uniform decay is obtained by using the multiplier technique. Received: 15 June 2000 / Accepted: 4 December 2000 / Published online: 29 April 2002     

Parents’ Attitudes Toward Mathematics and the Influence on Their Students’ Attitudes toward Mathematics: A Quantitative Study

The purpose of this study was to investigate parents’ attitudes toward mathematics, their students' attitude toward mathematics, and the influence of the parents’ attitude on the students' attitude toward mathematics. Data analyses revealed statistically significant positive correlations between parents’ and students’ attitudes toward mathematics. Additionally, parents’ mathematics attitude significantly predicted students’ attitudes toward mathematics (n=146). By understanding the influence of parents’ attitudes on students’ attitudes toward mathematics, school efforts can be geared toward fostering favorable attitudes toward mathematics among parents.     

广义Bethe树上奇偶马尔可夫链场上的若干极限性质

通过构造两个非负鞅证明了一个强极限定理,然后把它应用到本文所定义的广义Bethe树上的奇偶马尔可夫链场上,从而获得了此马氏链场上的一类强极限定理.     

Oxidation of organotrifluoroborates via oxone

A method for the oxidation of organotrifluoroborates using Oxone was developed. A variety of aryl-, heteroaryl-, alkenyl-, and alkyltrifluoroborates were converted into the corresponding oxidized products in excellent yields. This method proved to be tolerant of a broad range of functional groups, and in secondary alkyl substrates it was demonstrated to be completely stereospecific.     

Compressibility study of quaternary phospholipid blend monolayers

The mechanical properties of liposome membranes are strongly dependent on type and ratio of lipid compounds, which can have important role in drug targeting and release processes when liposome is used as drug carrier. In this work we have used Brewster's angle microscopy to monitor the lateral compression process of lipid monolayers containing as helper lipids either distearoyl phosphatidylethanolamine (DSPE) or dioleoyl phophatidylethanolamine (DOPE) molecules on the Langmuir trough. The compressibility coefficient was determined for lipid blend monolayers containing the helper lipids above, cholesterol, distearoyl phosphatidylcholine (DSPC) and pegylated-DSPE at room temperature. Two variables, the cholesterol fraction and the ratio ρ between the helper lipid (either DSPE or DOPE) and the reference lipid DSPC, were studied by multivariate analysis to evaluate their impact on the compressibility coefficient of the monolayers. The cholesterol level was found to be the most significant variable for DSPE blends while the ratio ρ was the most significant one for DOPE blend monolayers. It was also found that these two variables can exhibit positive interaction and the same compressibility value can be obtained with different blend compositions.