Boundedness of solutions of retarded functional differential equations with variable impulses via generalized ordinary differential equations

In this paper, we give sufficient conditions for the uniform boundedness and uniform ultimate boundedness of solutions of a class of retarded functional differential equations with impulse effects acting on variable times. We employ the theory of generalized ordinary differential equations to obtain our results. As an example, we investigate the boundedness of the solution of a circulating fuel nuclear reactor model.

GROUND STATE AND NON-GROUND STATE SOLUTIONS OF SOME STRONGLY COUPLED ELLIPTIC SYSTEMS

We study an elliptic system of the form Lu = vertical bar v vertical bar(p-1) v and Lv = vertical bar u vertical bar(q-1) u in Omega with homogeneous Dirichlet boundary condition, where Lu := -Delta u in the case of a bounded domain and Lu := -Delta u + u in the cases of an exterior domain or the whole space R-N. We analyze the existence, uniqueness, sign and radial symmetry of ground state solutions and also look for sign changing solutions of the system. More general non-linearities are also considered.

Size-dependent phase transitions in nanostructured zirconia-scandia solid solutions

The dependences of phase stability and solid state phase transitions on the crystallite size in ZrO2-10, 12 and 14 mol% Sc2O3 nanopowders are investigated by X-ray powder diffraction using a synchrotron source (S-XPD). The average crystallite sizes lie within the range of 35 to 100 nm, approximately. At room temperature these solid solutions were previously characterised as mixtures of a cubic phase and one or two rhombohedral phases, beta and gamma, with their fractions depending on composition and average crystallite sizes. In this study, it is shown that at high temperatures these solid solutions become cubic single-phased. The size-dependent temperatures of the transitions from the rhombohedral phases to the cubic phase at high temperature are determined through the analyses of a number of S-XPD patterns. These transitions were studied on cooling and on heating, exhibiting hysteresis effects whose relevant features are size and composition dependent.

Invariant Solutions of Richards' Equation for Water Movement in Dissimilar Soils

Scaling methods allow a single solution to Richards' equation (RE) to suffice for numerous specific cases of water flow in unsaturated soils. During the past half-century, many such methods were developed for similar soils. In this paper, a new method is proposed for scaling RE for a wide range of dissimilar soils. Exponential-power (EP) functions are used to reduce the dependence of the scaled RE on the soil hydraulic properties. To evaluate the proposed method, the scaled RE was solved numerically considering two test cases: infiltration into relatively dry soils having initially uniform water content distributions, and gravity-dominant drainage occurring from initially wet soil profiles. Although the results for four texturally different soils ranging from sand to heavy clay (adopted from the UNSODA database) showed that the scaled solution were invariant for a wide range of flow conditions, slight deviations were observed when the soil profile was initially wet in the infiltration case or deeply wet in the drainage case. The invariance of the scaled RE makes it possible to generalize a single solution of RE to many dissimilar soils and conditions. Such a procedure reduces the numerical calculations and provides additional opportunities for solving the highly nonlinear RE for unsaturated water flow in soils.

Exact cosmological solutions of models with an interacting dark sector

In this work we extend the first order formalism for cosmological models that present an interaction between a fermionic and a scalar field. Cosmological exact solutions describing universes filled with interacting dark energy and dark matter have been obtained. Viable cosmological solutions with an early period of decelerated expansion followed by late acceleration have been found, notably one which presents a dark matter component dominating in the past and a dark energy component dominating in the future. In another one, the dark energy alone is the responsible for both periods, similar to a Chaplygin gas case. Exclusively accelerating solutions have also been obtained.

Comparative experimental study of myocardial protection with crystalloid solutions for heart transplantation

Background: There is a growing need to improve myocardial protection, which will lead to better performance of cardiac operations and reduce morbidity and mortality. Therefore, the objective of this study was to compare the efficacy of myocardial protection solution using both intracellular and extracellular crystalloid type regarding the performance of the electrical conduction system, left ventricular contractility and edema, after being subjected to ischemic arrest and reperfusion. Methods: Hearts isolated from male Wistar (n=32) rats were prepared using Langendorff method and randomly divided equally into four groups according the cardioprotective solutions used Krebs-Henseleit-Buffer (KHB), Bretschneider-HTK (HTK), St. Thomas-1 (STH-1) and Celsior (CEL). After stabilization with KHB at 37 degrees C, baseline values (control) were collected for heart rate (HR), left ventricle systolic pressure (LVSP), maximum first derivate of rise left ventricular pressure (+dP/dt), maximum first derivate of fall left ventricular pressure (-dP/dt) and coronary flow (CF). The hearts were then perfused at 10 degrees C for 5 min and kept for 2 h in static ischemia at 20 degrees C in each cardioprotective solution. Data evaluation was done using analysis of variance in completely randomized One-Way ANOVA and Tukey's test for multiple comparisons. The level of statistical significance chosen was P<0.05. Results: HR was restored with all the solutions used. The evaluation of left ventricular contractility (LVSP, +dP/dt and -dP/dt) showed that treatment with CEL solution was better compared to other solutions. When analyzing the CF, the HTK solution showed better protection against edema. Conclusion: Despite the cardioprotective crystalloid solutions studied are not fully able to suppress the deleterious effects of ischemia and reperfusion in the rat heart, the CEL solution had significantly higher results followed by HTK>KHB>STH-1.

Antimicrobial effect of endodontic solutions used as final irrigants on a dentine biofilm model

Aim To evaluate the residual biovolume of live bacterial cells, the mean biofilm thickness and the substratum coverage found in mixed biofilms treated with different endodontic irrigant solutions. Methodology Twenty-five bovine dentine specimens were infected intraorally using a removable orthodontic device. Five samples were used for each irrigant solution: 2% chlorhexidine, 1% sodium hypochlorite (NaOCl), 10% citric acid, 17% EDTA and distilled water. The solutions were used for 5 min. The samples were stained using the Live/Dead technique and evaluated using a confocal microscope. Differences in the amount of total biovolume (mu m3), number of surviving cells (mu m3), mean biofilm thickness (mu m) and substratum coverage (%) of the treated biofilms were determined using nonparametric statistical tests (P < 0.05). Results Similar values of biovolume total, biovolume of live subpopulations and substratum coverage were found in 2% chlorhexidine, 10% citric acid, 17% EDTA and distilled water-treated biofilms (P > 0.05). The lower values of the studied parameters were found in 1% NaOCl-treated dentine (P < 0.05) with the exception of the mean biofilm height criteria that did not reveal significant differences amongst the irrigant solutions (P > 0.05). Conclusions One per cent sodium hypochlorite was the only irrigant that had a significant effect on biofilm viability and architecture.

Periodic solutions of abstract neutral functional differential equations

We characterize the existence of periodic solutions of some abstract neutral functional differential equations with finite and infinite delay when the underlying space is a UMD space. (C) 2011 Elsevier Inc. All rights reserved.

Comparison of lung preservation solutions in human lungs using an ex vivo lung perfusion experimental model

OBJECTIVE: Experimental studies on lung preservation have always been performed using animal models. We present ex vivo lung perfusion as a new model for the study of lung preservation. Using human lungs instead of animal models may bring the results of experimental studies closer to what could be expected in clinical practice. METHOD: Brain-dead donors whose lungs had been declined by transplantation teams were used. The cases were randomized into two groups. In Group 1, Perfadex (R) was used for pulmonary preservation, and in Group 2, LPDnac, a solution manufactured in Brazil, was used. An ex vivo lung perfusion system was used, and the lungs were ventilated and perfused after 10 hours of cold ischemia. The extent of ischemic-reperfusion injury was measured using functional and histological parameters. RESULTS: After reperfusion, the mean oxygenation capacity was 405.3 mmHg in Group 1 and 406.0 mmHg in Group 2 (p=0.98). The mean pulmonary vascular resistance values were 697.6 and 378.3 dyn.s.cm(-5), respectively (p=0.035). The mean pulmonary compliance was 46.8 cm H2O in Group 1 and 49.3 ml/cm H2O in Group 2 (p=0.816). The mean wet/dry weight ratios were 2.06 and 2.02, respectively (p=0.87). The mean Lung Injury Scores for the biopsy performed after reperfusion were 4.37 and 4.37 in Groups 1 and 2, respectively (p=1.0), and the apoptotic cell counts were 118.75/mm(2) and 137.50/mm(2), respectively (p=0.71). CONCLUSION: The locally produced preservation solution proved to be as good as Perfadex (R). The clinical use of LPDnac may reduce costs in our centers. Therefore, it is important to develop new models to study lung preservation.

MULTIPLICITY OF NONRADIAL SOLUTIONS FOR A CLASS OF QUASILINEAR EQUATIONS ON ANNULUS WITH EXPONENTIAL CRITICAL GROWTH

In this paper, we establish the existence of many rotationally non-equivalent and nonradial solutions for the following class of quasilinear problems (p) {-Delta(N)u = lambda f(vertical bar x vertical bar, u) x is an element of Omega(r), u > 0 x is an element of Omega(r), u = 0 x is an element of Omega(r), where Omega(r) = {x is an element of R-N : r < vertical bar x vertical bar < r + 1}, N >= 2, N not equal 3, r >0, lambda > 0, Delta(N)u = div(vertical bar del u vertical bar(N-2)del u) is the N-Laplacian operator and f is a continuous function with exponential critical growth.

Evidence of the participation of electronic excited states in the mechanism of positronium formation in substitutional Tb1-xEux(dpm)(3) solid solutions studied by optical and positron annihilation spectroscopies

Positronium formation in the bimary molecular solid solutions Tb1-xEux (dpm)(3) (dpm = dipivaloylmethanate) has been investigated. A strong linear correlation between the D-5(4) Tb(III) energy level excited state lifetime and the positronium formation probability has been observed. This correlation indicates that the ligand-to-metal charge transfer LMCT states act in both luminescence quenching and positronium formation inhibition, as previously proposed. A kinetic mechanism is proposed to explain this correlation and shows that excited electronic states have a very important role in the positronium formation mechanism.

A NOTE ON THE UNIQUENESS OF SOLUTIONS FOR THE YAMABE PROBLEM

Using recent results on the compactness of the space of solutions of the Yamabe problem, we show that in conformal classes of metrics near the class of a nondegenerate solution which is unique (up to scaling) the Yamabe problem has a unique solution as well. This provides examples of a local extension, in the space of conformal classes, of a well-known uniqueness criterion due to Obata.

MULTI-BUMP SOLUTIONS FOR A CLASS OF QUASILINEAR EQUATIONS ON R

This paper is concerned with the existence of multi-bump solutions to a class of quasilinear Schrodinger equations in R. The proof relies on variational methods and combines some arguments given by del Pino and Felmer, Ding and Tanaka, and Sere.

Multibrane solutions in cubic superstring field theory

Using the elements of the so-called KBc gamma subalgebra, we study a class of analytic solutions depending on a single function F(K) in the modified cubic superstring field theory. We compute the energy associated to these solutions and show that the result can be expressed in terms of a contour integral. For a particular choice of the function F(K), we show that the energy is given by integer multiples of a single D-brane tension.

Existence of Solutions for Abstract Non-Autonomous Neutral Differential Equations

In this paper we discuss the existence of mild and classical solutions for a class of abstract non-autonomous neutral functional differential equations. An application to partial neutral differential equations is considered.