Schwarzschild and de Sitter solutions from the argument by Lenz and Sommerfeld

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A note about the appearance of non-hyperbolic solutions in a mechanical pendulum system

The investigation of the behavior of a nonlinear system consists in the analysis of different stages of its motion, where the complexity varies with the proximity of a resonance region. Near this region the stability domain of the system undergoes sudden changes due basically to competition and interaction between periodic and saddle solutions inside the phase portrait, leading to the occurrence of the most different phenomena. Depending of the domain of the chosen control parameter, these events can reveal interesting geometric features of the system so that the phase portrait is not capable to express all them, since the projection of these solutions on the two-dimensional surface can hide some aspects of these events. In this work we will investigate the numerical solutions of a particular pendulum system close to a secondary resonance region, where we vary the control parameter in a restrict domain in order to draw a preliminary identification about what happens with this system. This domain includes the appearance of non-hyperbolic solutions where the basin of attraction in the center of the phase portrait diminishes considerably, almost disappearing, and afterwards its size increases with the direction of motion inverted. This phenomenon delimits a boundary between low and high frequency of the external excitation.

Effects of acetylsalicylic acid and acetic acid solutions on VX2 liver carcinoma in rabbits: in vivo analysis

OBJETIVO: Analisar os efeitos das soluções de aspirina e de ácido acético, in vivo, em fígado de coelhos portadores de tumor hepático VX2, verificando o efeito histolítico e anatomo-patológico das soluções e eventuais alterações bioquímicas hepáticas. MÉTODOS: Utilizou-se 48 coelhos, divididos em 2 protocolos experimentais(3 e 4), subdivididos em 3 grupos cada. Após 4 dias da implantação do tumor no fígado, procedeu-se a laparotomia mediana, com injeção de 0,4 ml da solução de aspirina (5,0%), de ácido acético (5,0%) e solução salina; o sacrifício ocorreu apos 24 horas (protocolo 3) e 11 dias (protocolo 4); avaliou-se o peso, evolução clinica, dosagens bioquímicas, cavidade abdominal e torácica e microscopia do fígado. RESULTADOS: Não foram observadas alterações na evolução clinica, peso e nas dosagens bioquímicas, apenas elevação da fosfatase alcalina no grupo controle do protocolo 4. Observamos desaparecimento do tumor em ambos os protocolos. CONCLUSÃO: As soluções de ácido acético e ácido acetilsalicílico acarretam destruição do tumor hepático experimental.

INTEGRATION OF THE NONLINEAR POISSON BOLTZMANN-EQUATION FOR CHARGED VESICLES IN ELECTROLYTIC SOLUTIONS

The Poisson-Boltzmann equation (PBE), with specific ion-surface interactions and a cell model, was used to calculate the electrostatic properties of aqueous solutions containing vesicles of ionic amphiphiles. Vesicles are assumed to be water- and ion-permeable hollow spheres and specific ion adsorption at the surfaces was calculated using a Volmer isotherm. We solved the PBE numerically for a range of amphiphile and salt concentrations (up to 0.1 M) and calculated co-ion and counterion distributions in the inside and outside of vesicles as well as the fields and electrical potentials. The calculations yield results that are consistent with measured values for vesicles of synthetic amphiphiles.

A general treatment for the conductivity of electrolytes in the whole concentration range in aqueous and nonaqueous solutions

Despite the great importance of ion transport, most of the widely accepted models and theories are valid only in the not very practical limit of low concentrations. Aiming to extend the range of applicability to moderate concentrations, a number of modified models and equations (some approximate, some fundamented on different assumptions, and some just empirical) have been reported. In this work, a general treatment for the electrical conductivity of ionic solutions has been developed, considering the electrical conductivity as a transport phenomenon governed by dissipation and feedback. A general expression for the dependence of the specific conductivity on the solution viscosity (and indirectly on concentration), from which the whole conductivity curve can be obtained, has been derived. The validity of this general approach is demonstrated with experimental results taken from the literature for aqueous and nonaqueous solutions of electrolytes.

On bifurcation and symmetry of solutions of symmetric nonlinear equations with odd-harmonic forcings

In this work we study existence, bifurcation, and symmetries of small solutions of the nonlinear equation Lx = N(x, p, epsilon) + mu f, which is supposed to be equivariant under the action of a group OHm, and where f is supposed to be OHm-invariant. We assume that L is a linear operator and N(., p, epsilon) is a nonlinear operator, both defined in a Banach space X, with values in a Banach space Z, and p, mu, and epsilon are small real parameters. Under certain conditions we show the existence of symmetric solutions and under additional conditions we prove that these are the only feasible solutions. Some examples of nonlinear ordinary and partial differential equations are analyzed. (C) 1995 Academic Press, Inc.

Behavior of plant tissue in osmotic solutions

The effect of the concentration of sucrose solutions on the cellular structure of potato tissue in equilibrium at 27 degreesC was Studied. Two different methods of investigation were used to determine the volume of the different phases composing the cellular tissue of the potato when in equilibrium with the solutions. one based on data of the concentration itself and the overall volume of 2 mm slices after 48 h at equilibrium, and the other on microscopic images of cells in thin slices of fresh tissue stained with neutral red after an hour in equilibrium to show protoplasts, vacuoles and plasmolysis spaces. The results of these methods were compared with those obtained by a predictive thermodynamic approach considering the semipermeability of cell membranes. Phase volume data obtained from microscopic analysis were more similar to what was predicted by the theoretical model than those obtained by means of composition measurement. where the long equilibrium time apparently led to the loss of semi permeability of the cell membranes, since total volumes calculated without consideration of the cell membranes were similar to those measured. This suggests that the length of time of osmotic dehydration brings about a change in cell structure and the consequent involvement of a different mechanism in mass transfer. (C) 2002 Elsevier B.V. Ltd. All rights reserved.

Nonlinear dynamics of short traveling capillary-gravity waves

We establish a Green-Nagdhi model equation for capillary-gravity waves in (2+1) dimensions. Through the derivation of an asymptotic equation governing short-wave dynamics, we show that this system possesses (1 + 1) traveling-wave solutions for almost all the values of the Bond number θ (the special case θ=1/3 is not studied). These waves become singular when their amplitude is larger than a threshold value, related to the velocity of the wave. The limit angle at the crest is then calculated. The stability of a wave train is also studied via a Benjamin-Feir modulational analysis. ©2005 The American Physical Society.

Evaluation of electrical conductivity, pH and refractive index as physico-chemical parameters for quality control of Aveloz homeopathic solutions

Euphorbia tirucalli Lineu (Aveloz) belongs to the family Euphorbiaceae and is used in the treatment of cancer and warts. Some studies have reported that phorbol esters are the active principles responsible for the antitumor activity of Aveloz. The production of these molecules occurs in greater quantity in May, during the morning. This study aimed to evaluate whether the physico-chemical parameters of Aveloz homeopathic aqueous solutions such as pH, electrical conductivity and refractive index change due to storage time. Such parameters were measured regularly for 180 days. All solutions were prepared according to the method of grinding with lactose and subsequent dissolution in aqueous medium, as described in the Brazilian Homeopathic Pharmacopoeia, using as starting point the Aveloz latex collected in May. Homeopathic aqueous solutions containing only lactose were also prepared and evaluated as a control group. The potencies that were analyzed for electrical conductivity, pH and refractive index were: 4cH, 7cH, 9cH, 12cH, 14cH, 15cH, 29cH, 30cH. As a result, we found out that there was only statistical difference (p=0.035) in electrical conductivity between the homeopathic solutions containing Aveloz and the homeopathic solutions without Aveloz, when 15cH potency was compared. We also observed that the electrical conductivity increased with the aging of the solutions but is not directly related to the pH or the refractive index of the solutions, indicating that the aging process may alter the electrical conductivity of the homeopathic medicines. The presence of gas inside the glass that stores these solutions may affect the electrical conductivity measurements. Finally, no statistically significant difference was observed (p> 0.05) in the pH and refractive index.

Absolute continuity and existence of solutions to dynamic inclusions in time scales

We provide some properties for absolutely continuous functions in time scales. Then we consider a class of dynamical inclusions in time scales and extend to this class a convergence result of a sequence of almost inclusion trajectories to a limit which is actually a trajectory of the inclusion in question. We also introduce the so called Euler solution to dynamical systems in time scales and prove its existence. A combination of the existence of Euler solutions with the compactness type result described above ensures the existence of an actual trajectory for the dynamical inclusion when the setvalued vector field is nonempty, compact, convex and has closed graph. © 2012 Springer-Verlag.

Rheological behavior of binary aqueous solutions of poly(ethylene glycol) of 1500 g·mol-1 as affected by temperature and polymer concentration

The rheological behavior of poly(ethylene glycol) of 1500 g·mol -1(PEG1500) aqueous solutions with various polymer concentrations (w = 0.05, 0.10, 0.15, 0.20 and 0.25) was studied at different temperatures (T = 283.15, 288.15, 293.15, 298.15 and 303.15) K. The analyses were carried out considering shear rates ranging from (20 to 350) s-1, using a cone-and-plate rheometer under controlled stress and temperature. Classical rheological models (Newton, Bingham, Power Law, Casson, and Herschel-Bulkley) were tested. The Power Law model was shown suitable to mathematically represent the rheological behavior of these solutions. Well-adjusted empirical models were derived for consistency index variations in function of temperature (Arrhenius-type model; R2 > 0.96), polymer concentration (exponential model; R2 > 0.99) or the combination of both (R 2 > 0.99). Additionally, linear models were used to represent the variations of behavior index in the functions of temperature (R2 > 0.83) and concentration (R2 > 0.87). © 2013 American Chemical Society.

On certain new exact solutions of a diffusive predator-prey system

We construct exact solutions for a system of two coupled nonlinear partial differential equations describing the spatio-temporal dynamics of a predator-prey system where the prey per capita growth rate is subject to the Allee effect. Using the G'/G expansion method, we derive exact solutions to this model for two different wave speeds. For each wave velocity we report three different forms of solutions. We also discuss the biological relevance of the solutions obtained. © 2012 Elsevier B.V.

Mineral loss and color change of enamel after bleaching and staining solutions combination

Pigments of food and beverages could affect dental bleaching efficacy. The aim of this investigation was to evaluate color change and mineral loss of tooth enamel as well as the influence of staining solutions normally used by adolescent patients undergoing home bleaching. Initial hardness and baseline color were measured on enamel blocks. Specimens were divided into five groups (n = 5): G1 (control) specimens were kept in artificial saliva throughout the experiment (3 weeks); G2 enamel was exposed to 10% carbamide peroxide for 6 h daily, and after this period, the teeth were cleaned and stored in artificial saliva until the next bleaching session; and G3, G4, and G5 received the same treatments as G2, but after bleaching, they were stored for 1 h in cola soft drink, melted chocolate, or red wine, respectively. Mineral loss was obtained by the percentage of hardness reduction, and color change was determined by the difference between the data obtained before and after treatments. Data were subjected to analysis of variance and Fisher's test (a = 0.05). G3 and G5 showed higher mineral loss (92.96 +/- 5.50 and 94.46 +/- 1.00, respectively) compared to the other groups (p = 0.05). G5 showed high-color change (9.34 +/- 2.90), whereas G1 presented lower color change (2.22 +/- 0.44) (p = 0.05). Acidic drinks cause mineral loss of the enamel, which could modify the surface and reduce staining resistance after bleaching. (C) 2013 Society of Photo-Optical Instrumentation Engineers (SPIE)

Corrosion kinetics and topography analysis of Ti-6Al-4V alloy subjected to different mouthwash solutions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Periodic solutions of el nino model through the vallis differential system

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)