Self-interacting scalar field cosmologies: unified exact solutions and symmetries

We investigate a mechanism that generates exact solutions of scalar field cosmologies in a unified way. The procedure investigated here permits to recover almost all known solutions, and allows one to derive new solutions as well. In particular, we derive and discuss one novel solution defined in terms of the Lambert function. The solutions are organised in a classification which depends on the choice of a generating function which we have denoted by x(phi) that reflects the underlying thermodynamics of the model. We also analyse and discuss the existence of form-invariance dualities between solutions. A general way of defining the latter in an appropriate fashion for scalar fields is put forward.

Reversible Photorheology in Solutions of Cetyltrimethylammonium Bromide, Salicylic Acid, and trans-2,4,4 '-Trihydroxychalcone

We show photorheology in aqueous solutions of weakly entangled wormlike micelles prepared with cetyltrimethylammonium bromide (CTAB), salicylic acid (HSal), and dilute amounts of the photochromic multistate compound trans-2,4,4'-trihydroxychalcone (Ct). Different chemical species of Ct are associated with different colorations and propensities to reside within or outside CTAB micelles. A light-induced transfer between the intra- and intermicellar space is used to alter the mean length of wormlike micelles and hence the rheological properties of the fluid, studied in steady-state shear Bow and in dynamic rheological measurements. Light-induced changes of fluid rheology are reversible by a the relaxation process. at relaxation rates which depend on pH and which are consistent with photochromic reversion rates measured by UV-vis absorption spectroscopy. Parameterizing viscoelostic rheological states by their effective relaxation time tau(c) and corresponding response modulus G(c), we find the light and dark states of the system to fall onto a characteristic state curve defined by comparable experiments conducted without photosensitive components. These reference experiments were prepared with the same concentration of CTAB, but different concentrations of HSal or sodium salicylote (NaSal), and tested at different temperatures.

Solutions of second-order and fourth-order ODEs on the half-line

We start by studying the existence of positive solutions for the differential equation u '' = a(x)u - g(u), with u ''(0) = u(+infinity) = 0, where a is a positive function, and g is a power or a bounded function. In other words, we are concerned with even positive homoclinics of the differential equation. The main motivation is to check that some well-known results concerning the existence of homoclinics for the autonomous case (where a is constant) are also true for the non-autonomous equation. This also motivates us to study the analogous fourth-order boundary value problem {u((4)) - cu '' + a(x)u = vertical bar u vertical bar(p-1)u u'(0) = u'''(0) = 0, u(+infinity) = u'(+infinity) = 0 for which we also find nontrivial (and, in some instances, positive) solutions.

Positive Solutions of the Dirichlet Problem for the One-dimensional Minkowski-Curvature Equation

We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation-(u' / root 1 - u'(2))' = f(t, u). Depending on the behaviour of f = f(t, s) near s = 0, we prove the existence of either one, or two, or three, or infinitely many positive solutions. In general, the positivity of f is not required. All results are obtained by reduction to an equivalent non-singular problem to which variational or topological methods apply in a classical fashion.

Coordination Chemistry of the (eta(6)-p-Cymene)ruthenium(II) Fragment with Bis-, Tris-, andTetrakis(pyrazol-1-yl)borate Ligands: Synthesis, Structural, Electrochemical, and CatalyticDiastereoselective Nitroaldol Reaction Studies

Novel [Ru(eta(6)-p-cymene)(kappa(2)-L)X] and [Ru(eta(6)-p-cymene)(kappa(3)-L)]X center dot nH(2)O complexes (L = bis-, tris-, or tetrakis-pyrazolylborate; X = Cl, N-3, PF6, or CF3SO3) are prepared by treatment of [Ru(eta(6)-p-cymene)Cl-2](2) with poly-(pyrazolyl)borate derivatives [M(L)] (L in general; in detail L = Ph(2)Bp = diphenylbis-(pyrazol-1-yl)borate; L = Tp = hydrotris(pyrazol-1-yl)borate; L = pzTp = tetrakis(pyrazol-1-yl)borate; L = Tp(4Bo) = hydrotris(indazol-1-yl)borate, L = T-p4Bo,T-5Me = (5-methylindazol-1-yl)borate; L = Tp(Bn,4Ph) = hydrotris(3-benzyl-4-phenylpyrazol-1-yl)borate; M = Na, K, or TI) and characterized by analytical and spectral data (IR, ESIMS, H-1 and C-13 NMR). The structures of [Ru(eta(6)-p-cymene)(Ph(2)Bp)Cl] (1) and [Ru(eta(6)-p-cymene)(Tp)Cl] (3) have been established by single-crystal X-ray diffraction analysis. Electrochemical studies allowed comparing the electron-donor characters of Tp and related ligands and estimating the corresponding values of the Lever E-L ligand parameter. The complexes [Ru(eta(6)-p-cymene)-(kappa(2)-L)X] and [Ru(eta(6)-p-cymene)(kappa(3)-L)]X center dot nH(2)O act as catalyst precursors for the diastereoselective nitroaldol reaction of benzaldehyde and nitroethane to the corresponding beta-nitroalkanol (up to 82% yield, at room temperature) with diastereoselectivity toward the formation of the threo isomer.

Positive solutions of fourth order problems with clamped beam boundary conditions

n this paper we make an exhaustive study of the fourth order linear operator u((4)) + M u coupled with the clamped beam conditions u(0) = u(1) = u'(0) = u'(1) = 0. We obtain the exact values on the real parameter M for which this operator satisfies an anti-maximum principle. Such a property is equivalent to the fact that the related Green's function is nonnegative in [0, 1] x [0, 1]. When M < 0 we obtain the best estimate by means of the spectral theory and for M > 0 we attain the optimal value by studying the oscillation properties of the solutions of the homogeneous equation u((4)) + M u = 0. By using the method of lower and upper solutions we deduce the existence of solutions for nonlinear problems coupled with this boundary conditions. (C) 2011 Elsevier Ltd. All rights reserved.

Comparative study of amine solutions used in CO2 absorption/desorption cycles

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia Química

Detection and diagnosis solutions for fault-tolerant VSI

This paper presents solutions for fault detection and diagnosis of two-level, three phase voltage-source inverter (VSI) topologies with IGBT devices. The proposed solutions combine redundant standby VSI structures and contactors (or relays) to improve the fault-tolerant capabilities of power electronics in applications with safety requirements. The suitable combination of these elements gives the inverter the ability to maintain energy processing in the occurrence of several failure modes, including short-circuit in IGBT devices, thus extending its reliability and availability. A survey of previously developed fault-tolerant VSI structures and several aspects of failure modes, detection and isolation mechanisms within VSI is first discussed. Hardware solutions for the protection of power semiconductors with fault detection and diagnosis mechanisms are then proposed to provide conditions to isolate and replace damaged power devices (or branches) in real time. Experimental results from a prototype are included to validate the proposed solutions.

Benchmark exact solutions for the static analysis of multi-layered piezoelectric composite using PVDF

The three-dimensional (3D) exact solutions developed in the early 1970s by Pagano for simply supported multilayered orthotropic composite plates and later in the 1990s extended to piezoelectric plates by Heyliger have been extremely useful in the assessment and development of advanced laminated plate theories and related finite element models. In fact, the well-known test cases provided by Pagano and by Heyliger in those earlier works are still used today as benchmark solutions. However, the limited number of test cases whose 3D exact solutions have been published has somewhat restricted the assessment of recent advanced models to the same few test cases. This work aims to provide additional test cases to serve as benchmark exact solutions for the static analysis of multilayered piezoelectric composite plates. The method introduced by Heyliger to derive the 3D exact solutions has been successfully implemented using symbolic computing and a number of new test cases are here presented thoroughly. Specifically, two multilayered plates using PVDF piezoelectric material are selected as test cases under two different loading conditions and considering three plate aspect ratios for thick, moderately thick and thin plate, in a total of 12 distinct test cases. (C) 2013 Elsevier Ltd. All rights reserved.

New RuII(arene) complexes with halogen-substituted bis- and tris(pyrazol-1-YL)borate ligands

[RuCl(arene)(-Cl)](2) dimers were treated in a 1:2 molar ratio with sodium or thallium salts of bis- and tris(pyrazolyl)borate ligands [Na(BpBr3)], [Tl(TpBr3)], and [Tl(Tp(iPr,4Br))]. Mononuclear neutral complexes [RuCl(arene)((2)-BpBr3)] (1: arene=p-cymene (cym); 2: arene=hexamethylbenzene (hmb); 3: arene=benzene (bz)), [RuCl(arene)((2)-TpBr3)] (4: arene=cym; 6: arene=bz), and [RuCl(arene)((2)-Tp(iPr,4Br))] (7: arene=cym, 8: arene=hmb, 9: arene=bz) have been always obtained with the exception of the ionic [Ru-2(hmb)(2)(-Cl)(3)][TpBr3] (5), which formed independently of the ratio of reactants and reaction conditions employed. The ionic [Ru(CH3OH)(cym)((2)-BpBr3)][X] (10: X=PF6, 12: X=O3SCF3) and the neutral [Ru(O2CCF3)(cym)((2)-BpBr3)] (11) have been obtained by a metathesis reaction with corresponding silver salts. All complexes 1-12 have been characterized by analytical and spectroscopic data (IR, ESI-MS, H-1 and (CNMR)-C-13 spectroscopy). The structures of the thallium and calcium derivatives of ligand TpBr3, [Tl(TpBr3)] and [Ca(dmso)(6)][TpBr3](2)2DMSO, of the complexes 1, 4, 5, 6, 11, and of the decomposition product [RuCl(cym)(Hpz(iPr,4Br))(2)][Cl] (7) have been confirmed by using single-crystal X-ray diffraction. Electrochemical studies showed that 1-9 and 11 undergo a single-electron (RuRuIII)-Ru-II oxidation at a potential, measured by cyclic voltammetry, which allows comparison of the electron-donor characters of the bis- and tris(pyrazol-1-yl)borate and arene ligands, and to estimate, for the first time, the values of the Lever E-L ligand parameter for BpBr3, TpBr3, and Tp(iPr,4Br). Theoretical calculations at the DFT level indicated that both oxidation and reduction of the Ru complexes under study are mostly metal-centered with some involvement of the chloride ligand in the former case, and also demonstrated that the experimental isolation of the (3)-binuclear complex 5 (instead of the mononuclear 5) is accounted for by the low thermodynamic stability of the latter species due to steric reasons.

From cellulosic based liquid crystalline sheared solutions to 1D and 2D soft materials

Liquid crystalline cellulosic-based solutions described by distinctive properties are at the origin of different kinds of multifunctional materials with unique characteristics. These solutions can form chiral nematic phases at rest, with tuneable photonic behavior, and exhibit a complex behavior associated with the onset of a network of director field defects under shear. Techniques, such as Nuclear Magnetic Resonance (NMR), Rheology coupled with NMR (Rheo-NMR), rheology, optical methods, Magnetic Resonance Imaging (MRI), Wide Angle X-rays Scattering (WAXS), were extensively used to enlighten the liquid crystalline characteristics of these cellulosic solutions. Cellulosic films produced by shear casting and fibers by electrospinning, from these liquid crystalline solutions, have regained wider attention due to recognition of their innovative properties associated to their biocompatibility. Electrospun membranes composed by helical and spiral shape fibers allow the achievement of large surface areas, leading to the improvement of the performance of this kind of systems. The moisture response, light modulated, wettability and the capability of orienting protein and cellulose crystals, opened a wide range of new applications to the shear casted films. Characterization by NMR, X-rays, tensile tests, AFM, and optical methods allowed detailed characterization of those soft cellulosic materials. In this work, special attention will be given to recent developments, including, among others, a moisture driven cellulosic motor and electro-optical devices.

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.

Investigation of structural effects and behaviour of pseudomonas aeruginosa amidase encapsulated in reserved micelles

The acetohydroxamic acid synthesis reaction was studied using whole cells, cell-free extract and purified amidase from the strains of Pseudomonas aeruginosa L10 and A13 entrapped in a reverse micelles system composed of cationic surfactant tetradecyltrimethyl ammonium bromide. The specific activity of amidase, yield of synthesis and storage stability were determined for the reversed micellar system as well as for free amidase in conventional buffer medium. The results have revealed that amidase solutions in the reverse micelles system exhibited a substantial increase in specific activity, yield of synthesis and storage stability. In fact, whole cells from P. aeruginosa L10 and AI3 in reverse micellar medium revealed an increase in specific activity of 9.3- and 13.9-fold, respectively, relatively to the buffer medium. Yields of approximately 92% and 66% of acetohydroxamic acid synthesis were obtained for encapsulated cell free extract from P. aeruginosa L10 and A13, respectively. On the other hand, the half-life values obtained for the amidase solutions encapsulated in reverse micelles were overall higher than that obtained for the free amidase solution in buffer medium. Half-life values obtained for encapsulated purified amidase from P. aeruginosa strain L10 and encapsulated cell-free extract from P. aeruginosa strain AI3 were of 17.0 and 26.0 days, respectively. As far as the different sources biocatalyst are concerned, the data presented in this work has revealed that the best results, in both storage stability and biocatalytic efficiency, were obtained when encapsulated cell-free extract from P. aeruginosa strain AI3 at 14/0 of 10 were used. Conformational changes occurring upon encapsulation of both strains enzymes in reverse micelles of TAB in heptane/octanol were additionally identified by FTIR spectroscopy which clarified the biocatalysts performances.

On the analytical solutions of the Hindmarsh-Rose neuronal model

In this article we analytically solve the Hindmarsh-Rose model (Proc R Soc Lond B221:87-102, 1984) by means of a technique developed for strongly nonlinear problems-the step homotopy analysis method. This analytical algorithm, based on a modification of the standard homotopy analysis method, allows us to obtain a one-parameter family of explicit series solutions for the studied neuronal model. The Hindmarsh-Rose system represents a paradigmatic example of models developed to qualitatively reproduce the electrical activity of cell membranes. By using the homotopy solutions, we investigate the dynamical effect of two chosen biologically meaningful bifurcation parameters: the injected current I and the parameter r, representing the ratio of time scales between spiking (fast dynamics) and resting (slow dynamics). The auxiliary parameter involved in the analytical method provides us with an elegant way to ensure convergent series solutions of the neuronal model. Our analytical results are found to be in excellent agreement with the numerical simulations.

Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations

An improved class of nonlinear bidirectional Boussinesq equations of sixth order using a wave surface elevation formulation is derived. Exact travelling wave solutions for the proposed class of nonlinear evolution equations are deduced. A new exact travelling wave solution is found which is the uniform limit of a geometric series. The ratio of this series is proportional to a classical soliton-type solution of the form of the square of a hyperbolic secant function. This happens for some values of the wave propagation velocity. However, there are other values of this velocity which display this new type of soliton, but the classical soliton structure vanishes in some regions of the domain. Exact solutions of the form of the square of the classical soliton are also deduced. In some cases, we find that the ratio between the amplitude of this wave and the amplitude of the classical soliton is equal to 35/36. It is shown that different families of travelling wave solutions are associated with different values of the parameters introduced in the improved equations.