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.

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.

Antioxidant activity and cytotoxicity of solubilized C60 and its conjugates with butylated hydroxytoluene

It has been described that fullerenes (C60) present interesting properties with potential application in clinical conditions related to oxidative stress. One of the most prominent features of fullerenes is the ability to quench free radicals. However, because of its poor solubility, this has been studied mostly in organic solutions, while the antioxidant activity and cytotoxicity of fullerenes and their derivates in aqueous medium is not well characterized. The antioxidant capacity of synthesised C60-conjugates has been investigated and its was higher comparing to C60 isolated. The aim of this study was to assess the viability of C60-conjugates by determining its antioxidant activity and cytotoxicity in bio-relevant media.

Nanofiltration of surface water for the removal of endocrine disruptors

The assessment of surface water nanofiltration (NF) for the removal of endocrine disruptors (EDs) Nonylphenol Ethoxylate (IGEPAL), 4-Nonylphenol (NP) and 4-Octylphenol (OP) was carried out with three commercial NF membranes - NF90, NF200, NF270. The permeation experiments were conducted in laboratory flat-cell units of 13.2 x 10(-4) m(2) of surface area and in a DSS Lab-unit M20 with a membrane surface area of 0.036 m2. The membranes hydraulic permeabilities ranged from 3.7 to 15.6 kg/h/m(2)/bar and the rejection coefficients to NaCl, Na2SO4 and Glucose are for NF90: 97%, 99% and 97%, respectively; for NF200: 66%, 98% and 90%, respectively and for NF270: 48%, 94% and 84%, respectively. Three sets of nanofiltration experiments were carried out: i) NF of aqueous model solutions of NP, IGEPAL and OP running in total recirculation mode; ii) NF of surface water from Rio Sado (Settibal, Portugal) running in concentration mode; iii) NF of surface water from Rio Sado inoculated with NP, IGEPAL and OP running in concentration mode. The results of model solutions experiments showed that the EDs rejection coefficients are approximately 100% for all the membranes. The results obtained for the surface water showed that the rejection coefficients to natural organic Matter (NOM) are 94%, 82% and 78% for NF90, NF200 and NF 270 membranes respectively, with and without inoculation of EDs. The rejection coefficients to EDs in surface water with and without inoculation of EDs are 100%, showing that there is a fraction of NOM of high molecular weight that retains the EDs in the concentrate and that there is a fraction of NOM of low molecular weight that permeates through the NF membranes free of EDs.

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.