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.

Waste Marble Dust Blended Cement

Marble processing activities generates a.significant amount of waste in dust form. This waste, which is nowadays one of the environmental problems worldwide, presents great potential of being used as mineral addition in blended cements production. This paper shows preliminary results of an ongoing project which ultimate goal is to investigate the viability of using waste marble dust (WMD), produced by marble Portuguese industry, as cement replacement material. In order to evaluate the effects of the WMD on mechanical behaviour, different mortar blended cement mixtures were tested. These mixtures were prepared with different partial substitution level of cement with WMD. Strength results of WMD blended cements were compared to control cements with same level of incorporation of natural limestone used to produce commercial Portland-limestone cements. The results obtained show that WMD blended cements perform better than limestone blended cements for same replacement level up to 20% w/w. Therefore, WMD reveals promising attributes for blended cements production.

Phase growth control in low temperature PLD Co: TiO2 films by pressure

This paper reports on the structural and optical properties of Co-doped TiO2 thin films grown onto (0001)Al2O3 substrates by non-reactive pulsed laser deposition (PLD) using argon as buffer gas. It is shown that by keeping constant the substrate temperature at as low as 310 degrees C and varying only the background gas pressure between 7 Pa and 70 Pa, it is possible to grow either epitaxial rutile or pure anatase thin films, as well as films with a mixture of both polymorphs. The optical band gaps of the films are red shifted in comparison with the values usually reported for undoped TiO2, which is consistent with n-type doping of the TiO2 matrix. Such band gap red shift brings the absorption edge of the Co-doped TiO2 films into the visible region, which might favour their photocatalytic activity. Furthermore, the band gap red shift depends on the films' phase composition, increasing with the increase of the Urbach energy for increasing rutile content. (C) 2012 Elsevier B.V. All rights reserved.