Electrical conductivity and pH of the substrate solution in gerbera cultivars under fertigation

The quality and the profitability on floriculture are intimately linked to the adequate plant nutrition. In the present research we aimed to evaluate the electrical conductivity (EC) and pH of the substrate solution on four different gerbera cultivars subjected to fertigation, with two nutritive solutions. The experiment was carried out in a greenhouse, from May to July 2006, on the Universidade Estadual Paulista, Botucatu, São Paulo state, Brazil. The experiment was carried out under an experimental design of random blocks, in 4×2 factorial arrangement, with four Gerbera cultivars (Cherry, Golden Yellow, Salmon Rose and Orange) and two nutritive solution concentrations: 0.92 and 1.76 dS m-1 EC) during the vegetative stage, and 1.07 and 2.04 dS m-1 during the reproductive stage (S1 and S2, respectively). The nutrients were applied through fertigation, manually performed every day. The EC and pH values of the substrate solution were evaluated weekly, using the 'pourthru' method. Orange and Cherry cultivars had, respectively, the highest and the lowest electrical conductivity of the substrate solution, and Cherry was the most efficient on the nutrient uptake. The solution S2 showed a trend to accumulate salts in the substrate, but without visual symptoms of plant toxicity, leading to the lowest pH values. The 'pourthru' method was efficient when compared to the 1:2 method and can be adopted for substrate solution analysis in gerbera culture.

The analytical solution and numerical solution of the fractional diffusion-wave equation with damping

Fractional partial differential equations have been applied to many problems in physics, finance, and engineering. Numerical methods and error estimates of these equations are currently a very active area of research. In this paper we consider a fractional diffusionwave equation with damping. We derive the analytical solution for the equation using the method of separation of variables. An implicit difference approximation is constructed. Stability and convergence are proved by the energy method. Finally, two numerical examples are presented to show the effectiveness of this approximation.

YBa2Cu3O7-x films on yttria-stabilized ZrO2 substrates : influence of the substrate morphology

c-axis-oriented YBa2Cu3O7-x (YBCO) thin films were laser deposited on (001) yttria-stabilized ZrO2 (YSZ) substrates with different surface morphologies. The in-plane orientation of the films on smooth substrates was sensitive to the deposition conditions, often resulting in mixed orientations. However, a strongly dominating [110] YBCO//[110]YSZ orientation was obtained at a deposition temperature of 770°C. Films on substrates with surface steps, induced by depositing a homoepitaxial buffer layer or by thermally annealing the substrate, had a [110]YBCO//[100]YSZ orientation when deposited at the same temperature. It was concluded that the [110]YBCO//[100] YSZ orientation was promoted by a graphoepitaxial mechanism. Films prepared under identical conditions on smooth and stepped substrates grew with extended c axes on the former. It is proposed that the extension can be induced by disorder, invoked by a low oxygen pressure and a low density of adsorption sites. The disorder may be eliminated by either an increase of the oxygen pressure or an increase of the density of adsorption sites in the form of steps. The film microstructure influenced the microwave surface resistance, which was similar for films with one exclusive in-plane orientation and higher for films with mixed orientations. The films on the stepped surfaces had superior superconducting properties; inductive measurements gave a Tc onset of 88 K, a ΔT(90%-10%) c of 0.2 K, and the transport jc was 1.5×106 A/cm2 at 83 K, for films on substrates with homoepitaxial buffer layers.

2.5-dimensional solution of the advective accretion disk:a self-similar approach

We provide a 2.5-dimensional solution to a complete set of viscous hydrodynamical equations describing accretion- induced outflows and plausible jets around black holes/compact objects. We prescribe a self-consistent advective disk-outflow coupling model, which explicitly includes the information of vertical flux. Inter-connecting dynamics of an inflow-outflow system essentially upholds the conservation laws. We provide a set of analytical family of solutions through a self-similar approach. The flow parameters of the disk-outflow system depend strongly on the viscosity parameter α and the cooling factor.

Some direct numerical approaches to the solution of the singular nonlinear transonic integral equation

The nonlinear singular integral equation of transonic flow is examined, noting that standard numerical techniques are not applicable in solving it. The difficulties in approximating the integral term in this expression were solved by special methods mitigating the inaccuracies caused by standard approximations. It was shown how the infinite domain of integration can be reduced to a finite one; numerical results were plotted demonstrating that the methods proposed here improve accuracy and computational economy.

Asymtotic solution of the Frieman and Book equation for the pair-correlation function

Using Thomé's procedure, the asymptotic solutions of the Frieman and Book equation for the two-particle correlation in a plasma have been obtained in a complete form. The solution is interpreted in terms of the Lorentz distance. The exact expressions for the internal energy and pressure are evaluated and they are found to be a generalization of the result obtained earlier by others.

Analytical solution of the laminar mean flow wave equation in a lined or unlined two-dimensional rectangular duct

The prediction of the sound attenuation in lined ducts with sheared mean flow has been a topic of research for many years. This involves solving the sheared mean flow wave equation, satisfying the relevant boundary condition. As far as the authors' knowledge goes, this has always been done using numerical techniques. Here, an analytical solution is presented for the wave propagation in two-dimensional rectangular lined ducts with laminar mean flow. The effect of laminar mean flow is studied for both the downstream and the upstream wave propagation. The attenuation values predicted for the laminar mean flow case are compared with those for the case of uniform mean flow. Analytical expressions are derived for the transfer matrices.

On the solution of the equation ut+unux+H(x, t, u)=0

We consider the equation u(t) + u(n)u(x) + H(x, t, u) = 0 and derive a transformation relating it to u(t) + u(n)u(x) = 0. Special cases of the equation appearing in applications are discussed. Initial value problems and asymptotic behaviour of the solution are studied.