Existence of asymptotically almost automorphic solutions to some abstract partial neutral integro-differential equations

The paper establishes the existence and uniqueness of asymptotically almost automorphic mild solution to an abstract partial neutral integro-differential equation with unbounded delay. An example is given to illustrate our results. (C) 2008 Elsevier Ltd. All rights reserved.

Almost automorphic mild solutions to some partial neutral functional-differential equations and applications

The paper considers the existence and uniqueness of almost automorphic mild solutions to some classes of first-order partial neutral functional-differential equations. Sufficient conditions for the existence and uniqueness of almost automorphic mild solutions to the above-mentioned equations are obtained. As an application, a first-order boundary value problem arising in control systems is considered. (C) 2007 Elsevier Ltd. All fights reserved.

Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C(0)-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations. (C) 2010 Elsevier Ltd. All rights reserved.

Asymptotically almost periodic solutions for abstract neutral integro-differential equations

We study the existence of asymptotically almost periodic classical solutions for a class of abstract neutral integro-differential equation with unbounded delay. A concrete application to partial neutral integro-differential equations which arise in the study of heat conduction in fading memory material is considered. (C) 2011 Elsevier Inc. All rights reserved.

Non-autonomous semilinear evolution equations with almost sectorial operators

Inspired by the theory of semigroups of growth a, we construct an evolution process of growth alpha. The abstract theory is applied to study semilinear singular non-autonomous parabolic problems. We prove that. under natural assumptions. a reasonable concept of solution can be given to Such semilinear singularly non-autonomous problems. Applications are considered to non-autonomous parabolic problems in space of Holder continuous functions and to a parabolic problem in a domain Omega subset of R(n) with a one dimensional handle.

Shelf-life of a 2.5% sodium hypochlorite solution as determined by arrhenius equation

Accelerated stability tests are indicated to assess, within a short time, the degree of chemical degradation that may affect an active substance, either alone or in a formula, under normal storage conditions. This method is based on increased stress conditions to accelerate the rate of chemical degradation. Based on the equation of the straight line obtained as a function of the reaction order (at 50 and 70 ºC) and using Arrhenius equation, the speed of the reaction was calculated for the temperature of 20 ºC (normal storage conditions). This model of accelerated stability test makes it possible to predict the chemical stability of any active substance at any given moment, as long as the method to quantify the chemical substance is available. As an example of the applicability of Arrhenius equation in accelerated stability tests, a 2.5% sodium hypochlorite solution was analyzed due to its chemical instability. Iodometric titration was used to quantify free residual chlorine in the solutions. Based on data obtained keeping this solution at 50 and 70 ºC, using Arrhenius equation and considering 2.0% of free residual chlorine as the minimum acceptable threshold, the shelf-life was equal to 166 days at 20 ºC. This model, however, makes it possible to calculate shelf-life at any other given temperature.

An analytical solution for the critical number of particles for stable bose-einstein condensation under the influence of an anisotropic potential

We have considered a Bose gas in an anisotropic potential. Applying the the Gross-Pitaevskii Equation (GPE) for a confined dilute atomic gas, we have used the methods of optimized perturbation theory and self-similar root approximants, to obtain an analytical formula for the critical number of particles as a function of the anisotropy parameter for the potential. The spectrum of the GPE is also discussed.

Enhanced response of the fricke solution doped with hematoporphyrin under X-rays irradiation

The vials filled with Fricke solutions were doped with increasing concentrations of Photogem®, used in photodynamic therapy. These vials were then irradiated with low-energy X-rays with doses ranging from 5 to 20 Gy. The conventional Fricke solution was also irradiated with the same doses. The concentration of ferric ions for the Fricke and doped-Fricke irradiated solutions were measured in a spectrophotometer at 220 to 340 nm. The results showed that there was an enhancement in the response of the doped-Fricke solution, which was proportional to the concentration of the photosensitizer. The use of such procedure for studying the radiosensitizing property of photosensitizers based on the production of free radicals is also discussed.

Nonexistence of regular stationary solution in a metric nonsymmetric theory of gravitation

It is proven that the field equations of a previously studied metric nonsymmetric theory of gravitation do not admit any non-singular stationary solution which represents a field of non-vanishing total mass and non-vanishing total fermionic charge.

Remoção de Pb2+ e Cr3+ em solução por zeólitas naturais associadas a rochas eruptivas da formação serra geral, bacia sedimentar do Paraná

The capacity of natural zeolites and its host rock (dacite) to remove Pb2+ and Cr3+ from aqueous solutions has been investigated. Results showed that both samples prefer to remove Pb2+ instead of Cr3+. Almost 100% of Pb2+ was removed from solutions with concentration until 50 mg L-1 and 100 mg L-1 of this metal, respectively by dacite and zeolite. The equilibrium of metals adsorption process was reached during the first 30 min by both materials. Na+ can be used to recover Pb2+, but not to remove Cr3+ from the treated samples. The Sips model showed a good fit for experimental data of this study.

Design methodology for multi-pumped discrete Raman amplifiers: case-study employing photonic crystal fibers

This paper proposes a new design methodology for discrete multi-pumped Raman amplifier. In a multi-objective optimization scenario, in a first step the whole solution-space is inspected by a CW analytical formulation. Then, the most promising solutions are fully investigated by a rigorous numerical treatment and the Raman amplification performance is thus determined by the combination of analytical and numerical approaches. As an application of our methodology we designed an photonic crystal fiber Raman amplifier configuration which provides low ripple, high gain, clear eye opening and a low power penalty. The amplifier configuration also enables to fully compensate the dispersion introduced by a 70-km singlemode fiber in a 10 Gbit/s system. We have successfully obtained a configuration with 8.5 dB average gain over the C-band and 0.71 dB ripple with almost zero eye-penalty using only two pump lasers with relatively low pump power. (C) 2009 Optical Society of America

UNIQUENESS AND NONUNIQUENESS RESULTS FOR A CERTAIN CLASS OF ALMOST PERIODIC DISTRIBUTIONS

We consider distributions u is an element of S'(R) of the form u(t) = Sigma(n is an element of N) a(n)e(i lambda nt), where (a(n))(n is an element of N) subset of C and Lambda = (lambda n)(n is an element of N) subset of R have the following properties: (a(n))(n is an element of N) is an element of s', that is, there is a q is an element of N such that (n(-q) a(n))(n is an element of N) is an element of l(1); for the real sequence., there are n(0) is an element of N, C > 0, and alpha > 0 such that n >= n(0) double right arrow vertical bar lambda(n)vertical bar >= Cn(alpha). Let I(epsilon) subset of R be an interval of length epsilon. We prove that for given Lambda, (1) if Lambda = O(n(alpha)) with alpha < 1, then there exists epsilon > 0 such that u vertical bar I(epsilon) = 0 double right arrow u 0; (2) if Lambda = O(n) is uniformly discrete, then there exists epsilon > 0 such that u vertical bar I(epsilon) = 0 double right arrow u 0; (3) if alpha > 1 and. is uniformly discrete, then for all epsilon > 0, u vertical bar I(epsilon) = 0 double right arrow u = 0. Since distributions of the above mentioned form are very common in engineering, as in the case of the modeling of ocean waves, signal processing, and vibrations of beams, plates, and shells, those uniqueness and nonuniqueness results have important consequences for identification problems in the applied sciences. We show an identification method and close this article with a simple example to show that the recovery of geometrical imperfections in a cylindrical shell is possible from a measurement of its dynamics.

Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems

This work develops a method for solving ordinary differential equations, that is, initial-value problems, with solutions approximated by using Legendre's polynomials. An iterative procedure for the adjustment of the polynomial coefficients is developed, based on the genetic algorithm. This procedure is applied to several examples providing comparisons between its results and the best polynomial fitting when numerical solutions by the traditional Runge-Kutta or Adams methods are available. The resulting algorithm provides reliable solutions even if the numerical solutions are not available, that is, when the mass matrix is singular or the equation produces unstable running processes.

The Relationship between Population Structure and Aluminum Tolerance in Cultivated Sorghum

Background: Acid soils comprise up to 50% of the world's arable lands and in these areas aluminum (Al) toxicity impairs root growth, strongly limiting crop yield. Food security is thereby compromised in many developing countries located in tropical and subtropical regions worldwide. In sorghum, SbMATE, an Al-activated citrate transporter, underlies the Alt(SB) locus on chromosome 3 and confers Al tolerance via Al-activated root citrate release. Methodology: Population structure was studied in 254 sorghum accessions representative of the diversity present in cultivated sorghums. Al tolerance was assessed as the degree of root growth inhibition in nutrient solution containing Al. A genetic analysis based on markers flanking Alt(SB) and SbMATE expression was undertaken to assess a possible role for Alt(SB) in Al tolerant accessions. In addition, the mode of gene action was estimated concerning the Al tolerance trait. Comparisons between models that include population structure were applied to assess the importance of each subpopulation to Al tolerance. Conclusion/Significance: Six subpopulations were revealed featuring specific racial and geographic origins. Al tolerance was found to be rather rare and present primarily in guinea and to lesser extent in caudatum subpopulations. Alt(SB) was found to play a role in Al tolerance in most of the Al tolerant accessions. A striking variation was observed in the mode of gene action for the Al tolerance trait, which ranged from almost complete recessivity to near complete dominance, with a higher frequency of partially recessive sources of Al tolerance. A possible interpretation of our results concerning the origin and evolution of Al tolerance in cultivated sorghum is discussed. This study demonstrates the importance of deeply exploring the crop diversity reservoir both for a comprehensive view of the dynamics underlying the distribution and function of Al tolerance genes and to design efficient molecular breeding strategies aimed at enhancing Al tolerance.

Magnetoconfined levels in a parabolic quantum dot: An analytical solution of a three-dimensional Fock-Darwin problem in a tilted magnetic field

The energy spectrum of an electron confined in a quantum dot (QD) with a three-dimensional anisotropic parabolic potential in a tilted magnetic field was found analytically. The theory describes exactly the mixing of in-plane and out-of-plane motions of an electron caused by a tilted magnetic field, which could be seen, for example, in the level anticrossing. For charged QDs in a tilted magnetic field we predict three strong resonant lines in the far-infrared-absorption spectra.