An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.

EXISTENCE RESULTS FOR NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

In this paper we discuss the existence of mild, strict and classical solutions for a class of abstract integro-differential equations in Banach spaces. Some applications to ordinary and partial integro-differential equations are considered.

GLOBAL SOLUTIONS FOR ABSTRACT FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

In this paper we study the existence of global solutions for a class of abstract functional differential equation with nonlocal conditions. An application is considered.

Weighted S-Asymptotically omega-Periodic Solutions of a Class of Fractional Differential Equations

We study the existence of weighted S-asymptotically omega-periodic mild solutions for a class of abstract fractional differential equations of the form u' = partial derivative (alpha vertical bar 1)Au + f(t, u), 1 < alpha < 2, where A is a linear sectorial operator of negative type.

EXISTENCE RESULTS FOR ABSTRACT NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper we discuss the existence of solutions for a class of abstract partial neutral functional differential equations.

SOLITON SOLUTIONS TO SYSTEMS OF COUPLED SCHRODINGER EQUATIONS OF HAMILTONIAN TYPE

We study the existence of positive solutions of Hamiltonian-type systems of second-order elliptic PDE in the whole space. The systems depend on a small parameter and involve a potential having a global well structure. We use dual variational methods, a mountain-pass type approach and Fourier analysis to prove positive solutions exist for sufficiently small values of the parameter.

LOCAL WELL POSEDNESS, ASYMPTOTIC BEHAVIOR AND ASYMPTOTIC BOOTSTRAPPING FOR A CLASS OF SEMILINEAR EVOLUTION EQUATIONS OF THE SECOND ORDER IN TIME

A class of semilinear evolution equations of the second order in time of the form u(tt)+Au+mu Au(t)+Au(tt) = f(u) is considered, where -A is the Dirichlet Laplacian, 92 is a smooth bounded domain in R(N) and f is an element of C(1) (R, R). A local well posedness result is proved in the Banach spaces W(0)(1,p)(Omega)xW(0)(1,P)(Omega) when f satisfies appropriate critical growth conditions. In the Hilbert setting, if f satisfies all additional dissipativeness condition, the nonlinear Semigroup of global solutions is shown to possess a gradient-like attractor. Existence and regularity of the global attractor are also investigated following the unified semigroup approach, bootstrapping and the interpolation-extrapolation techniques.

Reverse engineering in many-body quantum physics: Correspondence between many-body systems and effective single-particle equations

The mapping, exact or approximate, of a many-body problem onto an effective single-body problem is one of the most widely used conceptual and computational tools of physics. Here, we propose and investigate the inverse map of effective approximate single-particle equations onto the corresponding many-particle system. This approach allows us to understand which interacting system a given single-particle approximation is actually describing, and how far this is from the original physical many-body system. We illustrate the resulting reverse engineering process by means of the Kohn-Sham equations of density-functional theory. In this application, our procedure sheds light on the nonlocality of the density-potential mapping of density-functional theory, and on the self-interaction error inherent in approximate density functionals.

Profiles of xylose reductase, xylitol dehydrogenase and xylitol production under different oxygen transfer volumetric coefficient values

BACKGROUND: Xylitol is a sugar alcohol (polyalcohol) with many interesting properties for pharmaceutical and food products. It is currently produced by a chemical process, which has some disadvantages such as high energy requirement. Therefore microbiological production of xylitol has been studied as an alternative, but its viability is dependent on optimisation of the fermentation variables. Among these, aeration is fundamental, because xylitol is produced only under adequate oxygen availability. In most experiments with xylitol-producing yeasts, low oxygen transfer volumetric coefficient (K(L)a) values are used to maintain microaerobic conditions. However, in the present study the use of relatively high K(L)a values resulted in high xylitol production. The effect of aeration was also evaluated via the profiles of xylose reductase (XR) and xylitol clehydrogenase (XD) activities during the experiments. RESULTS: The highest XR specific activity (1.45 +/- 0.21 U mg(protein)(-1)) was achieved during the experiment with the lowest K(L)a value (12 h(-1)), while the highest XD specific activity (0.19 +/- 0.03 U mg(protein)(-1)) was observed with a K(L)a value of 25 h(-1). Xylitol production was enhanced when K(L)a was increased from 12 to 50 h(-1), which resulted in the best condition observed, corresponding to a xylitol volumetric productivity of 1.50 +/- 0.08 g(xylitol) L(-1) h(-1) and an efficiency of 71 +/- 6.0%. CONCLUSION: The results showed that the enzyme activities during xylitol bioproduction depend greatly on the initial KLa value (oxygen availability). This finding supplies important information for further studies in molecular biology and genetic engineering aimed at improving xylitol bioproduction. (C) 2008 Society of Chemical Industry

Anaerobic sequencing batch biofilm reactor applied to automobile industry wastewater treatment: Volumetric loading rate and feed strategy effects

This paper presents a technological viability study of wastewater treatment in an automobile industry by an anaerobic sequencing batch biofilm reactor containing immobilized biomass (AnSBBR) with a draft tube. The reactor was operated in 8-h cycles, with agitation of 400 rpm, at 30 degrees C and treating 2.0 L wastewater per cycle. Initially the efficiency and stability of the reactor were studied when supplied with nutrients and alkalinity. Removal efficiency of 88% was obtained at volumetric loading rate (VLR) of 3.09 mg COD/L day. When VLR was increased to 6.19 mg COD/L day the system presented stable operation with reduction in efficiency of 71%. In a second stage the AnSBBR was operated treating wastewater in natura, i.e., without nutrients supplementation, only with alkalinity, thereby changing feed strategy. The first strategy consisted in feeding 2.0 L batch wise (10 min), the second in feeding 1.0 L of influent batch wise (10 min) and an additional 1.0 L fed-batch wise (4 h), both dewatering 2.0 L of the effluent in 10 min. The third one maintained 1.0 L of treated effluent in the reactor, without discharging, and 1.0 L of influent was fed fed-batch wise (4 h) with dewatering 1.0 L of the effluent in 10 min. For all implemented strategies (VLR of 1.40, 2.57 and 2.61 mg COD/L day) the system presented stability and removal efficiency of approximately 80%. These results show that the AnSBBR presents operational flexibility, as the influent can be fed according to industry availability. In industrial processes this is a considerable advantage, as the influent may be prone to variations. Moreover, for all the investigated conditions the kinetic parameters were obtained from fitting a first-order model to the profiles of organic matter, total volatile acids and methane concentrations. Analysis of the kinetic parameters showed that the best strategy is feeding 1.0 L of influent batchwise (10 min) and 1.0 L fed-batch wise (4 h) in 8-h cycle. (c) 2007 Elsevier B.V. All rights reserved.

Volumetric reconstruction of the mean flow around circular cylinders fitted with strakes

The volumetric reconstruction technique presented in this paper employs a two-camera stereoscopic particle image velocimetry (SPIV) system in order to reconstruct the mean flow behind a fixed cylinder fitted with helical strakes, which are commonly used to suppress vortex-induced vibrations (VIV). The technique is based on the measurement of velocity fields at equivalent adjacent planes that results in pseudo volumetric fields. The main advantage over proper volumetric techniques is the avoidance of additional equipment and complexity. The averaged velocity fields behind the straked cylinders and the geometrical periodicity of the three-start configuration are used to further simplify the reconstruction process. Two straked cylindrical models with the same pitch (p = 10d) and two different heights (h = 0.1 and 0.2d) are tested. The reconstructed flow shows that the strakes introduce in the wake flow a well-defined wavelength of one-third of the pitch. Measurements of hydrodynamic forces, fluctuating velocity, vortex formation length, and vortex shedding frequency show the interdependence of the wake parameters. The vortex formation length is increased by the strakes, which is an important effect for the suppression of vortex-induced vibrations. The results presented complement previous investigations concerning the effectiveness of strakes as VIV suppressors and provide a basis of comparison to numerical simulations.

NDT flaw mapping of steel surfaces by continuous magnetic Barkhausen noise: Volumetric flaw detection case

This paper reports the use of a non-destructive, continuous magnetic Barkhausen noise (CMBN) technique to investigate the size and thickness of volumetric defects, in a 1070 steel. The magnetic behavior of the used probe was analyzed by numerical simulation, using the finite element method (FEM). Results indicated that the presence of a ferrite coil core in the probe favors MBN emissions. The samples were scanned with different speeds and probe configurations to determine the effect of the flaw on the CMBN signal amplitude. A moving smooth window, based on a second-order statistical moment, was used for analyzing the time signal. The results show the technique`s good repeatability, and high capacity for detection of this type of defect. (C) 2009 Elsevier Ltd. All rights reserved.

Generalized Coupled Algebraic Riccati Equations for Discrete-time Markov Jump with Multiplicative Noise Systems

In this paper we consider the existence of the maximal and mean square stabilizing solutions for a set of generalized coupled algebraic Riccati equations (GCARE for short) associated to the infinite-horizon stochastic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The weighting matrices of the state and control for the quadratic part are allowed to be indefinite. We present a sufficient condition, based only on some positive semi-definite and kernel restrictions on some matrices, under which there exists the maximal solution and a necessary and sufficient condition under which there exists the mean square stabilizing solution fir the GCARE. We also present a solution for the discounted and long run average cost problems when the performance criterion is assumed be composed by a linear combination of an indefinite quadratic part and a linear part in the state and control variables. The paper is concluded with a numerical example for pension fund with regime switching.

New Analytic Solution Related to the Richards, Philip, and Green-Ampt Equations for Infiltration

Based on physical laws of similarity, an analytic solution of the soil water potential form of the Richards equation was derived for water infiltration into a homogeneous sand. The derivation assumes a similarity between the soil water retention function and that of the soil water content profiles taken at fixed times. The new solution successfully described soil water content profiles experimentally measured for water infiltrating downward, upward, and horizontally into a homogeneous sand and agrees with that presented by Philip in 1957. The utility of this analysis is still to be verified, but it is expected to hold for soils that have a narrow pore-size distribution before wetting and that manifest a sharp increase of water content at the wetting front during infiltration. The effect of van Genuchten`s parameters alpha and n on the application of the solution to other porous media was investigated. The solution also improves and provides a more realistic description of the infiltration process than that pioneered by Green and Ampt in 1911.

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.