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We study the existence of local and global mild solutions of the fractional-order differential equations in an arbitrary Banach space by using the semigroup theory and the Schauder fixed-point theorem. We also give some examples to illustrate the applications of abstract results. [ABSTRACT FROM AUTHOR]

Definition and validation of the ranges of normal values and agreement among echocardiographic measures of mechanical synchrony in healthy subjects are mostly lacking. The aims of this study were (1) to assess the ranges of normal values for 5 tissue Doppler imaging parameters, real-time 3-dimensional echocardiographic measures, and speckle-tracking measures of mechanical synchrony; (2) to evaluate interinstitutional variability; (3) to compare the ranges of normal values with those reported in previous research; and (4) to analyze the agreement among all parameters in the same healthy subject. Time to peak systolic velocity (Ts), the delay between Ts at the basal septal and lateral segments, peak velocity difference, strain derived by tissue Doppler imaging, Ts derived by tissue synchronization imaging, systolic synchrony index (SSI) derived by real-time 3-dimensional echocardiography, and longitudinal and radial strain derived by speckle tracking were prospectively collected and analyzed at 2 different institutions in 160 consecutive healthy subjects. The ranges of normal values, expressed as means +/- 2 SDs, were 30.32 +/- 29.36 ms for the SD of Ts, 15.51 +/- 99.88 ms for septal-lateral delay, 60.75 +/- 81.62 ms for peak velocity difference, 33.07 +/- 29.96 ms for tissue synchronization imaging, 34.16 +/- 23.26 ms for the SD of strain, 2.74 +/- 2.16% for SSI, 28.91 +/- 23.02 ms for the SD of longitudinal strain, and 10.4 +/- 6.31 ms for radial strain. There was large interinstitutional variability for all parameters. Three-dimensional SSI and radial strain were within the published upper range limit for healthy subjects. Ninety percent of healthy subjects were consistently classified to be synchronous by 1 parameter. With a composite index, more subjects than expected showed dyssynchrony (10% vs 2.5%). In conclusion, 3-dimensional SSI and radial strain were the most reproducible parameters and consistently discriminated normal healthy subjects from the cardiac resynchronization therapy volume responders. [ABSTRACT FROM AUTHOR]

In this work, we consider low contrast periodic media and we study the dependence of the effective or homogenized tensor and the dispersion tensor in terms of the microstructure. We treat both one-dimensional structures and some laminated structures in higher dimension. Interesting properties of the sign of these coefficients are found. Surprisingly, these depend on the microstructure only through the local proportion parameter, and in some cases, they do not depend on the microstructure at all. [ABSTRACT FROM AUTHOR]

We consider a periodically heterogeneous and perforated medium filling an open domain Ω of ℝN. Assuming that the size of the periodicity of the structure and of the holes is O(ε), we study the asymptotic behavior, as ε → 0, of the solution of an elliptic boundary value problem with strongly oscillating coefficients posed in Ωε (Ωε being Ω minus the holes) with a Neumann condition on the boundary of the holes. We use Bloch wave decomposition to introduce an approximation of the solution in the energy norm which can be computed from the homogenized solution and the first Bloch eigenfunction. We first consider the case where Ωis ℝN and then localize the problem for a bounded domain Ω, considering a homogeneous Dirichlet condition on the boundary of Ω. [ABSTRACT FROM AUTHOR]

The classical problem of homogenization deals with elliptic operators in periodically oscillating media of small period ℇ>0 and the asymptotic behavior of solution uℇ of boundary value problems associated with such operators. In a previous work [Conca et al., SIAM J. Math. Anal. 33 (2002), 1166–1198], the authors introduced what is called Bloch approximation which provided energy norm approximation for the solution in $\mathbb{R}^{N}$. This paper continues with the above development and proposes a modified Bloch approximation. This function takes into account boundary effects. Its connection with the first order classical correctors is also established with the corresponding error estimate. All the proofs are worked out entirely in the Fourier–Bloch space. [ABSTRACT FROM AUTHOR]

In the book by Hornung, Chap. 6, the author proposes a homogenization strategy for the effective behavior of some chemical processes involving adsorption and reactions arising in porous media. Rigorous proofs of the convergence results are given in the case of linear adsorption rates and linear chemical reactions. The author leaves as an open question the case of a nonlinear adsorption rate. Our goal in this paper is to study two well-known examples of such nonlinear models, namely the so-called Freundlich and Langmuir kinetics. [ABSTRACT FROM AUTHOR]

This paper presents two methods for the numerical solution of the classical homogenization problem of elliptic operators with periodically oscillating coefficients. The numerical solution of such problems is difficult because of the presence of rapidly oscillating coefficients. The first method based on the classical one which consists of the homogenized solution, the first- and second-order correctors, whereas the second one is based on the Bloch wave approach. Further, for the calculation of the homogenized coefficients and some auxiliary functions involved in this method, we applied both methods and compared their accuracies. The Bloch approximation consists in determining an oscillating integral, numerically. The Bloch method provides a better approximation to the exact solution than the classical first-order corrector term in the smooth coefficients case. Moreover, we provided Taylor approximations for the Bloch approximation function and implemented it numerically. In order to show the efficiency of these methods, exhaustive numerical examples in both one and two-dimensional cases are presented. [Copyright &y& Elsevier]

We study the stationary Stokes and Navier-Stokes equations with nonhomogeneous Navier boundary conditions in a bounded domain Ω ⊂ R 3 of class C 1 , 1. We prove the existence and uniqueness of weak and strong solutions in W 1 , p (Ω) and W 2 , p (Ω) for all 1 < p < ∞ , considering minimal regularity on the friction coefficient α. Moreover, we deduce uniform estimates for the solution with respect to α which enables us to analyze the behavior of the solution when α → ∞. [ABSTRACT FROM AUTHOR]

Articulated solid bodies (ASB) is a basic model for the study of shape-changing underwater vehicles made of rigid parts linked together by pivoting joints. In this paper we study the locomotion of such swimming mechanisms in an ideal fluid. Our study ranges over a wide class of problems: several ASBs can be involved (without being hydrodynamically decoupled), the fluid-bodies system can be partially or totally confined and fluid circulation, buoyancy force and possible collisions between bodies are taken into account. We derive the Euler-Lagrange equation governing the dynamics of the system, study its well-posedness and describe a numerical scheme implemented in a Matlab toolbox (Biohydrodynamics Toolbox). [ABSTRACT FROM AUTHOR]

The equations that govern elastostatic equilibrium between a prescribed force field and an unknown displacement field for materials with periodic skeletal micro-structures are studied. It is shown that as the size of the micro-structure tends to zero, the displacement field will converge to the solution of a constant coefficient partial differential equation. This equation is shown to be either a classical or a micro-polar continuum elasticity equation, depending on the micro-structural geometry and the nature of the external load field. Convergence is proved for representative model problems in Sobolev energy norms and in the maximum norm. In addition, it is shown that by considering pseudo-differential homogenized equations, any order of convergence can be achieved. [ABSTRACT FROM AUTHOR]

Elliptic problems on unbounded domains with periodic coefficients and geometries are analyzed and two-scale regularity results for the solution are given. These are based on a detailed analysis in weighted Sobolev spaces of the so-called unit-cell problem in which the critical parameters (the period ∊ the wave number t, and the differentiation order) enter explicitly. [ABSTRACT FROM AUTHOR]

An abstract of the article "Registration of three-dimensional coronary sinus computed tomographic images with projection images obtained using fluoroscopy," by A. Sorgente and colleagues is presented.

The paper presents a theoretical study of an identification problem by shape optimization methods. The question is to detect an object immersed in a fluid. Here, the problem is modeled by the Stokes equations and treated as a nonlinear least-squares problem. We consider both the Dirichlet and Neumann boundary conditions. Firstly, we prove an identifiability result. Secondly, we prove the existence of the first-order shape derivatives of the state, we characterize them and deduce the gradient of the least-squares functional. Moreover, we study the stability of this setting. We prove the existence of the second-order shape derivatives and we give the expression of the shape Hessian. Finally, the compactness of the Riesz operator corresponding to this shape Hessian is shown and the ill-posedness of the identification problem follows. This explains the need of regularization to numerically solve this problem. [ABSTRACT FROM AUTHOR]