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Appropriate Assumptions (appropriate + assumption)

Distribution by Scientific Domains
Mathematics and Statistics66%

Selected Abstracts

Uniform stability of spectral nonlinear Galerkin methods

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2004
Yinnian He
Abstract This article provides a stability analysis for the backward Euler schemes of time discretization applied to the spatially discrete spectral standard and nonlinear Galerkin approximations of the nonstationary Navier-Stokes equations with some appropriate assumption of the data (,, u0, f). If the backward Euler scheme with the semi-implicit nonlinear terms is used, the spectral standard and nonlinear Galerkin methods are uniform stable under the time step constraint ,t , (2/,,1). Moreover, if the backward Euler scheme with the explicit nonlinear terms is used, the spectral standard and nonlinear Galerkin methods are uniform stable under the time step constraints ,t = O(,) and ,t = O(,), respectively, where , , ,, which shows that the restriction on the time step of the spectral nonlinear Galerkin method is less than that of the spectral standard Galerkin method. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004 [source]

A two-scale model for liquid-phase epitaxy

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2009
Ch. Eck
Abstract We study a model for liquid-phase epitaxy that is based on a continuum description of the transport processes in the liquid and a Burton,Cabrera,Frank (BCF) model for the growth of the solid by epitaxy. In order to develop a model that is capable to incorporate structures of a very small scale in the solid phase within a computation for a technically relevant macroscopic length scale, we apply homogenization methods. The result of the homogenization procedure is a two-scale model that consists of macroscopic equations for fluid flow and solute diffusion in the fluid volume, coupled to microscopic BCF models for the evolution of the microstructure in the solid phase. The obtained two-scale model is justified by an estimate for the model error that is valid under appropriate assumptions on the regularity of the solutions. This estimate is proved for a phase field approximation of the BCF model. Copyright © 2008 John Wiley & Sons, Ltd. [source]

On a class of PDEs with nonlinear distributed in space and time state-dependent delay terms

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2008
Alexander V. Rezounenko
Abstract A new class of nonlinear partial differential equations with distributed in space and time state-dependent delay is investigated. We find appropriate assumptions on the kernel function which represents the state-dependent delay and discuss advantages of this class. Local and long-time asymptotic properties, including the existence of global attractor and a principle of linearized stability, are studied. Copyright © 2008 John Wiley & Sons, Ltd. [source]

AFM measurement of the stiffness of layers of agarose gel patterned with polylysine

MICROSCOPY RESEARCH AND TECHNIQUE, Issue 10 2010
Marco Salerno
Abstract Films of agarose gel microspotted with polylysine aqueous solution have been characterized by atomic force microscopy carried out in deionized water. Thickness and surface morphology of the layers have been checked, and the effect of polylysine impregnation on the local elasticity has been investigated. An increase in contact stiffness of the organic layer at the spotted areas has been observed, correlated with the polylysine concentration. For the considered agarose layer thickness of ,0.9 ,m in dry condition, the concentration threshold at which stiffening appears is ,0.1 mg/mL. Above this threshold, the stiffening coefficient becomes approximately twofold and seems not to increase significantly with concentration in the range 0.3,0.7 mg/mL. For concentrations above the stiffening threshold, this effect is also accompanied by a locally lower film thickness. For quantitative determination of the stiffness, force,distance curves extracted from the regions of interest of spots and agarose substrate have been selected and processed. These curves were fitted to the Hertz model of purely elastic tip-surface interaction, under appropriate assumptions on both tip shape and optimum indentation depth. In this way, we could determine the Young's modulus of the agarose layer to be ,50 kPa and quantitatively confirm the stiffening due to polylysine. Microsc. Res. Tech. 73:982,990, 2010. © 2010 Wiley-Liss, Inc. [source]

On the mixed finite element method with Lagrange multipliers

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2003
Ivo Babu
Abstract In this note we analyze a modified mixed finite element method for second-order elliptic equations in divergence form. As a model we consider the Poisson problem with mixed boundary conditions in a polygonal domain of R2. The Neumann (essential) condition is imposed here in a weak sense, which yields the introduction of a Lagrange multiplier given by the trace of the solution on the corresponding boundary. This approach allows to handle nonhomogeneous Neumann boundary conditions, theoretically and computationally, in an alternative and usually easier way. Then we utilize the classical Babu,ka-Brezzi theory to show that the resulting mixed variational formulation is well posed. In addition, we use Raviart-Thomas spaces to define the associated finite element method and, applying some elliptic regularity results, we prove the stability, unique solvability, and convergence of this discrete scheme, under appropriate assumptions on the mesh sizes. Finally, we provide numerical results illustrating the performance of the algorithm for smooth and singular problems. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 192,210, 2003 [source]

A comparison of alternative approaches for determining the downside risk of hedge fund strategies

THE JOURNAL OF FUTURES MARKETS, Issue 3 2009
Daniel Giamouridis
In this study, we compare a number of different approaches for determining the Value at Risk (VaR) and Expected Shortfall (ES) of hedge fund investment strategies. We compute VaR and ES through both model-free and mean/variance and distribution model-based methods. Certain specifications of the models that we considered can technically address the typical characteristics of hedge fund returns such as autocorrelation, asymmetry, fat tails, and time-varying variances. We find that conditional mean/variance models coupled with appropriate assumptions on the empirical distribution can improve the prediction accuracy of VaR. In particular, we observed the highest prediction accuracy for the predictions of 1% VaR. We also find that the goodness of ES prediction models is primarily influenced by the distribution model rather than the mean/variance specification. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:244,269, 2009 [source]