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The aim of this paper is to establish a precise illustration for the structure of the nonconstant steady states for a Beddington–DeAngelis and Tanner predator–prey reaction–diffusion system with prey‐taxis. We treat the nonlinear prey‐taxis as a bifurcation parameter to analyze the bifurcation structure of the system. Furthermore, the exported global bifurcation theorem, under a rather natural condition, offers the existence of nonconstant steady states. In the proof, a priori estimates of steady states will play an important role. The local stability analysis with a numerical simulation and bifurcation analysis are given. Finally, some conclusions including biological meanings are performed to summarize our main analytic results and future investigations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the time‐dependent Stokes problem in a three‐dimensional domain with mixed boundary conditions. The discretization relies on spectral methods with respect to the space variables and Euler's implicit scheme with respect to the time variable, then by the second order BDF method. A detailed numerical analysis leads to a priori error estimates for each numerical scheme. [ABSTRACT FROM AUTHOR]

Digital holographic microscope allows imaging of opaque and transparent specimens without staining. A digitally recorded hologram must be reconstructed numerically at the actual depth of the object to obtain a focused image. We have developed a high-resolution digital holographic microscope for imaging amplitude and phase objects with autofocusing capability. If the actual depth of an object is not known a priori, it is estimated by comparing the sharpness of several reconstructions at different distances, which is very demanding in means of computational power when the recorded hologram is large. In this paper, we present 11 different sharpness metrics for estimating the actual focus depths of objects. The speed performance of focusing is discussed, and a scaling technique is introduced where the speed of autofocusing increases on the order of square of the scale ratio. We measured the performance of scaling on computer-generated holograms and on recorded holograms of a biological sample. We show that simulations are in good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

It is well known that conforming finite element schemes exhibit Poisson locking in the incompressible limit as the Poisson ratio ν tends to 1/2. A remedy for this is to use a non-conforming method (Math. Comput. 1992; 59:321-328) in which an a priori error bound is proved for the Crouzeix–Raviart scheme. In this paper we derive a new a priori estimate for the error in energy for the Fortin–Soulie finite element method using a method similar to that used in Brenner and Sung. We then illustrate the new error bound by presenting some numerical examples. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]