A new symmetrized solution for phase retrieval using the transport of intensity equation

We propose a novel symmetrization method for solving the transport of intensity equation (TIE) using fast Fourier transforms for situations where the input images may or may not exhibit spatial periodicity. The method is derived from the analysis of intensity conservation law and the internal symmetry of the TIE, and is illustrated for both a computational and an experimental data set.     

Demagnetization factors of the general ellipsoid: An alternative to the Maxwell approach

A transparent, exhaustive, and self-contained method for the calculation of the demagnetization tensor of the uniformly magnetized ellipsoid is presented. The method is an alternative to the established Maxwell derivation and is based on a Fourier-space approach to the micromagnetics of magnetized bodies. The key to the success of the procedure lies in the convenient treatment of shape effects through the Fourier representation. The scaled form of the demagnetization factors which depends on two dimensionless aspect ratios is argued to be their natural integral representation. Amongst other advantages, it allows for the immediate implementation of symmetry arguments such that only one of the principal factors needs to be computed. The oblate and prolate ellipsoids of revolution are examined from the same general point of view. The demagnetization factors for these distinct types of spheroid are seen to be related by analytic continuation of well-known Gaussian hypergeometric functions.     

Synthesis and biological activity of simplified belactosin C analogues

Successful biochemical studies of the natural products belactosin A and C and their acylated congeners have shown a β-lactonecarboxamide moiety to be a possible core structure of powerful proteasome inhibitors. As a part of further investigations, variously decorated simplified β-lactonecarboxamides have been synthesized in order to understand structure-biological activity relations in detail, to find ways of improving their biological activity and stability and to reduce the complexity of their preparation. Biological tests showed that the best compounds possess a high potential against phytopathogenic fungi in the greenhouse.     

Upper and lower estimates of the positive solutions of a higher order boundary value problem

The authors consider a higher order boundary value problem that originates from the study of boundary value problems for the beam equation. Upper and lower estimates for positive solutions of the problem are obtained.     

Periodic solutions of some models with strong Allee effects

In this paper, the authors obtain sufficient conditions for the existence of two positive periodic solutions to models representing the dynamics of a renewable resource that is subject to a strong Allee effect. The Leggett-Williams multiple fixed point theorem is used to prove the results.     

Demagnetization factors for cylindrical shells and related shapes

Magnetostatic self and interaction energies can be computed via demagnetization factors whenever the magnetic state is close to a uniform state, e.g. in the presence of a strong applied field, or when the dimensions involved are within the single-domain limit. We derive analytical expressions for the demagnetization factors of cylindrical shells and rings with rectangular and square cross-sections. The factors are given either as a combination of elliptic integrals or as a series expansion in powers of the dimensionless ratio between inner and outer radii. Limiting cases are analysed for particular ranges of the shape parameters. We also investigate the ring with a square cross-section, and the elliptic ring, where analytical expressions are provided only for small eccentricity. Finally, we introduce the dipolar coupling integral encoding magnetostatic interactions between a magnetized cylinder and a thin coating on its lateral surface.     

泥沙输运模拟综述——现状及其发展趋势

随着流体力学中数值方法的飞速发展,计算模型已经成为研究流体运动,泥沙输运和不同环境(诸如河流,湖泊及沿海地区)中相应污染物归趋过程等方面非常有吸引力的工具,在过去的30多年里,发展了许多计算水动力学/泥沙输运模型.文章追溯当前具有代表性的(一维、二维、三维)模型的发展历程,描述他们各自的特点,优势及局限,力图作为对模型方面感兴趣读者的第一指南,同时也为大家讨论模型的局限性,未来的发展趋势和研究需求方面搭建一个平台.给出了模型的表达,时空特性,水动力学和沉积物的耦合方式,处理非恒定流,推移质和悬移质,泥沙交换过程,泥沙类型(粘性或非粘性)及非均匀泥沙输运的能力.总结了不同模型的应用实例,读者可以运用这些例子作为研究模型设置,模型率定及模型验证的参考.给出了选择泥沙输运模型应遵循的原则,模型输入及率定方面存在的问题及改进的途径.探讨了现有水动力学/泥沙输运模型在处理复杂湍流,泥沙携带,流动与输沙耦合,非均匀泥沙,离散和扩散系数,河岸来沙处理等方面的局限性及改进的方向.最后,对基于多相流思想的泥沙输运模型及其它一些交叉性问题作了评述与展望.     

Multiple Solutions for Systems of Sturm–Liouville Boundary Value Problems

In this paper, the authors discuss the existence of multiple solutions to a class of second-order Sturm–Liouville boundary value systems. Their proofs are based on variational methods and critical point theory.     

Dhage iteration method for initial value problems for nonlinear first order hybrid integrodifferential equations

In this paper, we prove algorithms for the existence as well as the approximation of solutions to initial value problems (IVPs) for nonlinear first order ordinary integrodifferential equations using operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration method embodied in the recent hybrid fixed point theorems of Dhage in a partially ordered normed linear space. The approximations to the solutions are obtained under weaker mixed partial continuity and Lipschitz conditions. The hypotheses and results are also illustrated by some examples.