A multigrid perspective on the parallel full approximation scheme in space and time

For the numerical solution of time‐dependent partial differential equations, time‐parallel methods have recently been shown to provide a promising way to extend prevailing strong‐scaling limits of numerical codes. One of the most complex methods in this field is the “Parallel Full Approximation Scheme in Space and Time” (PFASST). PFASST already shows promising results for many use cases and benchmarks. However, a solid and reliable mathematical foundation is still missing. We show that, under certain assumptions, the PFASST algorithm can be conveniently and rigorously described as a multigrid‐in‐time method. Following this equivalence, first steps towards a comprehensive analysis of PFASST using blockwise local Fourier analysis are taken. The theoretical results are applied to examples of diffusive and advective type.     

Double-knife EDGE problems with elastic/plastic type screens

A problem of diffraction of a wave by a pair of semi-infinite screens is considered. The screens are lined with two different wave bearing materials that can support surface waves. This type of problem arises in the propagation and, scattering of acoustic and electromagnetic waves by surface wave guides. To be specific, we shall couch our problem in terms of acoustics. These diffraction problems for two parallel wave bearing screens lead to boundary value problems which are governed by the Helmholtz equation, and some specific third kind boundary conditions. Such problems are shown to be well-posed for finite energy space solutions. Their representation is given by means of the canonical factorization of a non-rational matrix function.This work was supported by DFG grant KO 634/32-1     

需求可变性降低对均值CVaR约束销售努力决策库存系统的影响

本文运用Levy提出的变换研究需求可变性降低对风险偏好零售商的库存决策、销售努力决策和期望效用的影响,用均值CVaR刻画零售商的风险偏好特性,它包括风险厌恶、风险追求,也具有损失规避的特性。首先,运用该变换定量刻画需求可变性的降低,证明该变换蕴含经典随机占优中的割准则序和二阶随机占优等。其次,给出系统的最优订货量、最优期望效用和最优销售努力水平,得到它们关于风险偏好系数的单调性,并给出降低需求可变性对期望效用的影响。第三,针对风险中性、风险厌恶(最大化CVaR)和风险追求(最小化CVaR)这三种特殊情况得到相应的结果,并给出企业在库存决策和促销决策的管理启示。最后,通过数值例子验证了得到的研究结果并给出相应的管理启示。     

由一类非线性常微分方程的抛物线解所确定的扭波

通过求解与平面动力系统的两个平衡点相连接的抛物线解,获得了6种非线性行波方程的扭波解存在条件,并给出了这些扭波解的参数表达式,以及上述解存在的参数条件．     

Finite Interval Convolution Operators with Transmission Property

We study convolution operators in Bessel potential spaces and (fractional) Sobolev spaces over a finite interval. The main purpose of the investigation is to find conditions on the convolution kernel or on a Fourier symbol of these operators under which the solutions inherit higher regularity from the data. We provide conditions which ensure the transmission property for the finite interval convolution operators between Bessel potential spaces and Sobolev spaces. These conditions lead to smoothness preserving properties of operators defined in the above-mentioned spaces where the kernel, cokernel and, therefore, indices do not depend on the order of differentiability. In the case of invertibility of the finite interval convolution operator, a representation of its inverse is presented in terms of the canonical factorization of a related Fourier symbol matrix function.     

一类求解抛物型方程侧边值问题的最优滤波方法

该文考虑一类特殊的抛物型方程侧边值问题,即一类含有对流项的非标准逆热传导问题. 给定在x=1处的温度测量值来确定区间(0,1)上的未知解u(x, t). 这是一类不适定问题,即问题的解(如果解存在)不连续依赖于数据.为了求解这一问题, 必须采用某些正则化技巧. 该文给出了一种最优滤波方法, 使得问题的真实解和近似解之间的误差估计达到了Hölder型最优. 同时还证明了问题的解在x=0处的收敛性.     

含联苯结构的环氧树脂固化性能的研究

以3,3′,5,5′-四甲基联苯二酚为单体,合成了一种含联苯结构的环氧树脂.用DDM和DDS为固化剂对环氧树脂的固化性能进行了研究,发现与双酚A型环氧树脂相比,含有联苯结构的环氧树脂具有更好的耐热性,同时在耐湿性方面也有很大改进.     

一种新型磺化聚醚醚酮的合成、表征和性能

以特丁基对苯二酚、3,3′-二磺酸钠基-4,4′-二氟二苯酮和4,4′-二氟二苯酮为单体,制备了具有高磺化度的聚醚醚酮.该系列聚合物可溶,并具有良好的成膜性.对聚合物及其膜的一些性能进行了研究.