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.     

基于MEMS微镜的傅里叶变换光谱仪原理与分析

提出了一种新型的基于可编程MEMS(micro-electro-mechanical systems)微镜的微型傅里叶变换红外光谱仪。该光谱仪采用可编程MEMS微镜和倾斜反射镜替代了传统傅里叶变换光谱仪的动镜系统。理论分析了该光谱仪的工作原理,并进行了计算机仿真,验证了该方法的可行性。结果表明,该光谱系统能够准确地还原光谱信息,其光谱分辨率在近红外区域小于5 nm,波长准确性约1 nm,系统理论上的信号采集周期约50 ms。适合于利用阿达玛变换提高信噪比,可应用于微量物质检测。     

碳酸二甲酯在固体碱上吸附和活化的原位红外光谱研究

采用原位红外技术研究了碳酸二甲酯在氧化镁、氟化镁、镁铝复合氧化物和氟改性的镁铝复合氧化物4种固体碱表面上的吸附和活化行为。结果表明:碳酸二甲酯以单、双齿两种形态吸附于固体碱的表面,双齿吸附的比单齿吸附的更易活化。碳酸二甲酯吸附于氧化镁和镁铝复合氧化物上活化生成甲氧基,吸附于氟化镁上活化生成甲氟基;而吸附于氟改性的镁铝复合氧化物上优先活化生成甲氟基,随着吸附表面温度的升高,逐渐有甲氧基生成,说明氟改性的镁铝复合氧化物是一种优良的甲基化反应催化剂。     

二维N－S方程的Fourier非线性Galerkin方法

本文对周期边界条件Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程，证明了其Ｆｏｕｒｉｅｒ非线性Ｇａｌｅｒｋｉｎ逼近解的存在唯一性，同时给出了逼近解的误差估计．     

On the counting function of the lattice profile of periodic sequences

The lattice profile analyzes the intrinsic structure of pseudorandom number sequences with applications in Monte Carlo methods and cryptology. In this paper, using the discrete Fourier transform for periodic sequences and the relation between the lattice profile and the linear complexity, we give general formulas for the expected value, variance, and counting function of the lattice profile of periodic sequences with fixed period. Moreover, we determine in a more explicit form the expected value, variance, and counting function of the lattice profile of periodic sequences for special values of the period.     

L~p(R~m× R~n) boundedness for the Marcinkiewicz integral on product spaces

Lp(Rm × Rn) boundedness is considered for the multiple Marcinkiewicz integral. Some size conditions implying the LP(Rm × Rn) boundedness of the multiple Marcinkiewicz integral for some fixed 1 < p <∞ are obtained.     

Optimal design of profit sharing rates by FFT

This paper addresses the calculation of a fair profit sharing rate for participating policies with a minimum interest rate guaranteed. The bonus credited to policies depends on the performance of a basket of two assets: a stock and a zero coupon bond and on the guarantee. The dynamics of the instantaneous short rates are driven by a Hull and White model, whereas the stocks follow a double exponential jump-diffusion model. The participation level is determined such that the return retained by the insurer is sufficient to hedge the interest rate guaranteed. Given that the return of the total asset is not lognormal, we rely on a Fast Fourier Transform to compute the fair value of bonus and guarantee options.     

Solutions for the fractional Landau-Lifshitz equation

This article considers the dynamic equation of a reduced model for thin-film micromagnetics deduced by A. DeSimone, R.V. Kohn and F. Otto in [A. DeSimone, R.V. Kohn, F. Otto, A reduced theory for thin-film micromagnetics, Comm. Pure Appl. Math. 55 (2002) 1-53]. To derive the existence of weak solutions under periodical boundary condition, the authors first prove the existence of smooth solutions for the approximating equation, then prove the convergence of the viscosity solution when the viscosity term vanishes, which implies the existence of solutions for the original equation.     

基于傅立叶变换的SVJ模型的欧式期权定价

为了更加精确的计算期权价格,将结合随机波动和跳扩散模型(以下简称SVJ模型)以更好的描述期权标的资产价格过程,然而这样的价格过程无法得到概率密度函数的封闭形式,而只能得到包含特殊函数和无限求和的复杂的表达式.不过它们的特征函数都是封闭且是唯一的,因而可以通过它们的特征函数,并运用两种傅立叶变换的方法来求出期权价格.其中FFT算法计算的结果将与Monte Carlo模拟得出的结果进行比较,然后再将SVJ模型的计算结果和Black-Scholes模型进行比较.     

平移不变线性算子的连续性

利用一类紧ａｂｅｌｉａｎ群Ｇ上的函数空间Ｌ２（Ｇ）上以及Ｄ（Ｒ）上平移不变线性泛函的自动连续性并结合闭图象定理证明这些空间上的平移不变线性算子连续。