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关键词： Detectors   Photonics   Optical arrays   Optical transmitters   Optical receivers   Adaptive optics   Error probability   free-space optical communications   Gaussian beam   photon counting detector arrays  

摘要： Photon counting detector arrays are commonly used for free-space optical communications in deep space. Such detector arrays-by virtue of their size-help in the collection of the optical signal even when there is some misalignment between the transmitter and receiver systems. In this paper, we argue that, for the common Gaussian beam profile, a detector array receiver is more useful for minimizing the probability of error than a single detector receiver of the same dimensions. Furthermore, the improvement in the error probability is more pronounced for low signal-to-noise ratio conditions, and the probability of error decreases monotonically as a function of the number of detectors in the array. However, communication with detector arrays results in a larger computational and hardware complexity at the receiver.

关键词： Micropolar materials   Crystal plasticity   Quaternions   Cosserat theory   Numerical simulations   Preconditioning  

摘要： This article deals with the mathematical derivation and the validation over benchmark examples of a numerical method for the solution of a finite-strain holonomic (rate-independent) Cosserat plasticity problem for materials, possibly with microstructure. Two improvements are made in contrast to earlier approaches: First, the micro-rotations are parameterized with the help of an Euler-Rodrigues formula related to quaternions. Secondly, as main result, a novel two-pass preconditioning scheme for searching the energy-minimizing solutions based on the limited memory Broyden-Fletcher-Goldstein-Shanno quasi-Newton method is proposed that consists of a predictor step and a corrector-iteration. After outlining the necessary adaptations to the model, numerical simulations compare the performance and efficiency of the new and the old algorithm. The proposed numerical model can be effectively employed for studying the mechanical response of complicated materials featuring large size effects.

关键词： 65Y05   65F08  

摘要： Convergence of domain decomposition methods rely heavily on the efficiency of the coarse space used in the second level. The GenEO coarse space has been shown to lead to a robust two-level Schwarz preconditioner which scales well over multiple cores (Spillane et al. in Numer Math 126(4):741-770, 2014. 10.1007/s00211-013-0576-y;Dolean et al. in An introduction to domain decomposition methods: algorithms, theory and parallel implementation, SIAM, Philadelphia, 2015). The robustness is due to its good approximation properties for problems with highly heterogeneous material parameters. It is available in the finite element packages FreeFem++ (Hecht in J Numer Math 20(3-4):251-265, 2012), Feel++ (Prud'homme in Sci Program 14(2):81-110, 2006), Dune (Blatt et al. in Arch Numer Softw 4(100):13-29, 2016) and is implemented as a standalone library in HPDDM (Jolivet and Nataf in HPDDM: high-Performance Unified framework for Domain Decomposition methods, MPI-C++ library, 2014. ) and as such is available as well as a PETSc (Balay et al. in: Arge, Bruaset, Langtangen, (eds) Modern software tools in scientific computing, Birkhauser Press, Basel, 1997) preconditioner. But the coarse component of the preconditioner can ultimately become a bottleneck if the number of subdomains is very large and exact solves are used. It is therefore interesting to consider the effect of inexact coarse solves. In this paper, robustness of GenEO methods is analyzed with respect to inexact coarse solves. Interestingly, the GenEO-2 method introduced in Haferssas et al. (SIAM J Sci Comput 39(4):A1345-A1365, 2017. 10.1137/16M1060066) has to be modified in order to be able to prove its robustness in this context.

关键词： Diagnosis  

摘要： A mathematical model is proposed to study the dynamics of the transmission of rabies, incorporating predation of dogs by humans. The model is shown to have a unique disease-free equilibrium which is globally asymptotically stable whenever Script capital R-0=1. Local sensitivity analysis suggests that the disease can be controlled through reducing contact with infected dogs, increasing immunization of dogs, screening recruited dogs, culling of infected dogs, and use of dog meat as a delicacy.

关键词： 数学师范专业   专业基础课程   教师教育   改革实践  

摘要： 数学学科是我国教育体系的重要组成部分,如何在数学教学过程中让学生更好更快的掌握知识,获得能力,树立正确观念是每一位数学教师在教学过程中需要掌握的基本功,这也要求教师在工作中要拥有较强的专业能力与综合素质。想要培养教师这方面的能力就要从源头抓起,因此,在数学师范专业基础课程的构建方面需要打牢基础,在数学师范专业教学过程中要做好数学课程的建设。从教师教育的视角考虑,通过分析数学师范专业基础课程数学分析的改革,为教师教育提供更好的指导。

关键词： Hysteresis   Dynamic Preisach model   Transient eddy current   Finite element method  

摘要： Hysteresis is a phenomenon that is observed in a great variety of physical systems, which leads to a nonlinear and multivalued behavior, making their modeling and control difficult. Even though the analysis and mathematical properties of several rate-independent and rate-dependent hysteresis models are known, this is not the case for the Bertotti's rate-dependent extension of the classical Preisach model;the so-called dynamic Preisach model for which current approaches lack a proper functional analytic framework which is essential to formulate optimization problems and develop stable numerics, both being crucial in practice. This paper deals with the description and mathematical analysis of the dynamic Preisach hysteresis model. Toward that end, we complete a widely accepted definition of the dynamic model commonly used to describe the constitutive relation between the magnetic field H and the magnetic induction B, in which, the values of B not only depends on the present values of H but also on the past history and its velocity. We first analyze mathematically some important properties of the model and compare them with known results for the static Preisach model. Then, we consider a parabolic problem with dynamic hysteresis motivated by electromagnetic field equations. Under suitable assumptions, we prove the existence of a solution of a weak formulation of the problem and solve it numerically. Finally, we report a numerical test in order to assess the order of convergence and to illustrate the behavior of the numerical solution for different configurations of the dynamic Preisach model. (C) 2019 Elsevier B.V. All rights reserved.

关键词： 初中   数学   应用   培养  

摘要： 初中数学中考中应用问题是必考的一个知识点,如何提高学生对数学问题的分析理解能力,解决实际问题,本文作者根据多年的教学经验,从课堂上,教材中,到走出校园,引领同学钻研教材,掌握知识点,培养学生的分析,解决问题能力。

关键词： American option pricing   Counterparty risk   (non)linear PDEs   Parabolic variational inequalities   Method of characteristics   Finite elements  

摘要： In this article we propose new linear and nonlinear partial differential equations (PDEs) models for pricing American options and total value adjustment in the presence of counterparty risk. An innovative aspect comes from the consideration of stochastic spreads, which increases the dimension of the problem. In this setting, we pose new complementarity problems associated to linear and nonlinear PDEs. Moreover, using the mathematical tools of semilinear variational inequalities for parabolic equations, we prove the existence and uniqueness of a solution for these models. For the numerical solution, we mainly combine a semi-Lagrangian time discretization scheme, a fixed point method to cope with nonlinear terms and a finite element method for the spatial discretization, jointly with an augmented Lagrangian active set method to solve the fully discretized complementarity problem. Finally, numerical examples illustrate the expected behaviour of the option prices and the corresponding total value adjustment, as well as the performance of the proposed numerical techniques. Moreover, we compare the numerical results from the PDEs approach with those obtained by applying Monte Carlo techniques. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： 信息与计算科学   数学分析   课程实践教学  

摘要： 文章通过目前《数学分析》课程的教学现状,针对信息与计算科学专业《数学分析》课程进行实践教学探索。在《数学分析》课程中引入数学软件教学,同时通过对教学效果进行研究分析,提出加强数学软件实践、改革教学方式、改进教学手段的必要性,并对实践教学改革提出可行性建议。

关键词： Maxwell's equations   Metamaterial   Finite element method   Perfectly matched layers   Edge element  

摘要： In this paper we investigate one Perfectly Matched Layer (PML) model proposed by Ziolkowski in 1999. Various schemes for solving this PML model have been developed and have been shown to be effective in absorbing outgoing waves when the wave propagation in unbounded domain problem is reduced to a bounded domain problem. However, a rigorous analysis of this model is lacking. In this paper we establish the stability of this PML model and propose a fully-discrete finite element scheme to solve this model with edge elements. Discrete stability and optimal error estimate of this scheme are proved. Numerical results justifying the analysis and demonstrating the effectiveness of this PML model are presented. (C) 2019 Elsevier B.V. All rights reserved.