关键词： Algebraic structure   constructivizible (computable) structure   Turing degrees   e-degrees (enumeration degrees)   degree spectra of models  

摘要： We describe all possible relations between certain reducibities of algebraic structures which are based on the mass problems of structure presentability.

关键词： satellite signals   non-parametric approaches   solution of inverse problem  

摘要： Mathematical algorithms for processing and analysis of near-infrared data from a satellite-borne Fourier transform spectrometer have been designed. The algorithms involve non-parametric approaches based on neural networks, random forest, and empirical orthogonal functions. The results obtained from processing of model data and real measurements performed by means of the GOSAT-borne Fourier transform spectrometer are presented.

关键词： Riccati equation   Bernoulli equation   Lyapunov equation   feedback stabilization   Navier-Stokes equations  

摘要： In this paper, we consider the stabilization of the nonstationary incompressible NavierStokes equations around a stationary solution by a boundary linear feedback control. The feedback operator is obtained from the solution of the algebraic Bernoulli equation associated with the penalized linearized NavierStokes equations around an unstable stationary solution and is used to locally stabilize the original nonlinear equations. We give the explicit factorized form of the stabilizing solution of the algebraic Bernoulli equation. The numerical effectiveness of this approach is demonstrated by stabilizing the vortex shedding behind a circular obstacle. Copyright (c) 2011 John Wiley & Sons, Ltd.

关键词： 图像去噪   高斯噪声   数学形态学   小波域增强  

摘要： 为了有效滤除图像高斯噪声,将数学形态学与小波域增强相结合,提出了一种高斯噪声新型滤波算法.该算法首先将噪声图像进行二维小波分解,得到低频和高频子图像;然后保留低频子图像不变,对各高频子图像根据其噪声分布特点分别设计出多角度、多结构逐级形态学滤波器进行滤波处理,并进行小波分解系数重构;最后对经过形态学滤波后的图像进行2层小波分解,通过设计出一种新型小波增强函数对不同幅值的小波系数进行不同程度的收缩处理,在此基础上进行分解系数重构.将自适应中值滤波与数学形态学滤波与本文算法进行比较,实验证明本文滤波算法其去噪效果优于前两种算法.

关键词： 小波分析   形态滤波   融合   降噪  

摘要： 本文建立了实际工程应用中信号的仿真模型和干扰模型,运用小波变换和数学形态学相融合的方法进行降噪,并将该方法与小波阈值方法、小波模极大值法、数学形态学方法的仿真结果进行对比分析,仿真分析结果发现小波-形态融合方法能够有效的消除噪声且能较好地保留原信号的形态特征。

关键词： 车辆路径问题   多时间窗   数学模型   遗传算法  

摘要： 研究了多时间窗车辆路径问题,增加了车容量及最大行驶距离等限制条件,以总成本最低为目标,建立了整数线性规划模型,并利用Lingo软件编写了求解该模型的精确算法程序。然后通过引入最优个体保留机制对传统的遗传算法进行改进,设计了求解多时间窗车辆路径问题的遗传算法,最后通过具体实例验证了模型及算法的有效性。

关键词： 傅里叶变换   数学算法   麻省理工学院   无线通信网络   计算机科学   数字世界   研究人员   医学成像  

摘要： 数学算法的升级为数字世界的提速带来了希望。今年1月，四位来自麻省理工学院的研究人员提出了一种新算法，以替代计算机科学领域最重要的算法之一。这四位研究者——蒂娜卡塔比（DinaKatabi）、海塞姆啥桑（HaithamHassanieh）、比欧特’因迪克（PiotrIndyk）和埃里克普里斯（EricPrice）——设计出了一种能更快执行傅里叶变换的算法。傅里叶变换是一种用于处理数据流的数学算法，是数字医学成像、Wi—Fi路由器和4G无线通信网络等众多技术的运算基础。

关键词： 算法分析与设计实验   教学改革   Python算法  

摘要： 《算法分析与设计》课程是计算机科学和应用数学类专业的核心课程之一,在数学类专业同样起着非常重要的作用。本文通过对实验课程教学过程中存在的问题进行分析,提出了提高学生上机实现算法的兴趣和能力,改善教学质量的方案,并且通过了课程实践的验证,改革后的措施获得了良好的效果。

关键词： Hybrid flow shop scheduling   Identical processors   Makespan   Genetic algorithm  

摘要： This paper presents a new mathematical model for a hybrid flow shop scheduling problem with a processor assignment that minimizes makespan (i.e., C (max)) and cost of assigning a number of processors to stages. In this problem, it is assumed that there are a number of parallel identical processors which are assigned to all of the stages with an unlimited intermediate storage between any two successive stages. To solve such a hard problem, first a new heuristic algorithm is proposed to compute the makespan that is embedded in the proposed genetic algorithm in order to find the best sequence of jobs, and then processors are assigned to the stages simultaneously. A number of test problems have been solved and related results are illustrated and analyzed.