关键词： 数学形态学   骨架   抽取算法   图象分析  

摘要： 骨架是图象几何形态的重要拓扑描述，在图象分析领域有广泛应用。本文给出了利用数学形态学方法抽取图象骨架的算法及对该算法的详细证明。利用骨架算法得到的骨架子集可部分或完全重建原始图象，因而可用于对原始图象编码或描述原始图象的特征。该算法适用于模拟空间，同时也适用于数字空间。本文还给出了数字空间中的快速骨架抽取算法。

关键词： Tomography   Linear algebraic algoritims   QR decomposition  

摘要： Computed tomography measurement was studied with linear algebraic methods of image reconstruction. The singular value and QR decompositions of the projection matrix give new types of series expansions of the plasma image and present stable and high speed imaging which might be useful for monitoring the time evolution of plasma in a fusion device with angular-limited, sparse and noisy data in projection observation. (C) 1997 Elsevier Science S.A.

关键词： 神经网络   数学神经网络   学习算法   梯度下降法  

摘要： 重点研究神经网络的学习算法，给出了单入单出、多入单出、单入多出及多入多出网络学习算法的通用公式．指出了目前人工神经网络研究的方法没有跑出计算数学的“圈子”，人工神经网络所具有的“优点”（如并行性处理）并没有真正的实现．

摘要： In this paper, we examine the problem of incrementally evaluating algebraic functions. In particular, if f(x(1), x(2),..., x(n)) = (y(1), y(2),..., y(m)) is an algebraic problem, we consider answering on-line requests of the form ''change input x(i) to value v'' or ''what is the value of output y(i)?'' We first present lower bounds for some simply stated algebraic problems such as multipoint polynomial evaluation, polynomial reciprocal, and extended polynomial GCD, proving an Omega(n) lower bound for the incremental evaluation of these functions. In addition, we prove two time-space trade-off theorems that apply to incremental algorithms for almost all algebraic functions. We then derive several general-purpose algorithm design techniques and apply them to several fundamental algebraic problems. For example, we give an O(root n) time per request algorithm for incremental DFT. We also present a design technique for serving incremental requests using a parallel machine, giving a choice of either optimal work with respect to the sequential incremental algorithm or superfast algorithms with O(log log n) time per request with a sublinear number of processors. (C) 1997 Academic Press.

摘要： Features Math Works Inc.'s Matlab 5.0 mathematics-based development tool that combines data modelling and analysis functions with the ability to interactively explore alternatives in complex-algorithm design. Graphical user interface development environment; Visual debugging function.

关键词： 决策系统   价格预测   大规模资源分配   分解协调   禁忌搜索   遗传算法   混合算法  

摘要： 该文首先介绍了一体化系统中的线性规划模型和系统开发的主要技术,对原有的启发式综合平衡模型和产品价格预测方法进行了分析,指出了原系统的不足.然后,分析了宝钢现有的价格管理系统以及一体化系统中的预测方法,提出了新的销售价格管理系统方案,建立了定量数据和定性信息相结合的多元模糊线性回归模型,通过产品价格数字模拟效果显著.其次,在分析一体化系统两步启发式综合平衡模型的基础上,用传统的Wolfe分解协调算法建立了新的综合平衡模型,通过模拟实验证明:在最优性和寻优效率方面,Wolfe算法优于两步启发式算法,同时也指出Wolfe算法求解大规模规划问题的不足.该文接着介绍了禁忌搜索算法基本思想,讨论了TS新型优化算法的改进方案.对于传统大规模规划问题,建立了资源分配模型;针对大规模规划的具体特点,研究了新编码、短期记忆、长期记忆、动态步长等TS的新改进方案.通过数字模拟,改进禁忌搜索算法解大规模资源分析问题十分有效.该文针对大规模资源分配问题,研究了遗传算法和禁忌搜索算法相结合的新混合算法.通过数字模拟验证了参数选用和算法改进的合理性,表明了新混合算法对完善综合平衡模型的有效性.

摘要： From the philosophical viewpoint, two interpretations of the quantum measurement process are possible: According to the first interpretation, when we measure an observable, the measured system moves into one of the eigenstates of this observable (''the wave function collapses'');in other words, the universe ''branches'' by itself, due to the very measurement procedure, even if we do not use the result of the measurement. According to the second interpretation, the system simply moves into a mixture of eigenstates, and the actual ''branching'' occurs only when an observer reads the measurement results. According to the first interpretation, a mixture is a purely mathematical construction, and in the real physical world, a mixture actually means that the system is in one of the ''component'' states. In this paper, we analyze this difference from the viewpoint of algorithmic information theory;as a result of this analysis, we argue that only pure quantum states are fundamental, while mixtures are simply useful mathematical constructions.

关键词： MAGNETIC fields   MATHEMATICAL models  

摘要： Proposes an analytical inverse solution for a dipole source location problem. Development of magnetic field algorithms based upon the method; Cases when the system produces a static magnetic field; Measurement algorithms; Probabilistic test of inverse solution; Numerical simulation which verifies validity of the solving method; Estimation of the results.

关键词： Jordan algebras   interior-point methods   complexity estimates  

摘要： We provide an introduction to the theory of interior-point algorithms of optimization based on the theory of Euclidean Jordan algebras. A short-step path-following algorithm for the convex quadratic problem on the domain, obtained as the intersection of a symmetric cone with an affine subspace, is considered. Connections with the Linear monotone complementarity problem are discussed. Complexity estimates in terms of the rank of the corresponding Jordan algebra are obtained. Necessary results from the theory of Euclidean Jordan algebras are presented.