关键词： Computer algorithms   Mathematical programming   Mathematical analysis   Algebra  

摘要： A computationally efficient algorithm is presented for 3-D near-field source localisation using a uniform circular array. Algebraic relations are demonstrated between the incident angles (elevation angle and azimuth angle) under the far-field assumption and the actual near-field location (range, elevation angle, and azimuth angle). Using these relations as paths to follow to the peak of the 3-D MUSIC spectrum, the proposed algorithm replaces the 3-D search required in the conventional 3-D MUSIC with a 1-D path-following after a 2-D initialisation, thereby reducing the computational burden.

关键词： 投资组合   有效前沿   借贷   可容许偏差   可能性理论   遗传算法   交易费用   效用函数  

摘要： 投资组合研究主要是围绕如何建立适合各种要求的模型和提出有效算法.随着数学新理论和新方法的不断出现,使得投资组合的理论、模型及方法能够得到进一步发展.该文将从理论和应用上系统研究一般投资约束条件下投资组合的若干新模型和新算法.该文研究的主要工作和创新性成果体现在以下几个方面:1.建立了一般投资约束条件下风险资产有效投资组合模型,分别给出了不允许卖空风险资产情形、投资数量有下界限制情形有效投资组合(有效前沿)的解析表示,提出了投资数量有上下界限制情形有效投资组合的遗传算法.2.建立了一般投资约束条件下存在无风险资产的有效投资组合模型.3.在假定资产的期望收益和风险具有可容许偏差条件下建立了可容许有效投资组合模型.4.建立了一般投资约束条件下具有交易费用的有效投资组合均值—绝对离差模型(MAD),提出了ε偏差逐段线性替换和ε偏差有效投资组合概念,给出了一个求ε偏差有效投资组合的修正分枝定界算法.5.定义了模糊数的上、下可能性方差和可能性协方差,修正了Carlsson和Fuller提出的可能性方差与概率方差意义不符和可能性协方差非负的缺陷,给出了类似于概率论的可能性方差有关理论结果,建立了有效投资组合的上、下可能性均值—方差模型和提出了上、下可能性有效投资组合(有效前沿)及算法.6.建立了连续支付红利并且市场模型系数r(t),α<,i>(t),σ<,ij>(t)(1≤i,j≤n)和β(t)都为连续变化及值函数V(x(t),π(t),c(t))为一般形式的最优投资消费模型,给出使总体消费折扣效用最大化且具有反馈形式的最优投资比例及最优消费的显式解.

关键词： 试井资料   多解性   储层   试井解释   数学算法   试井设计  

摘要： 试井成果是油田制定开发方案、措施选井及评估的重要依据 ,但资料的多解性严重制约着试井成果的准确性和可靠性 ,从而降低了使用价值。从产生试井资料多解性的来源入手 ,分析了试井设计、资料录取、模型选择、数学算法等因素对试井解释结果的影响 。

关键词： polynomial-time primal-dual interior-point methods   JB-algebras   infinite-dimensional problems   optimal control problems  

摘要： We consider primal-dual algorithms for certain types of infinite-dimensional optimization problems. Our approach is based on the generalization of the technique of finite-dimensional Euclidean Jordan algebras to the case of infinite-dimensional JB-algebras of finite rank. This generalization enables us to develop polynomial-time primal-dual algorithms for "infinite-dimensional second-order cone programs." We consider as an example a long-step primal-dual algorithm based on the Nesterov-Todd direction. It is shown that this algorithm can be generalized along with complexity estimates to the infinite-dimensional situation under consideration. An application is given to an important problem of control theory: multi-criteria analytic design of the linear regulator. The calculation of the Nesterov-Todd direction requires in this case solving one matrix differential Riccati equation plus solving a finite-dimensional system of linear algebraic equations on each iteration. The number of equations and unknown variables of this algebraic system is m+1, where m is a number of quadratic performance criteria.

关键词： continuous casting of steel   mathematical modeling   optimization methods   genetic algorithm  

摘要： The control of quality in continuous casting products cannot be achieved without a knowledge base which incorporates parameters and variables of influence such as: equipment characteristics, steel, each component of the system and operational conditions. This work presents the development of a computational algorithm (software) applied to maximize the quality of steel billets produced by continuous casting. A mathematical model of solidification works integrated with a genetic search algorithm and a knowledge base of operational parameters. The optimization strategy selects a set of cooling conditions (mold and secondary cooling) and metallurgical criteria in order to attain highest product quality, which is related to a homogeneous thermal behavior during solidification. The results of simulations performed using the mathematical model are validated against both experimental and literature results and a good agreement is observed. Using the numerical model linked to a search method and the knowledge base, results can be produced for determining optimum settings of casting conditions, which are conducive to the best strand surface temperature profile and metallurgical length. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： quantum algorithms   Pell's equation   quantum Fourier transform  

摘要： Pell's equation is x(2) - dy(2) = 1, where d is a square-free integer and we seek positive integer solutions x, y > 0. Let (x(0), y(0)) be the smallest solution (i.e., having smallest A = x(0) + y(0) rootd). Lagrange showed that every solution can easily be constructed from A so given d it suffices to compute A. It is known that A can be exponentially large in d so just to write down A we need exponential time in the input size log d. Hence we introduce the regulator R = lnA and ask for the value of R to n decimal places. The best known classical algorithm has sub-exponential running time O(exp rootlog d, poly(n)). Hallgren's quantum algorithm gives the result in polynomial time O(poly(log d), poly(n)) with probability 1/poly(log d). The idea of the algorithm falls into two parts: using the formalism of algebraic number theory we convert the problem of solving Pell's equation into the problem of determining R as the period of a function on the real numbers. Then we generalise the quantum Fourier transform period finding algorithm to work in this situation of an irrational period on the (not finitely generated) abelian group of real numbers. This paper is intended to be accessible to a reader having no prior acquaintance with algebraic number theory;we give a self-contained account of all the necessary concepts and we give elementary proofs of all the results needed. Then we go on to describe Hallgren's generalisation of the quantum period finding algorithm, which provides the efficient computational solution of Pell's equation in the above sense. (C) 2003 Elsevier Science (USA). All rights reserved.

关键词： adaptive algorithm   partial differential-algebraic equation  

摘要： This paper describes an adaptive algorithm for optimal control of time-dependent partial differential-algebraic equation (PDAE) systems. A direct method based on a modified multiple shooting type technique and sequential quadratic programming (SQP) is used for solving the optimal control problem, while an adaptive mesh refinement (AMR) algorithm is employed to dynamically adapt the spatial integration mesh. Issues of coupling the AMR solver to the optimization algorithm are addressed. For time-dependent PDAEs which can benefit from the use of an adaptive mesh, the resulting method is shown to be highly efficient. Copyright (C) 2003 John Wiley Sons, Ltd.

关键词： 图像分割   小波分析   多分辨率分析   边缘检测   多尺度分析   阈值选择   数学形态学  

摘要： 该文对图像分割技术进行了综述和探讨.在此基础上,以图像分割技术中的边缘检测技术为突破口,结合了近年来具有\"数学显微镜\"美誉的小波分析工具和发展迅速的数学形态学处理方法,在Mallat小波模多尺度边缘检测算法的基础上,提出了以体现侧抑制现象的Bubble函数作为平滑函数进行多尺度小波模边缘检测,并利用数学形态学方法进行边缘连接的多尺度边缘检测算法.该文算法能够进行单像素宽的边缘检测,并能够将检测出的边缘进行连接和标记,得到较好的边缘检测结果.由于采用多尺度处理方法,对于噪声较多的图像,采用较大的尺度参数能够很好的过滤噪声,对于没有噪声的图像,采用较小的尺度参数能够有效的检测出细节.由于阈值采用自适应的方法获得,该算法不仅能够处理反差较小的图像也能处理具有较大反差的图像,并且能够得到较好的处理效果.

关键词： 算法多样化   创新思维   小学   数学教学   教学研究  

关键词： KIDNEY tubules   URINE   EXAMPLE  

摘要： A nonlinear optimization technique, in conjunction with a single-nephron, single-solute mathematical model of the quail urine concentrating mechanism, was used to estimate parameter sets that optimize a measure of concentrating mechanism efficiency, viz., the ratio of the free-water absorption rate to the total NaCl active transport rate. The optimization algorithm, which is independent of the numerical method used to solve the model equations, runs in a few minutes on a 1000 MHz desktop computer. The parameters varied were: tubular permeabilities to water and solute;maximum active solute transport rates of the ascending limb of Henle and the collecting duct (CD);length of the prebend enlargement (PBE) of the descending limb;fractional solute delivery to the CD;solute concentration of tubular fluid entering the CD at the cortico-medullary boundary;and rate of exponential CD population decrease along the medullary cone. Using a base-case parameter set and parameter bounds suggested by physiologic experiments, the optimization algorithm identified a maximum-efficiency set of parameter values that increased efficiency by 40% above base-case efficiency;a minimum-efficiency set reduced efficiency by about 41%. When maximum-efficiency parameter values were computed as medullary length varied over the physiologic range, the PBE was found to make up 88% of a short medullary cone but only 8% of a long medullary cone. (C) 2003 Society for Mathematical Biology. Published by Elsevier Science Ltd. All rights reserved.