一次不定方程在数学竞赛及其数学综合训练题中是有其特殊的地位的,这一内容在中学阶段未作系统的教学,许多学生在遇到这类问题时往往会感到不知所措。本文将简略地介绍一些求解一次不定方程的知识。我们把形如 p1x1+p2x2+…+pnxn=r ① ...一次不定方程在数学竞赛及其数学综合训练题中是有其特殊的地位的,这一内容在中学阶段未作系统的教学,许多学生在遇到这类问题时往往会感到不知所措。本文将简略地介绍一些求解一次不定方程的知识。我们把形如 p1x1+p2x2+…+pnxn=r ① （p1、p2、…、pr为正理数,r为整数,n≥2）的方程叫做n元一次不定方程。一般地说,它有无穷多个解。但它的解如只限定在非负整数集或正整数集内,有时,它的解也可以是有限的或无解。如二元一次方程x+y=3,展开更多
The subset threshold auto regressive (SSTAR) model, which is capable of reproducing the limit cycle behavior of nonlinear time series, is introduced. The algorithm for fitting the sampled data with SSTAR model is pr...The subset threshold auto regressive (SSTAR) model, which is capable of reproducing the limit cycle behavior of nonlinear time series, is introduced. The algorithm for fitting the sampled data with SSTAR model is proposed and applied to model and forecast power load. Numerical example verifies that desirable accuracy of short term load forecasting can be achieved by using the SSTAR model.展开更多
To smooth the correlation process from bio-virus diffusion to emergency relief response,the Gaussian plume model is used to describe the diffusion of dangerous sources,where the bio-virus concentration at any given po...To smooth the correlation process from bio-virus diffusion to emergency relief response,the Gaussian plume model is used to describe the diffusion of dangerous sources,where the bio-virus concentration at any given point in affected areas can be calculated.And the toxic load rule is introduced to define the borderline of the dangerous area at different levels.Combined with this,different emergency levels of different demand points in dangerous areas are confirmed using fuzzy clustering,which allows demand points at the same emergency level to cluster in a group.Some effective emergency relief centers are chosen from the candidate hospitals which are located in different emergency level affected areas by set covering.Bioterrorism experiments which were conducted in Nanjing,Jiangsu province are simulated,and the results indicate that the novel method can be used efficiently by decision makers during an actual anti-bioterrorism relief.展开更多
The container loading problem (CLP) is a well-known NP-hard problem. Due to the computation complexity, heuristics is an often-sought approach. This article proposes two heuristics to pack homogeneous rectangular boxe...The container loading problem (CLP) is a well-known NP-hard problem. Due to the computation complexity, heuristics is an often-sought approach. This article proposes two heuristics to pack homogeneous rectangular boxes into a single container. Both algorithms adopt the concept of building layers on one face of the container, but the first heuristic determines the layer face once for all, while the second treats the remaining container space as a reduced-sized container after one layer is loaded and, hence, selects the layer face dynamically. To handle the layout design problem at a layer's level, a block-based 2D packing procedure is also developed. Numerical studies demonstrate the efficiency of the heuristics.展开更多
文摘非负矩阵分解(non-negative matrix factorization,NMF)是一种常用的非负多元数据描述方法。处理数据矩阵集时,NMF描述力不强、推广性差。基于双线性型的非负矩阵集分解(bilinear form-based non-negative matrix set factorization,BFBNMSF)是对NMF的扩展,处理数据矩阵集时,BFBNMSF比NMF描述力强、推广性好。但BFBNMSF在初始化时使用随机分布,为使BFBNMSF更快收敛,该文提出一种基于奇异值分解(Singular value decomposition,SVD)初始化的BFBNMSF,即SVD-BFBNMSF,对系数矩阵进行初始化,已达到快速收敛的目的。实验结果表明:与传统BFBNMSF比较,该方法在收敛速度确有所改善。
文摘一次不定方程在数学竞赛及其数学综合训练题中是有其特殊的地位的,这一内容在中学阶段未作系统的教学,许多学生在遇到这类问题时往往会感到不知所措。本文将简略地介绍一些求解一次不定方程的知识。我们把形如 p1x1+p2x2+…+pnxn=r ① （p1、p2、…、pr为正理数,r为整数,n≥2）的方程叫做n元一次不定方程。一般地说,它有无穷多个解。但它的解如只限定在非负整数集或正整数集内,有时,它的解也可以是有限的或无解。如二元一次方程x+y=3,
文摘The subset threshold auto regressive (SSTAR) model, which is capable of reproducing the limit cycle behavior of nonlinear time series, is introduced. The algorithm for fitting the sampled data with SSTAR model is proposed and applied to model and forecast power load. Numerical example verifies that desirable accuracy of short term load forecasting can be achieved by using the SSTAR model.
基金The National Natural Science Foundation of China(No.70671021)the National Key Technology R&D Program of China during the 11th Five-Year Plan Period(No.2006BAH02A06)
文摘To smooth the correlation process from bio-virus diffusion to emergency relief response,the Gaussian plume model is used to describe the diffusion of dangerous sources,where the bio-virus concentration at any given point in affected areas can be calculated.And the toxic load rule is introduced to define the borderline of the dangerous area at different levels.Combined with this,different emergency levels of different demand points in dangerous areas are confirmed using fuzzy clustering,which allows demand points at the same emergency level to cluster in a group.Some effective emergency relief centers are chosen from the candidate hospitals which are located in different emergency level affected areas by set covering.Bioterrorism experiments which were conducted in Nanjing,Jiangsu province are simulated,and the results indicate that the novel method can be used efficiently by decision makers during an actual anti-bioterrorism relief.
基金the Natural Sciences and Engineering Research Council of Canada (NSERC) under the Discovery Grant Program
文摘The container loading problem (CLP) is a well-known NP-hard problem. Due to the computation complexity, heuristics is an often-sought approach. This article proposes two heuristics to pack homogeneous rectangular boxes into a single container. Both algorithms adopt the concept of building layers on one face of the container, but the first heuristic determines the layer face once for all, while the second treats the remaining container space as a reduced-sized container after one layer is loaded and, hence, selects the layer face dynamically. To handle the layout design problem at a layer's level, a block-based 2D packing procedure is also developed. Numerical studies demonstrate the efficiency of the heuristics.
