This note explores the relations between two different methods. The first one is the Alternating Least Squares (ALS) method for calculating a rank<em>-k</em> approximation of a real <em>m</em>&...This note explores the relations between two different methods. The first one is the Alternating Least Squares (ALS) method for calculating a rank<em>-k</em> approximation of a real <em>m</em>×<em>n</em> matrix, <em>A</em>. This method has important applications in nonnegative matrix factorizations, in matrix completion problems, and in tensor approximations. The second method is called Orthogonal Iterations. Other names of this method are Subspace Iterations, Simultaneous Iterations, and block-Power method. Given a real symmetric matrix, <em>G</em>, this method computes<em> k</em> dominant eigenvectors of <em>G</em>. To see the relation between these methods we assume that <em>G </em>=<em> A</em><sup>T</sup> <em>A</em>. It is shown that in this case the two methods generate the same sequence of subspaces, and the same sequence of low-rank approximations. This equivalence provides new insight into the convergence properties of both methods.展开更多
In this paper, we extend the alternate Broyden's method to the multiple version fbi solving lincar leastsquarc systems with multiple right-hand sides. We show that the method possesses property of a finite tcrmina...In this paper, we extend the alternate Broyden's method to the multiple version fbi solving lincar leastsquarc systems with multiple right-hand sides. We show that the method possesses property of a finite tcrmination.Some numerical cxperiments are gi von to inustrate the effectiveness of the method.展开更多
In factor analysis, a factor loading matrix is often rotated to a simple target matrix for its simplicity. For the purpose, Procrustes rotation minimizes the discrepancy between the target and rotated loadings using t...In factor analysis, a factor loading matrix is often rotated to a simple target matrix for its simplicity. For the purpose, Procrustes rotation minimizes the discrepancy between the target and rotated loadings using two types of approximation: 1) approximate the zeros in the target by the non-zeros in the loadings, and 2) approximate the non-zeros in the target by the non-zeros in the loadings. The central issue of Procrustes rotation considered in the article is that it equally treats the two types of approximation, while the former is more important for simplifying the loading matrix. Furthermore, a well-known issue of Simplimax is the computational inefficiency in estimating the sparse target matrix, which yields a considerable number of local minima. The research proposes a new rotation procedure that consists of the following two stages. The first stage estimates sparse target matrix with lesser computational cost by regularization technique. In the second stage, a loading matrix is rotated to the target, emphasizing on the approximation of non-zeros to zeros in the target by least squares criterion with generalized weighing that is newly proposed by the study. The simulation study and real data examples revealed that the proposed method surely simplifies loading matrices.展开更多
信道仿真器中不同通道之间的幅相不一致会使系统性能恶化,通常的解决方法是在接收信道中加入校准均衡器,以校正信号传输路径中的幅度和相位失真。为了降低通道间的幅相误差、提高信道均衡效果,文中设计了一种正则化交替频域最小二乘优...信道仿真器中不同通道之间的幅相不一致会使系统性能恶化,通常的解决方法是在接收信道中加入校准均衡器,以校正信号传输路径中的幅度和相位失真。为了降低通道间的幅相误差、提高信道均衡效果,文中设计了一种正则化交替频域最小二乘优化算法(Regularized Alternating Frequency Domain Least Squares Optimization,RA-ALO)。该算法采用正则化来确保矩阵求逆时解的正确性,并使用交替最小二乘法(Alternating Least Squares,ALS)寻找最优解来增强均衡器性能。仿真结果表明,在信道均衡方面,与正则化算法和求伪逆算法相比,该算法具有更低的幅相误差、更优的校准性能。展开更多
The Global Position System(GPS)is a reliable method for positioning in most scenarios,but it falls short in harsh environments like urban vehicular scenarios,where numerous trees or flyovers obstruct the signals.This ...The Global Position System(GPS)is a reliable method for positioning in most scenarios,but it falls short in harsh environments like urban vehicular scenarios,where numerous trees or flyovers obstruct the signals.This presents an unprecedented challenge for autonomous vehicles or applications requiring high accuracy.Fortunately,vehicular ad-hoc networks(VANET)offer an effective solution,where vehicle-to-vehicle(V2V)and vehicle-to-infrastructure(V2I)communications are used to enhance location awareness.In V2I communications,the roadside units(RSU)transmit beacon packets,and the vehicle receives numerous packets from different RSUs to establish communication.To further improve localization accuracy,a cross-covariance matrices-alternating least square(CCM-ALS)algorithm is proposed.The algorithm relies on ALS of the CCM for obtaining the position of vehicles in V2I communications.The algorithm is highly precise compared to traditional angle of arrival(AOA)positioning and not inferior to direct position determination(DPD)approaches while being low in complexity,which is crucial for moving vehicles.The numerical results verify the superiority of the proposed method.展开更多
随着互联网的快速发展,人们对个性化网页搜索、个性化广告投放、个性化社会标注等三维推荐服务的需求越来越紧迫。这些三维立方体数据高度稀疏,且与二维推荐系统相比三维推荐系统中对象之间的关系更加复杂。为了更好地模拟三维对象之间...随着互联网的快速发展,人们对个性化网页搜索、个性化广告投放、个性化社会标注等三维推荐服务的需求越来越紧迫。这些三维立方体数据高度稀疏,且与二维推荐系统相比三维推荐系统中对象之间的关系更加复杂。为了更好地模拟三维对象之间的关系并解决三维数据高度稀疏的问题,提出了一种新的三维协同过滤推荐算法CubeALS(cube alternating least squares)。该算法对三维协同过滤推荐算法CubeSVD(cube singular value decomposition)进行了改进,尝试使用不同于SVD的算法进行矩阵分解。在真实的个性化社会标注数据集上的实验结果表明,与CubeSVD算法相比,CubeALS的性能得到了显著提高。展开更多
目的:应用多元曲线分辨-交替最小二乘(MCR-ALS)法,对7-乙基-10-羟基喜树碱与喜树碱的色谱重叠峰进行分辨,并对杂质喜树碱进行定量。方法:以渐进因子分析(EFA)解析结果作为初始值对喜树碱与7-乙基-10-羟基喜树碱的色谱重叠峰进行 ALS 迭...目的:应用多元曲线分辨-交替最小二乘(MCR-ALS)法,对7-乙基-10-羟基喜树碱与喜树碱的色谱重叠峰进行分辨,并对杂质喜树碱进行定量。方法:以渐进因子分析(EFA)解析结果作为初始值对喜树碱与7-乙基-10-羟基喜树碱的色谱重叠峰进行 ALS 迭代优化,直至收敛。结果:采用此方法分辨所得光谱还原率高,定量结果的浓度值与真实值之间线性关系良好。结论:本方法用于药物色谱重叠峰分辨结果可靠。展开更多
Hexagonal metal honeycomb is widely used in energy absorption field for its special construction. However, many other metal honeycomb structures also show good energy absorption characteristics. Currently, most of the...Hexagonal metal honeycomb is widely used in energy absorption field for its special construction. However, many other metal honeycomb structures also show good energy absorption characteristics. Currently, most of the researches focus on hexagonal honeycomb, while few are performed into different honeycomb structures. Therefore, a new alternative square honeycomb is developed to expand the non-hexagonal metal honeycomb applications in the energy absorption fields with the aim of designing low mass and low volume energy absorbers. The finite element model of alternative square honeycomb is built to analyze its specific energy absorption property. As the diversity of honeycomb structure, the parameterized metal honeycomb finite element analysis program is conducted based on PCL language. That program can automatically create finite element model. Numerical results show that with the same foil thickness and cell length of metal honeycomb, the alternative square has better specific energy absorption than hexagonal honeycomb. Using response surface method, the mathematical formulas of honeycomb crashworthiness properties are obtained and optimization is done to get the maximum specific energy absorption property honeycomb. Optimal results demonstrate that to absorb same energy, alternative square honeycomb can save 10% volume of buffer structure than hexagonal honeycomb can do. This research is significant in providing technical support in the extended application of different honeycomb used as crashworthiness structures, and is absolutely essential in low volume and low mass energy absorber design.展开更多
A novel current feed style, alternating pulse current, was proposed in electrocoagulation aiming at preventing the passivation of electrode materials. The open circuit potential （OCP） measurements after anodic and c...A novel current feed style, alternating pulse current, was proposed in electrocoagulation aiming at preventing the passivation of electrode materials. The open circuit potential （OCP） measurements after anodic and cathodic potentiodynamic polarization showed that cathodic polarization could activate Al electrode. The surface of Al electrode after alternating pulse current electrocoagulation was investigated by scanning electron microscope （SEM） and X-ray photoelectron spectroscopy （XPS）, and the results indicate that passivation of Al is not observed. Furthermore, the simulated wastewater treatment tests show that alternating pulse current electrocoagulation has a visible energy saving effect and is worthy of generalization.展开更多
Alternating current electrical dynamometer is a common device to measure the torque of engines, such as the gasoline engine. In order to solve the problems such as high cost, high energy consumption and complicated me...Alternating current electrical dynamometer is a common device to measure the torque of engines, such as the gasoline engine. In order to solve the problems such as high cost, high energy consumption and complicated measurement system which exists in the direct measurement on the torque of alternating current electrical dynamometer, copper loss and iron loss are taken as two key factors and a soft-sensing model on the torque of alternating current electrical dynamometer is established using the fuzzy least square support vector machine (FLS-SVM). Then, the FLS-SVM parameters such as penalty factor and kernel parameter are optimized by adaptive genetic algorithm, torque soft-sensing is investigated in the alternating current electrical dynamometer, as well as the energy feedback efficiency and energy consumption during the measurement phase of a gasoline engine loading continual test is obtained. The results show that the minimum soft-sensing error of torque is about 0.0018, and it fluctuates within a range from -0.3 to 0.3 N·m. FLS-SVM soft-sensing method can increase by 1.6% power generation feedback compared with direct measurement, and it can save 500 kJ fuel consumption in the gasoline engine loading continual test. Therefore, the estimation accuracy of the soft measurement model on the torque of alternating current electrical dynamometer including copper loss and iron loss is high and this indirect measurement method can be feasible to reduce production cost of the alternating current electrical dynamometer and energy consumption during the torque measurement phase of a gasoline engine, replacing the direct method of torque measurement.展开更多
Square piles of reinforced concrete(RC)in marine environments are susceptible to chloride-inducedcorrosion.A novel reverse-seepage technique(RST)is applied to square piles to block the intrusion of chlorides.Thisresea...Square piles of reinforced concrete(RC)in marine environments are susceptible to chloride-inducedcorrosion.A novel reverse-seepage technique(RST)is applied to square piles to block the intrusion of chlorides.Thisresearch introduces a computational model designed to predict the lifespan of corrosion initiation in reinforced concretesquare piles when applied reverse-seepage pressure.The model considers the impacts of chloride binding and the tripletime-dependence property among the permeability,the corrected surface chloride concentration,and the diffusioncoefficient.The proposed numerical model is solved using the alternating direction implicit(ADI)approach,and itsaccuracy and reliability are evaluated by contrasting the computational outcomes with the analytical solution andexperimental results.Furthermore,the primary factors contributing to the corrosion of reinforced concrete square pilesare analyzed.The results indicate that applying RST can decrease the chloride penetration depth and prolong the lifespanof corrosion initiation in square piles.The water-cement ratio and reverse seepage pressure are the most influentialfactors.A water pressure of 0.4 MPa can double the life of concrete,and the durable life of concrete with a water-cementratio of 0.3 can reach 100 years.展开更多
为了更有效地向用户推荐其感兴趣的菜品,提升餐营业的精准服务水平,本文基于Alternating Least Squares交替最小二乘法和Apache Spark计算引擎,开发了一款根据用户周期性消费行为的菜品智能推荐系统。系统将采集历史消费数据存于HBase...为了更有效地向用户推荐其感兴趣的菜品,提升餐营业的精准服务水平,本文基于Alternating Least Squares交替最小二乘法和Apache Spark计算引擎,开发了一款根据用户周期性消费行为的菜品智能推荐系统。系统将采集历史消费数据存于HBase并训练推荐模型,通过Thymleaf展示推荐信息。系统采用冷热两种启动模式来满足用户需求。展开更多
The effect of a novel low-voltage alternating current pulse(ACP)controlled by transformer and silicon controlled rectifier on the solidification structure of Al-20%Si alloy was investigated.The results indicated that ...The effect of a novel low-voltage alternating current pulse(ACP)controlled by transformer and silicon controlled rectifier on the solidification structure of Al-20%Si alloy was investigated.The results indicated that the remarkable segregation of primary Si occurred during the solidification,and even dendrites of a-Al phase appeared at the center of samples under ACP.The thickness of segregation layer decreased first and then increased with current density increasing from 0 to 300 Acm^(-2).The primary Si existed with long pole or five petal star-shaped without ACP.However, the morphology of primary Si phases changed to block under ACP,and the sizes of blocky Si decreased obviously with increasing current density from 110 to 300 Acm^(-2).The formation mechanism of the structure of hypereutectic AI-20%Si alloy was also discussed under ACP.展开更多
We study the eight infinite sequences of triples of natural numbers A=(F2n+1,4F2n+3,F2n+7), B=(F2n+1,4F2n+5,F2n+7), C=(F2n+1,5F2n+1,F2n+3), D=(F2n+3,4F2n+1,F2n+3) and A=(L2n+1,4L2n+3,L2n+7), B=(L2n+1,4L2n+5,L2n+7), C=...We study the eight infinite sequences of triples of natural numbers A=(F2n+1,4F2n+3,F2n+7), B=(F2n+1,4F2n+5,F2n+7), C=(F2n+1,5F2n+1,F2n+3), D=(F2n+3,4F2n+1,F2n+3) and A=(L2n+1,4L2n+3,L2n+7), B=(L2n+1,4L2n+5,L2n+7), C=(L2n+1,5L2n+1,L2n+3), D=(L2n+3,4L2n+1,L2n+3. The sequences A,B,C and D are built from the Fibonacci numbers Fn while the sequences A, B, C and D from the Lucas numbers Ln. Each triple in the sequences A,B,C and D has the property D(-4) (i. e., adding -4 to the product of any two different components of them is a square). Similarly, each triple in the sequences A, B, C and D has the property D(20). We show some interesting properties of these sequences that give various methods how to get squares from them.展开更多
文摘This note explores the relations between two different methods. The first one is the Alternating Least Squares (ALS) method for calculating a rank<em>-k</em> approximation of a real <em>m</em>×<em>n</em> matrix, <em>A</em>. This method has important applications in nonnegative matrix factorizations, in matrix completion problems, and in tensor approximations. The second method is called Orthogonal Iterations. Other names of this method are Subspace Iterations, Simultaneous Iterations, and block-Power method. Given a real symmetric matrix, <em>G</em>, this method computes<em> k</em> dominant eigenvectors of <em>G</em>. To see the relation between these methods we assume that <em>G </em>=<em> A</em><sup>T</sup> <em>A</em>. It is shown that in this case the two methods generate the same sequence of subspaces, and the same sequence of low-rank approximations. This equivalence provides new insight into the convergence properties of both methods.
文摘In this paper, we extend the alternate Broyden's method to the multiple version fbi solving lincar leastsquarc systems with multiple right-hand sides. We show that the method possesses property of a finite tcrmination.Some numerical cxperiments are gi von to inustrate the effectiveness of the method.
文摘In factor analysis, a factor loading matrix is often rotated to a simple target matrix for its simplicity. For the purpose, Procrustes rotation minimizes the discrepancy between the target and rotated loadings using two types of approximation: 1) approximate the zeros in the target by the non-zeros in the loadings, and 2) approximate the non-zeros in the target by the non-zeros in the loadings. The central issue of Procrustes rotation considered in the article is that it equally treats the two types of approximation, while the former is more important for simplifying the loading matrix. Furthermore, a well-known issue of Simplimax is the computational inefficiency in estimating the sparse target matrix, which yields a considerable number of local minima. The research proposes a new rotation procedure that consists of the following two stages. The first stage estimates sparse target matrix with lesser computational cost by regularization technique. In the second stage, a loading matrix is rotated to the target, emphasizing on the approximation of non-zeros to zeros in the target by least squares criterion with generalized weighing that is newly proposed by the study. The simulation study and real data examples revealed that the proposed method surely simplifies loading matrices.
文摘信道仿真器中不同通道之间的幅相不一致会使系统性能恶化,通常的解决方法是在接收信道中加入校准均衡器,以校正信号传输路径中的幅度和相位失真。为了降低通道间的幅相误差、提高信道均衡效果,文中设计了一种正则化交替频域最小二乘优化算法(Regularized Alternating Frequency Domain Least Squares Optimization,RA-ALO)。该算法采用正则化来确保矩阵求逆时解的正确性,并使用交替最小二乘法(Alternating Least Squares,ALS)寻找最优解来增强均衡器性能。仿真结果表明,在信道均衡方面,与正则化算法和求伪逆算法相比,该算法具有更低的幅相误差、更优的校准性能。
基金supported by the National Natural Science Foundation of China(62371225).
文摘The Global Position System(GPS)is a reliable method for positioning in most scenarios,but it falls short in harsh environments like urban vehicular scenarios,where numerous trees or flyovers obstruct the signals.This presents an unprecedented challenge for autonomous vehicles or applications requiring high accuracy.Fortunately,vehicular ad-hoc networks(VANET)offer an effective solution,where vehicle-to-vehicle(V2V)and vehicle-to-infrastructure(V2I)communications are used to enhance location awareness.In V2I communications,the roadside units(RSU)transmit beacon packets,and the vehicle receives numerous packets from different RSUs to establish communication.To further improve localization accuracy,a cross-covariance matrices-alternating least square(CCM-ALS)algorithm is proposed.The algorithm relies on ALS of the CCM for obtaining the position of vehicles in V2I communications.The algorithm is highly precise compared to traditional angle of arrival(AOA)positioning and not inferior to direct position determination(DPD)approaches while being low in complexity,which is crucial for moving vehicles.The numerical results verify the superiority of the proposed method.
文摘随着互联网的快速发展,人们对个性化网页搜索、个性化广告投放、个性化社会标注等三维推荐服务的需求越来越紧迫。这些三维立方体数据高度稀疏,且与二维推荐系统相比三维推荐系统中对象之间的关系更加复杂。为了更好地模拟三维对象之间的关系并解决三维数据高度稀疏的问题,提出了一种新的三维协同过滤推荐算法CubeALS(cube alternating least squares)。该算法对三维协同过滤推荐算法CubeSVD(cube singular value decomposition)进行了改进,尝试使用不同于SVD的算法进行矩阵分解。在真实的个性化社会标注数据集上的实验结果表明,与CubeSVD算法相比,CubeALS的性能得到了显著提高。
文摘目的:应用多元曲线分辨-交替最小二乘(MCR-ALS)法,对7-乙基-10-羟基喜树碱与喜树碱的色谱重叠峰进行分辨,并对杂质喜树碱进行定量。方法:以渐进因子分析(EFA)解析结果作为初始值对喜树碱与7-乙基-10-羟基喜树碱的色谱重叠峰进行 ALS 迭代优化,直至收敛。结果:采用此方法分辨所得光谱还原率高,定量结果的浓度值与真实值之间线性关系良好。结论:本方法用于药物色谱重叠峰分辨结果可靠。
基金supported by Guangdong Province and Chinese Academy of Science Comprehensive Strategic Cooperation of China(Grant No. 2011A090100019)College Discipline Innovation Wisdom Plan of China (Grant No. B07018)
文摘Hexagonal metal honeycomb is widely used in energy absorption field for its special construction. However, many other metal honeycomb structures also show good energy absorption characteristics. Currently, most of the researches focus on hexagonal honeycomb, while few are performed into different honeycomb structures. Therefore, a new alternative square honeycomb is developed to expand the non-hexagonal metal honeycomb applications in the energy absorption fields with the aim of designing low mass and low volume energy absorbers. The finite element model of alternative square honeycomb is built to analyze its specific energy absorption property. As the diversity of honeycomb structure, the parameterized metal honeycomb finite element analysis program is conducted based on PCL language. That program can automatically create finite element model. Numerical results show that with the same foil thickness and cell length of metal honeycomb, the alternative square has better specific energy absorption than hexagonal honeycomb. Using response surface method, the mathematical formulas of honeycomb crashworthiness properties are obtained and optimization is done to get the maximum specific energy absorption property honeycomb. Optimal results demonstrate that to absorb same energy, alternative square honeycomb can save 10% volume of buffer structure than hexagonal honeycomb can do. This research is significant in providing technical support in the extended application of different honeycomb used as crashworthiness structures, and is absolutely essential in low volume and low mass energy absorber design.
基金National 863 Plan(No.2005AA601010-02-2)Water Environment Research & Data Sharing Platform in the Middle Reaches of the Yangtse River(Wuhan University)(No.WERDSPMYR-0602)
文摘A novel current feed style, alternating pulse current, was proposed in electrocoagulation aiming at preventing the passivation of electrode materials. The open circuit potential （OCP） measurements after anodic and cathodic potentiodynamic polarization showed that cathodic polarization could activate Al electrode. The surface of Al electrode after alternating pulse current electrocoagulation was investigated by scanning electron microscope （SEM） and X-ray photoelectron spectroscopy （XPS）, and the results indicate that passivation of Al is not observed. Furthermore, the simulated wastewater treatment tests show that alternating pulse current electrocoagulation has a visible energy saving effect and is worthy of generalization.
基金Project(11772126) supported by the National Natural Science Foundation of China
文摘Alternating current electrical dynamometer is a common device to measure the torque of engines, such as the gasoline engine. In order to solve the problems such as high cost, high energy consumption and complicated measurement system which exists in the direct measurement on the torque of alternating current electrical dynamometer, copper loss and iron loss are taken as two key factors and a soft-sensing model on the torque of alternating current electrical dynamometer is established using the fuzzy least square support vector machine (FLS-SVM). Then, the FLS-SVM parameters such as penalty factor and kernel parameter are optimized by adaptive genetic algorithm, torque soft-sensing is investigated in the alternating current electrical dynamometer, as well as the energy feedback efficiency and energy consumption during the measurement phase of a gasoline engine loading continual test is obtained. The results show that the minimum soft-sensing error of torque is about 0.0018, and it fluctuates within a range from -0.3 to 0.3 N·m. FLS-SVM soft-sensing method can increase by 1.6% power generation feedback compared with direct measurement, and it can save 500 kJ fuel consumption in the gasoline engine loading continual test. Therefore, the estimation accuracy of the soft measurement model on the torque of alternating current electrical dynamometer including copper loss and iron loss is high and this indirect measurement method can be feasible to reduce production cost of the alternating current electrical dynamometer and energy consumption during the torque measurement phase of a gasoline engine, replacing the direct method of torque measurement.
基金Projects(52178371,52108355,52178321)supported by the National Natural Science Foundation of ChinaProject(202305)supported by the Research Project of Engineering Research Centre of Rock-Soil Drilling&Excavation and Protection,Ministry of Education,China。
文摘Square piles of reinforced concrete(RC)in marine environments are susceptible to chloride-inducedcorrosion.A novel reverse-seepage technique(RST)is applied to square piles to block the intrusion of chlorides.Thisresearch introduces a computational model designed to predict the lifespan of corrosion initiation in reinforced concretesquare piles when applied reverse-seepage pressure.The model considers the impacts of chloride binding and the tripletime-dependence property among the permeability,the corrected surface chloride concentration,and the diffusioncoefficient.The proposed numerical model is solved using the alternating direction implicit(ADI)approach,and itsaccuracy and reliability are evaluated by contrasting the computational outcomes with the analytical solution andexperimental results.Furthermore,the primary factors contributing to the corrosion of reinforced concrete square pilesare analyzed.The results indicate that applying RST can decrease the chloride penetration depth and prolong the lifespanof corrosion initiation in square piles.The water-cement ratio and reverse seepage pressure are the most influentialfactors.A water pressure of 0.4 MPa can double the life of concrete,and the durable life of concrete with a water-cementratio of 0.3 can reach 100 years.
文摘为了更有效地向用户推荐其感兴趣的菜品,提升餐营业的精准服务水平,本文基于Alternating Least Squares交替最小二乘法和Apache Spark计算引擎,开发了一款根据用户周期性消费行为的菜品智能推荐系统。系统将采集历史消费数据存于HBase并训练推荐模型,通过Thymleaf展示推荐信息。系统采用冷热两种启动模式来满足用户需求。
基金Item Sponsored by NPU Foundation for Fundamental ResearchChina[Grant No.JC201272]
文摘The effect of a novel low-voltage alternating current pulse(ACP)controlled by transformer and silicon controlled rectifier on the solidification structure of Al-20%Si alloy was investigated.The results indicated that the remarkable segregation of primary Si occurred during the solidification,and even dendrites of a-Al phase appeared at the center of samples under ACP.The thickness of segregation layer decreased first and then increased with current density increasing from 0 to 300 Acm^(-2).The primary Si existed with long pole or five petal star-shaped without ACP.However, the morphology of primary Si phases changed to block under ACP,and the sizes of blocky Si decreased obviously with increasing current density from 110 to 300 Acm^(-2).The formation mechanism of the structure of hypereutectic AI-20%Si alloy was also discussed under ACP.
文摘We study the eight infinite sequences of triples of natural numbers A=(F2n+1,4F2n+3,F2n+7), B=(F2n+1,4F2n+5,F2n+7), C=(F2n+1,5F2n+1,F2n+3), D=(F2n+3,4F2n+1,F2n+3) and A=(L2n+1,4L2n+3,L2n+7), B=(L2n+1,4L2n+5,L2n+7), C=(L2n+1,5L2n+1,L2n+3), D=(L2n+3,4L2n+1,L2n+3. The sequences A,B,C and D are built from the Fibonacci numbers Fn while the sequences A, B, C and D from the Lucas numbers Ln. Each triple in the sequences A,B,C and D has the property D(-4) (i. e., adding -4 to the product of any two different components of them is a square). Similarly, each triple in the sequences A, B, C and D has the property D(20). We show some interesting properties of these sequences that give various methods how to get squares from them.
