On Methods of Constructing Sets of Mutually Orthogonal Latin Squares Using a Computer. I

This paper deals with the problem of finding sets of mutually orthogonal Latin squares of order 4t (where 4t – 1 is a prime power) based on orthogonal mappings of a group. For the group G we take the module G(2, 2t) whose elements are vectors (a ₁, a ₂,) where a ₁ is a residue class (mod 2) and a ₂ is a residue class (mod 2t), the addition being defined by (a ₁, a ₂) + (b ₁, b ₂) = (c ₁, c ₂) where a ₁ + b ₁ = C ₁ (mod 2) and a ₂ + b ₂ = c ₂ (mod 2t). Then the search for orthogonal mappings is materially simplified by using a configuration based on the balanced incomplete block design with parameters v = b = 4t – 1, r = k = 2t – 1, λ = t – 1. Using this method, two sets of five mutually orthogonal Latin squares of order 12 were obtained.     

On Methods of Constructing Sets of Mutually Orthogonal Latin Squares Using a Computer. II

A new class of triplets of mutually orthogonal latin squares is derived. These are the consequence of attempts to extend the results described in Part I of this paper which appears in Technometrics, 1960, Vol. 2, No. 4, p. 507.     

Construction of Orthogonal Nearly Latin Hypercubes

Orthogonal Latin hypercubes (OLHs) are available for only a limited collection of run sizes. This paper presents a simple algorithm for constructing orthogonal designs that are nearly Latin hypercubes. The algorithm is based on the approach developed by Steinberg and Lin for OLH designs and can generate designs for all run sizes for which a Plackett‐Burman design exists. The designs have good univariate projections, although they are not perfectly uniform. They also provide good spatial coverage in higher dimensions. The great gain in sample size flexibility requires just a small sacrifice in the univariate spread of points. Copyright © 2014 John Wiley & Sons, Ltd.     

The Analysis of Latin Squares with a Certain Type of Row-Column Interaction

A serious limitation in the use of latin squares is the confounding of the main effect of each factor with the interaction of the remaining two factors. In some cases, the interaction of rows and columns can be expressed as a multiplicative term of assigned factors associated with rows and columns. The analysis of such designs is presented in detail. An example is discussed. The method ia extended to the case where the treatment effects are linearly related to a given concomitant variable. A brief discussion is given of the relation of the proposed method with other tests for non-additivity.     

正轴测投影的基本方程组及其应用

基于投影、坐标系和向量的基本概念和基本性质,可以十分简明地导出正轴测投影由4个约束方程构成的基本方程组。为确定6个轴测参数,应在合理选定2个参数后,从该方程组求出其他4个待定的参数,从而解决了正轴测投影的基本问题。对于选定2个参数的各种情况,文中都给出了求这些参数的解析解,并通过数值计算验证了这些解析解的正确性。     

Enumeration and Evaluation of Small Orthogonal Latin Hypercube Designs for Polynomial Regression Models

In this paper, we construct and evaluate all nonisomorphic Latin hypercube designs with n≤16 runs, the use of which guarantee that the estimates of the first‐order effects are uncorrelated with each other and also uncorrelated with the estimates of the second‐order effects, in polynomial regression models. The produced designs are evaluated using well‐known and popular criteria, and optimal designs are presented in every case studied. An effort to construct nonisomorphic small Latin hypercubes in which only the estimates of the first‐order effects are required to be uncorrelated with each other has also been made, and new designs are presented. All the constructed designs, besides their stand‐alone properties, are useful for the construction of bigger orthogonal Latin hypercubes with desirable properties, using well‐known techniques proposed in the literature. Copyright © 2015 John Wiley & Sons, Ltd.     

三轴正交机器人运动误差的建模与分析

借助齐次坐标变换法建立了三轴正交机器人运动误差的模型,给出了实际运动轨迹和目标位置的关系。首先,只考虑坐标轴安装不准确引入的垂直度误差;然后添加上直线度、偏转角、定位误差共计21项形位公差;最后再加上坐标轴弹性形变引入的误差。介绍了获取建立模型所需的参数的方法,计算出机器人的真实运动轨迹的包络面。经过仿真计算,x、y、z方向的最大运动误差分别是 1.7 mm、 1.0 mm,、0.4 mm。通过实验验证了计算结果和模型的可行性。     

A Bound for the Order of Characteristic Set Elements of an Ordinary Prime Differential Ideal and some Applications

With respect to an elimination ordering, we give an upper bound for the order of characteristic set elements of an ordinary prime differential ideal. Using some results of complexity in the algebraic case, we show that computing characteristic sets of ordinary prime differential ideals, by change of ordering, is single exponential time. Received: January 8, 1997; revised version: May 6, 1999     

谐波对35kV三相三元件组合互感器电能计量影响之分析以及防范之措施

针对重庆市某县发电厂使用的35kV三相三元件组合互感器受谐波影响,计量严重失准的现象.本文将简要分析谐波的来源,并提出相应的防范措施.     

一类正交基插值尺度函数

本文给出一类正交基插值尺度函数,讨论了这类尺度函数的光滑性和衰减性,特别研究了两种情况下这类尺度函数的光滑性和衰减性。     

A Tutorial on Latin Hypercube Design of Experiments

The growing power of computers enabled techniques created for design and analysis of simulations to be applied to a large spectrum of problems and to reach high level of acceptance among practitioners. Generally, when simulations are time consuming, a surrogate model replaces the computer code in further studies (e.g., optimization, sensitivity analysis, etc.). The first step for a successful surrogate modeling and statistical analysis is the planning of the input configuration that is used to exercise the simulation code. Among the strategies devised for computer experiments, Latin hypercube designs have become particularly popular. This paper provides a tutorial on Latin hypercube design of experiments, highlighting potential reasons of its widespread use. The discussion starts with the early developments in optimization of the point selection and goes all the way to the pitfalls of the indiscriminate use of Latin hypercube designs. Final thoughts are given on opportunities for future research. Copyright © 2015 John Wiley & Sons, Ltd.     

A Least Squares Fit Method for Precision Evaluation of Waveguide-Resonator Measurements

The resonance frequencies of waveguide resonators, e.g., for the measurement of dielectric constants, are evaluated using a least squares fit method based on the analytic eigenfrequency equation. This yields a reliable estimate of the number of order of the resonances even for long resonators and averages random measurement errors.     

Allocating A Replenishment Order Among A Family of Items

Inventory control models which provide coordinated control (or joint replenishment) of families of items are very useful in practice. An important component of these models is the algorithm for allocating a total reorder quantity among the items in the family. In this paper the allocation algorithm from a new class of coordinated control models is discussed. Inventory position is modelled as a diffusion process, and both continuous review and periodic review situations are considered. This new class of coordinated control models has been shown to outperform existing models (IBM's IMPACT Inventory Control Package).     

非奇异$H$-矩阵的一组新判定法

非奇异 $H$-矩阵作为矩阵论中一类重要的特殊矩阵,在计算数学、统计学、弹性力学和神经网络等众多学科领域里都有广泛应用,因此对其判定条件的研究具有重大意义．本文探讨非奇异 $H$-矩阵的直接判定问题,通过构造不同的正对角因子及新的参数方法,得到了一组简捷实用的非奇异 $H$-矩阵判定新条件,改进和推广了近期一些相关成果,达到了扩充非奇异 $H$-矩阵判定范围的目的．最后,用三个数值例子说明了新判定条件的优越性．     

保障型不间断供冷系统设计

本文介绍了一套保障型不间断供冷系统的设计。系统利用已有的两个区域供冷站同时向用户供冷,双冷源互为备用,并利用复杂的矩阵型管网实现多种方式的切换和配置,达到全年365天不间断供冷的目的。     

非奇异H-矩阵的一组判定条件

非奇异H-矩阵在计算方法、物理数学、生物学、矩阵论、控制理论等领域有着广泛的应用,如何有效地判定一个矩阵是否为非奇异H-矩阵,一直是人们关心的问题.本文利用矩阵指标集的k-级划分,给出了非奇异H-矩阵的一组判定条件,改进和推广了近期的相关结果,并用数值算例说明本文判定方法的有效性.     

A Note on Moments of Gamma Order Statistics

Previously quadrature approximations were developed to determine the moments of a distribution of the response of a multivariable function when each of the variables is a random variable from a normal distribution. The error was shown to be of the order of the sixth power of the standard deviations of the random variables, but a more useful bound is desired in applied work. Only limited success has been achieved in this direction. It is shown that the best approximating distribution is a Beta distribution of the first kind with β₂ equal to 3 and mean, variance, and β₁ obtained by quadrature, where β₁ and β₂ are standard measures of skewness and kurtosis, respectively. A parametric study of the function X = C_o (a _o, ± y ₁ ± y ₂ ± … ±y_n ) ^m + b _o where the y_i all have the same standard deviation, σ, is conducted both analytically and by quadrature. The mean and variance obtained by quadrature are essentially exact in the range of interest. It is shown that for a large range of σ the above distribution is both a good approximation and a much better approximation than either a normal approximation with the same mean and variance or a linear approximation. The example also shows that the β₂ obtained by quadrature is a poor indicator of the precision of the quadrature approximation.     

基于FPGA的正交信号细分系统研究

介绍了一种新的基于FPGA的纯硬件细分系统,该系统主要由模拟信号处理和集成于同一FPGA芯片上的坐标变换、FIFO存储器、FIR滤波器几个部分组成.采用了集成化和模块化设计,具有精度高、实时性好等特点.将此方法应用于2 m比长仪的测长系统,通过实验验证了该细分系统的准确性及实用性.     

一类对称正交反对称矩阵反问题

设P是n阶对称正交矩阵,如果n阶矩阵A满足AT=-A和(PA)T=-PA,则称A为对称正交反对称矩阵。讨论了问题IPLS:给定n阶矩阵 A,n×m矩阵X和B,求n阶对称正交反对称矩阵A使得‖AX-B‖F=min和‖ A-A‖F=min。给出了该问题解的表达式及其数值方法,并将所得结果应用于研究对称正交反对称矩阵特征值反问题。