Nearly orthogonal Latin squares are useful for conducting experiments eliminating heterogeneity in two directions and using different interventions each at each level.In this paper,some constructions of mutually nearl...Nearly orthogonal Latin squares are useful for conducting experiments eliminating heterogeneity in two directions and using different interventions each at each level.In this paper,some constructions of mutually nearly orthogonal Latin squares are provided.It is proved that there exist 3 MNOLS（2m） if and only if m ≥3 nd there exist 4 MNOLS（2m） if and only if m ≥4 with some possible exceptions.展开更多
Two Latin squares of order v are r-orthogonal if their superposition produces exactly r distinct ordered pairs. The two squares are said to be r-orthogonal idempotent Latin squares and denoted by r-MOILS（v）if they a...Two Latin squares of order v are r-orthogonal if their superposition produces exactly r distinct ordered pairs. The two squares are said to be r-orthogonal idempotent Latin squares and denoted by r-MOILS（v）if they are all idempotent. In this paper, we show that for any integer v≥28, there exists an r-MOILS（v） if and only if r∈[v, v^2]／ {v ＋ 1, v^2-1}.展开更多
Let N = {0, 1, ···, n-1}. A strongly idempotent self-orthogonal row Latin magic array of order n（SISORLMA（n） for short） based on N is an n × n array M satisfying the following properties：（1）...Let N = {0, 1, ···, n-1}. A strongly idempotent self-orthogonal row Latin magic array of order n（SISORLMA（n） for short） based on N is an n × n array M satisfying the following properties：（1） each row of M is a permutation of N, and at least one column is not a permutation of N;（2） the sums of the n numbers in every row and every column are the same;（3） M is orthogonal to its transpose;（4） the main diagonal and the back diagonal of M are 0, 1, ···, n-1 from left to right. In this paper, it is proved that an SISORLMA（n）exists if and only if n ？ {2, 3}. As an application, it is proved that a nonelementary rational diagonally ordered magic square exists if and only if n ？ {2, 3}, and a rational diagonally ordered magic square exists if and only if n ≠2.展开更多
生鲜牛肉的含水率对其牛肉的加工、储藏、贸易与食用质量有重要影响,为了提高牛肉的经济价值和食用品质,需要研究牛肉含水率的无损检测技术。以取自不同超市的内蒙小黄牛和鲁西黄牛背最长肌为研究对象,有效样本86个,其中,75%的样本作为...生鲜牛肉的含水率对其牛肉的加工、储藏、贸易与食用质量有重要影响,为了提高牛肉的经济价值和食用品质,需要研究牛肉含水率的无损检测技术。以取自不同超市的内蒙小黄牛和鲁西黄牛背最长肌为研究对象,有效样本86个,其中,75%的样本作为校正集,25%的样本作为验证集。采集牛肉新鲜切口处400～1170nm波长范围内的漫反射光谱,用国标方法测定牛肉含水率。经过多元散射校正(multiplicative scatter correction,MSC)、变量标准化(standard normalized variate,SNV)和直接正交信号校正(direct orthogonal signal correction,DOSC)等方法预处理,在400～1170nm范围内分别建立多元线性回归(multiple linear regression,MLR)模型、主成分回归(principal component Regression,PCR)模型和偏最小二乘回归(partial least squares regression,PLSR)模型。结果表明使用MSC预处理方法建立的模型预测效果最佳,其中用PLSR建模结果最好,校正集的相关系数和校正标准差分别是0.92和0.0069,验证集的相关系数和验证标准差分别是0.92和0.0047,外部验证的相关系数和验证标准差分别是0.85和0.0054。结果表明,可见/近红外光谱结合MSC预处理方法建立的PLSR模型,可以对牛肉含水率进行准确的快速无损评价,为生鲜牛肉含水率快速无损检测技术的应用提供理论参考。展开更多
基金Supported by the National Natural Science Foundations of China(Nos.11071207,11371308,11301457,11501181)
文摘Nearly orthogonal Latin squares are useful for conducting experiments eliminating heterogeneity in two directions and using different interventions each at each level.In this paper,some constructions of mutually nearly orthogonal Latin squares are provided.It is proved that there exist 3 MNOLS（2m） if and only if m ≥3 nd there exist 4 MNOLS（2m） if and only if m ≥4 with some possible exceptions.
基金Supported by the National Natural Science Foundation of China under Grant No.61373007,11371208Zhejiang Provincial Natural Science Foundation of China under Grant No.LY13F020039Sponsored by K.C.Wong Magna Fund in Ningbo University
文摘Two Latin squares of order v are r-orthogonal if their superposition produces exactly r distinct ordered pairs. The two squares are said to be r-orthogonal idempotent Latin squares and denoted by r-MOILS（v）if they are all idempotent. In this paper, we show that for any integer v≥28, there exists an r-MOILS（v） if and only if r∈[v, v^2]／ {v ＋ 1, v^2-1}.
基金Supported by the National Natural Science Foundation of China(No.11271089)Guangxi Nature Science Foundation(No.2012GXNSFAA053001)+1 种基金Key Foundation of Guangxi Education Department(No.201202ZD012)Guangxi “Ba Gui” Team for Research and Innovation
文摘Let N = {0, 1, ···, n-1}. A strongly idempotent self-orthogonal row Latin magic array of order n（SISORLMA（n） for short） based on N is an n × n array M satisfying the following properties：（1） each row of M is a permutation of N, and at least one column is not a permutation of N;（2） the sums of the n numbers in every row and every column are the same;（3） M is orthogonal to its transpose;（4） the main diagonal and the back diagonal of M are 0, 1, ···, n-1 from left to right. In this paper, it is proved that an SISORLMA（n）exists if and only if n ？ {2, 3}. As an application, it is proved that a nonelementary rational diagonally ordered magic square exists if and only if n ？ {2, 3}, and a rational diagonally ordered magic square exists if and only if n ≠2.
文摘生鲜牛肉的含水率对其牛肉的加工、储藏、贸易与食用质量有重要影响,为了提高牛肉的经济价值和食用品质,需要研究牛肉含水率的无损检测技术。以取自不同超市的内蒙小黄牛和鲁西黄牛背最长肌为研究对象,有效样本86个,其中,75%的样本作为校正集,25%的样本作为验证集。采集牛肉新鲜切口处400～1170nm波长范围内的漫反射光谱,用国标方法测定牛肉含水率。经过多元散射校正(multiplicative scatter correction,MSC)、变量标准化(standard normalized variate,SNV)和直接正交信号校正(direct orthogonal signal correction,DOSC)等方法预处理,在400～1170nm范围内分别建立多元线性回归(multiple linear regression,MLR)模型、主成分回归(principal component Regression,PCR)模型和偏最小二乘回归(partial least squares regression,PLSR)模型。结果表明使用MSC预处理方法建立的模型预测效果最佳,其中用PLSR建模结果最好,校正集的相关系数和校正标准差分别是0.92和0.0069,验证集的相关系数和验证标准差分别是0.92和0.0047,外部验证的相关系数和验证标准差分别是0.85和0.0054。结果表明,可见/近红外光谱结合MSC预处理方法建立的PLSR模型,可以对牛肉含水率进行准确的快速无损评价,为生鲜牛肉含水率快速无损检测技术的应用提供理论参考。
