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To overcome this problem, many authors proposed some biased estimators to alternate the least squared estimator. In some sense, these estimators improved the least squared estimator.However, the biased estimator was apart from the true value of parameter, so some statisticians proposed the notation of the almost unbiased estimator.

人们发现设计阵的"病态"是导致Stein现象的根源,为了克服共线性性,人们在文献中相继提出了许多有偏估计来替代最小二乘估计,这些估计从某种意义上讲,都改进了最小二乘估计。

Based on the projection theorem in the finite-dimensional inner product space, by making use of the generalized singular value decomposition and the canonical correlation decomposition of matrix pair simultaneously, we transform the least-squares problems of the abovementioned inconsistent matrix equations into the problems of solving the consistent matrix equations over given matrix set, and obtain the general expressions of the corresponding least-squares solutions.

S使得‖-X~*‖=‖-X~*‖,其中‖·‖为Frobenius范数,S分别表示矩阵方程 AXB=D,AXA~T+BYB~T=D,AXB+CYD=E和矩阵方程组=,=在一般矩阵集合或对称矩阵集合上不相容时的最小二乘解集合。

In Chapter 5, the least-squares solutions bisymmetric matrix set of the matrix equation ATXA = B on two linear manifolds Si ={X BSRnxn\\\XY - Z\\ = min} and S2 ={X BSRnXn\XY = Z, YtTZi = ZjYu ZtffYi = Zi,i = 1,2, Y, Z e Rnxm}, by applying the singular value decomposition of matrix and the canonical correlation decomposition of matrix pairs, we obtain a general expression of the least-squares solutions of the matrix equation ATXA = B on two linear manifolds.

在第五章,我们研究了两类线性流形S_1={X∈BSR~|‖XY-Z‖=min}和S_2={X∈BSR~|XY=Z,Y_i~TZ_i=Z_i~TY_i,Z_iY_i+Y_i=Z_i,i=1,2,Y,Z∈R~}上矩阵方程A~TXA=B的双对称最小二乘解。

According to the results of thermodynamic calculations and the flyash-sodium carbonate sintering experiments, contrasting the energy consumption, material resource consumption and the expellant of the greenhouse gas CO2 during the two sintering processes, it demonstrates that the procedure could be the least consumptions of the mineral resources and energy, the least expellant of the greenhouse gas CO2, and that the terminal products with high value could be manufactured when sodium carbonate is taken as the flux agent.

基于热力学计算结果,对比了两种工艺的能耗、物耗、温室气体排放量等因素,结合粉煤灰-碳酸钠烧结反应实验,证明以碳酸钠为配料,高铝粉煤灰烧结过程具有一次性资源消耗量少,能耗最低,温室气体CO2排放量最小,且可生产高附加值产品,实现完全清洁生产等优点。

However, the generalized moving least squares approximation makes require least squares approximation with regard to functional and its derivative value on all nodes.

而广义移动最小二乘近似要求近似函数及其导数在所有节点处的误差的平方和最小。

The moving least squares approximation makes only require least squares approximation with regard to functional value on all nodes. It makes no require for the residual of derivative approximation.

移动最小二乘近似只要求近似函数在各节点处的误差的平方和最小,对近似函数导数的误差没有任何约束。

Pubescens community and mixed plant species belonged to 56 families, 85 genera, 122 species. The layers of arbors, shrubs, liane, and herbages could be distinguished clearly. The community of Jiulian Mountain Nature Reserve in Jiangxi Province had the highest diversity indices of tree layer in four T. ciliata var. pubescens forest communities, the least was community in Changgang, Longquan of Zhejiang Province. The community of Changgang had the highest index evenness, the least was in Jiulong Mountain of Zhejiang Province. The importance value of T. ciliata var.

研究结果表明:毛红椿天然林群落的物种多样性丰富,与毛红椿混生的植物种类有56科85属122种,而且层次性较强,分为乔木层、灌木层、藤本层和草本层4层。4个毛红椿天然林群落乔木层中,江西九连山群落Simpson多样性指数最高,浙江龙泉昌岗毛红椿群落为最低;浙江龙泉昌岗群落的均匀度指数最高,浙江九龙山群落为最低。

The value of a scalar variance at a general point can be estimated from the measurement at a limitary data points,and the deviation between the estimated value and the measured value is the least.

使用该阵列有限个点上的观测值可以客观地分析出该变量的瞬间空间分布,使它与其真值之间的偏差达到最小值。

Therefore, it has the important scientific research value in studying the relationship between the changing of the parameters (including the temperature, the humidity, the grain radius and so on) and the electricity and radioactivity of the medium. Applied the count statistics and the numeral value analysis, the paper analyzes, concludes and contrasts the data sufficiently through the experimentation, and acquires the following results that the resistivity and the polarizability both have the negative relationship with the temperature variety of medium from 0℃ to 200 ℃. The parallactic poalarizability is consistent with the temperature variety in the plan as well as the section, but their trends are exactly opposite. Power supply voltage has no considerable influence to the resistivity and polarizability by using duality variance analysis, however, the detecting depth and the plan position influence them greatly. Different AB/2 interval that increases by degree does not influence variance and the average value of the resistivity and the polarizability remarkably. By using the least double multiplication, the relationship of temperature-time-the influence radius of the fire source is carried up by the mathematic drawing up. After discussing their correl ation, I educe the influence radius of the fire source and carry out the 'trend analysis and forecast to the spacial changing of the temperature and the parallactic polarizability in the end.

本文通过试验并应用数理统计和数值分析等相关理论对所得到的试验数据进行了分析、归纳和对比,得出了介质温度变化在0-200℃内视电阻率和视极化率与温度均表现为负相关性;视极化率与温度在剖面和平面上的变化形态具有很好的一致性,但变化趋势相反;由二元方差分析可得供电电压对视电阻率和视极化率无显著影响,但探测深度和平面位置对视电阻率和视极化率有显著影响;通过假设检验可证不同AB/2递增间隔,对视电阻率和视极化率的方差和平均数影响都无显著性差异;应用最小二乘法对温度——时间——火源影响半径之间的关系进行了数学拟合,讨论了它们之间的相互关系,得出了火源影响的有效半径,太原理工大学硕士研究生学位论文并对温度和视极化率的空间变化作了趋势分析和预测。

If the tectonic uplift is not considered, the relief of Dabie orogen will reach at least 3km in Late-Cretaceous. As to the value of the relief reduction factor in Dabie orogen at 90Ma, the largest value appeared in northeast region, followed consecutively by the core and southeast Tanlu fault zone, with the smalleast value appeared in northwest and southwest region. The results reflect the strong uplift difference between core and North Huaiyang flank in Dabie orogen during doming extension period. Relief in the core region and southeast Tanlu fault zone is higher than those in the peripheral regions, northwest and southwest flanks are more stable than other regions.

如果不考虑构造抬升,大别造山带在晚白垩世地形起伏至少可达3km.90Ma时大别造山带地形起伏变化率在空间上呈现如下特征:东北区块最大,热窿核部其次,东南郯庐断裂区块再次,西北、西南区块最小,反映大别造山带热窿伸展期,核部与北淮阳翼之间强烈差异隆升,核部地形和东南郯庐断裂区块起伏高于周边地区,西北、西南两个翼部比其他地区稳定。

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Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克,果实色泽鲜艳,汁多味浓,甜酸适口,离核仁甜,清末时就驰名陕、甘两省,清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异:红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感,ED90值分别为47.65、71.67和29.17g/hm2;春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感,ED90值分别为96.91、114.20g/hm2;而番茄不敏感。

However, I have an idea.

不过,我有个主意。