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SVD is the general method for linear decomposition of a matrix into independent principal components, and is a form of Eigenvalue-Eigenvector analysis or principal components decomposition and, in a more general sense, of multi-dimensional scaling.

SVD分解根据矩阵的运算计算出矩阵的奇异值，然后根据奇异值计算出矩阵的两个奇异矩阵，将矩阵分解为三个矩阵的乘积形式。

The principal amount of each person is limited, so we have to do is to make good use of the maximum principal, the enemy when the rapid weak attack, scored the goal with minimal cost.

每个人的本金是有限的，所以，我们要做的，就是最大限度地用好本金，在敌人疲软的时候迅速出击，以最小代价拿下目标。

The multivariate analysis for structure simplification includes principal component analysis, principal component factor analysis and maximum likelihood factor analysis.

为简化形態性状多样性结构所进行之多变数统计分析包括主成分分析、主成分因子分析及最大可能率因子分析。

Triaxial stress presents minimum horizontal principal stress increasing and maximum horizontal principal stress being a "bottleneck".

三轴应力表现为最小水平主应力增加和最大水平主应力减小的"瓶颈"现象。

In order to compare the results for the three different die gaps, the ratio of the two principal strains is introduced, being min/max, where max and min are the major and the minor principal strains, respectively. Hosford and Caddell [5] have shown that if the absolute value of is greater than a critical value, wrinkling is supposed to occur, and the larger the absolute value of , the greater is the possibility of wrinkling.

为了比较三种不同模具间隙的结果，两种主要张力的比率被介绍-是最小值/最大值，这里最小值/最大值是主要的和次要的张力，分别的， Hosford and Caddell [5] 显示如果他的绝对值比临界值大，起皱应该会产生，越大的绝对值，则越大的起皱产生。

Considering the effect of the angle of internal friction on the inclination of sliding plane of soils behind retaining wall, circular and catenary, the two shapes of minor principal stress arch are theoretically analyzed. According to the shapes of minor principal stress arch, the coefficients of earth pressure corresponding to different angle of internal friction and that of wall friction are gained.

为克服现有考虑土拱效应的土压力计算方法不能考虑墙土摩擦角变化对挡土墙后土体滑裂面的影响的不足，考虑墙土摩擦角变化对挡土墙后上体滑裂面倾角的影响，对圆弧和悬链线两种拱形分别进行了分析，并与现有方法计算结果进行了比较。

Under the given loading method, the experimental results about new granite in Laxiwa show that the resilient deformation is found and acoustic emission counts rate is evidently enhanced when the minor principal stress is unloaded. The enhancing extent of acoustic emission counts rate increases with the intermediate principal stress.

在设定的加载方式下，针对拉西瓦新鲜花岗岩的试验结果表明：当卸载最小主应力时，岩石发生回弹变形，声发射计数率比卸载前显著增加，增加的幅度随中间主应力的增加而逐渐提高。

Vesic's solutions to cavity expansion that include cylindrical cavity expansion and spherical cavity expansion are introduced. Then cylindrical cavity expansion theory is applied to study compaction effect of pile driving in saturated soil. Based on the results of conventional triaxial tests, a trilinear curve model is used to simulate stress-strain curve of strain-softening materials. Meanwhile, trilinear curves are also used to simulate curves of volumetric strain, minor principal strain and major principal strain. By using elasto-plastic theory, analytical solutions to cylindrical cavity expansion in strain-softening soil are presented. According to the mechanism of statically pressed pile driving, compaction effect of pile tip can be viewed as hemispheric cavity expansion. Therefore spherical cavity expansion theory is applied to obtain the solutions to stress, strain, displacement fields and final pressure. Resistance force of pile tip is calculated to estimate static pressure.

介绍了Vesic关于圆孔扩张问题的解答，其中包括柱形孔扩张问题和球形孔扩张问题，并应用柱形孔扩张理论分析了饱和软土中的沉桩挤土效应问题；在常规三轴试验成果的基础上，采用三折线模型模拟具有应变软化性质的岩土材料的应力应变关系曲线，分析了在应变软化土体中沉桩时桩周土的位移场、应力场和应变场的变化，得到了解析解答；分析了静压桩的沉桩机理，并利用球形孔扩张理论，视桩端处的挤土为半个球形孔的扩张，分析了桩端处土的位移场、应力场和应变场的变化，并根据最终扩张压力计算出沉桩时的桩端阻力，可作为压桩力的估算。

However, the pseudo-triaxial strengths of several rocks from the best fitting solutions have great scatterness from the real magnitudes. Also, it does not correspond to the experimental results that rock has the same strength under conventional triaxial compression and tension; the maximum increase of strength from intermediate principal stress has a linear relation with the minor principal stress; and the first-order derivative of strength has an interruption at the peak point.

此外，统一强度理论认为岩石三轴伸长强度与常规三轴压缩强度相同，在最小主应力恒定时中间主应力引起的强度最大增加值随最小主应力线性增加，且强度关于中间主应力的一阶导数在峰值点是不连续的，这些都与试验结果不能完全协调。

On the basis of the achieved result and the effect of stress such as minor principal stress, intermediate principal stress, hydrostatic pressure, stress Lode degree, a generalized hyperbolic failure function adapted naturally with the envelope form of Mohr-Coulomb criterion is proposed for brittle rocks; and a smooth failure function acquired by Yu Maohong is also presented. Thus, a generalized polyaxial strain energy strength criterion is created.

在分析脆性岩石强度的静水压力、中间主应力、最小主应力以及应力Lode角等4种效应的基础上，提出子午面上与Mohr-Coulomb准则包络线自然衔接的广义双曲线型破坏函数及八面体偏平面上光滑角隅型破坏函数，从而建立非线性广义多轴应变能强度准则。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。