最大值

Theorem 1 (Boundedness and max-min theorem) If is a continuous function on a closed interval, then has an absolute maximum and an absolute minimum on the interval.

定理 1 (有界性与最大值最小值定理)在闭区间上连续的函数在该区间上有界且一定能取得它的最大值和最小值。

Property 1 (Boundedness and max-min theorem) Let be a continuous function of several variables on a closed region D, then has an absolute maximum and an absolute minimum on the region.

性质1（有界性与最大值最小值定理）在有界闭区域D上的多元留恋许函数，必定在D上有界且一定能取得它的最大值和最小值。

The results show that there will be slight decrease of the control efforts when the mean absolute value or the root mean square value of the optimal control force is taken as the maximum designed control force, while the maximum control force of MR damper can be decreased by 85% compared with the maximum optimal control force. The decrease in the designed control force can not only significantly increase the capability of MR dampers, but also reduce the dimension of MR dampers for pratical application in engineering.

研究表明，当设计值取最优控制力的平均绝对值或均方根值时，MR阻尼器的最大控制力比最优控制力的最大值降低了85%，而控制效果降低不多，可以满足对结构的控制要求；降低最大控制力设计值后，不但可以充分发挥MR阻尼器的出力性能，而且可以缩小MR阻尼器的设计尺寸，便于工程应用。

From this test results, it is obtained that the maximum lateral displacement occurs at a depth of about 0.75L; land upheaval build up rapidly and reach the maximum when the pile tip arrive at depth of about 6 m; and the increment. of excess pore water pressure reaches the maximum when the pile tip arrive at the piezometer level; while the maximum excess pore pressure presents a hysteresis quality with radial distance.

由测试结果可知，最大的侧向位移发生在距地表0.75L附近，地面隆起从桩贯入开始迅速发展，并在桩压入到6m左右时达到最大值，测点处超静孔压增量的最大值发生在桩端到达该点所在水平面时，而超孔压的最大值沿径向有滞后性。

Carleman不等式及其在最优控制问题中的应用.Optimal control theory of distributed parameter systems mainly includes: Pontryagin's maximum principle; controllability; Hamilton-Jacobi equation (i.e., dynamic programming equation); time optimal control, etc.In this dissertation, we establish Pontryagin's maximum principle of optimal control problems governed by some nonlinear differential equations (parabolic differential equations, elliptic differential equations and 3-dimensional Navier-Stokes equations), which in particular could have local solut...

在这篇博士论文中，我们建立了非线性微分方程(包括抛物型微分方程，椭圆型微分方程以及3维Navier-Stokes方程)最优控制问题的庞特里雅金最大值原理，特别地，这些方程可能只有局部解或存在多解(我们称这样的系统为非适定系统，相应的最优控制问题为非适定最优控制问题)，以及适定的非线性发展方程最优控制问题的庞特里雅金最大值原理；我们研究了phase-field系统的时间最优控制问题以及Boussinesq系统的局部内可控性。

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。

The mean, maximum and minimum value of the area of transverse section and the major axis length of ellipse and the maximum centroid displacement can be used to discriminate width of pulse tracing.

长轴长度周期平均值、最大值、最小值，面积周期平均值、最大值、最小值，以及轴心在平行于皮肤表面的最大位移等参数可以作为初步判别脉宽的参数。

It was concluded that there are direct relationships between amplitude and initial phase in vertical orientation by numerical analysis. There are maximum and minimum of amplitude, and the way to ensure them was proposed.

经过数值分析，得出在竖直方向上激振力的幅值与初相角有直接的关系，并且幅值存在最大值和最小值，提出了最大值和最小值的确定方法。

The amount of drainage in 1998-1999 was caudated by the equation, the average was 149.4mm, the maximum value was 197.5mm and the minimum was 93.1mm, coefficient variability was 2.9%. The average amount of drainage in 1999-2000 was 286.4 mm, the maximum value was 391.9 mm and the minimum was 193.9 mm, the maximum value was two times than minimum value, and CV was 6.4%.

通过上面建立的关系式，计算得到了1998-1999年10个小区的渗漏量，其平均值为149.4mm，最大值为197.5mm，最小值为93.1mm，变异系数为2.9％。1999-2000年的渗漏量平均值为286.4mm，最大值为391.9mm，最小值为193.9mm，最大值约是最小值的2倍，变异系数为6.4％。

The results indicated Paecilomyces farinosus was aerobic fungus and rotate speed of rocking bed exceeded 150r/min would benefit the mycelium growth.Initial inoculum could affect the time of reaching maximal mycelial bioass and could not affect the maximal mycelial bioass.inoculum exceeding 5% would benefit t...

结果表明粉拟青霉是一种好气性真菌，摇床转速大于150r/min有利于该菌生长；接种量对菌丝最大产量影响不大，但是能够影响菌丝量达到最大值的时间；接种量大于5%，有利于菌丝产量迅速达到最大值；粉拟青霉菌在pH值为3～10的培养基中都能够生长，生长过程中能够分泌代谢产物主动调节pH值，该菌在pH为5～7的微酸环境中生长最快；液体发酵过程中粉拟青霉生长量与发酵时间的关系符合逻辑斯蒂生长模型。

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。