极限点

On the basis of method of derivative on the left and the right of separable function,the derivability of separable function on demarcation point was simply distinguished,and derivative continuity on demarcation point discussed.

运用研究分段函数的导函数的左、右极限的方法，简便地判明分段函数在分界点处的可导性；同时讨论了分界点处导数的连续

In favour of arc length algorithm, the curve of fix points of balanced rotor to rotor speed, harmonious and subharmonious unbalance reponse curves are given. The Hopf bifurcation of balance rotor is computed by use of extent equation method.

同时应用扩展方程方法计算了平衡转子的Hopf分叉点，并用求得的Hopf分叉点参数进行数字仿真，证明极限环的存在，因此说明Hopf分叉点的计算是正确的。

Consistency of change-point estimator is proved and its rate of convergence is established under weak assumptions. To construct confidence interval, the limiting distribution of change-point estimator is obtained.

在较弱的条件下证明了变点估计的一致性，并得到了佑计的收敛率；为构造变点的置信区间给出了变点的极限分布。

The action point of limiting force on retaining structure is not always at 1/3 of the height of retaining structures, but varies with the friction angle δ between soil and retaining structures, the type of limiting state, the failure mode, the internal friction angle φ, and cohesion c of the soil, ranging from 1/5 to 2/3 of the height of retaining structures.

3土体极限荷载P〓的作用点位置不象Coulomb理论中假定的那样，总是作用在墙高的1／3处，而是与土体极限状态的类型、土体的破坏形式、墙土之间的摩擦角δ、土体的内摩擦角φ和粘聚力c有关系，在挡土结构物高度的1／5到2／3的范围内取值。

The main work and innovation1 In general , a image compression method has different effect to different image . Some are fit for image which has much high frequency . Some are fit for image which has much low frequency .This paper analysis the applicability of fractal algorithm . In this dissertation , an improved algorithum is given . The basic algorithum without eight change and the joint use of quantitative coding , The compression ratio and PSNR can be adjusted , and it can get more quickly speed of coding .2 To a group of exact fractal code , the decoding image can be any resolution .With this characteristic ,choose the proper domain block and range block,this paper get an algorithum which can get higher decoding PSNR and speed than the basic fractal algorithum.3 Give a new method to calculate the scale factor . The calculation of basic algorithum is complex and enormous . The factor of scale is an important variable of the basic algorithm. Now there are two methods to calculate the factor of scale .A new method was given to calculate the factor of scale. The calculation load and complexity are reduced by the new method. Compared with the basic algorithm , the method can reduce coding time.4 The basic fractal algorithum is based on the Collage theorem and contraction mapping theorem . A mathematic model based on basic fractal algorithum is given .

本文的主要工作及创新点主要包括以下几点：1一般情况下，一种图像压缩的方法对不同特点的图像，压缩效果会有所不同，本文利用分形压缩编码对不同特点的图像进行编码，分析了分形编码对不同图像的编码适用性，利用去掉8种变换的分形编码算法与简单的均匀量化编码方案相结合，得到了一种可以调节压缩比与解码质量的分形编码方案，该提高编码速度6倍以上。2分形编码的特点之一是分形解码的分辨率无关性，即对于一组分形编码可以将其解码到任意分辨率下，本文利用分形编码的这一特点，结合不同的量化编码方案，选择合适的定义域块与值域块及适当的编解码分辨率，得到了一种提高解码质量，编码速度提高12倍以上的加速算法。3比例因子是基本分形算法中的一个重要变量，目前有两种计算比例因子的方法，文中给出了一种新的求比例因子的方法，该方法简化了求比例因子的计算，从整体上减小了基本分形算法的计算量，简化了算法4分形压缩的数学基础是不动点定理与拼贴定理，本文根据基本的自动分形编码方法，建立数学模型对其进行推导，得到了用普通数学的极限理论解释分形编码的数学表达式，从而对由基本分形编码得到的解码图像中的像素点的值给出了确定的表达式。

Unless otherwise stated in the design brief, the North Atlantic scatter diagram should be used in ULS and FLS for unrestricted world wide operation.

除设计概要中另有说明外，北大西洋散点图应用于非限制全球作业的极限状态和疲劳极限状态。我翻译，我存在！

The following exciting results are revealed: 1 When considering the influence of some nonlinear elements such as hard-limit of exciters, the effects of some devices such as Power System Stabilizer and Static Var Compensator which can introduce positive damping in power system, the reasonability of system parameter values in simulation, the SNB surface and HB surface on the boundary of SSSR will turn close to each other and even coalesce together; 2 Under some conditions, coupling between slow exciters and shunt capacitors will bring negative damping in power system dynamics, which increases the possibility of oscillatory instability. So the power system with mass shunt compensators is easily subjected to the oscillatory instability. In recent years, chaotic phenomena of power system have been reported many times. Some simulation studies even found chaos existing inside the power system SSSR. In this dissertation, chaotic phenomena in power systems are thoroughly studied in order to make clear the relation of chaos and SSSR. The following results are derived: 1 Based on Li-Yorke Theorem and their definition on the chaos, the existence of chaos in power system is verified; 2 Three possible routes of causing chaos in power system are found and deeply investigated. They are route of cascading period doubling, route of directly initial energizing and route of torus bifurcation (or quasi-periodicity). The latter two routes are investigated for the first time in power system stability studies; 3 When the stability conditions of chaos are broken, it is found they can lead to voltage collapse, angle divergence, or voltage collapse with angle divergence simultaneously.

针对在电力系统小扰动稳定区域内可能存在混沌吸引域的有关报道，本文深入研究了电力系统混沌现象的出现途径和与系统失稳模式之间的关系：1利用Li-Yorke定理和Li-Yorke的混沌定义，从理论上证明了电力系统混沌现象的存在性；2发现了电力系统中导致混沌出现的三种可能途径：倍周期分岔导致混沌、初始能量直接激发混沌和经由环面分岔导致混沌，并对后两种新发现的途径进行了较为细致的研究；3发现了混沌极限环破裂导致电压崩溃、角度失稳以及电压崩溃和角度失稳同时出现的现象，其中混沌极限环破裂导致系统角度失稳和电压崩溃及角度失稳同时出现的现象均属首次报道；4证明由微分-代数方程描述的系统模型，其小扰动稳定域的边界只包含HB、SNB和SIB三种分岔界面，在SSSR的内部和边界上，均不可能存在会导致混沌的点，从而将混沌现象排除在小扰动稳定域的研究之外，简化了后者的研究工作。

The foundation soil is divided for finding the ultimate bearing capacity of a foundation with given buried depth and size. Supposing a uniform load acts on the foundation, Mindlin's integral formula and comer points method are used to get extra stress of every mesh knot by MATLAB program, then the principal stress is found. Combining with failure criterion, MATLAB program is used to find coordinates of points which are destroyed. Using graphic processing function of MATLAB, the failure points are showed in the coordinate.

为确定作用在已知埋深、给定基础形状地基土上的极限承载力，对基底下的土体进行网格划分，先假定一均布荷载作用在此地基土上，运用明德林解的积分公式，结合角点法，编制MATLAB语言程序，求出每个网格节点上附加应力，进而求得每个网格节点上主应力，根据破坏准则，结合程序找出破坏点的坐标，利用MATLAB的图形处理功能，把破坏点的坐标在坐标图中显示出来。

The permanent wilting point is reached when the plant has wilted to a point where it will not recover, even if more water is added, because the cells have plasmolyzed.

当植物的萎蔫达到一定程度就不可以再复原，这一极限被称为永久萎蔫点。超过此极限，补充再多水分也不能被吸收，因为已经胞质浓缩已经到达质壁分离的程度。

Adjust cam of the height limiter beside the hoisting drum, so as to hook the limited height(the point of the root of tower crane jib frame should reduce 2.5m, it's the limited height), enable the limit switch, the hook can not hoist, then if the hook can't act, then start it again just load onto the ground.

2调整起升卷筒旁边高度限位器中的凸轮，使吊钩达到预定的极限高度(起重机臂架根部铰点高度减去 2.5 米，即为预定极限高度)时，限位开关动作，吊钩不能上升，再启动时只能下降。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。