极限

We obtain that if any 〓 is discrete or elementaryand 〓 satisfies Condition A,then the algebraic limit G of group sequence 〓is discrete or elementary.

首先，我们不再仅仅考虑离散非初等群集〓的代数极限G，而是离散群或初等群群集〓的代数极限G，我们对〓上〓变换群中斜驶元及其不动点进行了细致研究，注意到任意一个斜驶元存在一个仅仅含有斜驶元的领域，从而证明了初等群群集〓的代数极限G仍然是初等群，进而我们得到了一个代数收敛定理：如果任一〓是离散群或者初等群并且〓满足条件A，那么，群列〓的代数极限G一定是离散群或者初等群。

Theoretical Part: Through theoretical analysis of chemothermodynamics, combustion and engineering thermodynamics, factors that affect explosion limit were determined, which include temperature, pressure, spark ignition energy, electrode shape, direction of flame propagation and size of explosion vessel.

理论部分：根据化学热力学、燃烧学和工程热力学的基础理论，从本质上定性地分析了爆炸极限的影响因素，包括温度、压力、爆炸容器的大小、点火能量大小、以及火焰传播方向等，得出了这些影响因素对爆炸极限的影响规律，以确保实验有完整的理论基础指导；在此基础上本文提出了一种新的推算在常温常压下可燃性纯质和混合工质制冷剂爆炸极限浓度的理论方法，该方法由可燃性气体的化学组成来推算上下限浓度，不需要其它条件；对混合工质制冷剂，只要再知道混合配比，即可以推算出爆炸极限，使预测爆炸极限的工作更简单、方便。

This paper presents the concepts of double limit, repeated limit , directional limit and weak double limit of binary function, and discusses the relationships among them.

给出了二元函数的二重极限、累次极限、方向极限、弱二重极限的概念，讨论了这几种极限之间的关系。

Moreover, we constructed the limit and inverse limit sturcture in the category of quantale.

此外，还讨论了范畴Quant中的极限，逆极限和定向极限，给出了Quant中极限和逆极限的结构。

Firstly, the connection matrices are strongly connected Boolean matrix, it is shown that the maximum length of limit cycles for FBAM is the period index of the product of the connection matrices. Thus, the maximum limit cycle is reachable. Secondly, two strongly connected components are connected by walks, it is proved that the maximum length of limit cycles for FBAM is the max. of the period index of the two strongly connected components if they are prime, otherwise, it is the least common multiple of the two period index. Finally, n strongly connected component are connected in succession, the method for computing the maximum length is described. By different patterns are presented to the networks, diminishing the number of the strongly connected components until only two components.

第一，连接权矩阵为强连通布尔矩阵，此时模糊双向联想记忆网络的最大极限环长度为连接权矩阵乘积的周期指数，从而极限环具有可达性；第二，两个强连通分支有路径连接，此时如果两个强连通分支的周期指数互素，那么网络的最大极限环长度为其最大者，否则，网络的最大极限环长度就等于二者的最小公倍数；第三，n个相邻强连通分支有路径连接，给出了计算最大极限环长度的方法，通过激发模式的变化，逐渐减少强连通分支的个数，直到只有两个分支。

The assumption of the variable tendency of slip-line in active zone is made based on the numerical results. Combining the slip-line equations and boundaries, the formula of bearing capacity is deduced which can consider the density of soil. The formula of bearing capacity of strip footing on ponderable soil is also deduced assuming that the slip-line field of ponderable soil is the same with that of weightless soil, which is proved to be an upper-limit solution, as its the same with that deduced by the upper-limit method in Prandtl mechanism.

在数值计算结果的基础上，对有重土地基主动区滑移线变化趋势进行了合理假设，根据边界条件和特征线方程求得了条形基础极限承载力的解析表达式，该表达式可以计算考虑土重度的条形基础的极限承载力；获得了不考虑重度对滑移线场影响时(即有重土在普朗特尔滑移线场下)极限承载力的解析表达式，该表达式与普朗特尔机动场对应的极限承载力上限解的表达式相同，这就从理论上证明了在土重度对滑移线场没有影响这一假定前提下得到的极限承载力是一个上限；(3)利用上限定理求解了极限承载力的最小上限。

Forming limit stress diagram was investigated theoretically and experimentally.

本课题通过试验，有限元仿真和理论分析，研究了应力成形极限的路径相关性问题，应力成形极限和应变成形极限的转换关系，材料各向异性对成形极限的影响，以及应力成形极限在板料成形分析中的应用等。

By the numerical analysis of the ultimate bearing capacity of two- and three-dimensional footing under combined loading mode, the results show that the effect of alteration of underground water lever on bearing capacity of three-dimensional foundation is more than on that of two-dimensional foundation, the effect of soil gravity on bearing capacity of three-dimensional foundation is more than that of two-dimensional foundation. At the same time, the numerical calculation process of ABAQUS indicates that whether the geostatic stress is balanced or not has great effect on the numerical convergence. In view of the effect extent of dilation angle of soil on the ultimate bearing capacity and the failure pattern of foundation, the condition of two-dimensional plane strain is higher than that of the three-dimensional foundation.

复合加载模式下，通过对三维矩形基础和二维条形基础进行数值分析，结果表明：黏性土地基中地下水位的变化，对三维矩形基础极限承载力的影响程度高于对二维条形基础的影响；在求解地基极限承载力的过程中，土体重度对三维矩形基础的影响明显高于对二维条形基础的影响，同时ABAQUS数值计算过程表明，地基土体地应力能否合理平衡，对数值求解过程中是否收敛有很大的影响；就土体剪胀角对地基极限承载力的影响程度而言，二维平面应变情况下土体剪胀角对极限承载力的影响比三维情况下的影响更明显，即土体剪胀角对条形基础极限承载力的影响高于三维矩形基础。

Model test shows that when raft is the principal bearing element, a single pile with cap has nearly the same behavior with a corresponding unpiled raft when subjected to vertical load. When the load acting on the pile cap exceeds the ultimate pile load, the pile carries less load than it's ultimate pile load. When the load exceeds 2 times of the ultimate pile load, pile is nearly at full capacity.

一、进行了室内模型试验，证明当以桩间土为主承担荷载时，带台单桩的荷载～沉降特性与天然地基上浅基础类似；当外荷载超过单桩极限承载力时单桩并不达到极限承载力，当外荷载超过2倍单桩极限承载力时桩顶反力才接近单桩极限承载力；此后加载台下单桩以接近极限承载力的状态继续承担外荷载。

For example, the class of all limit ordinals is closed and unbounded : this translates the fact that there is always a limit ordinal greater than a given ordinal, and that a limit of limit ordinals is a limit ordinal (a fortunate fact if the terminology is to make any sense at all!).

例如，所有极限序数的类是闭合且无界的：这解释了总是有一个极限序数大于给定序数，而且极限序数的极限是极限序数的事实。

It is also known as one of the most poisonous naturally occurring substances.

它也被称为一个最自然发生的有毒物质。

The greatest stress is found at the location on the cross section where V is the largest.

最大应力出现在横截面上V为最大的地方。