查询词典 exponential function

On the basis of extending the concepts of the derived function, primitive function and integration of interval-valued function to complex interval-valued function and using the descomposition theorem of complex fuzzy set, the derived function, primitive function and integration of complex fuzzy set-valued function and some properties of them are proved.

2在国际上最先引入了复模糊集合与复模糊数的基本概念，证明了它们的基本代数运算的封闭性，并且其运算可通过α水平复集合的相应运算来进行

The total of these two sorts of functions is called S-functions The indicial function, sinusoidal function, cosinusoidal function, hyperbolic sinusoidal function, hyperbolic cosinusoidal function, trigonometric function of n-order and hyperbolic function of n-order etch are all belong to S-functions.

指数函数、正弦函数、余弦函数、双曲正弦、双曲余弦、n阶三角函数和n阶双曲函数等。都是S－函数的特殊形式。文中证明了关于S－函数及其各阶导数的性质的三个定理。

By utilizing an exponential transformation and piecewise linearization technique,transforming the exponential terms into the sum of absolute terms,and linearizing each absolute term,the original problem can be transformed into a linear programming problem which can be easily solved.

使用指数变换及利用分段线性化技术转变每个指数项为一些带绝对值项的和，再将绝对值项线性化，最终将原问题转化为一个线性规划问题。

Experiments of flow conductivity closure stress of typical propping agent are done, propping agent short-term flow conductivity alteration index is defined, by this, the relation between fissure short-term flow conductivity and closure stress, it is close to exponential relation. 4. Establishing the mathematical simulator of hydraulic fractured well's production in a steady state, finding the relation curve between dimensionless flow conductivity and fracture penetration coefficient by means of calculation and analyses, it is the basis of hydraulic fracture. 5. Expatiating the importance of optimized hydraulic fracturing design in reservoir engineering, advancing the optimizing design method, fracture dimension can be calculated easily when the physical parameters are known. 6. Production rate decline standard curve of vertical fractured wells is achieved by mathematical simulation, when the flow pressure is certain , by asymptotic analyze, this decline curve is close to exponential relation.

完成了国内外典型支撑剂的导流能力闭合应力影响实验，在数据分析中定义了支撑剂短期导流能力变异系数，并由此发现裂缝短期导流能力随闭合应力变化的近似符合指数关系式； 4 建立了一种水力压裂井稳态产能的数学模拟器，计算分析找到了最优无量纲导流能力与裂缝穿透比之间的新型关系曲线，它是水力压裂优化设计的基础； 5 阐述了水力压裂油藏工程优化设计的重要性，提出了优化设计方法，在已知支撑剂物性参数条件下可简洁计算最优裂缝尺寸； 6 数学模拟给出了垂直裂缝井产量递减标准曲线，在井底定压条件下通过渐近分析表明，该递减曲线满足指数关系式。

Based on the analysis of the mechanism of robot manipulators, a trajectory tracking controlling research model is first built up with ADAMS, and its mathematical model is formulated through the study of robot kinematics and dynamics. After the modeling errors are analyzed in practical robotic systems, a conception of centralized error is brought forward according to the theory of weighting functions. In the case of modeling errors' exist, the robotic uncertain model is derived by introducing an auxiliary control variable into inverse dynamic analysis. The control strategy of robust exponential convergence is applied to the robotic uncertain model, the applicable conditions and the applicable controller with this application are presented. The stable control effect under three main model uncertainties (parametric errors, joint disturbs, joint frictions) are systematically studied on the previously built research model. The problems of robust exponential convergence controller which often results in unstable output and so produces a large relative error when the input trajectory is in a small range are resolved by adjusting the control parameters based on the controller's structure.

本文在机械手的机械结构分析基础上，利用ADAMS建立了用于机械手轨线跟踪控制研究的机械手模型；通过对机器人运动学和动力学问题的研究，建立了机械手研究的数学模型；分析了机器人系统中模型误差的主要来源，根据加权函数法分析，提出了模型集中误差的概念；在存有模型误差的情况下，采用逆动力学结构并引入辅助控制量，由机器人误差模型推导了机器人非确定性模型；提出了采用鲁棒指数收敛法对上述机器人非确定性模型进行鲁棒镇定的控制策略，并给出了对机器人进行鲁棒指数收敛控制时系统不确定因素应满足的匹配条件；针对机械手研究模型，深入研究了鲁棒指数收敛控制器对机器人系统中常见的模型参数误差、关节扰动、关节摩擦等不确定因素的镇定控制效果；针对鲁棒指数收敛控制器易产生控制量振荡的问题以及在小范围内系统轨线跟踪的稳态误差过大问题，本文分别提出了基于控制器结构的控制参数调整法和基于轨线跟踪范围大小的控制参数分段切换法。

The exponential model and double exponential model were the most practical and applied models for secondary clarifier simulation.

在二沉池模拟中，指数模型和双指数模型较为实用且应用较多。

Our main results are as follows: we have given a non-trivial estimate for a class of rational exponential sums,and the best possible upper bound for a class of characters sums with exponential functions.

我们的主要结果是：给出了一类有理指数和的非平凡估计，以及一类特征和的最佳上界。

Also, by using exponential dichotomy, contraction map theorem and matrix theory, some sufficient conditions are obtained to ensure the existence and global exponential stability of almost periodic solution for MAM neural network with distributed delays.

利用矩阵的谱半径、指数二分法结合运用压缩映射原理获得了分布时滞多向联想记忆神经网络模型概周期解的存在性，并在相同条件下证明了概周期解的全局指数稳定性。

A sufficient condition is obtained to ensure the existence and uniqueness of almost periodic solution for MAM neural network with time-varying delays by way of exponential dichotomy and contraction map theorem. Moreover, the global exponential stability of the almost periodic solution for this type of MAM neural network is proved by using Halanay inequality.

利用指数二分法结合运用压缩映射原理获得了变时滞多向联想记忆神经网络模型概周期解的唯一存在性，利用Halanay不等式证明了变时滞多向联想记忆神经网络概周期解的全局指数稳定性。

According to Lemaitre's damage evolution law and the assumption of this paper that the cyclic loading maximum tensile stress has the most contribution to the cyclic damage and assume that the stress is the maximum stress .The material parameters S which are expressed in exponential form and generalize the variation in the process of cyclic loading is exponential experience equation which provide the expectation of cyclic damage of 63Sn/37Pb material and lead it into the calculation of damaged incremental form and assume that damage keeps constant during the same cycle. The results match the experimental data. It proves that the Endochronic plasticity theorem adopt the calculation of damage environment.

根据Lemaitre损伤演化律及本文假设循环负载下拉应力在最大值附近对循环损伤的贡献最大，文中应力对各循环之损伤而言假设应力为最大拉应力，将材料参数S以指数型式表示，归纳出疲劳损伤在循环负载过程中的变化为指数型经验式，提供63Sn/37Pb材料在循环负载作用时损伤情况的预测，并引入含损伤增量式内涵时间之计算中，假设同一循环的损伤为定值，其计算结果与实验数据吻合，说明内涵时间塑性理论亦适用於损伤环境下的计算。

Fostering the concept of multi-culture firmly and mastering the development of advanced culture correctly are conductive to resisting terrorism, separatism of nationalities and ultraism of religion, which is of great academic theoretical, immediate and profound historical si...

牢固树立多元文化的理念和正确把握先进文化的发展方向，有助于在世界范围内自觉地抵制恐怖主义，民族分裂主义和宗教极端主义。不仅具有重大的学术理论意义，而且也具有重大的现实意义和深远的历史意义。

But if anyone walks in the night, he stumbles, because the light is not in him.

11：10 若在黑夜行走，就必碰跌，因为那光不在他里面。