最后，让我们的双曲函数反三角函数和照顾。
Finally, let's take care of the inverse trig and hyperbolic functions.
对双曲函数法进行了探讨，且对其进行了推广。
We studied the hyperbola function method and generalized it.
用双曲函数法，成功得到了非线性浅水长波近似方程组的精确孤立波解。
We successfully derived some exact solitary wave solutions of the nonlinear approximate equations with long waves in shallow water by using the hyperbola function method.
通过对注水井压降曲线形态的分析，提出了压降曲线的等轴双曲函数的数学表达式。
The axisymmertyical hyperbola function mathematical formulation of pressure fall-off curves is given by analysing the pattern of the generous pressure fall-off curves of the injection wells.
栓钉剪切刚度与滑移呈双曲函数关系，影响其剪切滑移刚度的因素是栓钉直径和混凝土强度。
The diameter of stud and strength of concrete are main factors to affect the shear stiffness.
采用双曲函数与幂函数结合的模式拟合沥青混凝土的三轴蠕变试验曲线，对大坝进行蠕变分析。
Furthermore, a function of hyperbola combined power is adopted in modeling the curves of long-term triaxial creep test of the asphalt concrete; and creep analysis is performed for the dam.
双曲正弦、双曲余弦和双曲正切函数也会以常见或特殊形式出现在各种计算中。
The sinh, cosh, and tanh functions also all appear in various calculations in special and general relativity.
采用了仪表化冲击试验设备和双曲正切函数回归计算的数据处理方法，因而确保了实验结果的准确性。
The advanced instrumented impact test equipment and the method for treating test data with the hyperbolic tangent function ensure the accuracy of results.
提出了“利用反双曲正弦函数变换提高数据列光滑程度”的新结论，获得了递增时间序列改善的自回归预测新方法。
A new conclusion is put forward, in which the smooth degree of the data row can be enhanced by means of the arc-hyperbolic sine function transformation.
针对文家坪磷矿地下开采岩体移动变形问题，给出了用于预测分析地下开采引起地表移动变形的双曲正切函数模型。
A theoretical model for predicting ground displacement and deformation due to mining of phosphate body in Wenjiaping by using hyperbolic tangent function was given in this paper.
之后，设计了双曲正切函数的鲁棒补偿项，从而得到一种没有抖振的平滑控制输入。
Then, a robust compensation term is developed in form of hyperbolic tangent function to obtain a smooth control input without chattering phenomena.
在详细分析现有变步长LMS算法的基础上，给出一种以双曲正切函数的改进形式为变步长的LMS算法。
A new variable step size LMS algorithm with improved hyperbolic tangent function is presented, which is derived by the extensive review about some existing LMS algorithms.
借用并修改金蛋模型，以拟双曲形贴现效用函数和预算约束中的短期储蓄目标，刻画了中国消费者的短视行为。
This paper establishes a model to analyze myopia of Chinese consumers who have hyperbolic discount functions and short-run saving targets by means of the method of Golden Eggs model.
所得脉冲包络为时间的双曲正割函数。
The pulse envelope we obtained is a hyperbolic secant function of time.
根据模糊推理估计集成不确定边界，利用双曲正切函数代替符号函数实现软切换连续控制。
The integration uncertain border value is estimated by fuzzy inference and the soft switch control is accomplished by tanh (x) function replacing SGN (x).
利用解析函数的性质，通过反双曲余弦计算出了由共焦点椭圆导体柱面组成的电容器内电场和单位长度的电容，并对结果作了进一步讨论。
The electric field and capacitance of a confocal elliptic capacitor are calculated by the inverse hyperbolic cosine analytic function, and discussion on them is performed.
在这篇文章中，我们得到了非线性函数在无穷远处超线性增长时一类高维半线性双曲方程的整体精确能控性。
In this paper, we obtain the global exact controllability for a class of multidimensional semilinear hyperbolic equations with a superlinear nonlinearity.
本文以两个自变量的拟线性双曲型方程的古尔沙问题为例，应用反函数和积分不等式证明了等价积分方程组解的存在唯一性，同时给出了解的存在区域和已知参量的依赖关系。
In this paper, we show the domain of the existence of the solution on Goursat problem for quasi—linear hyperbolic equation and obtain the Theorem of the existence and uniqueness in above domain.
利用扩展的双曲正切函数法获得了(2 +1)维长波短波共振相互作用方程的多组新显式精确行波解。
Applying the modified extended tanh-function methods, many types of new explicit traveling wave solutions of the (2 + 1) dimensional long wave-short wave resonance interaction equations are obtained.
针对不同情形，通过恰当地利用双曲正切函数，提出了三种连续有界的协同控制器。
According to different cases, three kinds of continuous and bounded coordination controllers are proposed with the novel use of hyperbolic tangent functions.
证明了利用反双曲正弦函数变换能提高数据列的光滑程度，给出了改善的自回归预测方法，并且举例加以论证。
This paper proves that the smooth degree of a data row can be increased by transforming the counter-hyperbolic sine function.
文中引用双曲数与双曲复函数，证明了上述边值问题的解在一般区域上的存在性。
The so called hyperbolic numbers and hyperbolic complex functions are introduced and used, and the existence of solutions for the above problem in the general domains is proved.
方法分析双曲对称群的特点，改造欧式平面上构造经典分形的IFS迭代函数系，利用这种迭代函数系与双曲平面对称变换构造出组合IFS，通过随机挑选组合IFS中的仿射变换，构造双曲排列的分形集。
We recall the characteristics of the groups with hyperbolic symmetry and improve the IFS iterated function systems which are used to construct the classical fractal sets in the Euclidian plane.
研究表明，6061铝合金热压缩塑性变形时的流变应力和应变速率之间的关系满足双曲正弦函数关系式；
The results show that relationship between flow stress and strain rate is applied to hyperbolic sine equation in the hot compressive deformation of 6061 aluminum alloy;
基于这种基函数，建立了一种带多个形状参数的二次双曲多项式曲线，该类曲线对于非均匀节点为C1连续。
Based on the basis functions, quadratic hyperbolic polynomial curves with multiple shape parameters are constructed. These curves are C1-continuous with a non-uniform knot vector.
基于这种基函数，建立了一种带多个形状参数的二次双曲多项式曲线，该类曲线对于非均匀节点为C1连续。
Based on the basis functions, quadratic hyperbolic polynomial curves with multiple shape parameters are constructed. These curves are C1-continuous with a non-uniform knot vector.
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