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Duffing equation has parameter and initial value sensitivity. It can generate chaotic state by adjusting the parameter and initial value, and it also can generate intermissive chaotic state, if the ideal signal and the measured signal applied to the system simultaneously. The actual measured signal can be measured by using this state.

Duffing方程具有参数敏感性和初值敏感性，通过调节Duffing方程的参数和初值可以产生混沌现象，且被测信号和理想信号如果共同作用在Duffing方程上，可以产生有规律间歇混沌现象，利用这种现象就可以实现周期信号的频率测量。

Based on the theory of two-phase fluids dynamics, the general governing equation is established, which is applied to the fields of seepage, consolidation and deposit. For the first time, the mechanics properties of the soil affected by seepage are studied by the means of experiment. The problems of the modified indexes of mechanics and constitutive relation are solved due to the formulations obtained of mechanics parameter under seepage condition. Applied fuzzy theory and modern project design method, the fuzzy probability model for stability analysis is stetted up; Considered variation of mechanics parameter and curtain effect, the deformation patterns of deep execution are systematically analyzed.

基于两相流理论，推导了适用于渗流、固结和沉积的统一形式的控制方程；试验研究了渗流作用下土的力学性质的变化规律，经综合分析得到力学指标的定量表达式，为工程设计和数值计算中力学参数的确定提供了参考；基于模糊理论和现代工程设计方法，建立了基坑失稳的模糊概率模型，为基坑稳定性预测提供了新的方法；对基坑变形规律作了系统分析，考虑了土性变化和帷幕防渗效果对支护结构变形的影响，得到了较满意的结果。

Based on the heating flow equation, the tip temperature of the cone field emitters were computed self-consistently in Nottingham effect and in Jouel heating. The temperature as a function of structure parameter and physical parameter of the cone emitter was calculated.

从热传导方程出发，考虑Nottingham效应和焦耳热情况下，采用自洽求解了圆锥形场发射体的尖端表面温度；定量讨论了温度与给定的圆锥形场发射体的结构参量与物理参中的关系。

Based on basic theory of elastic wave propagation, wave equation forpropagation of elastic wave in 2 dimension vertical inhomogeneous mediumof similar concrete cutoff wall model is developed. 2 dimension elastic sheetof concrete cutoff wall is established to research law and energy distributionrelations between propagation, attenuation, reflection and transmission ofelastic wave in concrete cutoff wall; Based on the concept of resolution, thecontent of vertical reflection method used to inspect concrete cutoff wallresolution is raised and factors will have influences on resolution are analyzed,expression of defective layer composite reflection factor and detectabledefective layer maximum thickness are developed; Relations between allsteps of sampling system of vertical reflection are build, the influence ofcentrum characteristics and receiving sensor on testing results are analyzed,therefore parameter requirements for testing instrument and parameter selection principle of collected parameters are raised.

2从弹性波传播的基本理论研究出发，推导了弹性波在类似混凝土防渗墙模型的二维垂向不均匀介质中传播的波动方程式；建立了混凝土防渗墙二维弹性薄板模型，研究弹性波在混凝土防渗墙中的传播、衰减、反射、透射规律及能量分配关系；从分辨率的概念出发，提出了垂直反射法检测混凝土防渗墙分辨率的内涵，对影响分辨率的因素进行了分析，推导出了缺陷层复合反射系数、可检测缺陷层极限厚度的表达式；建立了垂直反射法采样系统各环节之间的关系，研究分析了震源特性、接收传感器对测试结果的影响，提出了对测试仪器参数的要求及采集参数的选择原则。

Based on two-dimensional elastic wave equation and adopts the well logs as constraint condition, a new imaging method of crosswell seismic data-elastic wave equation inversion and imaging with the well logs constraint is given by using adjoint theory of distribution-parameter control system.

基于二维弹性波动方程，利用分布参数控制系统的伴随理论，采用测井资料作为约束条件，本文给出了一种井间地震资料速度成像的新方法——井间测井约束弹性波动方程反演成像。

The derivative nonlinear Schrodinger equation is, however, an open and important issue both in theoretical and applied aspects. The DNLS equation with nonvanishing boundary conditions is solved by introducting an affine parameter and we find that it supports a rich set of soliton solutions.

大部分完全可积的(1+1)维非线性偏微分方程，特别是有明确物理应用的方程的孤子解已经用反散射变换等方法得到，但还剩下一些难题，变形的非线性薛定谔方程在非零边值下的反散射变换就是其中一个。

An analytical coupled water-energy balance equation at arbitrary time acale was derived by dimension analysis and mathematical derivation. The equation has only one parameter.

本文通过量纲分析和数学推导得到能用于任意时间尺度上的水热耦合平衡方程，该方程含有唯一参数。

Assuming a condition cont-rol reserve calculation,combimatively solve the material balance equation of gas recovery and binomial gas recovery equation for gas well,calculate the production curve of gas well and match it with the actual production curve,finally determine the reserve and productivity parameter,this method doesn't need much pressure build-up data,and can calculate the c...

该方法的推导思路是：假设在某一控制储量条件下，联立求解气藏物质平衡方程式和气井二项式采气方程，计算气井采气曲线并将其与实际的采气曲线相匹配，最后确定储量、产能参数。该方法不需要较长的多次关井复压资料，在气藏受水驱影响较小时，还可计算一口探井或气藏试采早期所反映出的气井控制储量，在气藏生产中得到应用，计算结果较为可靠

As long as the root of the characteristic equation is within the unit circle of z-plane and the corresponding PID parameter is got, the closed loop control system is sure to be stable. Although the root of the characteristic equation can vary within the unit circle of z-plane,different value may affect the control property differently.

本文所采用的这种确定PID参数的方法，虽然可以使特征方程的根在z平面的单位圆内任意取值，但各种取值情况对变风量空调系统的控制品质的影响却不同，因此，要对各种特征方程的根的取值情况进行寻优，本文采用遗传算法对特征方程的根进行寻优，从而使控制器的参数得以优化。

The basic idea of Tikhonov regularization is that linear compact operator equation of the first kind is replaced by the minimization problem of Tikhonov functional, the paper demonstrates the minimization of Tikhonov functional is an well-posed problem. In the end, the paper suggests a new type of iterative algorithm to solve inverse problems of parameter identification for one-dimension parabolic partial differential equation .

本文论证了Tikhonov泛函极小化问题是适定的，即满足西安理工大学硕士学位论文解的存在性、解的唯一性和解连续依赖于数据的稳定性：并且此极小化问题等价丁求解第一类方程的正规方程。

Diabetes is a social disease that affects several million people worldwide.

糖尿病是一个社会性疾病，全世界有数百万人罹患此病。

I'll call you on Friday to see if we can reschedule our luncheon meeting at your convenience.

我星期五会给您打电话在您方便的时候我们重新安排我们的午餐约会。