指数方程

Under the assumption that a differential Riccati equation is solvable, an exponential reduced-order observer is developed by means of coordinate transformation and the gain matrix of the proposed observer depends on the solution of the differential equation.

在一微分Riccati方程有正定解的前提下，通过坐标变换方法对该类系统提出了一种指数型降维观测器设计方法，该观测器的增益矩阵取决于微分Riccati方程的正定解。

Through the hypersingular integral equations of 3-d crack perpendicular to the interface given in the preceding, the principles of finite-part integrals and of limit are further made use of to pick the hypersingular integral equations of 3-d crack terminating at the interface On the basis of the equations, starting strictly from 3-d theory of elasticity, stress singularities of intersection-line near the front edge of the 3-d crack terminating at the interface are analyzed by virtue of dominant-part analysis of 2-d hypersingular integrals.

根据前面所得到的与界面垂直的单片裂纹超奇异积分方程，进一步运用有限部积分原理和极限理论，推导出了与界面垂直相抵的三维平片裂纹的超奇异积分方程。在此基础上，严格从三维理论出发，使用二维超奇异积分的主部分析方法，对与界面垂直相抵的三维平片裂纹前沿交线上的应力奇性指数进行了分析。

The main goal of the thesis is to study such some problems as theexistence of weak solutions of quasilinear elliptic equations involvingcritical Sobolev exponents on a bounded domain and〓,the unique-ness of weak solutions、regularity of weak solutions、stability ofweak solution on exponent p、continuity of very weak solutions ondomains、the fusion problem of weak solutions and the existenceof minimal positive solution of a class of quasilinear elliptic obstacleproblems,which have been extensively concerned,but have not beensolved satisfactorily in the latest several years.

本文主要对近年来人们普遍关注而又没有完全解决的几个问题——有界域及无界域上带临界增长的拟线性椭圆方程弱解的存在性，弱解、很弱解的唯一性、正则性，解关于区域的连续依赖性，解关于指数的稳定性，弱解、很弱解的合并问题，以及椭圆型偏微分方程对应的障碍问题极小正解的存在性等进行研究。

Under the conclusion of this, we prove the exponential asymptotical stability of the solution.

本文主要研究了一类无穷区间正倒向随机微分方程，利用连续性方法证明了此类方程在M~(2，k)(0，∞；R~n)空间中解的存在唯一性，并指出了k的范围，通过所得到的结论，进一步证明了FBSDE解的指数渐进稳定性。

Tolksdorf [62] to prove the weak solutions of equation (2) are of C1,a if fand u are bounded with the help of some results in [40]. And by Morse iteration,we prove that the solutions are of C1,a even if f is of critical growth.

Tolksdor[62]的方法以及[40]中的一些定理证明了方程(1)弱解的C1，a的正则性；当f满足临界指数增长时，应用Morse迭代，我们首先证明了解的有界性，然后证明方程(1)的解也有C1，a的正则性。

In the formulas of stochastic input and output, when the coefficient of direct consumption and final demand are exponentially distributed, the interrelationship between parameters of stochastic variables can be divided into three types: all the parameters are the same; parameters are inequivalent to each other; some of the parameters are the same, but the rest are inequivalent to each other.

在随机投入产出方程中，当直接消耗系数和最终需求为指数型随机变量时，方程中随机变量分布中参数间的关系有3种基本情况：所有参数都相等、所有参数两两不相等、有部分相等而其余则两两不相等。实际上，前2种情况是第3种情况的特殊形式。

The bifurcation and chaos behavior of impact and rubbing fault rotor system caused by the parameters of nonlinear rigidity, rotor rotating speed, eccentric mass is analyzed, in the numerical value analysis method. The bifurcation diagrams, maximum Lyapunov exponent diagrams, Poincaré maps, phase plane portraits, trajectories of journal center, time-history curve, amplitude spectra diagrams of the rotor motion are used. The convert and evolution course of periodical response, quasi-periodical response, double-periodical bifurcation, chaos of the system response is analyzed.(3). It is deduced that the general differential equation of bending-torsional-pendular coupling vibration about rotor with the gyroscopic moment. On the basis of this equation, the general differential equations of coupled bending, torsional and pendular nonlinear vibration about rotor with unbalance character and rubbing character are deduced.

2建立了具有非线性刚度的转子系统在非稳态非线性油膜力作用下的径向碰摩动力学微分方程，并应用含高阶余项的非线性动力方程的线性化数值法研究了此类系统响应的复杂动力学行为，利用转子响应的分岔图、最大Lyapunov指数曲线、Poincaré截面映射、时域波形、相轨线、轴心轨迹、幅值谱等图形分析了系统响应的周期运动、拟周期运动、倍周期分岔、混沌等运动形式的转化与演变过程，重点研究了非线性刚度、转子转速、偏心质量等系统参数对碰摩故障转子系统的分岔和混沌行为的影响。

To estimate the bioconcentration factor of benzene derivatives in fish by gas chromatography retention time, this paper measured the BCF of chlorobenzene, o-chloro-toluene, p-dichlorobenzene, m-dichlorobenzene, 1,2-dichlorobenzene, nitrobenzene, p-chloro-aniline, p-chloro-nitrobenzene, and 4-chlorodiphenyl in grass crap, and the t_R of test derivatives on the stationary phases of six kinds polarity.

为了用气相色谱保留时间估算取代苯类化合物在鱼体内的生物富集系数，测定了草鱼对氯苯、邻氯甲苯、对二氯苯、间二氯苯、邻二氯苯、硝基苯、对氯苯胺、对硝基氯苯、4-氯联苯9种取代苯类化合物的BCF和不同取代苯化合物在6种不同极性固定相上的tR，建立了tR与BCF的一元回归方程及tR一阶分子连接性指数(1XV)与BCF的二元回归估算方程。

The database consists of nodimensional data of load carring capacities, maximum pressures and their positions, flow factors, and power loss factors by solving full 2D Reynolds equation including oil feed features of 360°, 180°partial groove, and single oil hole, corresponding to a series of power law index, length/diameter, groove width/length, hole diameter/length, hole diameter/bearing diameter, eccentricity, angle between the attitude angle line and centre line of oil groove/hole, rotary, squezze, and oil feed pressure factors.

数据库中的数据通过求解全二维Reynolds方程和热平衡方程获得。数据库由对应于360°全油槽，180°半油槽和单孔的三类轴承的一系列的幂率指数，宽径比、槽宽／轴瓦宽、油孔直径／轴瓦宽、油孔直径／轴承直径、偏心率、偏位线与油槽中心线之间的夹角、挤压因子、旋转因子、进油压力因子的一系列的轴承无量纲的特性参数组成：油膜承载力、最大油膜压力及位置、流量系数和消耗功系数。

The formula concerning how to control the oil contamination of coal mining machine hydraulic system was built based on the theory of the contamination control ,it is shown that the change of the oil contamination is in index regularity.

根据污染控制理论导出了采煤机液压系统油液污染控制方程，由方程知液压系统油液污染度的变化是按指数规律变化的，并分析了影响采煤机液压系统油液污染度的主要因素，提出在液压系统的设计阶段就要考虑液压系统的过滤净化性能，正确控制液压系统油液污染。

In the United States, chronic alcoholism and hepatitis C are the most common ones.

在美国，慢性酒精中毒，肝炎是最常见的。

If you have any questions, you can contact me anytime.

如果有任何问题，你可以随时联系我。