不等式

Here, we will try our best to use the unit-speed outward normal flow to prove this result, and therefore to strengthen Gage's inequality as a more "" isoperimetric-type"" inequality. It will be the main task of the first part of the present thesis.

这是本文第一部分的主要任务，在这里我们还利用Minkowski支撑函数将Gage不等式叙述成一个积分不等式，这可以视为Gage不等式的分析形式。

The solvability of quadratic matrix inequalities of singular H∞ control problems with infinite zeros is studied in this paper. It is proved that the quadratic matrix inequality can be solved directly via the generalized eigenvalue problems. The previous method of solving the quadratic matrix inequality involving complicated decompositions and transformations of the systems is avoided.

摘要研究具有无穷远零点的奇异H∞控制问题的二次矩阵不等式的可解性，证明了通过求解广义特征值问题，可以直接求得二次矩阵不等式的解，从而简化了原需通过复杂的系统分解和变换来求解二次矩阵不等式的方法。

Motivated by the newψfunctional stability,we can establish some new kinds of stabilities which are different from the exponential stability.With the help of semimartingale convergence theorem,stochastic calculous,moment inequality,Burkholder-Davis-Gundy inequality,Gronwall inequality etc.,we find that the product ofψfunction and the solutions of neutral equations will approach a nonempty set if some specific conditions are satisfied.

我们应用半鞅收敛定理、随机微积分的相关知识以及矩不等式、Burkholder-Davis-Gundy不等式和Gronwall不等式等技巧，得到中立型随机泛函微分方程的解与特定的"ψ函数"的乘积在一定的条件下将趋向某非空集合这一结论，并建立了该中立型方程的随机LaSalle型定理。

By using the analysis method,this paper gets a inequality about the relation of the interior product and the norm in the separable,complex Hilbert space.

用分析法得到了可分复Hilbert空间中一个内积与范数关系的不等式，由此不等式可推出几个可以看作是Cauchy-Schwarz不等式的反向不等

A necessary and sufficient condition for the existence of guaranteed cost control is derived. Furthermore, it is shown that this condition is equivalent to the solvability of a system of linear matrix inequalities, and its solution provides a parameterized representation of guaranteed cost controllers. Based on that, the design of the optimal guaranteed cost controller is formulated as a convex optimization problem, which can be solved by the existing convex optimization techniques.

通过采用线性矩阵不等式的方法，导出了存在保性能控制律的一个充要条件，进而，证明了该条件等价於一组线性矩阵不等式的可解性问题，并用这组线性矩阵不等式的可行解给出了保性能控制律的一个参数化表示。

In Chapter 2,we first generalize a waterman inequality by usering Clliffordmatrix represenation of n-dimensional 〓 transformation group 〓.

在第二章中，我们研究了关于离散群的一些不等式。首先，我们利用CHifford矩阵研究了〓上的〓变换群不等式，给以一定的限制条件，通过大量复杂的、技巧性计算，改进了Wateman不等式。

The research of the triangle geometric inequality has obtained very rich of the outcomes. This paper studies mainly some new linear triangle geometric inequalities, focusing on the linear geometric inequalities which are known, and it also includes some conjectures of the author.

三角形中的几何不等式研究已取得了非常丰富的成果，本文主要围绕已知的线性几何不等式进行研究，给出三角形中一些新的线性几何不等式，并包含了作者的某些猜想。

Next,similar to the studies of Friedland-Hersonsky inequalities in norm form and Martininequalities for discrete groups of 〓,we establish 〓 type inequalitiesfor subgroups of unitary transformation group U(1,n,C)in complex hyperbolicspace 〓 and we also give several 〓 type inequalities in the form of fgfg〓for the norm algebra 〓 in C.

其次，我们对复双曲空间〓上的酉变换群U(1，n，C)的子群建立了〓型不等式，推广了Martin的相应结果。最后，我们对复数域C上的范数代数〓建立了形如〓的〓型不等式，推广了Friedland-Hersonsky不等式。

For example, classic Doob s inequality, good A inequalities and Burkholder-Davis-Gundy inequalities and so on, are very important results in martingale theory and the basis of discussion of the general martingale spaces.

如古典的Doob不等式，good λ不等式，Burkholder-Davis-Gundy不等式等，都是鞅论中的重要结果，也是讨论一般鞅空间的基础。

We get the sufficient and necessary conditions for the reaction process to be stochastic monotonic under certain conditions e.g.

第三部分推广了[29]中的结果，对较广的有限系统证明了若干泛函不等式与底过程对应的泛函不等式的等价性以及不等式常数之间的关系。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。