非条件不等式

Some nonexistence results for p-degenerate sub-elliptic first order evolution inequalities associated with the generalized Baouendi-Grushin vector fields are given. The method is an improvement of the admissible function method in Euclidean space. The proof hardly depends on the properties of the generalized Baouendi-Grushin vector fields.

通过改进欧氏的容许函数法，应用广义Baouendi-Grushin向量场的一些性质，选取特殊的容许函数，利用Hlder不等式和Young不等式，证明了由广义Baouendi-Grushin向量场构成的p-退化次椭圆一阶发展不等方程，在适当条件下非平凡弱解的不存在性。

In this paper we generalize Bernstein inequality of t he sequence of independent random variables to the martingale difference s, then we give an application of this inequality.

本文将独立随机变量序列的Bernstein型不等式推广到鞅差序列情形，给出该不等式的一个应用，并在一定条件下证明了非参数回归中函数估计的强相合性。

Instead of Gronwall\'s inequality,the non-linear Bihari inequality is crutial in dealing with the non-Lipschitz equations.Moreover,we emphasize that the dominating functions in non-Lipschitz conditions always satisfy concavity and some non-integrability near zero.The concavity is for using Jensen\'s inequality.Because of the non-integrability near zero,we can apply the comparison theorem of ordinary differential equations together with Bihari\'s inequality to yield many results.

3作为Gronwall不等式的推广，Bihari不等式在处理具有非Lipschitz系数的方程时不可或缺；同时应当注意，非Lipschitz条件中所涉及的控制函数总是满足凹性和某种零点处的不可积性：凹性是为了利用Jensen不等式；零点处的不可积性使得Bihari不等式与常微分方程中的比较定理结合在一起从而完成很多结论的证明。

In chapter three, we prove that there exist solutions to the Ky Fan variation inequality, as the set-valued mappings are defined on spheres in infinite dimensional Banach spaces or odd dimensional Euclidean spaces, following from these theorems, we obtain some fixed point theorems for set-valued mappings defined on a sphere. When G is an approximate compact convex subset of E, or G is a almost quasi-convex set-valued mapping, we prove that there exist solutions to and type generalized Ky Fan variation inequality, following these theorems, we prove several best approximation theorems and coincidence theorems involving two set-valued mappings and two different spaces. In chapter four, we first present a new Simplicial algorithm for computing the Leray - Schauder fixed points, the algorithm can solve the set-valued nonlinear complementarily problem. We give a condition to guarantee the computation proceeding in a bounded region. We present integer-labeling algorithms for computing fixed points of some set-valued mappings, the best approximation points and solutions to a kind of set-valued variation inequalities.

第四章给出了计算定义在非凸集上的非自映射的Leray-Schauder不动点的算法，而现有的不动点算法都是计算凸集的上半连续集值自映射的不动点；给出了保证计算有界的一个充分条件，我们的条件大大弱于Mdrrill条件，我们的算法也可用来计算Eaves不动点；给出了集值非线性互补问题存在解的一个充分条件，此时可利用Leray-Schauder不动点算法来求解；向量标号算法以往是计算集值映射不动点的唯一有效算法，我们给出用整数标号算法计算一类集值映射的Kakutani 不动点的算法；定义在紧凸集上的连续映射不一定有不动点，但一定有最近点，最近点是不动点概念的推广，我们给出了计算最近点的算法；集值映射变分不等式尚无有效的求解算法，我们给出求解一类集值映射变分不等式的算法。

In the fourth chapter, we discussion the characterization of admissible in the general linear model under equality constraint and inequality constraint, we give the necessary and sufficient condition that homogeneous linear estimator is admissible estimator, and by using the relationship between homogeneous and inhomogeneous linear estimator, we obtain the characterization of admissible inhomogeneous linear estimator.

第四章分别在带等式约束条件以及不等式约束条件下，讨论了一般线性模型线性估计的可容许性特征，给出了在约束条件下齐次线性估计为可容许估计的充分必要条件，同时利用齐次线性估计与非齐次线性估计之间的关系，把齐次线性估计的可容许性特征推广到了非齐次线性估计的可容许性特征。

Under the assumptuion that the lower bound of the density of the observed nonlinear AR (1) time series is known, we prove that the nonlinear wavelet estimator of the conditional mean function g, which is similiar with the one introduced in Chapter 2, still has the same good adaptive properties for this kind of nonlinear AR (1) series on account of the moment inequalities and exponential type inequalities for strong mixing processes.

在假设观测序列的的密度函数的下界已知的条件下，我们利用关于强混合过程的矩不等式以及指数型不等式证明了类似于上一章的小波估计对于非线性AR（1）模型中条件均值函数的非参数函数估计仍然具有优良的自适应性质，并同样给出了数值模拟的结果分析。

The contents are the following:In chapter two, the existence and multiplicity results for the following equation of p-Laplacian type are obtained.For the elliptic quasilinear hemivariational inequality involving the p-Laplacian operator,in order to use the mountain pass theorem proving the existence result, the authors usually need to use the uniform convexity of the Sobolev space to prove the energy function satisfies the PS condition. But for the p-Laplacian type equation mentioned above, this method is no use. To overcome this difficulty, the potential function is assumed to be convex, then I prove the existence result and by using the extension of the Ricceri theorem, the multiplicity result for the problem is obtained.

在第二章我们首先考虑关于以下p-Laplacian型(p-Laplacian type)方程非平凡解及多解的存在性对于带有p-Laplacian算子的椭圆拟线性半边分不等式问题，为应用非光滑的山路引理证明解的存在性，在证明方程所对应的能量泛函满足非光滑的PS条件时，需利用Sobolev空间的一致凸性，但是对于具有更一般形式的算子的p-Laplacian型方程，不具备上述性质，在文中为克服这一困难，本人对位势泛函做了一致凸的假设，从而证明了解的存在性，并应用推广的Ricceri定理，证明了方程三个解的存在性。

We call L n=1-matrices for N_0~1-matrices. Meyer introduced the concept of the Perron complement of a nonnegative and irreducible matrix in 1989 and used it to construct an algorithm for computing the stationary distribution vector for Markov chains. We extend the Perron complements of nonnegative and irreducible matrices to the Perron complements of nonpositive and irreducible matrices.

我们这里是把Perron余的概念推广到了非正不可约矩阵，显然它也具有非负矩阵相类似的性质，逆N 01矩阵又是特殊的非负矩阵，我们证明了在一定条件下，逆N 01矩阵和N 02矩阵的广义Perron余的继承性，并给出了相关的不等试：逆N 01矩阵和N 02矩阵的广义Perron余逆矩阵的不等式；逆N 01矩阵的主子阵与其逆矩阵的不等式。

The notion of - resolvent operator of set-valued mappings is introduced.

利用η-预解算子在有限维空间中探讨了集值混合拟类变分不等式问题和广义集值变分包含问题存在唯一解的条件；利用分析的方法在实Hilbert空间中讨论了集值混合拟类变分不等式问题解集的非空性。

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。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失