文中通过几个不等式的证明阐明了常用的概率思想方法。
In this paper, we illustrate probability thinking method through several inequalities proof.
其次，拉格朗日中值定理在一些等式和不等式的证明中应用十分广泛。
Secondly, the Lagrange mean value theorem in some proof of identity and the inequality in a wide range of applications.
在分析数学中有些不等式的证明往往比较复杂，而且具体的直观含义也比较抽象。
In analysis mathematics, some identifications of inequalities are often more complicated, and concrete ocular meaning is more abstract.
文中在分析数学的几个重要不等式的证明之中引进了概率方法，取得较好的效果。
Better results are got during the course of the proofs of several inequalities in analysis mathematics by using probabilistic method.
凸(凹)函数有很多特性，这些性质可广泛应用于不等式的证明及误差估计等方面。
There are convex function and concave function, Which are of expansive application in many aspects, especially in inequality proof and error estimate.
第二部分将通常的积分平均值不等式推广成一般形式，并利用它给出一些不等式的证明。
The part two general forms was derived with general integral average inequality and Some inequality was proved with this result was obtained above.
文章给出了几种常用方法，通过这些方法，可以较为简洁，方便地解决一些不等式的证明。
This paper gives out a few methods to prove inequation and by which we can simply and quickly solve the problem.
本文介绍了用微分法讨论不等式有关证明方法，利用这些方法使不等式的证明变得非常简单。
The paper introduces the methods of proving the inequality with differentiation, which make it easy to prove some inequalities.
本文通过构造向量，将向量的内积的性质运用于不等式的证明中，使得一些不等式的证明更加简捷。
A property of inner product is used for proving inequalities by constructing some spacial vectors, it can simplify the processes of the proof.
利用齐次线性方程组解的理论讨论矩阵的秩，给出几个关于矩阵秩的著名不等式的证明，并证明了两个命题。
The article discusses rank of a matrix by the solution theorem of system of homogeneous linear equations, and proves several famous inequalities and two propositions on rank of a matrix.
利用齐次线性方程组解的理论讨论矩阵的秩，给出几个关于矩阵秩的著名不等式的证明，并证明了两个命题。
The judgment theorems for locating correctness were concluded by skillfully combining the solutions of homogenous linear equations with locating schemes.
阐述了利用导数知识研究函数的单调区间、大值最小值等问题的基本方法，以及导数方法为解决某些不等式的证明、列求和等问题提供了捷径。
It explains some basic ways of how to use derivative to study monotonous zone in function, to calculate maximum and minimum, and how to solve some problems on inequality and number sequence, etc.
然而，JohnBell后来通过实验反驳Bell不等式(正是它使epr思维实验正式化)证明了真实粒子间的纠缠。
John Bell, however, later demonstrated entanglement in real particles by experimental refutation of the Bell Inequality (which formalized the EPR thought experiment).
证明了有关函数平均值的一个估值不等式，应用它推出了若干重要的不等式。
An inequality of estimate for function means is proved, and by using it some classical inequalities are proposed.
通过给出几个实例，介绍了利用二次型的半正定性证明不等式的方法。
The author introduce the method of applying positive semi-definite quadratic form to prove inequality by giving several examples.
利用数学归纳法证明了一个关于正值函数的不等式，并举例说明了其应用。
This paper proves an inequality based on a positive function with mathematical induction and demonstrates its application with examples.
介绍几种常用的证明不等式的方法。
This article introduces several common methods about the demonstration of Inequality.
并举例说明柯西不等式在不等式证明中应用的广泛性和灵活性。
The application widespread and flexibility of Cauchy inequality are show by the examples.
在适当的条件下，通过建立一个先验不等式，证明了其唯一非负解是平凡的。
By establishing a prior inequality, we prove that, under suitable conditions, the unique non-negative solutions of the problems are trivial.
提出了函数的双参数加权平均的定义，证明了一个凸函数的双参数加权平均不等式，加强和推广了有关文献中的结果。
The two - parameters weighted mean in defined and an inequality for two - parameters weighted mean of convex function is prove, they have generalized and improved the results in literatures.
采用线性矩阵不等式和多凸性处理方法，证明了该问题等价于线性矩阵不等式的可解性问题。
In terms of multiconvexity and linear matrix inequality, this problem is proved to be equivalent to an LMI feasible problem.
我们只证明这个不等式方程，而没有证明标准数据流方程(8)，原因是我们所感兴趣的只是解的正确性而不是解的最优性。
We only prove an inequation rather than the standard dataflow equation (8) because we are interested only in the correctness of the solution, not in its optimality.
给出了利用积分和证明不等式的原理以及积分和在不等式证明中的应用。
This paper displays the principle of using integral sum to prove inequality and the application of the principle.
本文对混合拟似变分包含问题提出新的辅助变分不等式，首先证明辅助变分不等式存在唯一解。
This paper presents a new auxiliary variational inequality for solving mixed quasi-variational-like inclusions. First, proved the auxiliary variational inequality has unique solution.
摘要：对“数学思想”这一概念进行定义，接着谈谈不等式证明中的几种数学思想。
Abstract: To "mathematics thought" this concept go on and define, then thin in inequality several kinds of mathematics thoughts in proving.
利用控制不等式理论简洁地证明了一些整幂函数不等式，大部分结果是一些常用不等式的推广。
By means of the theory of majorization, some inequalities with the integer power function simply are proved, and most of results is extension of applied inequalities.
给出了二维数组的体差不等式测试算法，并证明二维数组的体差不等式测试算法具有多项式时间复杂度。
This paper presents a new dependence difference inequality test algorithm for two-dimensional arrays, and proves that the time complexity of the algorithm is polynomial.
我们利用边界层校正法以及微分不等式理论证明了解的存在定理，并构造出其解的一致有效渐近展开式。
Using the method of boundary layer correction and the differential inequality theory, we prove the existence theorem of solutions and construct the uniformly valid asymptotic expansions of.
我们利用边界层校正法以及微分不等式理论证明了解的存在定理，并构造出其解的一致有效渐近展开式。
Using the method of boundary layer correction and the differential inequality theory, we prove the existence theorem of solutions and construct the uniformly valid asymptotic expansions of.
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