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 basic inequality 基本不等式(22)基本不等式(22)
 基本不等式
 Spread and application of basic inequality deformation a 2b 2≥2ab is given. 给出基本不等式a2 +b2 ≥ 2ab某一变形的推广及其应用 短句来源 In this paper,we give an elementary proof for the basic inequality that if A and B are positive definite symmetric matrices by n×n,then (det(A)+det(B))~(1n)≥(det(A))~(1n)+(det(B))~(1n),which is widely used in completely nonlinear elliptic equations. 给出了在完全非线性椭圆方程中被广泛使用的一个基本不等式的初等证明,用最优化的方法证明了不等式:(det(A)+det(B))1n≥(det(A))1n+(det(B))1n 短句来源 An important basic inequality for triangles is employed to prove a conjectured inequality for the sum of triangle's inner angular bisector:Let wa,wb,wc,s,r,R be the three inner angular bisectors semi-cirumference inradius and circumradius respectively,then(w++wb+wc)2≤s2+102Rr/5+66r2/5.A televant question worthy of further delvement is put forward. 应用三角形一个重要的基本不等式,证明了有关三角形内角平分线之和的一个猜想不等式:设wa,wb,wc与s分别是三角形三条内角平分线和半周长,R,r分别为三角形的外接圆半径,则(wa+wb+wc)2s2+102Rr/5+66r2/5.指出了一个相关的值得进一步探讨的问题. 短句来源 Demonstrated through the variants and deductions of basic inequality a2+b2≥±2ab, it is proved t simple mathematical forms which can solve many complicated problems, are to be paid more attention. 通过基本不等式a2+b2≥±2ab的变形和引伸证明已有定理,表明简单的数学形式可以解决许多复杂的问题,应予以重视。 短句来源 Spread and Application of Basic Inequality Deformation 基本不等式变形的推广及应用 短句来源 更多
 基本不等式
 Spread and application of basic inequality deformation a 2b 2≥2ab is given. 给出基本不等式a2 +b2 ≥ 2ab某一变形的推广及其应用 短句来源 In this paper,we give an elementary proof for the basic inequality that if A and B are positive definite symmetric matrices by n×n,then (det(A)+det(B))~(1n)≥(det(A))~(1n)+(det(B))~(1n),which is widely used in completely nonlinear elliptic equations. 给出了在完全非线性椭圆方程中被广泛使用的一个基本不等式的初等证明,用最优化的方法证明了不等式:(det(A)+det(B))1n≥(det(A))1n+(det(B))1n 短句来源 An important basic inequality for triangles is employed to prove a conjectured inequality for the sum of triangle's inner angular bisector:Let wa,wb,wc,s,r,R be the three inner angular bisectors semi-cirumference inradius and circumradius respectively,then(w++wb+wc)2≤s2+102Rr/5+66r2/5.A televant question worthy of further delvement is put forward. 应用三角形一个重要的基本不等式,证明了有关三角形内角平分线之和的一个猜想不等式:设wa,wb,wc与s分别是三角形三条内角平分线和半周长,R,r分别为三角形的外接圆半径,则(wa+wb+wc)2s2+102Rr/5+66r2/5.指出了一个相关的值得进一步探讨的问题. 短句来源 Demonstrated through the variants and deductions of basic inequality a2+b2≥±2ab, it is proved t simple mathematical forms which can solve many complicated problems, are to be paid more attention. 通过基本不等式a2+b2≥±2ab的变形和引伸证明已有定理,表明简单的数学形式可以解决许多复杂的问题,应予以重视。 短句来源 Spread and Application of Basic Inequality Deformation 基本不等式变形的推广及应用 短句来源 更多
 “basic inequality”译为未确定词的双语例句
 A Basic Inequality of Semi-Invariant Submanifolds in Cosymplectic Space Forms 关于余辛流形的半不变子流形的一个不等式 短句来源 In this paper it is shown that the basic inequality G(a)≤A(a),Cauchy inequality,Tchebychef inequality,Holder inequality,Lyapunov inequality,triangle inequality and Minkowski inequality are all equivalent to the simple proposition that a~2≥0 for every a∈R(set of real number),provided the proposition that the closure of the set of rational number equals R is known. 本文在实数集合的紧致性为已知的前提下,证明算术平均值与几何平均值不等式,Cauchy不等式,不等式,Holder不等式,不等式,三角不等式和Minkowski不等式之间的互相等价性,而旦它们都等价于一个实数的平方不小于零。 短句来源 The author defines a symmetric mean of convex function and sets up its basic inequality. He also generalizes "Fanky inequality" and Jensen inequality" by means of the basic inequality. And finally, the second korder symmetric mean and the third k-order symmetric mean are proved there. 定义了一类凸函数的对称平均，建立了其基本定理，推广了 Fanky不等式和 Jensen不等式．最后证明了第二k次和第三k次对称平均，说明基本定理的应用。 短句来源 We replace the “Good λ” inequality on X by the rearrangement inequality (Tf)  ω(t)≤C(M μf)  ω(t2)+(Tf)  ω(2t). This inequality is better than the “Good λ” inequality in that it is easier to use in many applications and seems to contain more information. By interating the basic inequality,we can obtain a new and interesting result. 利用一定的证明技巧，得到对算子进行估计时非常有用、能替代齐型空间上相应的“Goodλ”不等式的关于重整函数的不等式：（Tf）＊ω（t）≤C·（Mμf）＊ω（t2）＋（Tf）＊ω（2t）以及由此通过迭代而推得有关重整函数、重整平均函数的新结果。 短句来源

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 basic inequality
 Grothendieck proved a basic inequality which shows that any bounded linear operator between L1(μ)-spaces maps (Lebesgue-) dominated sequences to dominated sequences. A basic inequality for submanifolds in locally conformal almost cosymplectic manifolds It was proved in part I that every CR-warped product in a Kaehler manifold satisfies a basic inequality: . A basic inequality and new characterization of Whitney spheres in a complex space form Chen proved a basic inequality between the intrinsic scalar invariants infK andτ ofMn, and the extrinsic scalar invariant |H|, being the length of the mean curvature vector fieldH ofMn in. 更多
 In this paper it is shown that the basic inequality G(a)≤A(a),Cauchy inequality,Tchebychef inequality,Holder inequality,Lyapunov inequality,triangle inequality and Minkowski inequality are all equivalent to the simple proposition that a~2≥0 for every a∈R(set of real number),provided the proposition that the closure of the set of rational number equals R is known. 本文在实数集合的紧致性为已知的前提下,证明算术平均值与几何平均值不等式,Cauchy不等式,不等式,Holder不等式,不等式,三角不等式和Minkowski不等式之间的互相等价性,而旦它们都等价于一个实数的平方不小于零。 The origin and developmant of Jensen inequality is analysed. It is pointed out that the mentality, such as observation, analogy association, induction, guess permeates through the course of forming Jensen basic inequa lity. Associating the disproporlionality from the proportionality in Jensen basic inequality leads to the generation of Jensen summation inequality. Associating the continuous variable from the discrete variable in Jensen summation inequality leads to the discovery of Jensen integral... The origin and developmant of Jensen inequality is analysed. It is pointed out that the mentality, such as observation, analogy association, induction, guess permeates through the course of forming Jensen basic inequa lity. Associating the disproporlionality from the proportionality in Jensen basic inequality leads to the generation of Jensen summation inequality. Associating the continuous variable from the discrete variable in Jensen summation inequality leads to the discovery of Jensen integral inequality. 分析了Jensen不等式的来胧去脉,指出,在Jensen基本不等式的形成过程中,渗透着观察、类比联想、归纳、猜想等思想方法;而由Jensen基本不等式中的均等性联想到非均等性,则导致了Jensen总和不等式的产生;由Jensen总和不等式中变量的离散性联想到变量的连续性,则导致Jensen积分不等式的发现。 This paper proves some basic inequalities of Nevanlinna type.A chara-cteristic of thesce inequalities is that the error terms are accurately expressed. 本文证明了一些Ｎｅｖａｎｌｉｎｎａ型基本不等式，其主要特点是所有不等式中的余项都能明确地表达出来，并且一些密指量的系数有所减少。 << 更多相关文摘
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