Symmetric duality with (p, r) − ρ − (η, θ)-invexity

In this paper we introduce a new type of generalized invex function, called (p, r) − ρ − (η, θ)-invex function and study symmetric duality results under these assumptions. In our study the nonnegative orthants for the constraints are replaced by closed convex cones and their polars. We establish weak and strong duality theorems under (p, r) − ρ − (η, θ)-invexity assumptions for the symmetric dual problems. We also give many examples to justify our results.     

以0≤K∈C0∞为Gauss曲率的曲面的正则性

在较弱的条件下 ,证明了以给定的具有紧支集的非负函数为Gauss曲率 ,以已知的空间曲线为边界的凸曲面是整体C^1,1的 .有例子表明这个正则性是最佳的.     

Computational study of decaying annular vortex flow using the Rε/k − ε turbulence model

In this article, we present three dimensional CFD study of turbulent vortex flow in an annular passage using OpenFOAM 1.6. The vortex flow is generated by introducing the flow through a tangential entry to the passage. For the analysis presented in this article, turbulence was modeled using the R_ε/k − ε model, in addition, a comparison between such model with the standard k − ε model was conducted and discussed. The main characteristics of the flow such as vortex structure and recirculation zone were investigated. It was found that flow is subjected to Rankine vortex structure with three forced vortex regimes and a free vortex region near to the outer wall. The phenomenon of vortex decay was investigated by depicting the swirl number trend along the axial direction of the flow domain. It was found that the vortex decay is subjected to an exponential decay behavior. New coefficients for the exponential decay correlation were derived based on local values of velocity components in different radial planes.     

新Dirichlet级数Σn=0∞aneλns收敛横坐标

本文给出新Dirichlet级数Σ_n=0^∞a_ne^λ_ns的收敛横坐标σ_c、一致收敛横坐标σ_u和绝对收敛横坐标σ_a的定义.通过指数λ_n和系数a_n的关系去估计三个横坐标,并补充证明两类Dirichlet级数Σ_n=0^∞a_ne^λ_ns和Σ_n=0^∞a_ne^-λ_ns的收敛条件是一致的.     

Converse and Smoothness Theorems for Erdo&#x030B;s Weights inL_(0<p?∞)

We prove converse and smoothness theorems of polynomial approximation in weightedL_pspaces with norm ‖fW‖_Lp()(0<p?∞) for Erdo&#x030B;s weights on the real line. In particular we prove characterization theorems involving realization functionals and thereby establish some interesting properties of our weighted modulus of continuity.     

不等式a~2/b≥2a-b(b&gt;0)的变式

高中《代数》下册给出的二元均值不等式是 :如果 a、b∈ R,那么　　　　 a2 +b2≥ 2 ab 1当且仅当 a =b时取“=”号 .此不等式可变形为 :定理　如果 a∈ R,b∈ R+,那么　　　　　　 a2b ≥ 2 a - b. 2当且仅当 a =b时取“=”号 .下面谈谈对不等式 2的思考 .变式 1　不等式 2的特征是左边是商式 ,右边是差式 ,即不等式从左到右的“缩小”过程是一个“裂项”的过程 ,在此我们不妨把不等式 2叫做裂项不等式 .如果结合数列中裂项—叠加求和的方法 ,那么可以编拟许多不等式的题目 .在不等式 2中 ,若分别用 xi 代 a,xi+1代 b,i = 1,2 ,… ,n.其中 xn+1=x1,则有x21x2≥ 2 x1- x2 ,x22x3≥ 2 x2 - x3,… ,x2nx1≥ 2 xn - x1,相加可得　　 x21x2 +x22x3+… +x2n- 1xn +x2nx1≥ x1+x2 +… +xn.这样得到 :题 1　如果 x1,x2 ,… ,xn都是正数 ,那么x21x2 +x22x3+… +x2n- 1xn +x2nx1≥ x1+x2 +… +xn.这是一道 1...     

0/0与∞/∞不定式的几何解释

文(1)中给出了∞—∞与0·∞的几何解释。在诸多的不定式中,由于教学中较先涉及到的是0/0与∞/∞型的不定式这两个类型。因此,本文试给出0/0与∞/∞型的一种简洁的几何解释。教学中利用它,有助于解决由于学生初学极限,对不定式感到不可捉摸和难于理解的问题。     

一元函数0/0型极限求解方法探讨

本文对一元函数0/0型极限求解方法进行了探讨,提出可以消去零因子、利用洛比达法则、利用等价无穷小代换、利用导数的定义、利用重要极限limx→0((sinx)/x=1)及带有佩亚诺(Peano)型余项的泰勒(Taylor)公式六种常用方法求解0/0型极限,并重点对每种方法的注意事项、使用技巧及适用范围进行了分析和说明.     

探究x0x+y0y=r2与x0x+y0y=x02+y02的几何意义

问题背景苏教版教材必修二P105有这样一道习题:已知圆C的方程是x2+y2=r2,求经过圆C上一点M(x0,y0)的切线的方程.同学们在处理该问题时给出以下的解答过程:如图1,设切线的斜率为k,半径OM的斜率为k1,因为圆的切线垂直于过切点的半径,于是k=     

Embeddability of L1(μ) in dual spaces, geometry of cones and a characterization of c0

In this article we suppose that (Ω,Σ,μ) is a measure space and T an one-to-one, linear, continuous operator of L₁(μ) into the dual E′ of a Banach space E. For any measurable set A consider the image T(L⁺₁(μ_A)) of the positive cone of the space L₁(μ_A) in E′, where μ_A is the restriction of the measure μ on A. We provide geometrical conditions on the cones T(L⁺₁(μ_A)) which yield that the measure μ is atomic, i.e., that L₁(μ) is lattice isometric to , where denotes the set of atoms of μ. This result yields also a new characterization of c₀(Γ).     

1+2x5y+5z11u=2v·11w,xuvw>0,y+z>0的非负整数解

借助计算机,用初等方法给出了指数丢番图方程1+2^x5^y+5^z11^u=2^v·11^w,xuvw>0,y+z>0的全部非负整数解.     

关于“矩阵方程X-A*XqA=I(0<q<1) Hermitian正定解的扰动分析”的注记

本文指出论文“矩阵方程X-A^*X^qA=I(0相似文献   

关于sup_{n≥1}(S_n/n^{1/r})(0<r<2)和sup_{n≥1}(S_n/sqat(n lnln n))的矩

设{X_n,n≥1}是φ混合的同分布的随机变量序列,记S_n=∑^n_{i=1}X_i(n≥1).该文的目的是要在一定的矩条件和混合速度限制下,讨论了sup_{n≥1}(S_n/n^{1/r})(0相似文献   

New approximation-solvability of general nonlinear operator inclusion couples involving (A, η, m)-resolvent operators and relaxed cocoercive type operators

In this paper, we consider and study a class of general nonlinear operator inclusion couples involving (A, η, m)-resolvent operators and relaxed cocoercive type operators in Hilbert spaces. We also construct a new perturbed iterative algorithm framework with errors and investigate variational graph convergence analysis for this algorithm framework in the context of solving the nonlinear operator inclusion couple along with some results on the resolvent operator corresponding to (A, η, m)-maximal monotonicity. The obtained results improve and generalize some well known results in recent literatures.     

Adams谱序列中α~s(n)h0hk的收敛性

证明了(i)在p≥ 5,2≤s≤p- 1 ,k≥ 2时, β_sh₀h_k+1收敛到E_∞ ;(ii)在p≥7,3≤s≤p-1,k≥3时, γ_sh₀h_k+1收敛到E_∞.     

解析形如a1/2（a>0）的无理数的取值范围

性质若01/m<2^1/n.应用二次根式的这条性质,就能用有理数去估计形如2^1/a（a>0）的无理数的取值范围.这类题在中考中常以客观题的形式出现,现举例解析:     

勿忘(0)~(1/2)=0

我们知道 0 =0 ,但在解题过程中 ,却常常忽视了 ,这反映了我们考虑问题的片面性 .例 1　当α、β取什么范围内的值时 ,式子sin2αcosβ有意义 ?错解　由 sin2 α≥ 0知　 sin2 αcosβ≥ 0等价于 cosβ≥ 0 .即β∈ [2 kπ - π2 ,2 kπ π2 ](k∈ Z) .分析　因为学生牢记“实数的平方为非负数”,即α∈ R时 ,sin2 α≥ 0 .所以由sin2 αcosβ≥ 0推导出 cosβ≥ 0 .事实上 ,这漏掉了另一种情况 :sinα =0 ,cosβ∈ R时原式也有意义 .即α =kπ,且β∈ R,k∈ Z.正解　原式有意义等价于 cosβ≥ 0或sinα =0 .解得β∈ [2 kπ - π2 ,2 k…     

Uniqueness of positive radial solutions for Δu−u+u=0 on an annulus

We prove uniqueness of positive radial solutions to the semilinear elliptic equation , subject to the Dirichlet boundary condition on an annulus in . As a by-product, our argument also provides a much simpler, if not the simplest, new proof for the uniqueness of positive solutions to the same problem in a finite ball or in the whole space .     

ON BIRKHOFF INTERPOLATION (0;2) CASE

P. Turan and his associates considered in detail the problem of (0.2) interpolation based on the zeros of πn(x). Motivated by these results and an earlier result of Szabados and Varma[9] here we consider the problem of existence, uniqueness and explicit representation of the interpolatory polynomial Rn (x) satisfying the function values at one set of nodes and the second derivative on the other set of nodes. It is important to note that this problem has a unique solution provided these two sets of nodes are chosen properly. We also promise to have an interesting convergence theorem in the second paper of this series, which will provide a solution to the related open problem of P. Turan.