双曲空间中Veljan-Korchmaros型不等式及应用

本文研究了双曲空间Hn(K)中n维高维单形的几何不等式问题.利用距离几何的理论与方法,获得了涉及n维双曲单形体积,侧面积与棱长的几个几何不等式,这些几何不等式是双曲单形几何不等式的基础.     

一类涉及两个单形的三角不等式及其应用

应用解析方法和几何不等式理论研究了n维欧氏空间En中涉及两个n维单形的几何不等式问题,建立了涉及两个单形的一类三角不等式.作为其应用,获得了涉及两个单形及其内点的几何不等式,特别,获得了n维单形与其垂足单形的体积的一类关系式,改进了关于垂足单形体积的几类几何不等式.     

预给二面角的单形嵌入E~n的充分必要条件的一个应用

本文利用预给二面角的单形嵌入 E~n 的充分必要条件,得到如下的定理 设 T 为 E~n 中的一个单形,它的任意两个侧面 f(?),f_j 所成的内角为(?)=θ_(ij)(1≤i相似文献   

n维双曲空间和n维球面空间中的正弦定理及应用(英文)

本文研究了n维双曲空间和n维球面空间中单形的正弦定理和相关几何不等式.应用距离几何的理论和方法,给出了n维双曲空间和n维球面空间中一种新形式的正弦定理,利用建立的正弦定理获得了Hadamard型和Veljan-Korchmaros型不等式.另外,建立了涉及两个n维双曲单形和n维球面单形的"度量加"的一些几何不等式.     

多元线性模型D—最优设计等价性定理的一个统计直观解释

<正> 对于多元线性模型:其中θ=θ(_1,θ_2,…θ_m)~T,Y=(Y_1,Y_2,…Y_k)~T,F(x)=(f(ij)(x)),∑(x)=(σ_(ij)(x)),设所有试验点组成的集合是x,F(x)和∑(x)是x上的已知函数。在x_1,x_2,…x_n∈x上进行了n次     

Hn+1(c)中的有限型旋转曲面

研究E1n+2中双曲空间Hn+1(c)的坐标函数是其Laplacian的特征函数的球型、双曲型及抛物型旋转曲面Ma的性质,得到Ma或为Hn+1(c)的极小超曲面.或者可与 (球型),或 (双曲型)叠合.     

关于高维单形的一个不等式及应用

本文推广文献 [1 ]的结果 ,获得 En中关于单形的一个不等式 ( 1 ) ,并由此导出 En中面型的彭——常不等式 [5] ( 7)和涉及 n维单形 ∑A内任一点的两个几何不等式 ( 9) ,( 1 0 ) .     

关于n维单形体积不等式的一个定理

<正> 本文将给出关于两个n维单形体积间的一个不等式定理的证明,以及它们体积相等时的充要条件. 定理.设G是n维单形∑(A)=(a_0,a_1,…,a_n)的重心,a_iG交单形∑(A)的     

涉及单形内一点和内外径的一类不等式

设 n维 Euclid空间 En(n≥ 2 )中单形 Ω(A)的顶点集为 A={ A0 ,A1,… ,An} .,Ω(A)内任一点 P至侧面 { A0 ,A1,… ,An} \{ Ai}的距离为 di(i=0 ,1,… ,n) ,Ω(A)的外接超球半径和内切超球半径分别为 R、r,记C( n,α) =(2 (n+ 1　 2 ) + (n+ 1) 2α- (n+ 1) α) / 4 (n+ 12 ) ) α(α≥ 1) ,本文建立了涉及Ω (A)内一点的不等式∑0≤ i相似文献   

含根式不等式的处理方法

含根式不等式因技巧性较强,历年来颇受命题者喜爱,下面请欣赏几例. 一、三角代换例1 已知xi≥0,x0=0,sum from i=0 to nxi=1.求证:sum from i=1 to n xi/(1+x0+…+xi-1)(xi+…+xn)~(1/2)<π/2.证明 令x0+…+xi-1=sinθi-1,0=θ0≤θ1≤θ2≤…≤θn=π/2.则原式=sum from i=1 to n sinθi-sinθi-1/cosθi-1     

Estimation of the measure of the image of the ball

Under study is the class of ring Q-homeomorphisms with respect to the p-module. We establish a criterion for a function to belong to the class and solve a problem that stems from M. A. Lavrentiev [1] on the estimation of the measure of the image of the ball under these mappings. We also address the asymptotic behavior of these mappings at a point.     

On the distributions of the ratios of the extreme roots to the trace of the Wishart matrix

In this paper, the authors cosider the derivation of the exact distributions of the ratios of the extreme roots to the trace of the Wishart matrix. Also, exact percentage points of these distributions are given and their applications are discussed.     

On the rational approximation of the sum of the reciprocals of the Fermat numbers

Let $\mathcal{G}(z):=\sum_{n\geqslant0} z^{2^{n}}(1-z^{2^{n}})^{-1}$ denote the generating function of the ruler function, and $\mathcal {F}(z):=\sum_{n\geqslant} z^{2^{n}}(1+z^{2^{n}})^{-1}$ ; note that the special value $\mathcal{F}(1/2)$ is the sum of the reciprocals of the Fermat numbers $F_{n}:=2^{2^{n}}+1$ . The functions $\mathcal{F}(z)$ and $\mathcal{G}(z)$ as well as their special values have been studied by Mahler, Golomb, Schwarz, and Duverney; it is known that the numbers $\mathcal {F}(\alpha)$ and $\mathcal{G}(\alpha)$ are transcendental for all algebraic numbers α which satisfy 0<α<1. For a sequence u, denote the Hankel matrix $H_{n}^{p}(\mathbf {u}):=(u({p+i+j-2}))_{1\leqslant i,j\leqslant n}$ . Let α be a real number. The irrationality exponent μ(α) is defined as the supremum of the set of real numbers μ such that the inequality |α?p/q|<q ^?μ has infinitely many solutions (p,q)∈?×?. In this paper, we first prove that the determinants of $H_{n}^{1}(\mathbf {g})$ and $H_{n}^{1}(\mathbf{f})$ are nonzero for every n?1. We then use this result to prove that for b?2 the irrationality exponents $\mu(\mathcal{F}(1/b))$ and $\mu(\mathcal{G}(1/b))$ are equal to 2; in particular, the irrationality exponent of the sum of the reciprocals of the Fermat numbers is 2.     

On the approximation of positive operators and the behaviour of the spectra of the approximants

LetT be a positive linear operator on the Banach latticeE and let (S _n ) be a sequence of bounded linear operators onE which converge strongly toT. Our main results are concerned with the question under which additional assumptions onS _n andT the peripheral spectra (S _n ) ofS _n converge to the peripheral spectrum (T) ofT. We are able to treat even the more general case of discretely convergent sequences of operators.     

Refinement of the asymptotics of the power of the quantile test

One investigates the asymptotic properties of the quantile test, similar to the properties of the Pearson's chi-square test of fit.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 153, pp. 5–15, 1986.The author is grateful to D. M. Chibisov for useful remarks.