共查询到20条相似文献,搜索用时 15 毫秒
1.
Based on [3] and [4],the authors study strong convergence rate of the k_n-NNdensity estimate f_n(x)of the population density f(x),proposed in [1].f(x)>0 and fsatisfies λ-condition at x(0<λ≤2),then for properly chosen k_nlim sup(n/(logn)~(λ/(1 2λ))丨_n(x)-f(x)丨C a.s.If f satisfies λ-condition,then for propeoly chosen k_nlim sup(n/(logn)~(λ/(1 3λ)丨_n(x)-f(x)丨C a.s.,where C is a constant.An order to which the convergence rate of 丨_n(x)-f(x)丨andsup 丨_n(x)-f(x)丨 cannot reach is also proposed. 相似文献
2.
Shen Zun 《数学年刊B辑(英文版)》1986,7(2):213-220
In this paper,, the author proves the following result:
Let $\[{E_{a,k}}(N)\]$ denote the number of natural numbers $\[n \le N\]$ for which equation
$$\[\sum\limits_{i = 0}^k {\frac{1}{{{x_i}}}} = \frac{a}{n}\]$$
is insolable in positive integers $\[{x_i}(i = 0,1, \cdots ,k)\]$.Then
$$\[{E_{a,k}}(N) \ll N\exp \{ - C{(\log N)^{1 - \frac{1}{{k + 1}}}}\} \]$$
where the implied constant depends on a and K. 相似文献
3.
Zheng Zukang 《数学年刊B辑(英文版)》1988,9(2):167-175
Let X_1,…,X_n be a sequence of independent identically distributed random variableswith distribution function F and density function f.The X_are censored on the right byY_i,where the Y_i are i.i.d.r.v.s with distribution function G and also independent of theX_i.One only observesLet S=1-F be survival function and S be the Kaplan-Meier estimator,i.e.,where Z_are the order statistics of Z_i and δ_((i))are the corresponping censoring indicatorfunctions.Define the density estimator of X_i by where =1-and h_n(>0)↓0. 相似文献
4.
Han Yongsheng 《数学年刊B辑(英文版)》1983,4(1):15-20
A measure μ is called Carleson measure,iff the condition of Carleson type μ(Q~*)≤C|Q|~α(a≥1)is satisfied,where C is a constant independent of the cube Q with edge lengthq>0 in R~n and Q~*={(y,t)∈R_+~(+1)|y∈Q,0相似文献
5.
Wu Liangsen 《数学年刊B辑(英文版)》1988,9(1):27-31
Let $A$, $B$ be unital $\[{C^*}\]$-algebras.
$\[{\chi _A} = \{ \varphi |\varphi \]$ are all completely postive linear maps from $\[{M_n}(C)\]$ to $A$ with $\[\left\| {a(\varphi )} \right\| \le 1\]$ $}$.
$\[(a(\varphi ) = \left( {\begin{array}{*{20}{c}}
{\varphi ({e_{11}})}& \cdots &{\varphi ({e_{1n}})}\{}& \cdots &{}\{\varphi ({e_{n1}})}& \cdots &{\varphi ({e_{nn}})}
\end{array}} \right),\]$ where $\[\{ {e_{ij}}\} \]$ is the matrix unit of $\[{M_n}(C)\]$.
Let $\[\alpha \]$ be the natural action of $\[SU(n)\]$ on $\[{M_n}(C)\]$
For $\[n \ge 3\]$, if $\[\Phi \]$ is an $\[\alpha \]$-invariant affine isomorphism between $\[{\chi _A}\]$ and $\[{\chi _B}\]$, $\[\Phi (0) = 0\]$, then $A$ and $B$ are $\[^*\]$-isomorphic
In this paper a counter example is given for the case $\[n = 2\]$. 相似文献
6.
Chen Jiading 《数学年刊B辑(英文版)》1987,8(4):471-482
Suppose that $\[{x_1},{x_2}, \cdots \]$ are i i d. random variables on a probability space $\[(\Omega ,F,P)\]$ and $\[{x_1}\]$ is normally distributed with mean $\[\theta \]$ and variance $\[{\sigma ^2}\]$, both of which are
unknown. Given $\[{\theta _0}\]$ and $\[0 < \alpha < 1\]$, we propose a concrete stopping rule T w. r. e.the
$\[\{ {x_n},n \ge 1\} \]$ such that
$$\[{P_{\theta \sigma }}(T < \infty ) \le \alpha \begin{array}{*{20}{c}}
{for}&{\begin{array}{*{20}{c}}
{all}&{\theta \le {\theta _0},\sigma > 0,}
\end{array}}
\end{array}\]$$
$$\[{P_{\theta \sigma }}(T < \infty ) = 1\begin{array}{*{20}{c}}
{for}&{\begin{array}{*{20}{c}}
{all}&{\theta > {\theta _0},\sigma > 0,}
\end{array}}
\end{array}\]$$
$$\[\mathop {\lim }\limits_{\theta \downarrow {\theta _0}} {(\theta - {\theta _0})^2}{({\ln _2}\frac{1}{{\theta - {\theta _0}}})^{ - 1}}{E_{\theta \sigma }}T = 2{\sigma ^2}{P_{{\theta _0}\sigma }}(T = \infty )\]$$
where $\[{\ln _2}x = \ln (\ln x)\]$. 相似文献
7.
In this paper, the authors prove following result:Let M~n be a complete Bechner-Kaehler submanifold of complex dimension (n≥4) in a complex projective space CP~(n p)(1) of complex dimension n p, endowed with the FubiniStudy metric of constant holomorphic sectional curvature 1. If the sectional curvature K of M~n satisfies K<1, then codimension p of M~n is not less then n(n 1)/2. 相似文献
8.
Bai zhengguo 《数学年刊B辑(英文版)》1988,9(1):32-37
A Riemannian manifold V~m which admits isometric imbedding into two spaces V~(m+p)ofdifferent constant curvatures is called a manifold of quasi constant curvature.TheRiemannian curvature of V~m is expressible in the formand conversely.In this paper it is proved that if M~n is any compact minimal submanifoldwithout boundary in a Riemannian manifold V~(n+p)of quasi constant curvature,then∫_(M~u)(2-1/p)σ~2-[na+1/2(b-丨b丨)(n+1)]σ+n(n-1)b~2*丨≥0,where σ is the square of the norm of the second fundamental form of M~n When V~(n+p)is amanifold of constant curvature,b=0,the above inequality reduces to that of Simons. 相似文献
9.
Huang Xinzhong 《数学年刊B辑(英文版)》1986,7(2):139-146
Let S~* be the class of functionsf(z)analytic,univalent in the unit disk|z|<1 andmap|z|<1 onto a region which is starlike with respect to w=0 and is denoted as D_f.Letr_0=r_0(f)be the radius of convexity of f(2).In this note,the author proves the following result:(d_0/d~*)≥0.4101492,where d_0= f(z),d~*=|β|. 相似文献
10.
Deng Guantie 《数学年刊B辑(英文版)》1986,7(3):330-338
In the present paper, we show that there exist a bounded, holomorphic function $\[f(z) \ne 0\]$ in the domain $\[\{ z = x + iy:\left| y \right| < \alpha \} \]$ such that $\[f(z)\]$ has a Dirichlet expansion $\[\sum\limits_{n = 0}^{ + \infty } {{d_n}{e^{ - {u_n}}}} \]$ in the halfplane $\[x > {x_f}\]$ if and only if $\[\frac{a}{\pi }\log r - \sum\limits_{{u_n} < r} {\frac{2}{{{u_n}}}} \]$ has a finite upperbound on $\[[1, + \infty )\]$, where $\[\alpha \]$ is a positive constant,$\[{x_f}( < + \infty )\]$ is the abscissa of convergence of $\[\sum\limits_{n = 0}^{ + \infty } {{d_n}{e^{ - {u_n}}}} \]$ and the infinite sequence $\[\{ {u_n}\} \]$ satisfies $\[\mathop {\lim }\limits_{n \to + \infty } ({u_{n + 1}} - {u_n}) > 0\]$. We also point out some necessary conditions and sufficient ones Such that a bounded holomorphic function in an angular(or half-band) domain is identically zero if an infinite sequence of its derivatives and itself vanish at some point of the domain. Here some result are generalizations of those in [4]. 相似文献
11.
Liao Ruijia 《数学年刊B辑(英文版)》1988,9(3):292-296
Let M~n (n≥2) be a complex Kaehler submanifold immersed in the complex projective space CP~m(1). Let K be the sectional curvature of M~n. Then K≥1/8 if and only if M~n is an imbedding submanifold congruent to the standard imbedding CP~n (1) or CP~n(1/2). 相似文献
12.
Zhan Tao 《数学年刊B辑(英文版)》1989,10(2):227-235
Let L(x) denote the number of square-full integers not exceeding x. It is proved in [1] thatL(x)~(ζ(3/2)/ζ(3))x~(1/2) (ζ(2/3)/ζ(2))x~(1/3) as x→∞,where ζ(s) denotes the Riemann zeta function. Let △(x) denote the error function in the asymptotic formula for L(x). It was shown by D. Suryanaryana~([2]) on the Riemann hypothesis (RH) that1/x integral from n=1 to x |△(t)|dt=O(x~(1/10 s))for every ε>0. In this paper the author proves the following asymptotic formula for the mean-value of △(x) under the assumption of R. H.integral from n=1 to T (△~2(t/t~(6/5))) dt~c log T,where c>0 is a constant. 相似文献
13.
In this paper we have extended the Putnam-Fuglede Theorem of nomal operators anddiscussed the condition for the Putnam-Fuglede Theorem holding.We have proved that ifA and B~* are hyponomal operators and AX=XB,then A~*X=XB~*;that if A and B~* aresemi-hyponomal operators and X is 相似文献
14.
Liu Quan-sheng 《数学年刊B辑(英文版)》1989,10(2):214-220
The paper considers the random L-Dirichlet seriesf(s,ω)=sum from n=1 to ∞ P_n(s,ω)exp(-λ_ns)and the random B-Dirichlet seriesψτ_0(s,ω)=sum from n=1 to ∞ P_n(σ iτ_0,ω)exp(-λ_ns),where {λ_n} is a sequence of positive numbers tending strictly monotonically to infinity, τ_0∈R is a fixed real number, andP_n(s,ω)=sum from j=1 to m_n ε_(nj)a_(nj)s~ja random complex polynomial of order m_n, with {ε_(nj)} denoting a Rademacher sequence and {a_(nj)} a sequence of complex constants. It is shown here that under certain very general conditions, almost all the random entire functions f(s,ω) and ψ_(τ_0)(s,ω) have, in every horizontal strip, the same order, given byρ=lim sup((λ_nlogλ_n)/(log A_n~(-1)))whereA_n=max |a_(nj)|.Similar results are given if the Rademacher sequence {ε_(nj)} is replaced by a steinhaus seqence or a complex normal sequence. 相似文献
15.
Wu Xiaolong 《数学年刊B辑(英文版)》1988,9(4):436-441
In this paper, the author proves the following resu: It Let K be a skew field and A be an automorphism of SL(2, K). Then there exists A∈GL(2, K), an automorphism σ or an anti-automorphism τ of K, such that A is of theform AX=AX~σA~(-1) for all X∈SL(2, K)or AX=A(X~τ~2)~(-1)A~(-1) for all X∈SL(2, K),where X~σ, X~τ are the matrices obtained by applying σ, τ on X respee tively and X' is thetranspose of X. 相似文献
16.
The paper proves on the basis of [1] the following theorem: Let $\[f(z)\]$ be an entire function of lower order $\[\mu < \infty \]$, and $\[{a_i}(z)(l = 1,2, \cdots ,k)\]$ be meromorphic functions which satisfy $\[T(r,{a_i}(z)) = o\{ T(r,f)\} \]$. If
$$\[\sum\limits_{i = 1}^k {\delta ({a_i}(z),f) = 1\begin{array}{*{20}{c}}
{({a_i}(z) \ne \infty )}&{(1)}
\end{array}} \]$$
then the deficiencies $\[\delta ({a_i}(z),f)\]$ are equal to $\[\frac{{{n_1}}}{\mu }\]$, where $\[{n_i}\]$ is an integer,$\[l = 1,2, \cdots ,k\]$. 相似文献
17.
Wang Shushi 《数学年刊B辑(英文版)》1986,7(2):243-250
This paper shows that if T∈C(X)is strongly S-decomposable,where S is a closedsubset of σ_(T)and S≠C_∞,then for any(e)spectral maximal subspace Y of T,T~Y is aclosed strongly S∩σ_(T~Y)-decomposable operator. 相似文献
18.
Hu Ke 《数学年刊B辑(英文版)》1983,4(2):187-190
AIn this paper, the author obtains the following results:(1) If Taylor coeffiients of a function satisfy the conditions:(i),(ii),(iii)A_k=O(1/k) the for any h>0 the function φ(z)=exp{w(z)} satisfies the asymptotic equality the case h>1/2 was proved by Milin.(2) If f(z)=z α_2z~2 …∈S~* and,then for λ>1/2 相似文献
19.
Ye Cinan 《数学年刊B辑(英文版)》1986,7(3):384-396
Suppose that there is a variance components model
$$\[\left\{ {\begin{array}{*{20}{c}}
{E\mathop Y\limits_{n \times 1} = \mathop X\limits_{n \times p} \mathop \beta \limits_{p \times 1} }\{DY = \sigma _2^2{V_1} + \sigma _2^2{V_2}}
\end{array}} \right.\]$$
where $\[\beta \]$,$\[\sigma _1^2\]$ and $\[\sigma _2^2\]$ are all unknown, $\[X,V > 0\]$ and $\[{V_2} > 0\]$ are all known, $\[r(X) < n\]$. The author estimates simultaneously $\[(\sigma _1^2,\sigma _2^2)\]$. Estimators are restricted to the class $\[D = \{ d({A_1}{A_2}) = ({Y^''}{A_1}Y,{Y^''}{A_2}Y),{A_1} \ge 0,{A_2} \ge 0\} \]$. Suppose that the loss function is $\[L(d({A_1},{A_2}),(\sigma _1^2,\sigma _2^2)) = \frac{1}{{\sigma _1^4}}({Y^''}{A_1}Y - \sigma _1^2) + \frac{1}{{\sigma _2^4}}{({Y^''}{A_2}Y - \sigma _2^2)^2}\]$.
This paper gives a necessary and sufficient condition for $\[d({A_1},{A_2})\]$ to be an equivariant D-asmissible estimator under the restriction $\[{V_1} = {V_2}\]$, and a sufficient condition and a necessary condition for $\[d({A_1},{A_2})\]$ to equivariant D-asmissible without the restriction. 相似文献
20.
Li Fuan 《数学年刊B辑(英文版)》1986,7(1):1-13
Let $V$ be a non-defective S-dimensional quadratic space over a field $F$ of characteristic 2, $\[F \ne {F_2}\]$. We prove that if there is an exceptional automorphism of either $\[{\Omega _S}(V)\]$ or $\[O_S^''(V)\]$ then $\[{V^\alpha }\]$ has a Cayley algebra structure for some $\[\alpha \]$ in F. Moreover, every exceptional automorphism of $\[O_S^''(V)\]$ has exactly one of the following forms:
$$\[{\varphi _1} \circ {\Phi _g}or{\varphi _2} \circ {\Phi _g}\]$$
where $\[{\Phi _g}\]$ is an automorphism of $\[O_S^''(V)\]$ given by conjugation by a semilinear automorphism of V which preserves the quadratic structure, and $\[{\varphi _1}\]$ and $\[{\varphi _2}\]$ are the automorphisms induced by triality principle. Every exceptional automorphism of $\[{\Omega _S}(V)\]$ is the restriction of a unique exceptional automorpliism of $\[O_S^''(V)\]$. 相似文献