共查询到20条相似文献,搜索用时 15 毫秒
1.
Zhu Yaochen 《数学年刊B辑(英文版)》1984,5(1):109-118
Letf_v(z)=∑a_(v,,k)z~(λ_(v,k))(v=1,…,s)be s power series with algebraic coefficients a_(v,k),convergence radii R_v>0 and sufficientlyrapidly increasing integers λ_(v,k).It is shown that under certain conditions depending only ona_(v,k) and λ_(v,k),(i)f_1(θ_1),…,f_s(θ_s)are algebraically independent for arbitrary algebraicnumbers θ_1,…,θ_s with θ<丨θ_v丨相似文献
2.
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
3.
Sun Hesheng 《数学年刊B辑(英文版)》1988,9(4):429-435
In practical problems there appears the higher-order equations of changing type. But,there is only a few of papers, which studied the problems for this kind of equations. In this paper a kind of the higher-order m 相似文献
4.
Ding Tongren 《数学年刊B辑(英文版)》1984,5(4):687-694
This note is concerned with the equation
$$\[\frac{{{d^2}x}}{{d{t^2}}} + g(x) = p(t)\begin{array}{*{20}{c}}
{}&{(1)}
\end{array}\]$$
where g(x) is a continuously differentiable function of a $\[x \in R\]$, $\[xg(x) > 0\]$ whenever $\[x \ne 0\]$, and
$\[g(x)/x\]$ tends to $\[\infty \]$ as \[\left| x \right| \to \infty \]. Let p(t) be a bounded function of $\[t \in R\]$. Define its norm by
$\[\left\| p \right\| = {\sup _{t \in R}}\left| {p(t)} \right|\]$
The study of this note leads to the following conclusion which improves a result due to
J. E. Littlewood,
For any given small constants $\[\alpha > 0,s > 0\]$, there is a continuous and roughly periodic(with respect to $\[\Omega (\alpha )\]$) function p(t) with $\[\left\| p \right\| < s\]$ such that the corresponding equation (1)
has at least one unbounded solution. 相似文献
5.
Let $\[(\Omega ,F,\mu )\]$ be a probabilty space with an increasing family $\[{\{ {F_t}\} _{t > 0}}\]$ of sub-fields satisfying the usual conditions. The following results are obtained: for $\[f \in BMO\]$, we have $\[f = g - h\]$ with $\[g,h \in BLO\]$; if in addition, f satisfies
then for $\[s > 0\]$ arbitrary, g,h can be chosen such that $\[g,h \in BLO\]$, and
$$\[E({\varepsilon ^{(a - \varepsilon )(g - {g_t})}}|{F_t}) \le {C_{a,\beta ,\varepsilon }},E({\varepsilon ^{(\beta - \varepsilon )(h - {h_t})}}|{F_t}) \le {C_{a,\beta ,\varepsilon }}\]$$
and for weights z, we have
$\[z \in {A_p} \cap S \Leftrightarrow z = {z_1}z_2^{1 - p}\]$ with $\[{z_i} \in {A_i} \cap S,i = 1,2\]$,
where $\[S = \{ \begin{array}{*{20}{c}}
{weight}&{z:C{z_{{T^ - }}} \le {z_T} \le C{z_{{T^ - }}}}
\end{array}\} \]$, $\[\forall \]$ stopping times T, outside a null set }. 相似文献
6.
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
7.
ON THE JOINT SPECTRUM FOR N-TUPLE OF HYPONORMAL OPERATORS 总被引:1,自引:0,他引:1
Let A=(A_1,…,A,)be an n-tuple of double commuting hyponormal operators.It is-proved that:1.The joint spectrum of A has a Cartesian decomposition:Re[Sp(A)]=S_p(ReA),Im[Sp(A)]=Sp(ImA);2.The.joint resolvent of A satisfies the growth condition:‖()‖=1/(dist(z,Sp(A)));3.If 0σ(A_i),i=1,2,…,n,then‖A‖=γ_(sp)(A). 相似文献
8.
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
9.
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
10.
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
11.
Li Dening 《数学年刊B辑(英文版)》1986,7(2):147-159
Consider the nonlinear inltial-boundary value problem for quasilinear hyperbolicsystem:Let k≥2[n/2] 6,(F,g)∈ H~k(R_ ;Ω)×H~k(R_ ;Ω),and their traces at t=0 are zeroup to the order k-1.If for u=0,the problem(*)at t=0 is a Kreiss hyperbolic system,and the boundaryconditions satisfy the uniformly Lopatinsky criteria,then there exists a T>0 such that(*)has a unique H~k soluton in(0,T).In the Appendix,for symmetric hyperbolic systems,a comparison between theuniformly Lopatinsky condition and the stable admissible condition is given. 相似文献
12.
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
13.
The authors establish sufficient conditions for the oscillation of all solution of neutral delay differential equations of even and odd order of the form
$$\[\frac{{{d^n}}}{{d{t^n}}}[y(t) + p(t)y(t - \tau )] + Q(t)y(t - C) = 0,t \ge {t_0},\]$$
where $\[P,Q \in C[[{t_0},\infty ),R],\tau ,\sigma \in {R^ + }\]$ and $\[n \ge 1\]$. 相似文献
14.
The number $\[A({d_1}, \cdots ,{d_n})\]$ of solutions of the equation
$$\[\sum\limits_{i = 0}^n {\frac{{{x_i}}}{{{d_i}}}} \equiv 0(\bmod 1),0 < {x_i} < {d_i}(i = 1,2, \cdots ,n)\]$$
where all the $\[{d_i}s\]$ are positive integers, is of significance in the estimation of the number $\[N({d_1}, \cdots {d_n})\]$ of solutiohs in a finite field $\[{F_q}\]$ of the equation
$$\[\sum\limits_{i = 1}^n {{a_i}x_i^{{d_i}}} = 0,{x_i} \in {F_q}(i = 1,2, \cdots ,n)\]$$
where all the $\[a_i^''s\]$ belong to $\[F_q^*\]$. the multiplication group of $\[F_q^{[1,2]}\]$. In this paper, applying the inclusion-exclusion principle, a greneral formula to compute $\[A({d_1}, \cdots ,{d_n})\]$ is obtained.
For some special cases more convenient formulas for $\[A({d_1}, \cdots ,{d_n})\]$ are also given, for
example, if $\[{d_i}|{d_{i + 1}},i = 1, \cdots ,n - 1\]$, then
$$\[A({d_1}, \cdots ,{d_n}) = ({d_{n - 1}} - 1) \cdots ({d_1} - 1) - ({d_{n - 2}} - 1) \cdots ({d_1} - 1) + \cdots + {( - 1)^n}({d_2} - 1)({d_1} - 1) + {( - 1)^n}({d_1} - 1).\]$$ 相似文献
15.
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
16.
Yao Biyun 《数学年刊B辑(英文版)》1982,3(1):85-88
Let $\sigma$ denote the family of univalent functions
$\[F(z) = z + \sum\limits_{n = 1}^\infty {\frac{{{b_n}}}{{{z^n}}}} \]$
in l< |z| <\infty if G(w) is the inverse of a function $F(z) \in \sigma ^'$, the expansion of G(w) in some neighborhood of w=\infty is
$\[G(w) = w - \sum\limits_{n = 1}^\infty {\frac{{{B_n}}}{{{w^n}}}} \]$
It is well known that |B_1|\leq 1 for any F(z) \in \sigma ^'. Springer^[1] proved that | B_3| \leq 1 and conjectured that
$\[|{B_{2n - 1}}| \le \frac{{(2n - 2)!}}{{n!(n - 1)!}}{\rm{ }}(n = 3,4, \cdots )\]$ (1)
Kubota^[2] proved (1) for n=3, 4, 5. Schober^[3] proved (1) for n = 6, 7. Ren Fuyao[4,5] has verified (1) for n=6, 7, 8. In this article we are going to verify (1) for n=9. 相似文献
17.
设α是环R的一个自同态,称环R是α-斜Armendariz环,如果在R[x;α]中,(∑_(i=0)~ma_ix~i)(∑_(j=0)~nb_jx~j)=0,那么a_ia~i(b_j)=0,其中0≤i≤m,0≤j≤n.设R是α-rigid环,则R上的上三角矩阵环的子环W_n(p,q)是α~—-斜Armendariz环. 相似文献
18.
DAVENPORT''''S THEOREM IN SHORT INTERVALS 总被引:1,自引:0,他引:1
Zhan Tao 《数学年刊B辑(英文版)》1991,12(4):421-431
Let μ be te Mbius function. It is proved that for any A>0sum from n=x0), which generalizes H. Davenport's theorem for Mbius function to short intervals. 相似文献
19.
Qin Tiehu 《数学年刊B辑(英文版)》1988,9(3):251-269
The paper deals with the following boundary problem of the second order quasilinear hyperbolic equation with a dissipative boundary condition on a part of the boundary:u_(tt)-sum from i,j=1 to n a_(ij)(Du)u_(x_ix_j)=0, in (0, ∞)×Ω,u|Γ_0=0,sum from i,j=1 to n, a_(ij)(Du)n_ju_x_i+b(Du)u_t|Γ_1=0,u|t=0=φ(x), u_t|t=0=ψ(x), in Ω, where Ω=Γ_0∪Γ_1, b(Du)≥b_0>0. Under some assumptions on the equation and domain, the author proves that there exists a global smooth solution for above problem with small data. 相似文献
20.
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