共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
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
3.
Li Jiangfan 《数学年刊B辑(英文版)》1989,10(1):85-93
This paper studios the existence of closed geodesics in the homotopy class of a given closed curve. Let M be a complete Riemannian manifold without boundary, f∈C~1(S~1, M). Look at S~1 as [0, 2π]/{0, 2π}. The following results are proved:A. The initial value problem of heat equation _if_t=τ(f_i), f_0=f always admits a global solution.B. (Existence of closed geodesics). If there exists a compact set KM such that f(S~1)∩K≠φ andE(f)≤(1/π)l(K)~2,then there exists a closed geodesic homotopic to f. If then the closed geodesic is minimal.C. Some estimates about injective radius are obtained.Some example is found showing that the inequalities in B are sharp. 相似文献
4.
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
5.
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
6.
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
7.
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
8.
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
9.
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
$$\[A({d_1}, \cdots ,{d_n}) = ({d_{n - 1}} - 1) \cdots ({d_1} - 1) - ({d_{n - 2}} - 1) \cdots ({d_1} - 1) + \cdots + {( - 1)^n}({d_2} - 1)({d_1} - 1) + {( - 1)^n}({d_1} - 1).\]$$ 相似文献
10.
Ye Cinan 《数学年刊B辑(英文版)》1986,7(3):384-396
Suppose that there is a variance components model
$$\[\left\{ {\begin{array}{*{20}{c}}
{E\mathop Y\limits_{n \times 1} = \mathop X\limits_{n \times p} \mathop \beta \limits_{p \times 1} }\{DY = \sigma _2^2{V_1} + \sigma _2^2{V_2}}
\end{array}} \right.\]$$
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
11.
Chen Yunmei 《数学年刊B辑(英文版)》1987,8(4):498-522
This paper deals with the following IBV problem of nonlinear parabolic equation:
$$\[\left\{ {\begin{array}{*{20}{c}}
{{u_t} = \Delta u + F(u,{D_x}u,D_x^2u),(t,x) \in {B^ + } \times \Omega ,}\{u(0,x) = \varphi (x),x \in \Omega }\{u{|_{\partial \Omega }} = 0}
\end{array}} \right.\]$$
where $\[\Omega \]$ is the exterior domain of a compact set in $\[{R^n}\]$ with smooth boundary and F satisfies $\[\left| {F(\lambda )} \right| = o({\left| \lambda \right|^2})\]$, near $\[\lambda = 0\]$. It is proved that when $\[n \ge 3\]$, under the suitable smoothness and compatibility conditions, the above problem has a unique global smooth solution for small initial data. Moreover, It is also proved that the solution has the decay property $\[{\left\| {u(t)} \right\|_{{L^\infty }(\Omega )}} = o({t^{ - \frac{n}{2}}})\]$, as $\[t \to + \infty \]$. 相似文献
12.
Liang Zhaojun 《数学年刊B辑(英文版)》1984,5(1):37-42
In this paper, we consider the relative position of limit cycles for the system
$$\[\begin{array}{*{20}{c}}
{\frac{{dx}}{{dt}} = \delta x - y + mxy - {y^2}}\{\frac{{dy}}{{dt}} = x + a{x^2}}
\end{array}\]$$
under the condition
$$\[a < 0,0 < \delta \le m,m \le \frac{1}{a} - a\]$$
The main result is as follows:
(i)Under Condition (2), if $\[\delta = \frac{m}{2} + \frac{{{m^2}}}{{4a}} \equiv {\delta _0}\]$, then system $\[{(1)_{{\delta _0}}}\] $ has no limit cycles and
on singular closed trajectory through a saddle point in the whole plane,
(ii)Under condition (2), the foci 0 and R'' cannot be surrounded by the limit cycles of system (1) simultaneously. 相似文献
13.
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
14.
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
15.
16.
Wang Zhicheng 《数学年刊B辑(英文版)》1991,12(3):243-254
Consider the higher-order neutral delay differential equationd~t/dt~n(x(t)+sum from i=1 to lp_ix(t-τ_i)-sum from j=1 to mr_jx(t-ρ_j))+sum from k=1 to Nq_kx(t-u_k)=0,(A)where the coefficients and the delays are nonnegative constants with n≥2 even. Then anecessary and sufficient condition for the oscillation of (A) is that the characteristicequationλ~n+λ~nsum from i=1 to lp_ie~(-λτ_i-λ~n)sum from j=1 to mr_je~(-λρ_j)+sum from k=1 to Nq_ke~(-λρ_k)=0has no real roots. 相似文献
17.
Lin Zhengsheng 《数学年刊B辑(英文版)》1984,5(3):363-373
By using the exponential dichotomy and the averaging method,a perturbation theoryis established for the almost periodic solutions of an almost differential system.Suppose that the almost periodic differential system(dx)/(dt)=f(x,t) ε~2g(x,t,ε)(1)has an almost periodic solution x=x_0(t,M)for ε=0,where M=(m_1,…,m_k)is theparameter vector.The author discusses the conditions under which(1)has an almostperiodic solution x=x(t,ε)such that x(t,ε)=x_0(t,M)holds uniformly.The results obtained are quite complete. 相似文献
18.
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
19.
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
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