GENERALIZED HILBERT OPERATOR AND FEJR-RIESZ TYPE INEQUALITIES ON THE POLYDISC

Let f be a holomorphic function on the unit polydisc Dn,with Taylor expansion f(z) = ∞ |k|=0 akzk ≡∞ (k1+···+kn=0) (ak1,···,kn zk1 1znkn)where k = (k1, , kn) ∈ Z+n. The authors define generalized Hilbert operator on Dn by Hγ,n(f)(z) = ∞ |k|=0 i1,···,in≥0 ai1,···,in n j=1 Γ(γj + kj + 1)Γ(kj + ij + 1) Γ(kj + 1)Γ(kj + ij + γj + 2) zk,where γ∈ Cn, such that R γj > -1, j = 1, 2, , n. An upper bound for the norm of the operator on Hardy spaces Hp(Dn) is found. The authors also present a Fejér-Riesz type inequalit...     

ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE

Let {X_n, n≥1} be a strictly stationary sequence of random variables, whichare either associated or negatively associated, f(·) be their common density. In this paper,the author shows a central limit theorem for a kernel estimate of f(·) under certain regularconditions.     

一类高阶非线性微分方程解的存在问题(英文)

This paper is concerned with the following n-th ordinary differential equation:{u～(n)(t)=f(t,u(t),u～(1)(t),···,u～(n-1) (t)),for t∈(0,1),u～(i) (0)=0,0 ≤i≤n3,au～(n-2)(0)du～(n-1)(0)=0,cu～(n-2)(1)+du～(n-1)(1)=0,where a,c ∈ R,,≥,such that a～2 + b～2 0 and c～2+d～20,n ≥ 2,f:[0,1] × R → R is a continuous function.Assume that f satisfies one-sided Nagumo condition,the existence theorems of solutions of the boundary value problem for the n-th-order nonlinear differential equations above are established by using Leray-Schauder degree theory,lower and upper solutions,a priori estimate technique.     

On the Growth of Solutions of a Class of Higher Order Linear Differential Equations

In this paper, we investigate the growth of solutions of the differential equations f(k)+Ak?1(z)f(k?1)+· · ·+A0(z)f =0, where Aj(z)(j=0, · · · , k?1) are entire functions. When there exists some coe?cient As(z)(s ∈ {1, · · · , k?1}) being a nonzero solution of f00+P(z)f =0, where P(z) is a polynomial with degree n(≥1) and A0(z) satisfiesσ(A0)≤1/2 or its Taylor expansion is Fabry gap, we obtain that every nonzero solution of such equations is of infinite order.     

一个局部波动方程组的解的全局存在性与爆破

我们研究初始值问题(e)u1/(e)t2=(e)2u1/(e)x2+‖u2(·,t)‖p, (e)2u2/(e)t2=(e)2u2/(e)x2+‖u1(·,t)‖q,-∞<x<∞,t>0,u1(x,0)=f1(x), (e)u1/(e)t(x,0)=g1(x),u2(x,0)=f2(x), (e)u2/(e)t(x,0)=g2(x),- ∞<x<∞,where‖ui(·,t)‖=∫∞-∞(4)i(x)|ui(x,t)|dx with (4)i(x)≥0 and ∫∞-∞(4)i(x)dx=1,i=1,2.然后建立解的全局存在和爆破的标准,提出爆破增长率.     

ASYMPTOTIC NORMALITY OF WAVELET ESTIMATOR IN HETEROSCEDASTIC REGRESSION MODEL

The following heteroscedastic regression model Y_i=g(x_i) σ_ie_i(1≤i≤n)is considered,where it is assumed thatσ_i~2=f(u_i),the design points(x_i,u_i)are known and nonrandom,g and f are unknown functions.Under the unobservable disturbance e_i form martingale differences,the asymptotic normality of wavelet estimators of g with f being known or unknown function is studied.     

相依MA(∞)误差下半参数模型小波估计的收敛速度(英文)

考虑半参数回归模型yi=xiβ+g(ti)+Vi(1≤i≤n), 其中(xi,ti)是已知的设计点, 斜率参数β是未知的, g(·)是未知函数, 误差Vi=sum from j=-∞ to ∞(cjei-j),sum from j=-∞ to ∞(|cj|∞)并且ei是负相关的随机变量. 在适当的条件下, 我们研究了β与g(·)小波估计量的强收敛速度. 结果显示g(·)的小波估计量达到最优收敛速度. 同时, 对β小波估计量也作了模拟研究.     

Irregular wavelet frames on L~2 (R~n)

In this paper, we present the conditions on dilation parameter {sj}j that ensure a discrete irregular wavelet system to be a frame on L2(Rn), and for the wavelet frame we consider the perturbations of translation parameter b and frame function ψ respectively.     

四层前向神经网络作为通用逼近器的一致性分析

如果转移函数σ:R→R是Tauber-Wiener函数,即σ∈(TW), 本文给出了四层前向神经网络∑pi=1ui(q∑j=1uijσ(Aij·x+θij))作为通用逼近器的一致性分析,且选取了该网络具有某类特殊性质的连结权.例如,若f,g是连续函数,且f≤g,则相应的连结权关于f,g是递增的,等等.最后为验证结论,给出了一个模拟例子.     

Galois环上本原序列压缩映射的单性

设Ω是 Ｇａｌｏｉｓ环 ＧＲ（２~ｄ,ｒ）的 Ｔｅｉｃｈｍｕｌｌｅｒ代表集,则 ＧＲ（２~ｄ,ｒ）上每条序列ａ有唯一的权位分解,　其中ａ-ｉ是Ω上序列,同时也可自然视为有限域Ｆ-（２~ｒ）,上序列．设ｆ（ｘ）是环 ＧＲ（２~ｄ,ｒ）上强本原多项式,Ｇ（ｆ（ｘ））表示 ＧＲ（２~ｄ,ｒ）上以ｆ（ｘ）为特征多项式的序列的全体,是Ｆ-（２~ｒ）上一类ｄ－１元多项式, 　本文证明了压缩映射是单射,即对 ａ＝ ｂ当且仅当对所有 ａ,ｂ ∈ Ｇ（ｆ（ｘ））．