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1.
杨瑛 《数学物理学报(B辑英文版)》1999,19(1):37-44
1IntroductionandResultConsiderthenonparametricmedianregressionlllodelwhereg:[0,1]-Risasmoothfunctiontobeestilllated.{xu,.15z57L}arelloll-ralldollldesignpointsintheinterval[0,1],{e,,i.15i相似文献
2.
《数学通报》2010年4月第1848号数学问题为:
已知函数:f(x)=x3+bx,数列{an},其中a1>0.
(1)若an=f(n),当数列{an}为递增数列时,求b的取值范围;
(2)若an+1=f(an),当数列{an}为递增数列 时,求首项a1的取值范围.(用b表示,且b≥0)
原解答对于(1),将数列{an=f(n)}递增数列转化为函数f(x) =x3 +bx在[1,+∞)单调递增,进而转化为f′(x) =3x2+b≥0在[1,+∞)上恒成立,从而求出b的范围是:b≥-3. 相似文献
3.
非参数回归函数的基于截尾数据的估计 总被引:4,自引:1,他引:3
本文考虑截尾数据情况下非参数回归函数m(x)=E(Y|x)的估计。具体地讲,我们面对的是这样的数学模型:T是与(X,Y)独立的随机变量,我们观测到的不是Y本身,而是Z=min(Y,T)及δ=[Y≤T]。今有训练样本{(X_i,Z_i,δ_i)}_(i-1)及当前样本(X,z,δ),记ξ_i(·)=[z_i≥·], N~ (·)=sum from i=1 to n ξ_i(·), V_n(·)=multiply from i=1 to n{1 N~ (z_i)/2 N~ (z_i)}~[δ_i=_i<0], U_n(·)=sum from i=1 to n Wnt(x)ξ_i(·), 令 m_n(x)=integral from 0 to u_n U_n(y)|V_n(y)dy, 其中u_n=F_2~(-1)(n~(-a)),0<α<1/2为一实常数,F_2(·)=P(Y≥·)为Y的(右侧)分布函数。在权函数{W_(ni)(x)}_(i=1)~n及(X,Y,T)的分布函数满足一组条件下,我们证明了m_n(x)为m(x)的强相合估计,即:m_n(x)→m(x),a.s.(n→ ∞). 相似文献
4.
X. G. Lu 《计算数学(英文版)》1997,15(1):81-96
1,Iotroduction.InthispaPerwe8tudytherepresentationofDaubechies'wavelets.DaubechiesI1]constructedaf4milyofcompartlysupportedregularscallngfUnctionsrk.(x)andtheassoci4tedregularwpeletsop.(x)(N32):where4.eL'(R)definedbythep0lyn0mia:withZq.(k)=1'q.(k)ER,k=0,1,')N-1.Itisknownthat[1]f0reachN32,k=Osuppgh.=[0,2N-l],suppop.=[-(N-1),N]andthewaveletop.generatesbyitsdilatiOnsandtranslati0nsan0rth0rn0rmalbasis{m.(2ix-k)}i,k6Z0fL'(R).Thefunctionsrk.andop.havebeenprovedtobeveryusefulinnumericalanal… 相似文献
5.
HONG Wenming 《数学年刊B辑(英文版)》1999,20(4):447-454
61.IntroductionLetW=[w,,ll.,.,s,t2o,aER']denoteastandardBrownianmotioninRdwithsendgroup{Pt,t2o},C(R')denotetheBanachspaceofcontinuousboundedfunctionsonRdequlppedwiththesupnorm.rk.(a):=(1 Ial')-p/',aERd,Cr(R'):-{feC(R'),lf(x)l5CIof.(x)}withsomeconstantCj,Mv(R'):={pisffedonmeasureonRdandJ(1 lxlp)-'p(dx)d.(P,i):=ff(x)p(dx),AisLebesgUemeasure.GiventheordinaryMP-valuedsuper-Brownianmotiono:=[o,,fl1,Ps,#,t2s2O,pEMP]asthecatalyticmedium,Dawsona… 相似文献
6.
Several Results on Systems of Residue Classes 总被引:2,自引:0,他引:2
Let (m,n) and a(n) denote the g.c.d, of m, n and the residue class {x∈Z∶x≡α (mod n)} respectively. Any period of the characteristic function ofkU a_i(n_i) is called a covering period of {a_i(n_i)}_(i-1)~k.i-ITheorem Let A = {a_i(n_i)}_(i-1)~k. be a disjoint system (i. e. a_I(n_I,...,a_k(n_k) are pairwise disjoint). Let [n_I,...,n_k] (the I.c.m. of n_1,...,n_k) have the prime faetorization [n_1,...,n_k] = Πp_i~ai and T = Πp_iβi(β_i≥0 be the smallest positive covering period of A. Then 相似文献
7.
Supposethatqisasufficientlylargepositiveinteger,(a,q)=1,letP(a,q)betheleastprimeinthearithmeticprogression{n=a(modq)}andxbetheDirichletcharacterofmodulusq.L(s,x)istheDirichletL-function.Everypositiveintegerqcanbeexpressedasq=qq2,q2iscubefree.Anintegerqiscalled"hasboundedcubicpart"iftheaboveq3isboundedabsolutely.Forgeneralintegerq,Heath-Brown[1]showedthatP(a,q)q5.5.Whenqisaprime,Motohashi[2]showedthat:Foranyfordpositiveintegeraandsmallpositiverealnumber>0,thereexistindnitelymanyprimesqsucht… 相似文献
8.
9.
《中学数学》2005,(Z1)
1.(辽宁卷,19)已知函数f(x)=x 3x 1(x≠-1).设数列{an}满足a1=1,an 1=f(an),数列{bn}满足bn=an-3,Sn=b1 b2 … bn(n∈N*).()用数学归纳法证明bn≤(32n--11)n;()证明Sn<233.2.(江西卷,21)已知数列{an}的各项都是正数,且满足:a0=1,an 1=21an(4-an),n∈N.(1)证明an相似文献
10.
§1.引言 设ω(t)是给定的连续模,H_ω={f;ω(f,t)≤ω(t)}。P_n~(α,β)(x)(α,β>-1)表示n阶Jacobi多项式;P_n(x)=P_n~(0,0)(x)为Legendre多项式。 定义1 (见[1,555页])设{x_κ~((n))}_(κ=1)~n(n=1,2,…)为属于区间[-1,1]的节点系。 相似文献
11.
12.
首先对现行教材中初等函数的定义提出了商讨意见,讨论了高等数学教材中出现的形式上的非初等函数与初等函数的关系,并通过一些有代表性的例子加以说明. 相似文献
13.
In this paper we derive certain suffcient conditions for starlikeness and con-vexity of orderαof meromorphically multivalent functions in the punctured unit disk. 相似文献
14.
In this paper we derive certain sufficient conditions for starlikeness and convexity of order α of meromorphically multivalent functions in the punctured unit disk. 相似文献
15.
研究negabent函数之间的关系,并利用bent-negabent函数构造出代数次数达到次最优的semibent-negabent函数. 相似文献
16.
In this article,the authors define the derived function of an algeboidal function in the unit disc,prove it is an algabriodal function,and study the order of algebroidal function and that of its derived function in unit circular disc. 相似文献
17.
姚卫红 《数学物理学报(B辑英文版)》2003,(1)
This paper proves a result that if two entire functions f(z) and g(z) share four small functions aj(z) (j = 1,2,3,4) in the sense of Ek)(aj, f) = Ek)(aj,g), (j = 1,2,3,4) (k ≥ 11), then there exists f(z) = g(z). 相似文献
19.
ON ENTIRE FUNCTIONS, BLOCH AND NORMAL FUNCTIONS 总被引:1,自引:0,他引:1
New criteria for an analytic function to be Bloch and for a meromorphic function to benormal are given. These criteria generalize the recently introduced area integral conditionsinvolving a Green's function. 相似文献
20.
In this paper,the characteristic function of the derivative of meromorphic func- tion is studied.A expression of characteristic function T(r,f~1)is given. 相似文献