一个点态“o”饱和定理

1. Suppose dμ_p(p∈Ω) is a non-negative Borel measure on [-π,π] with 1/π integral from -π to π(dμ_p(t))=1For k∈N, denote a_(kp)=1/π integral from -π to π(coskx) dμ_p(x),     

NUMERICALLY SOLVING PERIODICALLY PERTURBED CONSERVATIVE SYSTEMS BY PARAMETER EMBEDDING METHODS

1　IntroductionConsider the system of differential equationsTu≡ u"+ F( t,u) =0 ( 1 )where F:R×Rn→Rnis a continuos function of2 π-period with respect to tand F( t,· )∈ C1( Rn,Rn) has a symmetric derivative for all t∈R and allξ∈Rn.When the system is of the formu"+ grad G( u) =e( t) ( 2 )where G∈C2 ( Rn,R) ,e:R→Rncontinuousand2 π-periodic.Equation( 2 ) can be interpreted asthe Newtonian equation ofmotion ofa mechanicalsystem subjectto conservative internal forcesand periodic e…     

A NEW FAMILY OF FILTRATION s＋6 IN THE STABLE HOMOTOPY GROUPS OF SPHERES

In the year 2002, Lin detected a nontrivial family in the stable homotopy groups of spheres πt-6S which is represented by hngor3 ∈ ExtA6,t(Zp,Zp) in the Adams spectral sequence, where t=2pn(p-1) 6(p2 p 1)(p-1) and p≥7 is a prime number.This article generalizes the result and proves the existence of a new nontrivial family of filtration s 6 in the stable homotopy groups of spheres πt1-s-6S which is represented by hngors 3 6 ExtAs 6,t1(Zp, Zp) in the Adams spectral sequence, where n≥4, 0≤s相似文献   

Tensor products of complementary series of rank one Lie groups

We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β)for small parameters α and β(in our parametrization). We prove further that for SO_0(n, 1) there are finitely many complementary series of the form π_(α+β+2j,)j = 0, 1,..., k, appearing in the tensor product π_α ? π_βof two complementary series π_α and π_β, where k = k(α, β, n) depends on α, β and n.     

对新题征展(31)第3题的订正

题　已知复数 z满足条件 | z| =1 ,求| z - i| .| z - 12 32 - i|的最大值 .解法 1　设 z =cosθ isinθ,其中θ∈[0 ,2π) ,| z - i| =| cosθ i( sinθ - 1 ) |= cos2 θ ( sinθ - 1 ) 2 =2 ( 1 - sinθ)= 2 [1 - cos( π2 -θ) ]=2 | sin( π4 - θ2 ) || z - 12 32 i|= | ( cosθ - 12 ) i( sinθ 32 ) |= ( cosθ - 12 ) 2 ( sinθ 32 ) 2= 2 2 sin(θ - π6 )=2 [1 cos( 2π3-θ) ]=2 .2 cos2 ( π3- θ2 )=2 | cos( π3- θ2 ) | .则　 | z - i| .| z - 12 32 i|=4 | sin( π4 - θ2 ) .cos( π3- θ2 ) |=…     

Errata for“The Approximate Valuesof Certain SeriesInvolving the Prowersof Generalized Fibonacciand Lucas Numbers

On page1 5 8,( 6) ,( 7) ,( 8) ,and( 9) should be,respectively:∑∞n=1α4nU22 n U22 n+ 2≈ ΔV2p2 α212 4 - 18lnα+ π296( lnα) 2 - 3α4p4,∑∞n=0α4nV22 n V22 n+ 2≈ V2Δα2 p218+ 18lnα+ π24 ( lnα) 2 ( eπ2 / ( 2 lnα) - 2 ) - 14Δα4p2 - 1Δα2 Δ p3 ,∑∞n=0α4nU22 n+ 1U22 n+ 3≈ ΔV2p2 α418lnα- π24 ( eπ2 / ( 2 lnα) + 2 ) ( lnα) 2 - 1α6p2 - 2α5p3 ,∑∞n=0α4nV22 n+ 1V22 n+ 3≈ V2Δα4p2π24 ( lnα) 2 ( 2 eπ2 / lnα + 1 ) + π232 ( lnα) 2 - 18lnα - 1Δα6p4- 2Δα5p4Δ.In t…     

不等式研究成果集锦(14)

169.在△ ABC中 ,i)若 m、n、k∈ N,则msin Am nsin Bn ksin Ck　≤ (m n k) sin πm n k;mcos Am ncos Bn kcos Ck　≤ (m n k) cos πm n k;ii)若 m、n、k∈ N,且 m、n、k≥ 2 ,则mtan Am ntan Bn ktan Ck　≥ (m n k) tan πm n k;mcot Am ncot Bn kcot Ck　≥ (m n k) cot πm n k,(郭成伟 ,2 0 0 0 ,4)1 70 .在△ ABC中 ,BC、CA、AB边上的高线、角平分线以及对应的傍切圆半径分别为ha、hb、hc、ta、tb、tc、ra、rb、rc.则i) ∑ rahb hc≥ ∑ raha ra;ii) ∑ r2at2b t2c≥ 2 ∑sin2 A2 .(万家练 ,2 0 …     

一道高考试题的几种解法

题目 ( 1994年全国高考文科试题 )如果函数ｙ =ｓｉｎ2ｘ ａｃｏｓ2ｘ的图象关于直线ｘ =- π8对称 ,那么ａ = (　　 )(Ａ) 2 .　 (Ｂ) - 2 .　 (Ｃ) 1.　 (Ｄ) - 1.解法 1　因 ｙ =ｓｉｎ2ｘ ａｃｏｓ2ｘ =1 ａ2·ｓｉｎ( 2ｘ φ) ,且其图象关于直线ｘ =- π8对称 ,所以 ,直线ｘ =- π8必经过图象的波峰或波谷 ,从而有ｓｉｎ( - π4 ) ａｃｏｓ( - π4 ) =± 1 ａ2 ,即 ( - 1 ａ) 2= 2 ( 1 ａ2 ) ,得ａ =- 1,应选 (Ｄ) .解法 2　因函数ｙ =ｓｉｎ2ｘ ａｃｏｓ2ｘ的图象关于直线ｘ =- π8对称 ,所以 ,把它沿着ｘ轴向右平移π8单位 ,得…     

2003年全国高考数学试题另解摘编（待续）

20 0 3年高考试题中 ,考生普遍反映计算量偏大 .考生由于客观题占用时间太长 ,导致后面的题做不完 .其实灵活应用多种解法 (如估算、图解法、排除法、特例处理等 )来处理客观题是完全可以避免这种情形的发生的 .以下是从来稿中撷取的关于客观题的非常规的解法 .理科 ( 1 )题　已知x∈ (- π2 ,0 ) ,cosx =45 ,则tan2x = (　　 )(A) 72 4 .　 (B) - 72 4 .　 (C) 2 47.　 (D) - 2 47.另解 1(估算 )　∵x∈ (- π2 ,0 ) ,cosx =45 ∈(22 ,32 ) ,∴ - π4 相似文献   

THE PERIODIC HARRY-DYM EQUATION

The development of the inverse scattering transform(I.S.T)has made it possible tosolve certain physically significant nonlinear evolution equations with periodic boundaryconditions.Date and Tanaka have considered kdv equation;Ma and Ablowitz havediscussed the cubic Schrodinger equation.In this paper,following closely the analysis in[2,3]the author considers Harry-Dym eqution(q~2)_t=-2r_(xxx)(Ⅰ)where q(x,t)is periodic in x with period π for all time q(x,t)=q(x π,t),q(x,t)=r~(-1)(x,t)>0