共查询到20条相似文献,搜索用时 234 毫秒
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在空间形式中, 我们构造了一类泛函, 其临界点包括极小与r 极小超曲面. 给出了临界超曲面的代数、微分和变分刻画. 我们证明了Simons 类不存在定理: 在单位球面中不存在稳定的临界超曲面. 同时证明了Alexandrov 类存在性定理: 在欧氏空间中球面是唯一的稳定的临界超曲面. 相似文献
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设Γ 是一些单t- 一致超图的集合. 填充设计Pλ(t, Γ, v) (或覆盖设计Cλ(t, Γ, v)) 是一个二元有序组(X, B), 其中X 是完全t- 一致超图λKv(t) 的顶点集, B 是λKv(t) 的一些子超图的集合, 要求每个子超图都同构于Γ 中的某一个超图, 每个子超图称为是一个区组, 并且满足λKv(t) 中的每一条边至多(或至少) 含在B 的λ 个区组中. 给定参数t, v, λ, Γ, 填充设计Pλ(t, Γ, v) 的最大可能的区组数称为填充数, 记为dλ(t, Γ, v); 覆盖设计Cλ(t, Γ, v) 的最小可能的区组数称为覆盖数, 记为Cλ(t, Γ, v). 本文将确定Γ 中仅含超图K4(3) + e 时的dλ(t, Γ, v) 和Cλ(t, Γ, v) 的精确值. 相似文献
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一般情况下,Gauss光束基模复参量q的ABCD定律对高阶模是不适用的.将某一特定谐振腔的Rayleigh长度ZR取代q参量虚部的光斑尺寸w,q参量的ABCD定律可由Gauss光束基模推广到高阶模或几个模的叠加.从理论和实验上研究并比较了当聚焦镜作长距离飞行时理想光学谐振腔和实际高功率激光谐振腔输出的Gauss光束不同模式的远场聚焦特性,纠正了国内外部分学者对这一问题的误解.飞行光束聚焦特性的研究,对于飞行光学激光加工、光学飞行器、大型激光工程空间滤波器等应用领域具有重要研究价值. 相似文献
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给定一个子群闭的饱和群系F ,定义群类Fpc ,使得G ∈Fpc 当且仅当对于每个子群X ≤G ,存在G的一个F 次正规子群S ,X≤S并且X在S中F 次反正规 .借助F投射子和F覆盖子群 ,给出了Fpc群的特征 . 相似文献
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O. M. Fomenko 《Journal of Mathematical Sciences》2005,129(3):3898-3909
Let Sk(N)+ be the set of primitive cusp forms of even weight k for Γ0(N) and let L(s, sym
2f) be the symmetric square L-function L(s, f) of a form f ∈ Sk(N)+. The moments of the variable L(1, sym
2f), f ∈ S2(N)+, are computed for N = p, and the corresponding limiting distribution is determined in N-aspect. Let f ∈ Sk(1)+, g ∈ Sl(1)+, and ωf = Γ(k - 1)/(4π)k-1 〈f, f〉. Asymptotic formulas for
and
as k → ∞ are obtained. Bibliography: 17 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 302, 2003, pp. 149–167. 相似文献
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O. M. Fomenko 《Journal of Mathematical Sciences》2006,133(6):1733-1748
Let Sk(Γ) be the space of holomorphic Γ-cusp forms f(z) of even weight k ≥ 12 for Γ = SL(2, ℤ), and let Sk(Γ)+ be the set of all Hecke eigenforms from this space with the first Fourier coefficient af(1) = 1. For f ∈ Sk(Γ)+, consider the Hecke L-function L(s, f). Let
It is proved that for large K,
where ε > 0 is arbitrary. For f ∈ Sk(Γ)+, let L(s, sym
2 f) denote the symmetric square L-function. It is proved that as k → ∞ the frequence
converges to a distribution function G(x) at every point of continuity of the latter, and for the corresponding characteristic
function an explicit expression is obtained. Bibliography: 17 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 314, 2004, pp. 221–246. 相似文献
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Valentin Blomer 《Mathematische Zeitschrift》2008,260(4):755-777
Let S
k
(N, χ) be the space of cusp forms of weight k, level N and character χ. For let L(s, sym2
f) be the symmetric square L-function and be the Rankin–Selberg square attached to f. For fixed k ≥ 2, N prime, and real primitive χ, asymptotic formulas for the first and second moment of the central value of L(s, sym2
f) and over a basis of S
k
(N, χ) are given as N → ∞. As an application it is shown that a positive proportion of the central values L(1/2, sym2
f) does not vanish.
The author was supported by NSERC grant 311664-05. 相似文献
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Hari Bercovici 《Complex Analysis and Operator Theory》2007,1(3):335-339
Consider a domain
, and two analytic matrix-valued functions functions
. Consider also points
and positive integers n
1, n
2, . . . , n
N
. We are interested in the existence of an analytic function
such that X(ω) is invertible, and G(ω) coincides with X(ω)F(ω)X(ω)−1 up to order n
j
at the point ω
j
. We will see that such a function exists provided that F(ω
j
),G(ω
j
) have cyclic vectors, and the characteristic polynomials of F,G coincide up to order n
j
at ω
j
. This allows one to give a short proof to a result of Huang, Marcantognini and Young concerning spectral interpolation in
the unit disk.
The author was partially supported by a grant from the National Science Foundation.
Received: September 8, 2006. Accepted: January 11, 2007. 相似文献
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P. Jacob 《Discrete Mathematics》2009,309(4):878-886
A bijection is presented between (1): partitions with conditions fj+fj+1≤k−1 and f1≤i−1, where fj is the frequency of the part j in the partition, and (2): sets of k−1 ordered partitions (n(1),n(2),…,n(k−1)) such that and , where mj is the number of parts in n(j). This bijection entails an elementary and constructive proof of the Andrews multiple-sum enumerating partitions with frequency conditions. A very natural relation between the k−1 ordered partitions and restricted paths is also presented, which reveals our bijection to be a modification of Bressoud’s version of the Burge correspondence. 相似文献
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M. S. Eremin 《Mathematical Notes》1976,20(6):1043-1048
For n2 we consider a differential operatorL [y] z
n
y
(n) +P
1(z)z
n–1
y
(n–1) +P
2
(z)z
n–2
y
n–2
+ ...+P
n
(z)y = y, p
1
(z), ..., P
n
(z) A
R
: here ar is the space of functions which are analytic in the disk ¦z¦ < R, equipped with the topology of compact convergence. We prove the existence of sequences {fk(z)}
k
=o, consisting of a finite number of associated functions of the operator L and an infinite number of its eigenfunctions; we show that the sequence forms a basis in Ar for an arbitrary r, 0 < r <- R; and we establish some additional properties of the sequence
0
(z),
1
(z),...,
d–1
(z), f
d
(z), f
d+1
(z),...
Translated from Matematicheskie Zametki, Vol. 20, No. 6, pp. 869–878, December, 1976. 相似文献
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In this paper, we consider the following Reinhardt domains. Let M = (M1, M2,..., Mn) : [0,1] → [0,1]^n be a C2-function and Mj(0) = 0, Mj(1) = 1, Mj″ 〉 0, C1jr^pj-1 〈 Mj′(r) 〈 C2jr^pj-1, r∈ (0, 1), pj 〉 2, 1 ≤ j ≤ n, 0 〈 C1j 〈 C2j be constants. Define
DM={z=(z1,z2,…,Zn)^T∈C^n:n∑j=1 Mj(|zj|)〈1}
Then DM C^n is a convex Reinhardt domain. We give an extension theorem for a normalized biholomorphic convex mapping f : DM -→ C^n. 相似文献
DM={z=(z1,z2,…,Zn)^T∈C^n:n∑j=1 Mj(|zj|)〈1}
Then DM C^n is a convex Reinhardt domain. We give an extension theorem for a normalized biholomorphic convex mapping f : DM -→ C^n. 相似文献
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O. M. Fomenko 《Journal of Mathematical Sciences》2007,143(3):3174-3181
Let f(z) be a holomorphic Hecke eigencuspform of even weight k with respect to SL(2, Z) and let L(s, sym
2 f) = ∑
n=1
∞
cnn−s, Re s > 1, be the symmetric square L-function associated with f.
Represent the Riesz mean (ρ ≥ 0)
as the sum of the “residue function” Γ(ρ+1)−1 Ł(0, sym2f)xρ and the “error term”
.
Using the Voronoi formula for Δρ(x;sym
2f), obtained earlier (see Zap. Nauchn. Semin. POMI. 314, 247–256 (2004)), the integral
is estimated. In this way, an asymptotics for 0 < ρ ≤ 1 and an upper bound for ρ = 0 are obtained. Also the existence of
a limiting distribution for the function
, and, as a corollary, for the function
, is established. Bibliography: 12 titles.
Dedicated to the 100th anniversary of G. M. Goluzin’s birthday
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 337, 2006, pp. 274–286. 相似文献
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We discuss the construction of finite difference schemes for the two-point nonlinear boundary value problem:y
(2n)+f(x,y)=0,y
(2j)(a)=A
2j
,y
(2j)(b)=B
2j
,j=0(1)n–1,n2. In the case of linear differential equations, these finite difference schemes lead to (2n+1)-diagonal linear systems. We consider in detail methods of orders two, four and six for two-point boundary value problems involving a fourth order differential equation; convergence of these methods is established and illustrated by numerical examples. 相似文献