共查询到20条相似文献,搜索用时 31 毫秒
1.
Kai WANG 《数学年刊B辑(英文版)》2007,28(3):321-326
Let M be an invariant subspace of Hv2. It is shown that for each f∈M⊥, f can be analytically extended across (?)Bd\σ(Sz1,…, Szd). 相似文献
2.
E.M.E.ZAYED 《数学学报(英文版)》2004,20(2):209-222
The asymptotic expansion for small |t| of the trace of the wave kernel ∧↑μ(t) =∑v=1^∞exp(-it μv^1/2), where i= √-1 and {μv}v=1^∞ are the eigenvalues of the negative Laplacian -△=-∑β=1^2(δ/δx^β)^2 in the (x^1, x^2)-plane, is studied for a multi-connected vibrating membrane Ω in R^2 surrounded by simply connected bounded domains Ωj with smooth boundaries δΩj(j=1,...,n), where a finite number of piecewise smooth Robin boundary conditions on the piecewise smooth components Гi(i=1 κj-1,...,κj) of the boundaries δΩj are considered, such that δΩj=∪i=1 κj-1^κj Гi and κ0=0. The basic problem is to extract information on the geometry of Ω using the wave equation approach. Some geometric quantities of Ω (e.g. the area of Ω, the total lengths of its boundary, the curvature of its boundary, the number of the holes of Ω, etc.) are determined from the asymptotic expansion of the trace of the wave kernel ∧↑μ(t) for small |t|. 相似文献
3.
By means of a method of analytic number theory the following theorem is proved. Letp be a quasi-homogeneous linear partial differential operator with degreem,m > 0, w.r.t a dilation
given by ( a1, …, an). Assume that either a1, …, an are positive rational numbers or
for some
Then the dimension of the space of polynomial solutions of the equationp[u] = 0 on ℝn must be infinite 相似文献
4.
Let Γ be the set of all permutations of the natural series and let α = {α j}
j∈ℕ, ν = {νj}
j∈ℕ, and η = {ηj}
j∈ℕ be nonnegative number sequences for which
is defined for all γ:= {γ(j)}
j∈ℕ ∈ Γ and η ∈ l
p. We find
in the case where 1 < p < ∞.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 10, pp. 1430–1434, October, 2005. 相似文献
5.
E.M.E.ZAYED 《数学学报(英文版)》2003,19(4):679-694
The asymptotic expansions of the trace of the heat kernel θ(t)=∑^∞v=1^exp(-tλv) for small positive t,where {λv} are the eigenvalues of the negative Laplacian -△n=-∑^ni=1(D/Dx^1)^2 in R^2(n=2 or 3),are studied for a general annular bounded domain Ω with a smooth inner boundary DΩ1 and a smooth outer boundary DΩ2,where a finite number of piecewise smooth Robin boundary conditions(D/Dnj γh)Ф=0 on the components Гj(j= 1,...,m) of (DΩ1 and on the components Гj (j=k 1,…,m) of of DΩ2 are considered such that DΩl=U^kj=lГj and DΩ2= U^m=k 1Гj and where the coefficients γj(j=1,...,m) are piecewise smooth positive functions. Some applications of θ(t) for an ideal gas enclosed in the general annular bounded domain Ω are given. Further results are also obtained. 相似文献
6.
S. Ya. Khavinson 《Mathematical Notes》1999,65(5):620-626
Suppose thatG is a finitely connected domain with rectifiable boundary γ, ∞εG, the domainsD
1,...,D
s
are the complements ofG, the subsetsF
j
⊂D
j
are infinite and compact,n
j
≥1,j=1,...,s, are integers, λ0 is a complex-valued measure on γ, and
We consider the extremum problem
where μ
j
,j=1,...,s, are complex-valued measures onF
j
and
are Golubev sums. We prove that β=Δ, where
We also establish several other relations between these and other extremal variables.
Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 738–745, May, 1999. 相似文献
7.
It is proposed that the Gaussian type distribution constantb
qi in the Gaussian model depends on the coordination numberq
i of sitei, and that the relation
holds amongb
qi
’s. The Gaussian model is then studied on a family of the diamond-type hierarchical (or DH) lattices, by the decimation real-space
renormalization group following spin-rescaling method. It is found that the magnetic property of the Gaussian model belongs
to the same universal class, and that the critical pointK* and the critical exponentv are given by
and
, respectively.
Project supported by the National Natural Science Foundation of China (Grant No. 19775008), the National Basic Research
Project supported by the National Natural Science Foundation of China (Grant No. 19775008), the National Basic Research
Project supported by the National Natural Science Foundation of China (Grant No. 19775008), the National Basic Research 相似文献
8.
9.
Let {A, B} and {C, D} be diagonalizable pairs of order n, i.e., there exist invertible matrices P, Q and X, Ysuchthat A = P∧Q, B = PΩQ, C =XГY, D= X△Y, where
∧ = diag(α1, α2, …, αn), Ω= diag(βl, β2, …βn),
Г=diag(γ1,γ2,…,γn), △=diag(δl,δ2,…,δn).
Let ρ((α,β), (γ,δ))=|αδ-βγ|/√|α|^2+|β|^2√|γ|^2+|δ|^2.In this paper, it will be proved that there is a permutation τ of {1,2,... ,n} such that
n∑i=1[ρ((αi,βi),(γτ(i),δτ(i)))]^2≤n[1-1/κ^2(Y)κ^2(Q)(1-d2F(Z,W)/n)],
where κ(Y) = ||Y||2||Y^-1||2,Z= (A,B),W= (C, D) and dF(Z,W) = 1/√2||Pz* -Pw*||F. 相似文献
∧ = diag(α1, α2, …, αn), Ω= diag(βl, β2, …βn),
Г=diag(γ1,γ2,…,γn), △=diag(δl,δ2,…,δn).
Let ρ((α,β), (γ,δ))=|αδ-βγ|/√|α|^2+|β|^2√|γ|^2+|δ|^2.In this paper, it will be proved that there is a permutation τ of {1,2,... ,n} such that
n∑i=1[ρ((αi,βi),(γτ(i),δτ(i)))]^2≤n[1-1/κ^2(Y)κ^2(Q)(1-d2F(Z,W)/n)],
where κ(Y) = ||Y||2||Y^-1||2,Z= (A,B),W= (C, D) and dF(Z,W) = 1/√2||Pz* -Pw*||F. 相似文献
10.
In studying local harmonic analysis on the sphere Sn, R.S. Strichartz introduced certain zonal functions ϕ2(d(x, y)) which satisfy the equation
, where Δz is the Laplace operator and δ−y the Dirac measure. The explicit expression of the constant a (λ) is given by R.S. Strichartz in the case that n is odd. Appyling
the Apéry identity, we show in this paper that
for n even, where wn-1 is the surface area of Sn-1,
.
The author's research was supported by a grant from NSFC. 相似文献
11.
Suppose that X is a complex Banach space with the norm ‖·‖ and n is a positive integer with dim X ⩾ n ⩾ 2. In this paper, we consider the generalized Roper-Suffridge extension operator $
\Phi _{n,\beta _2 ,\gamma _2 , \ldots ,\beta _{n + 1} ,\gamma _{n + 1} } (f)
$
\Phi _{n,\beta _2 ,\gamma _2 , \ldots ,\beta _{n + 1} ,\gamma _{n + 1} } (f)
on the domain $
\Omega _{p_1 ,p_2 , \ldots ,p_{n + 1} }
$
\Omega _{p_1 ,p_2 , \ldots ,p_{n + 1} }
defined by
$
\Phi _{n,\beta _2 ,\gamma _2 , \ldots ,\beta _{n + 1} ,\gamma _{n + 1} } (f)(x) = {*{20}c}
{\sum\limits_{j = 1}^n {\left( {\frac{{f(x_1^* (x))}}
{{x_1^* (x)}}} \right)} ^{\beta _j } (f'(x_1^* (x)))^{\gamma _j } x_1^* (x)x_j } \\
{ + \left( {\frac{{f(x_1^* (x))}}
{{x_1^* (x)}}} \right)^{\beta _{n + 1} } (f'(x_1^* (x)))^{\gamma _{n + 1} } \left( {x - \sum\limits_{j = 1}^n {x_1^* (x)x_j } } \right)} \\
$
\Phi _{n,\beta _2 ,\gamma _2 , \ldots ,\beta _{n + 1} ,\gamma _{n + 1} } (f)(x) = \begin{array}{*{20}c}
{\sum\limits_{j = 1}^n {\left( {\frac{{f(x_1^* (x))}}
{{x_1^* (x)}}} \right)} ^{\beta _j } (f'(x_1^* (x)))^{\gamma _j } x_1^* (x)x_j } \\
{ + \left( {\frac{{f(x_1^* (x))}}
{{x_1^* (x)}}} \right)^{\beta _{n + 1} } (f'(x_1^* (x)))^{\gamma _{n + 1} } \left( {x - \sum\limits_{j = 1}^n {x_1^* (x)x_j } } \right)} \\
\end{array}
相似文献
12.
We give the “boundary version” of the Boggess-PolkingCR extension theorem. LetM andN be real generic submanifolds of ℂ
n
withN ⊂M and letV be a “wedge” inM with “edge”N and “profile” Σ ⊂T
NM in a neighborhood of a pointz
o.We identify in natural manner
and assume that for a holomorphic vector fieldL tangent toM and verifying
we have that the Levi form
takes a value
. Then we prove thatCR functions onV extend ∀ω to a wedgeV
1 “attached” toV in direction of a vector fieldiV such that |pr(iV(z
0))−iv
0| < ε (where pr is the projection pr:T
NX →T
MX |
N
).We then prove that when the Levi cone “relative to Σ”iZ
Σ = convex hull
is open inT
MX, thenCR functions extend to a “full” wedge with edgeN (that is, with a profile which is an open cone ofT
NX). Finally, we prove that iff is defined in a couple of wedges ±V with profiles ±Σ such thatiZ
Σ =T
MX, and is continuous up toN, thenf is in fact holomorphic atz
o. 相似文献
13.
For x = (x 1, x 2, ..., x n ) ∈ ℝ+ n , the symmetric function ψ n (x, r) is defined by $\psi _n (x,r) = \psi _n \left( {x_1 ,x_2 , \cdots ,x_n ;r} \right) = \sum\limits_{1 \leqslant i_1 < i_2 \cdots < i_r \leqslant n} {\prod\limits_{j = 1}^r {\frac{{1 + x_{i_j } }}
{{x_{i_j } }}} } ,$\psi _n (x,r) = \psi _n \left( {x_1 ,x_2 , \cdots ,x_n ;r} \right) = \sum\limits_{1 \leqslant i_1 < i_2 \cdots < i_r \leqslant n} {\prod\limits_{j = 1}^r {\frac{{1 + x_{i_j } }}
{{x_{i_j } }}} } , 相似文献
14.
In this paper,we explore some weakly consistent properties of quasi-maximum likelihood estimates(QMLE) concerning the quasi-likelihood equation in=1 Xi(yi-μ(Xiβ)) = 0 for univariate generalized linear model E(y |X) = μ(X'β).Given uncorrelated residuals {ei = Yi-μ(Xiβ0),1 i n} and other conditions,we prove that βn-β0 = Op(λn-1/2) holds,where βn is a root of the above equation,β0 is the true value of parameter β and λn denotes the smallest eigenvalue of the matrix Sn = ni=1 XiXi.We also show that the convergence rate above is sharp,provided independent non-asymptotically degenerate residual sequence and other conditions.Moreover,paralleling to the elegant result of Drygas(1976) for classical linear regression models,we point out that the necessary condition guaranteeing the weak consistency of QMLE is Sn-1→ 0,as the sample size n →∞. 相似文献
15.
S. V. Kislyakov 《Journal of Mathematical Sciences》2009,156(5):824-833
Let 1 < r < 2 and let b is a weight on ℝ such that satisfies the Muckenhoupt condition Ar′/2 (r′ is the exponent conjugate to r). If fj are functions whose Fourier transforms are supported on mutually disjoint intervals, then
16.
V. A. Kofanov 《Ukrainian Mathematical Journal》2008,60(10):1557-1573
We obtain a new sharp inequality for the local norms of functions x ∈ L
∞, ∞
r
(R), namely,
17.
If P(z) is a polynomial of degree n which does not vanish in |z| 1,then it is recently proved by Rather [Jour.Ineq.Pure and Appl.Math.,9 (2008),Issue 4,Art.103] that for every γ 0 and every real or complex number α with |α|≥ 1,{∫02π |D α P(e iθ)| γ dθ}1/γ≤ n(|α| + 1)C γ{∫02π|P(eiθ)| γ dθ}1/γ,C γ ={1/2π∫0 2π|1+eiβ|γdβ}-1/γ,where D α P(z) denotes the polar derivative of P(z) with respect to α.In this paper we prove a result which not only provides a refinement of the above inequality but also gives a result of Aziz and Dawood [J.Approx.Theory,54 (1988),306-313] as a special case. 相似文献
18.
Feng-de Chen Jin-lin Shi School of Mathematics Computer Fuzhou University Fuzhou China 《应用数学学报(英文版)》2005,21(1):49-60
With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of the following nonlinear state dependent delays predator-prey system where a_i(t),c_j(t),d_i(t) are continuous positive periodic functions with periodic ω>0, b_1(t),b_2(t) are continuous periodic functions with periodic ωand ∫_0~ωbi(t)dt>0. T_i,σ_j, p_i (i=1,2,…,n, j=1, 2,…,m) are continuous and ω-periodic with respect to their first arguments, respectively, α_i, β_j,γ_i(i=1,2,…,n, j=1,2, …, m) are positive constants. 相似文献
19.
Jiecheng CHEN Dashan FAN Huoxiong WU Xiangrong ZHU 《Frontiers of Mathematics in China》2011,6(1):49-59
Let Q
2 = [0, 1]2 be the unit square in two-dimensional Euclidean space ℝ2. We study the L
p
boundedness of the oscillatory integral operator T
α,β
defined on the set ℒ(ℝ2+n
) of Schwartz test functions by
|
设为首页 | 免责声明 | 关于勤云 | 加入收藏 |
Copyright©北京勤云科技发展有限公司 京ICP备09084417号 |