共查询到20条相似文献,搜索用时 406 毫秒
1.
We prove that, starting at an initial metric
g(0)=e2u0(dx2+dy2)g(0)=e^{2u_{0}}(dx^{2}+dy^{2})
on ℝ2 with bounded scalar curvature and bounded u
0, the Ricci flow ∂
t
g(t)=−R
g(t)
g(t) converges to a flat metric on ℝ2. 相似文献
2.
Clustering of linearly interacting diffusions and universality of their long-time limit distribution
J. M. Swart 《Probability Theory and Related Fields》2000,118(4):574-594
Let K⊂ℝ
d
(d≥ 1) be a compact convex set and Λ a countable Abelian group. We study a stochastic process X in K
Λ, equipped with the product topology, where each coordinate solves a SDE of the form dX
i
(t) = ∑
j
a(j−i) (X
j
(t) −X
i
(t))dt + σ (X
i
(t))dB
i
(t). Here a(·) is the kernel of a continuous-time random walk on Λ and σ is a continuous root of a diffusion matrix w on K. If X(t) converges in distribution to a limit X(∞) and the symmetrized random walk with kernel a
S
(i) = a(i) + a(−i) is recurrent, then each component X
i
(∞) is concentrated on {x∈K : σ(x) = 0 and the coordinates agree, i.e., the system clusters. Both these statements fail if a
S
is transient. Under the assumption that the class of harmonic functions of the diffusion matrix w is preserved under linear transformations of K, we show that the system clusters for all spatially ergodic initial conditions and we determine the limit distribution of
the components. This distribution turns out to be universal in all recurrent kernels a
S
on Abelian groups Λ.
Received: 10 May 1999 / Revised version: 18 April 2000 / Published online: 22 November 2000 相似文献
3.
Sébastien Gouëzel 《manuscripta mathematica》2001,106(3):365-403
We study spectral properties of a transfer operator ℳΦ(x)=∑ω
g
ω(x)Φ(ψω
x) acting on functions of bounded variation. Using a symmetrical integral, we first obtain bounds on its spectral and essential
spectral radii. We then consider the dynamical determinant Det#(Id +zℳ). Our main theorem generalizes to discontinuous weights the result of Baladi and Ruelle (for continuous weights) on the
link between zeroes of the sharp determinant and eigenvalues of the transfer operator. The proof is based on regularizing
the weights and uses a (new) spectral result giving the surjectivity of some applications between eigenspaces of operators.
Received: 8 May 2001 相似文献
4.
We consider the periodic boundary-value problem u
tt
− u
xx
= g(x, t), u(0, t) = u(π, t) = 0, u(x, t + ω) = u(x, t). By representing a solution of this problem in the form u(x, t) = u
0(x, t) + ũ(x, t), where u
0(x, t) is a solution of the corresponding homogeneous problem and ũ(x, t) is the exact solution of the inhomogeneous equation such that ũ(x, t + ω) u x = ũ(x, t), we obtain conditions for the solvability of the inhomogeneous periodic boundary-value problem for certain values of the
period ω. We show that the relation obtained for a solution includes known results established earlier.
__________
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 7, pp. 912–921, July, 2005. 相似文献
5.
You Ming Liu 《数学学报(英文版)》2001,17(3):501-506
Let g(x) ∈L
2(R) and ğ(ω) be the Fourier transform of g(x). Define g
mn
(x) = e
imx
g(x−2πn). In this paper we shall give a sufficient and necessary condition under which {g
mn
(x)} constitutes an orthonormal basis of L
2(R) for compactly supported g(ω) or ˘(ω).
Received March 25, 1999, Revised November 5, 1999, Accepted September 6, 2000 相似文献
6.
Hans M. Dietz 《Statistical Inference for Stochastic Processes》2001,4(3):249-258
Suppose one observes a path of a stochastic processX = (Xt)t≥0 driven by the equation
dXt=θ a(Xt)dt + dWt, t≥0, θ ≥ 0
with a(x) = x or a(x) = |x|α for some α ∈ [0,1) and given initial condition X
0. If the true but unknown parameter θ0 is positive then X is non-ergodic. It is shown that in this situation a trajectory fitting estimator for θ0 is strongly consistent and has the same limiting distribution as the maximum likelihood estimator, but converges of minor
order.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
7.
8.
Let gzs(m, 2k) (gzs(m, 2k+1)) be the minimal integer such that for any coloring Δ of the integers from 1, . . . , gzs(m, 2k) by (the integers from 1 to gzs(m, 2k+1) by ) there exist integers
such that
1. there exists jx such that Δ(xi) ∈ for each i and ∑i=1m Δ(xi) = 0 mod m (or Δ(xi)=∞ for each i);
2. there exists jy such that Δ(yi) ∈ for each i and ∑i=1m Δ(yi) = 0 mod m (or Δ(yi)=∞ for each i); and
1. 2(xm−x1)≤ym−x1.
In this note we show gzs(m, 2)=5m−4 for m≥2, gzs(m, 3)=7m+−6 for m≥4, gzs(m, 4)=10m−9 for m≥3, and gzs(m, 5)=13m−2 for m≥2.
Supported by NSF grant DMS 0097317 相似文献
9.
Let I≥1 be an integer, ω
0=0<ω
1<⋯<ω
I
≤π, and for j=0,…,I, a
j
∈ℂ, a-j=[`(aj)]a_{-j}={\overline{{a_{j}}}}, ω
−j
=−ω
j
, and aj 1 0a_{j}\not=0 if j 1 0j\not=0. We consider the following problem: Given finitely many noisy samples of an exponential sum of the form
[(x)\tilde](k) = ?j=-II ajexp(-iwjk) +e(k), k=-2N,?,2N,\tilde{x}(k)= \sum_{j=-I}^I a_j\exp(-i\omega _jk) +\epsilon (k), \quad k=-2N,\ldots,2N, 相似文献
10.
P. V. Tsynaiko 《Ukrainian Mathematical Journal》1998,50(9):1478-1482
We study a periodic boundary-value problem for the quasilinear equation u
tt
−u
xx
=F[u, u
t
, u
x
], u(x, 0)=u(x, π)=0, u(x + ω, t) = u(x, t), x ∈ ℝ t ∈ [0, π], and establish conditions that guarantee the validity of a theorem on unique solvability.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 9, pp. 1293–1296, September, 1998. 相似文献
11.
The aim of this study is to prove global existence of classical solutions for systems of the form ${\frac{\partial u}{\partial t} -a \Delta u=-f(u,v)}
12.
Jorge J. Betancor Juan C. Fariña Teresa Martinez Lourdes Rodríguez-Mesa 《Arkiv f?r Matematik》2008,46(2):219-250
In this paper we investigate Riesz transforms R
μ
(k) of order k≥1 related to the Bessel operator Δμ
f(x)=-f”(x)-((2μ+1)/x)f’(x) and extend the results of Muckenhoupt and Stein for the conjugate Hankel transform (a Riesz transform of order one). We
obtain that for every k≥1, R
μ
(k) is a principal value operator of strong type (p,p), p∈(1,∞), and weak type (1,1) with respect to the measure dλ(x)=x
2μ+1
dx in (0,∞). We also characterize the class of weights ω on (0,∞) for which R
μ
(k) maps L
p
(ω) into itself and L
1(ω) into L
1,∞(ω) boundedly. This class of weights is wider than the Muckenhoupt class of weights for the doubling measure dλ. These weighted results extend the ones obtained by Andersen and Kerman. 相似文献
13.
We consider the existence and uniqueness of singular solutions for equations of the formu
1=div(|Du|p−2
Du)-φu), with initial datau(x, 0)=0 forx⇑0. The function ϕ is a nondecreasing real function such that ϕ(0)=0 andp>2.
Under a growth condition on ϕ(u) asu→∞, (H1), we prove that for everyc>0 there exists a singular solution such thatu(x, t)→cδ(x) ast→0. This solution is unique and is called a fundamental solution. Under additional conditions, (H2) and (H3), we show the
existence of very singular solutions, i.e. singular solutions such that ∫|x|≤r
u(x,t)dx→∞ ast→0. Finally, for functions ϕ which behave like a power for largeu we prove that the very singular solution is unique. This is our main result.
In the case ϕ(u)=u
q, 1≤q, there are fundamental solutions forq<p*=p-1+(p/N) and very singular solutions forp-1<q<p*. These ranges are optimal.
Dedicated to Professor Shmuel Agmon 相似文献
14.
Yu Liu 《Monatshefte für Mathematik》2012,127(2):41-56
Let
Lf(x)=-\frac1w?i,j ?i(ai,j(·)?jf)(x)+V(x)f(x){\mathcal{L}f(x)=-\frac{1}{\omega}\sum_{i,j} \partial_i(a_{i,j}(\cdot)\partial_jf)(x)+V(x)f(x)} with the non-negative potential V belonging to reverse H?lder class with respect to the measure ω(x)dx, where ω(x) satisfies the A
2 condition of Muckenhoupt and a
i,j
(x) is a real symmetric matrix satisfying l-1w(x)|x|2 £ ?ni,j=1ai,j(x)xixj £ lw(x)|x|2.{\lambda^{-1}\omega(x)|\xi|^2\le \sum^n_{i,j=1}a_{i,j}(x)\xi_i\xi_j\le\lambda\omega(x)|\xi|^2. } We obtain some estimates for VaL-a{V^{\alpha}\mathcal{L}^{-\alpha}} on the weighted L
p
spaces and we study the weighted L
p
boundedness of the commutator [b, Va L-a]{[b, V^{\alpha} \mathcal{L}^{-\alpha}]} when b ? BMOw{b\in BMO_\omega} and 0 < α ≤ 1. 相似文献
15.
We build a version of a thermodynamic formalism for maps
of the form f(z) = ∑
j = 0
p + q
a
j
e
(j−p)z
where p, q > 0 and
. We show in particular the existence and uniqueness of (t,α)-conformal measures and that the Hausdorff dimension HD(J
f
r
) = h is the unique zero of the pressure function t ↦ P(t) for t > 1, where the set J
f
r
is the radial Julia set.
Partially supported by NSF Grant DMS 0100078.
Partially supported by Warsaw University of Technology Grant No. 504G11200023000, Polish KBN Grant No. 2PO3A03425 and Chilean
FONDECYT Grant No. 11060280. 相似文献
16.
Jin Ru Wang 《数学学报(英文版)》2010,26(10):1981-1992
We consider the problem uxx(x, t) = ut(x, t), 0 ≤ x 〈 1, t ≥ 0, where the Cauchy data g(t) is given at x = 1. This is an ill-posed problem in the sense that a small disturbance on the boundary g(t) can produce a big alteration on its solution (if it exists). We shall define a wavelet solution to obtain the well-posed approximating problem in the scaling space Vj. In the previous papers, the theoretical results concerning the error estimate are L2-norm and the solutions aren't stable at x = 0. However, in practice, the solution is usually required to be stable at the boundary. In this paper we shall give uniform convergence on interval x ∈ [0, 1]. 相似文献
17.
Suppose on a probability space (Ω, F, P), a partially observable random process (xt, yt), t ≥ 0; is given where only the second component (yt) is observed. Furthermore assume that (xt, yt) satisfy the following system of stochastic differential equations driven by independent Wiener processes (W1(t)) and (W2(t)): dxt=−βxtdt+dW1(t), x0=0, dyt=αxtdt+dW2(t), y0=0; α, β∞(a,b), a>0. We prove the local asymptotic normality of the model and obtain a large deviation inequality for the maximum likelihood estimator (m.l.e.) of the parameter θ = (α, β). This also implies the strong consistency, efficiency, asymptotic normality and the convergence of moments for the m.l.e. The method of proof can be easily extended to obtain similar results when vector valued instead of one-dimensional processes are considered and θ is a k-dimensional vector. 相似文献
18.
Guoxiang Chen Meiying Wang 《分析论及其应用》2007,23(3):266-273
For a continuous, increasing function ω: R → R \{0} of finite exponential type, this paper introduces the set Z(A, ω) of all x in a Banach space X for which the second order abstract differential equation (2) has a mild solution such that [ω(t)]-1u(t,x) is uniformly continues on R , and show that Z(A, ω) is a maximal Banach subspace continuously embedded in X, where A ∈ B(X) is closed. Moreover, A|z(A,ω) generates an O(ω(t))strongly continuous cosine operator function family. 相似文献
19.
Let ξ,ξ
1,ξ
2,… be positive i.i.d. random variables, S=∑
j=1∞
a(j)ξ
j
, where the coefficients a(j)≥0 are such that P(S<∞)=1. We obtain an explicit form of the asymptotics of −ln P(S<x) as x→0 for the following three cases:
20.
Edgar Reich 《Israel Journal of Mathematics》1977,28(1-2):91-97
Letf(t, z)=z+tω(1/z) be schlicht for ⋎z⋎>1, ω(z) = Σ
n
= 0/∞
a
n
z
n
,t>0. The paper considers first-order estimates for the dilatation of extremal quasiconformal extensions off ast→0.
This work was initiated during the Special Year in Complex Analysis at the Technion, and was supported in parts by the Samuel
Neaman Fund, the Forschungsinstitut für Mathematik, ETH, Zürich, and the National Science Foundation. 相似文献
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