共查询到20条相似文献,搜索用时 31 毫秒
1.
2.
In this paper, we study the ill-posdness of the Cauchy problem for semilinear wave equation with very low regularity, where
the nonlinear term depends on u and ∂
t
u. We prove a ill-posedness result for the “defocusing” case, and give an alternative proof for the supercritical “focusing”
case, which improves the result in Fang and Wang (Chin. Ann. Math. Ser. B 26(3), 361–378, 2005).
Supported by NSF of China 10571158. 相似文献
3.
The paper presents the theory of the discontinuous Galerkin finite element method for the space-time discretization of a linear
nonstationary convection-diffusion-reaction initial-boundary value problem. The discontinuous Galerkin method is applied separately
in space and time using, in general, different nonconforming space grids on different time levels and different polynomial
degrees p and q in space and time discretization, respectively. In the space discretization the nonsymmetric interior and boundary penalty
approximation of diffusion terms is used. The paper is concerned with the proof of error estimates in “L
2(L
2)”-and “
”-norms, where ɛ ⩾ 0 is the diffusion coefficient. Using special interpolation theorems for the space as well as time discretization,
we find that under some assumptions on the shape regularity of the meshes and a certain regularity of the exact solution,
the errors are of order O(h
p
+ τ
q
). The estimates hold true even in the hyperbolic case when ɛ = 0. 相似文献
4.
Grahame Bennett 《Positivity》2007,11(2):231-238
We show how certain simple ℓp–inequalities may be proved by “ignoring the p.” An application to moment sequences is considered. 相似文献
5.
James Borger 《Mathematische Annalen》2011,351(4):877-933
6.
The score tests of independence in multivariate extreme values derived by Tawn (Tawn, J.A., “Bivariate extreme value theory:
models and estimation,” Biometrika 75, 397–415, 1988) and Ledford and Tawn (Ledford, A.W. and Tawn, J.A., “Statistics for near independence in multivariate
extreme values,” Biometrika 83, 169–187, 1996) have non-regular properties that arise due to violations of the usual regularity conditions of maximum
likelihood. Two distinct types of regularity violation are encountered in each of their likelihood frameworks: independence
within the underlying model corresponding to a boundary point of the parameter space and the score function having an infinite
second moment. For applications, the second form of regularity violation has the more important consequences, as it results
in score statistics with non-standard normalisation and poor rates of convergence. The corresponding tests are difficult to
use in practical situations because their asymptotic properties are unrepresentative of their behaviour for the sample sizes
typical of applications, and extensive simulations may be needed in order to evaluate adequately their null distribution.
Overcoming this difficulty is the primary focus of this paper.
We propose a modification to the likelihood based approaches used by Tawn (Tawn, J.A., “Bivariate extreme value theory: models
and estimation,” Biometrika 75, 397–415, 1988) and Ledford and Tawn (Ledford, A.W. and Tawn, J.A., “Statistics for near independence in multivariate
extreme values,” Biometrika 83, 169–187, 1996) that provides asymptotically normal score tests of independence with regular normalisation and rapid convergence.
The resulting tests are straightforward to implement and are beneficial in practical situations with realistic amounts of
data.
AMS 2000 Subject Classification Primary—60G70
Secondary—62H15 相似文献
7.
L.C. Evans R.F. Gariepy 《Calculus of Variations and Partial Differential Equations》1999,9(4):357-372
We prove a partial regularity assertion for a Lipschitz continuous mapping u in the plane that minimizes an appropriate convex (or quasiconvex) energy functional, under the “hard” constraint that det
D
u = 1 a.e. The primary technical assumption is that u be nondegenerate, meaning that, locally, at least one of its partial derivatives is bounded away from zero a.e. The method of proof is to
convert to a related minimization problem for a generating function w, the advantage being that we now have the “soft” constraint .
Received March 16, 1999 / Accepted April 23, 1999 相似文献
8.
It is shown that thep-summing norm of any operator withn-dimensional domain can be well-aproximated using only “few” vectors in the definition of thep-summing norm. Except for constants independent ofn and logn factors, “few” meansn if 1<p<2 andn
p/2 if 2<p<∞.
Supported in part by NSF #DMS90-03550 and the U.S.-Israel Binational Science Foundation.
Supported in part by the U.S.-Israel Binational Science Foundation. 相似文献
9.
Jussi Klemelä 《Probability Theory and Related Fields》2006,134(4):539-564
Estimation of a quadratic functional of a function observed in the Gaussian white noise model is considered. A data-dependent
method for choosing the amount of smoothing is given. The method is based on comparing certain quadratic estimators with each
other. It is shown that the method is asymptotically sharp or nearly sharp adaptive simultaneously for the “regular” and “irregular”
region. We consider lp bodies and construct bounds for the risk of the estimator which show that for p=4 the estimator is exactly optimal and for example when p ∈[3,100], then the upper bound is at most 1.055 times larger than the lower bound. We show the connection of the estimator
to the theory of optimal recovery. The estimator is a calibration of an estimator which is nearly minimax optimal among quadratic
estimators.
Writing of this article was financed by Deutsche Forschungsgemeinschaft under project MA1026/6-2, CIES, France, and Jenny
and AnttiWihuri Foundation. 相似文献
10.
François Ledrappier Mark Pollicott 《Bulletin of the Brazilian Mathematical Society》2005,36(2):143-176
In this paper we study the ergodic properties of the linear action of lattices Γ of SL(2,ℚp) on ℚp × ℚp and distribution results for orbits of Γ. Following Serre, one can define a “geodesic flow” for an associated tree (actually
associated to GL(2,ℚp)). The approach we use is based on an extension of this approach to “frame flows” which are a natural compact group extension
of the geodesic flow. 相似文献
11.
This paper deals with sparse approximations by means of convex combinations of elements from a predetermined “basis” subsetS of a function space. Specifically, the focus is on therate at which the lowest achievable error can be reduced as larger subsets ofS are allowed when constructing an approximant. The new results extend those given for Hilbert spaces by Jones and Barron,
including, in particular, a computationally attractive incremental approximation scheme. Bounds are derived for broad classes
of Banach spaces; in particular, forL
p spaces with 1<p<∞, theO (n
−1/2) bounds of Barron and Jones are recovered whenp=2.
One motivation for the questions studied here arises from the area of “artificial neural networks,” where the problem can
be stated in terms of the growth in the number of “neurons” (the elements ofS) needed in order to achieve a desired error rate. The focus on non-Hilbert spaces is due to the desire to understand approximation
in the more “robust” (resistant to exemplar noise)L
p, 1 ≤p<2, norms.
The techniques used borrow from results regarding moduli of smoothness in functional analysis as well as from the theory of
stochastic processes on function spaces. 相似文献
12.
The authors consider quasilinear parabolic systems
in two space dimensions. The function a has p-growth behaviour, 1< p < ∞, and the ellipticity “constant” behaves like (1+|∇u|)
p
− 2. The author prove full regularity of the weak solution on interior subdomains, but globally in time. The key idea in the
proof is a technique to obtain boundedness of the gradient based on logarithmic estimates.
Received: 8 July 1998 / Revised version: 19 February 1999 相似文献
13.
Dmitrii Zinoviev 《Israel Journal of Mathematics》1998,106(1):29-77
We relate the “Fourier” orbital integrals of corresponding spherical functions on thep-adic groups SO(5) and PGL(2). The correspondence is defined by a “lifting” of representations of these groups. This is a
local “fundamental lemma” needed to compare the geometric sides of the global Fourier summation formulae (or relative trace
formulae) on these two groups. This comparison leads to conclusions about a well known lifting of representations from PGL(2)
to PGSp(4). This lifting produces counter examples to the Ramanujan conjecture. 相似文献
14.
Gregory Hill 《manuscripta mathematica》1994,82(1):293-311
15.
We study the R-controllability (the controllability within the attainability set) and the R-observability of time-varying linear differential-algebraic equations (DAE). We analyze DAE under assumptions guaranteeing
the existence of a structural form (which is called “equivalent”) with separated “differential” and “algebraic” subsystems.
We prove that the existence of this form guarantees the solvability of the corresponding conjugate system, and construct the
corresponding “equivalent form” for the conjugate DAE. We obtain conditions for the R-controllability and R-observability, in particular, in terms of controllability and observability matrices. We prove theorems that establish certain
connections between these properties. 相似文献
16.
Shyūichi Izumiya 《manuscripta mathematica》1979,28(4):337-360
In his paper [2], Bierstone proves the equivariant Gromov theorem which is an integrability theorem for “open regularity condition”
of equivariant sections of a smooth G-fibre bundle under the assumption that all orbit bundles of base manifold are non-closed.
Here, we prove the result without his assumption under a nice “open regularity condition” which we call “G-extensible”.
One of the examples of “G-extensible condition” is given by notions of Thom-Boardman singularities. 相似文献
17.
We consider the boundary value problem Δu+⋎x⋎2α
u
p
=0, α>0, in the unit ballB with homogeneous Dirichlet boundary condition andp a large exponent. We find a condition which ensures the existence of a positive solutionu
p
concentrating outside the origin atk symmetric points asp goes to +∞. The same techniques lead also to a more general result on general domains. In particular, we find that concentration
at the origin is always possible, provided α⊄IN.
The first author is supported by M.U.R.S.T., project “Variational methods and nonlinear differential equations” and a PIMS
Postdoctoral Fellowship.
The second author is supported by M.U.R.S.T., project “Metodi variazionali e topologici nello studio di fenomeni non lineari.”
The third author is supported by an Earmarked Grant from RGC of HK. 相似文献
18.
Jesper M. Møller 《Mathematische Zeitschrift》1999,231(1):51-74
Normalizers and p-normalizers of maximal tori in p-compact groups can be characterized by the Euler characteristic of the associated homogeneous spaces. Applied to centralizers
of elementary abelian p-groups these criteria show that the normalizer of a maximal torus of the centralizer is given by the centralizer of a preferred
homomorphism to the normalizer of the maximal torus; i.e. that “normalizer” commutes with “centralizer”.
Received April 1, 1995; in final form August 11, 1997 相似文献
19.
We define the notion of “stable Banach space” by a simple condition on the norm. We prove that ifE is a stable Banach space, then every subspace ofL
p(E) (1≦p<∞) is stable. Our main result asserts that every infinite dimensional stable Banach space containsl
p, for somep, 1≦p<∞. This is a generalization of a theorem due to D. Aldous: every infinite dimensional subspace ofL
1 containsl
p, for somep in the interval [1, 2]. 相似文献
20.
Jilali Assim 《manuscripta mathematica》1995,86(1):499-518
In this paper, we give a codescent criterion for the higher tame kernelK
2i
−2/ét
O
E
for a Galoisp-extensionE/F of algebraic number fields (p odd). As an application, we give fori∈ℤ a “going-up” theorem for certain property called (p, i)-regularity, which allows us in particular to construct examples of number fields verifying “twisted” Leopoldt conjectures.
相似文献