共查询到20条相似文献,搜索用时 31 毫秒
1.
Barrett John W.; Garcke Harald; Nurnberg Robert 《IMA Journal of Numerical Analysis》2008,28(2):292-330
2.
An adaptive semi-Lagrangian scheme for solving the Cauchy problem associated to the periodic 1+1-dimensional Vlasov-Poisson
system in the two- dimensional phase space is proposed and analyzed. A key feature of our method is the accurate evolution
of the adaptive mesh from one time step to the next one, based on a rigorous analysis of the local regularity and how it gets
transported by the numerical flow. The accuracy of the scheme is monitored by a prescribed tolerance parameter ε which represents the local interpolation error at each time step, in the L
∞ metric. The numerical solutions are proved to converge in L
∞ towards the exact ones as ε and Δt tend to zero provided the initial data is Lipschitz and has a finite total curvature, or in other words, that it belongs
to . The rate of convergence is , which should be compared to the results of Besse who recently established in (SIAM J Numer Anal 42(1):350–382, 2004) similar
rates for a uniform semi-Lagrangian scheme, but requiring that the initial data are in . Several numerical tests illustrate the effectiveness of our approach for generating the optimal adaptive discretizations. 相似文献
3.
Let M be a compact orientable manifold, and F be an essential closed surface which cuts M into two 3-manifolds M
1 and M
2. Let be a Heegaard splitting for i = 1, 2. We denote by d(S
i
) the distance of . If d(S
1), d(S
2) ≥ 2(g(M
1) + g(M
2) − g(F)), then M has a unique minimal Heegaard splitting up to isotopy, i.e. the amalgamation of and .
Ruifeng Qiu is supported by NSFC(10625102). 相似文献
4.
A partial tube in PG(3, q) is a pair
, where
is a collection of mutually disjoint lines of PG(3, q) with the property that for each plane π of PG(3, q) through L, the intersection of π with the lines of
is an arc. Here, we generalize the notion of partial tube allowing the ground field to be any algebraically closed field.
To a generalized partial tube we will associate an irreducible surface of degree d in
providing upper bounds on d.
The authors were partially supported by MIUR and GNSAGA of INdAM (Italy). 相似文献
5.
Let Δ(1) be the uniform three direction mesh of the plane whose vertices are integer points of
.Let
(respectively
of degree d=3r (respectively d=3r+1 ) for r odd (respectively even) on the triangulation
, and of degree d=2r (respectively d=2r+1) for r odd (respectively even) on the triangulation
. Using linear combinations of translates of these splines we obtain Lagrange interpolants whose corresponding order of approximation
is optimal.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
6.
Yves Dumont 《Journal of Computational Analysis and Applications》2000,2(1):11-47
The evolutionary motion of surfaces or curves by their meancurvature has found much interest during the last years. The problem withmean curvature flow is that singularities can appear during the evolutioneven if the initial surface is convex. To prove the existence of a viscositysolution u of the mean curvature flow, Evans and Spruck [4] builtthe -regularized mean curvature flow. For practicalpurposes, i.e., numerical computations, it would be interesting to knowhow fast the solution of the regularized problem converges to the viscocitysolution of the original problem. The goal in this paper is to presentsome results concerning the -regularized mean curvatureflow in the one-dimension space. It is proved that there exists anasymptotic expansion of the solution of the regularized problem, in powers of theparameter , such that the first term of the asymptoticexpansion is the viscosity solution of the mean curvature flow problem.Moreover, that this asymptotic expansion is true in appropriate topologies,in particular in weighted Sobolev spaces is proved. Finally, an estimateof the rate of convergence in these topologies is given. 相似文献
7.
Dietmar Vogt 《Archiv der Mathematik》2006,87(2):163-171
It is shown that for open convex
, d > 1 and a nontrivial polynomial P the space
does not have property
. If P is elliptic or homogeneous, then this holds for every open Ω. For
even
cannot occur and if it occurs for some Ω, then P must be hypoelliptic.
Received: 18 July 2005 相似文献
8.
We analyze the convergence rate of a multigrid method for multilevel linear systems whose coefficient matrices are generated
by a real and nonnegative multivariate polynomial f and belong to multilevel matrix algebras like circulant, tau, Hartley, or are of Toeplitz type. In the case of matrix algebra
linear systems, we prove that the convergence rate is independent of the system dimension even in presence of asymptotical
ill-conditioning (this happens iff f takes the zero value). More precisely, if the d-level coefficient matrix has partial dimension n
r
at level r, with , then the size of the system is , , and O(N(n)) operations are required by the considered V-cycle Multigrid in order to compute the solution within a fixed accuracy. Since the total arithmetic cost is asymptotically
equivalent to the one of a matrix-vector product, the proposed method is optimal. Some numerical experiments concerning linear
systems arising in 2D and 3D applications are considered and discussed. 相似文献
9.
O. Scherzer 《Numerische Mathematik》1993,66(1):259-279
Summary In this paper we investigate iterated Tikhonov regularization for the solution of nonlinear ill-posed problems. In the case of linear ill-posed problems it is well-known that (under appropriate assumptions) then-th iterated regularized solutions can converge likeO(22
/(2n+1)), where denotes the noise level of the data perturbation. We give conditions that guarantee this convergence rate also for nonlinear ill-posed problems, and motivate these conditions by the mapping degree. The results are derived by a comparison of the iterated regularized solutions of the nonlinear problem with the iterated regularized solutions of its linearization. Numerical examples are presented.Supported by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung,project P-7869 PHY, and by the Christian Doppler Society 相似文献
10.
Hiroaki Shimomura 《Mathematische Zeitschrift》2008,259(2):355-361
This paper concerns positive-definite functions on infinite-dimensional groups G. Our main results are as follows: first, we claim that if G has a σ-finite measure μ on the Borel field whose right admissible shifts form a dense subgroup G
0, a unique (up to equivalence) unitary representation (H, T) with a cyclic vector corresponds to through a method similar to that used for the G–N–S construction. Second, we show that the result remains true, even if we
go to the inductive limits of such groups, and we derive two kinds of theorems, those taking either G or G
0 as a central object. Finally, we proceed to an important example of infinite-dimensional groups, the group of diffeomorphisms
on smooth manifolds M, and see that the correspondence between positive-definite functions and unitary representations holds for under a fairy mild condition. For a technical reason, we impose condition (c) in Sect. 2 on the measure space throughout this paper. It is also a weak condition, and it is satified, if G is separable, or if μ is Radon.
This research was partially supported by a Grant-in-Aid for Scientific Research (No.18540184), Japan Socieity of the Promotion
of Science. 相似文献
11.
Let V be an
rn-dimensional linear
subspace of
. Suppose the smallest
Hamming weight of non-zero vectors in V is d. (In coding-theoretic terminology,
V is a linear code of length
n, rate
r and distance
d.) We settle two extremal
problems on such spaces.First, we prove a (weak form) of a conjecture by Kalai and
Linial and show that the fraction of vectors in
V with weight
d is exponentially small.
Specifically, in the interesting case of a small
r, this fraction does not
exceed
.We also answer a question of Ben-Or and show that if
, then for every
k, at most
vectors of
V have weight
k.Our work draws on a simple connection between extremal
properties of linear subspaces of
and the distribution of
values in short sums of
-characters.* Supported in part by grants from the Israeli
Academy of Sciences and the Binational Science Foundation
Israel-USA. This work was done while the author was a student
in the Hebrew University of Jerusalem, Israel. 相似文献
12.
Summary In this paper we examine quadrature rules
for the integral
which are exact for all
with +d. We specify three distinct families of solutions which have properties not unlike the standard Gauss and Radau quadrature rules. For each integerd the abscissas of the quadrature rules lie within the closed integration interval and are expressed in terms of the zeros of a polynomialq
d(y). These polynomialsq
d(y), (d=0, 1, ...), which are not orthogonal, satisfy a three term recurrence relation of the type Qd+1(y)=(y+d+1)qd(y)–d+1yqd–1(y) and have zeros with the standard interlacing property.This work was supported by the Applied Mathematical Sciences Research Program (KC-04-02) of the Office of Energy Research of the U.S. Department of Energy under Contract W-31-109-Eng-38 相似文献
13.
We study the functionb(n, d), the maximal number of atoms defined byn d-dimensional boxes, i.e. parallelopipeds in thed-dimensional Euclidean space with sides parallel to the coordinate axes.
We characterize extremal interval families definingb(n, 1)=2n-1 atoms and we show thatb(n, 2)=2n
2-6n+7.
We prove that for everyd,
exists and
.
Moreover, we obtainb*(3)=8/9. 相似文献
14.
Summary.
Let
We say that
preserves the distance d 0 if
for each
implies
Let A
n
denote the set of all positive numbers
d such that any map
that preserves unit distance preserves also distance
d.
Let D
n
denote the set of all positive numbers
d with the property: if
and
then there exists a finite set
S
xy
with
such that any map
that preserves unit distance preserves also the distance between
x and y.
Obviously,
We prove:
(1)
(2)
for n 2
D
n
is a
dense subset of
(2) implies that each mapping
f
from
to
(n 2)
preserving unit distance preserves all distances,
if f is continuous with respect to the product topologies
on
and
相似文献
15.
Paul-Emile Maingé 《Positivity》2008,12(2):269-280
This paper deals with a viscosity iteration method, in a real Hilbert space , for minimizing a convex function over the fixed point set of , a mapping in the class of demicontractive operators, including the classes of quasi-nonexpansive and strictly pseudocontractive
operators. The considered algorithm is written as: x
n+1
:= (1 − w) v
n
+ w
T
v
n
, v
n
:= x
n
− α
n
Θ′(x
n
), where w ∈ (0,1) and , Θ′ is the Gateaux derivative of Θ. Under classical conditions on T, Θ, Θ′ and the parameters, we prove that the sequence (x
n
) generated, with an arbitrary , by this scheme converges strongly to some element in Argmin
Fix(T) Θ.
相似文献
16.
Franc Forstnerič Björn Ivarsson Frank Kutzschebauch Jasna Prezelj 《Mathematische Annalen》2007,338(3):545-554
Given a Stein manifold x of dimension n > 1, a discrete sequence , and a discrete sequence where , there exists a proper holomorphic embedding satisfying f(a
j
) = b
j
for every j = 1,2,...
Forstnerič and Prezelj supported by grants P1-0291 and J1-6173, Republic of Slovenia.
Kutzschebauch supported by Schweizerische National fonds grant 200021-107477/1.
Ivarsson supported by The Wenner-Gren Foundations. 相似文献
17.
The celebrated Erd?s, Faber and Lovász Conjecture may be stated as follows: Any linear hypergraph on ν points has chromatic index at most ν. We show that the conjecture is equivalent to the following assumption: For any graph , where ν(G) denotes the linear intersection number and χ(G) denotes the chromatic number of G. As we will see for any graph G = (V, E), where denotes the complement of G. Hence, at least G or fulfills the conjecture.
相似文献
18.
Mikhail Kapranov 《Selecta Mathematica, New Series》2007,13(2):277-319
We construct algebraic and algebro-geometric models for the spaces of unparametrized paths. This is done by considering a
path as a holonomy functional on indeterminate connections. For a manifold X, we construct a Lie algebroid which serves as the tangent space to X (punctual paths) inside the space of all unparametrized paths. It serves as a natural receptacle of all “covariant derivatives
of the curvature” for all bundles with connections on X.
If X is an algebraic variety, we integrate to a formal groupoid which can be seen as the formal neighborhood of X inside the space of paths. We establish a relation between and the stable map spaces of Kontsevich.
相似文献
19.
We discuss the analytic properties of curves γ whose global curvature function ρ
G
[γ]−1 is p-integrable. It turns out that the L
p
-norm is an appropriate model for a self-avoidance energy interpolating between “soft” knot energies in form of singular repulsive
potentials and “hard” self-obstacles, such as a lower bound on the global radius of curvature introduced by Gonzalez and Maddocks.
We show in particular that for all p > 1 finite -energy is necessary and sufficient for W
2,p
-regularity and embeddedness of the curve. Moreover, compactness and lower-semicontinuity theorems lead to the existence of
-minimizing curves in given isotopy classes. There are obvious extensions to other variational problems for curves and nonlinearly
elastic rods, where one can introduce a bound on to preclude self-intersections. 相似文献
20.
Let G be a Lie group with Lie algebra g and a
i,...,a
d and algebraic basic of g. Futher, if A
i=dL(ai) are the corresponding generators of left translations by G on one of the usual function spaces over G, let% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamXvP5wqonvsaeHbfv3ySLgzaGqbciab-Heaijaab2dadaaeqbqa% aiaadogadaWgaaWcbaqedmvETj2BSbacgmGae4xSdegabeaakiaadg% eadaahaaWcbeqaaiab+f7aHbaaaeaacqGFXoqycaGG6aGaaiiFaiab% +f7aHjaacYhatuuDJXwAK1uy0HMmaeXbfv3ySLgzG0uy0HgiuD3BaG% Wbbiab9rMiekaaikdaaeqaniabggHiLdaaaa!5EC1!\[H{\rm{ = }}\sum\limits_{\alpha :|\alpha | \le 2} {c_\alpha A^\alpha } \] be a second-order differential operator with real bounded coefficients c
. The operator is defined to be subelliptic if% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiGacMgacaGGUbGaaiOzamXvP5wqonvsaeHbfv3ySLgzaGqbaKaz% aasacqWF7bWEcqWFTaqlkmaaqafabaGaam4yamaaBaaaleaarmWu51% MyVXgaiyWacqGFXoqyaeqaaaqaaiab+f7aHjaacQdacaGG8bGae4xS% deMaaiiFaiabg2da9iaaikdaaeqaniabggHiLdGccqWFOaakiuGacq% qFNbWzcqWFPaqkcqaH+oaEdaahaaWcbeqaamaaBaaameaacqGFXoqy% aeqaaaaakiaacUdacqqFNbWzcqGHiiIZcqqFhbWrcqqFSaalcqqFGa% aicqaH+oaEcqGHiiIZrqqtubsr4rNCHbachaGaeWxhHe6aaWbaaSqa% beaacqqFKbazcqqFNaWjcqaFaC-jaaGccaGGSaGaaiiFaiabe67a4j% aacYhacqGH9aqpjqgaGeGae8xFa0NccqGH+aGpcaaIWaGaaiOlaaaa% !7884!\[\inf \{ - \sum\limits_{\alpha :|\alpha | = 2} {c_\alpha } (g)\xi ^{_\alpha } ;g \in G, \xi \in ^{d'} ,|\xi | = \} > 0.\]We prove that if the principal coefficients {c
; ||=2} of the subelliptic operator are once left differentiable in the directions a
1,...,a
d with bounded derivatives, then the operator has a family of semigroup generator extensions on the L
p-spaces with respect to left Haar measure dg, or right Haar measure d, and the corresponding semigroups S are given by a positive integral kernel,% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamXvP5wqonvsaeHbfv3ySLgzaGqbaiab-HcaOGqbciab+nfatnaa% BaaaleaacaWG0baabeaaruqqYLwySbacgiGccaqFgpGae8xkaKIae8% hkaGIae43zaCMae8xkaKIae8xpa0Zaa8qeaeaacaqGKbaaleaacqGF% hbWraeqaniabgUIiYdGcceWGObGbaKaacaWGlbWaaSbaaSqaaiaads% haaeqaaOGae8hkaGIae43zaCMae43oaSJae4hAaGMae8xkaKIaa0NX% diab-HcaOiab+HgaOjab-LcaPiab-5caUaaa!5DFA!\[(S_t \phi )(g) = \int_G {\rm{d}} \hat hK_t (g;h)\phi (h).\]The semigroups are holomorphic and the kernel satisfies Gaussian upper bounds. If in addition the coefficients with ||=2 are three times differentiable and those with ||=1 are once differentiable, then the kernel also satisfies Gaussian lower bounds.Some original features of this article are the use of the following: a priori inequalities on L
in Section 3, fractional operator expansions for resolvent estimates in Section 4, a parametrix method based on reduction to constant coefficient operators on the Lie group rather than the usual Euclidean space in Section 5, approximation theory of semigroups in Section 11 and time dependent perturbation theory to treat the lower order terms of H in Sections 11 and 12. 相似文献