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1.
Consider a smooth bounded domain , and the Navier–Stokes system in with initial value and external force f = div F, where , are so-called Serrin exponents. It is an important question what is the optimal (weakest possible) initial value condition
in order to obtain a unique strong solution in some initial interval [0, T), . Up to now several sufficient conditions on u
0 are known which need not be necessary. Our main result, see Theorem 1.1, shows that the condition , A denotes the Stokes operator, is sufficient and necessary for the existence of such a strong solution u. In particular, if , , then any weak solution u in the usual sense does not satisfy Serrin’s condition for each 0 < T ≤ ∞.
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2.
Iuliana Stanculescu 《Annali dell'Universita di Ferrara》2008,54(1):145-168
This report studies an abstract approach to modeling the motion of large eddies in a turbulent flow. If the Navier-Stokes
equations (NSE) are averaged with a local, spatial convolution type filter, , the resulting system is not closed due to the filtered nonlinear term . An approximate deconvolution operator D is a bounded linear operator which is an approximate filter inverse
Using this general deconvolution operator yields the closure approximation to the filtered nonlinear term in the NSE
Averaging the Navier-Stokes equations using the above closure, possible including a time relaxation term to damp unresolved
scales, yields the approximate deconvolution model (ADM)
Here , χ ≥ 0, and w
* is a generalized fluctuation, defined by a positive semi-definite operator. We derive conditions on the general deconvolution
operator D that guarantee the existence and uniqueness of strong solutions of the model. We also derive the model’s energy balance.
The author is partially supported by NSF grant DMS 0508260. 相似文献
3.
Liselott Flodén Anders Holmbom Marianne Olsson Nils Svanstedt 《Annali dell'Universita di Ferrara》2007,53(2):217-232
Reiterated homogenization is studied for divergence structure parabolic problems of the form . It is shown that under standard assumptions on the function a(y
1,y
2,t,ξ) the sequence of solutions converges weakly in to the solution u of the homogenized problem .
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4.
Let R be a prime ring and δ a σ-derivation of R, where σ is an automorphism of R. It is proved that the skew polynomial ring is a GPI-ring (PI-ring resp.) if and only if R is a GPI-ring (PI-ring resp.), δ is quasi-algebraic, and σ is quasi-inner. If is a GPI-ring then soc , where Q is the symmetric Martindale quotient ring of R and where denotes the extended centroid of . If is a PI-ring, its PI-degree is determined as follows: if δ is X-outer, and if δ is X-inner. 相似文献
5.
Shahar Mendelson Alain Pajor Nicole Tomczak-Jaegermann 《Geometric And Functional Analysis》2007,17(4):1248-1282
We present a randomized method to approximate any vector from a set . The data one is given is the set T, vectors of and k scalar products , where are i.i.d. isotropic subgaussian random vectors in , and . We show that with high probability, any for which is close to the data vector will be a good approximation of , and that the degree of approximation is determined by a natural geometric parameter associated with the set T.
We also investigate a random method to identify exactly any vector which has a relatively short support using linear subgaussian
measurements as above. It turns out that our analysis, when applied to {−1, 1}-valued vectors with i.i.d. symmetric entries,
yields new information on the geometry of faces of a random {−1, 1}-polytope; we show that a k- dimensional random {−1, 1}-polytope with n vertices is m-neighborly for
The proofs are based on new estimates on the behavior of the empirical process when F is a subset of the L
2 sphere. The estimates are given in terms of the γ
2 functional with respect to the ψ
2 metric on F, and hold both in exponential probability and in expectation.
Received: November 2005, Revision: May 2006, Accepted: June 2006 相似文献
6.
Krishnendu Chatterjee Rupak Majumdar Thomas A. Henzinger 《International Journal of Game Theory》2008,37(2):219-234
The value of a finite-state two-player zero-sum stochastic game with limit-average payoff can be approximated to within in time exponential in a polynomial in the size of the game times polynomial in logarithmic in , for all . 相似文献
7.
On Approximate Efficiency in Multiobjective Programming 总被引:2,自引:0,他引:2
This paper is focused on approximate (
-efficient) solutions of multiobjective mathematical programs. We introduce a new
-efficiency concept which extends and unifies different notions of approximate solution defined in the literature. We characterize these
-efficient solutions in convex multiobjective programs through approximate solutions of linear scalarizations, which allow us to obtain parametric representations of different
-efficiency sets. Several classical
-efficiency notions are considered in order to show the concepts introduced and the results obtained.This research was partially supported by Ministerio de Ciencia y Tecnología (Spain), project BFM2003-02194. 相似文献
8.
We study the boundary value problem in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in with smooth boundary, λ is a positive real number, and the continuous functions p
1, p
2, and q satisfy 1 < p
2(x) < q(x) < p
1(x) < N and for any . The main result of this paper establishes the existence of two positive constants λ0 and λ1 with λ0 ≤ λ1 such that any is an eigenvalue, while any is not an eigenvalue of the above problem. 相似文献
9.
Hoang Xuan Phu 《Mathematical Methods of Operations Research》2008,67(2):207-222
A real-valued function f defined on a convex subset D of some normed linear space is said to be inner γ-convex w.r.t. some fixed roughness degree γ > 0 if there is a such that holds for all satisfying ||x
0 − x
1|| = νγ and . This kind of roughly generalized convex functions is introduced in order to get some properties similar to those of convex
functions relative to their supremum. In this paper, numerous properties of their supremizers are given, i.e., of such satisfying lim . For instance, if an upper bounded and inner γ-convex function, which is defined on a convex and bounded subset D of some inner product space, has supremizers, then there exists a supremizer lying on the boundary of D relative to aff D or at a γ-extreme point of D, and if D is open relative to aff D or if dim D ≤ 2 then there is certainly a supremizer at a γ-extreme point of D. Another example is: if D is an affine set and is inner γ-convex and bounded above, then for all , and if 2 ≤ dim D < ∞ then each is a supremizer of f.
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10.
Let be a convex function and be its Legendre tranform. It is proved that if is invariant by changes of signs, then . This is a functional version of the inverse Santaló inequality for unconditional convex bodies due to J. Saint Raymond.
The proof involves a general result on increasing functions on together with a functional form of Lozanovskii’s lemma. In the last section, we prove that for some c > 0, one has always . This generalizes a result of B. Klartag and V. Milman.
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11.
Jean-Paul Bézivin 《manuscripta mathematica》2008,126(1):41-47
Résumé Let with |q| > 1, and a be a rational number such that a
2 is not equal to for . In this note, we prove that the sum is irrational. 相似文献
12.
Tyler Lawson 《K-Theory》2006,37(4):395-422
For finitely generated groups G and H, we prove that there is a weak equivalence
G H (G × H) of ku-algebra spectra, where denotes the “unitary deformation K-theory” functor. Additionally, we give spectral sequences for computing the homotopy groups of G and HG in terms of connective K-theory and homology of spaces of G-representations. 相似文献
13.
Jens Habermann 《Mathematische Zeitschrift》2008,258(2):427-462
For weak solutions of higher order systems of the type , for all , with variable growth exponent p : Ω → (1,∞) we prove that if with , then . We should note that we prove this implication both in the non-degenerate (μ > 0) and in the degenerate case (μ = 0). 相似文献
14.
New variational principles based on the concept of anti-selfdual (ASD) Lagrangians were recently introduced in “AIHP-Analyse
non linéaire, 2006”. We continue here the program of using such Lagrangians to provide variational formulations and resolutions
to various basic equations and evolutions which do not normally fit in the Euler-Lagrange framework. In particular, we consider
stationary boundary value problems of the form as well ass dissipative initial value evolutions of the form where is a convex potential on an infinite dimensional space, A is a linear operator and is any scalar. The framework developed in the above mentioned paper reformulates these problems as and respectively, where is an “ASD” vector field derived from a suitable Lagrangian L. In this paper, we extend the domain of application of this approach by establishing existence and regularity results under
much less restrictive boundedness conditions on the anti-selfdual Lagrangian L so as to cover equations involving unbounded operators. Our main applications deal with various nonlinear boundary value
problems and parabolic initial value equations governed by transport operators with or without a diffusion term.
Nassif Ghoussoub research was partially supported by a grant from the Natural Sciences and Engineering Research Council of
Canada. The author gratefully acknowledges the hospitality and support of the Centre de Recherches Mathématiques in Montréal
where this work was initiated.
Leo Tzou’s research was partially supported by a doctoral postgraduate scholarship from the Natural Science and Engineering
Research Council of Canada. 相似文献
15.
Ruben Jakob 《Annals of Global Analysis and Geometry》2008,33(3):231-244
In the present article, the author proves two generalizations of his “finiteness-result” (I.H.P. Anal. Non-lineaire, 2006,
accepted) which states for any extreme simple closed polygon that every immersed, stable disc-type minimal surface spanning Γ is an isolated point of the set of all disc-type minimal
surfaces spanning Γ w.r.t. the C
0-topology. First, it is proved that this statement holds true for any simple closed polygon in , provided it bounds only minimal surfaces without boundary branch points. Also requiring that the interior angles at the
vertices of such a polygon Γ have to be different from the author proves the existence of some neighborhood O of Γ in and of some integer , depending only on Γ, such that the number of immersed, stable disc-type minimal surfaces spanning any simple closed polygon
contained in O, with the same number of vertices as Γ, is bounded by .
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16.
Arvind Singh 《Journal of Theoretical Probability》2007,20(2):153-166
We consider a diffusion process X in a random potential of the form , where is a positive drift and is a strictly stable process of index with positive jumps. Then the diffusion is transient and converges in law towards an exponential distribution. This behaviour contrasts with the case where is a drifted Brownian motion and provides an example of a transient diffusion in a random potential which is as “slow” as
in the recurrent setting.
相似文献
17.
Euisung Park 《Mathematische Zeitschrift》2007,256(3):685-697
In this article we study nondegenerate projective curves of degree d which are not arithmetically Cohen-Macaulay. Note that for a rational normal curve and a point . Our main result is about the relation between the geometric properties of X and the position of P with respect to . We show that the graded Betti numbers of X are uniquely determined by the rank of P with respect to . In particular, X satisfies property N
2,p
if and only if . Therefore property N
2,p
of X is controlled by and conversely can be read off from the minimal free resolution of X. This result provides a non-linearly normal example for which the converse to Theorem 1.1 in (Eisenbud et al., Compositio
Math 141:1460–1478, 2005) holds. Also our result implies that for nondegenerate projective curves of degree d which are not arithmetically Cohen–Macaulay, there are exactly distinct Betti tables. 相似文献
18.
Neculai Andrei 《Numerical Algorithms》2008,47(2):143-156
Another hybrid conjugate gradient algorithm is subject to analysis. The parameter β
k
is computed as a convex combination of (Hestenes-Stiefel) and (Dai-Yuan) algorithms, i.e. . The parameter θ
k
in the convex combination is computed in such a way so that the direction corresponding to the conjugate gradient algorithm
to be the Newton direction and the pair (s
k
, y
k
) to satisfy the quasi-Newton equation , where and . The algorithm uses the standard Wolfe line search conditions. Numerical comparisons with conjugate gradient algorithms show
that this hybrid computational scheme outperforms the Hestenes-Stiefel and the Dai-Yuan conjugate gradient algorithms as well
as the hybrid conjugate gradient algorithms of Dai and Yuan. A set of 750 unconstrained optimization problems are used, some
of them from the CUTE library.
相似文献
19.
Morton E. Harris 《Results in Mathematics》2008,51(3-4):249-259
As in Finite Group Modular Representation Theory, let be a commutative complete noetherian ring with an algebraically closed residue field k. Let G be a finite group and let N be a normal subgroup of G. First suppose that V is an indecomposable -module, so that Inf
G
G/N
(V) is an indecomposable G-module. We relate the Green invariants of V as an -module to those of Inf
G
G/N
(V) as an G-module. Secondly, let V and W be indecomposable G-modules. Assume that W is an endo-permutation lattice and that is also an indecomposable G-module. We relate the Green invariants of the G-modules V and . (This situation arises under important Morita equivalences.)
Received: December 11, 2006. Revised: August 22, 2007. 相似文献
20.
Yu LI 《数学学报(英文版)》2008,24(2):285-304
Let G be a Lie group whose Lie algebra g is quadratic. In the paper "the non-commutative Weil algebra", Alekseev and Meinrenken constructed an explicit G-differential space homomorphism £, called the quantization map, between the Well algebra Wg = S(g^*) χ∧A(g^*) and Wg= U(g) χ Cl(g) (which they call the noncommutative Weil algebra) for g. They showed that £ induces an algebra isomorphism between the basic cohomology rings Hbas^*(Wg) and Hbas^*(Wg). In this paper, we will interpret the quantization map .~ as the super Duflo map between the symmetric algebra S(Tg[1]) and the universal enveloping algebra U(Tg[1]) of a super Lie algebra T9[1] which is canonically associated with the quadratic Lie algebra g. The basic cohomology rings Hbas^*(Wg) and Hbas^*(Wg) correspond exactly to S(Tg[1])^inv and U(Tg[1])^inv, respectively. So what they proved is equivalent to the fact that the super Duflo map commutes with the adjoint action of the super Lie algebra, and that the super Duflo map is an algebra homomorphism when restricted to the space of invariants. 相似文献