共查询到20条相似文献,搜索用时 46 毫秒
1.
Hang YU 《数学年刊B辑(英文版)》2012,33(1):149-160
The paper deals with the controllability of a heat equation.It is well-known that the heat equation yt y = uχE in(0,T)×Ω with homogeneous Dirichlet boundary conditions is null controllable for any T > 0 and any open nonempty subset E of Ω.In this note,the author studies the case that E is an arbitrary measurable set with positive measure. 相似文献
2.
Given an operator T : X → Y between Banach spaces, and a Banach lattice E consisting of measurable functions, we consider the point-wise extension of the operator to the vector-valued Banach lattices
T
E
: E(X) → E(Y) given by T
E
(f)(ω) = T(f(ω)). It is proved that for any Banach lattice E which does not contain c
0, the operator T is an isomorphism on a subspace isomorphic to c
0 if and only if so is T
E
. An analogous result for invertible operators on subspaces isomorphic to ℓ
1 is also given. 相似文献
3.
Arnaud Münch 《Computational Optimization and Applications》2009,42(3):443-470
We consider in this paper the homogeneous 1-D wave equation defined on Ω⊂ℝ. Using the Hilbert Uniqueness Method, one may define,
for each subset ω⊂Ω, the exact control v
ω
of minimal L
2(ω×(0,T))-norm which drives to rest the system at a time T>0 large enough. We address the question of the optimal position of ω which minimizes the functional
. We express the shape derivative of J as an integral on ∂
ω×(0,T) independently of any adjoint solution. This expression leads to a descent direction for J and permits to define a gradient algorithm efficiently initialized by the topological derivative associated with J. The numerical approximation of the problem is discussed and numerical experiments are presented in the framework of the
level set approach. We also investigate the well-posedness of the problem by considering a relaxed formulation. 相似文献
4.
Jan Wiegerinck 《Arkiv f?r Matematik》2000,38(1):201-208
In this paper we show that the pluripolar hull ofE={(z, ω)∈C2:ω=e
−1/z,z≠0} is equal toE. This implies thatE is plurithin at 0, which answers a question of Sadullaev. The result remains valid ife
−1/z is replaced by certain other holomorphic functions with an essential singularity at 0. 相似文献
5.
Suppose that E and F are two Banach spaces and that B(E, F) is the space of all bounded linear operators from E to F. Let T
0∈B(E, F) with a generalized inverse T
0
+∈B(F, E). This paper shows that, for every T∈B(E, F) with ‖T
0
+ (T−T
0)‖<1, B ≡ (I + T
0
+(T−T
0))−1
T
0
+ is a generalized inverse of T if and only if (I−T
0
+
T
0)N(T) = N(T
0), where N(·) stands for the null space of the operator inside the parenthesis. This result improves a useful theorem of Nashed and
Cheng and further shows that a lemma given by Nashed and Cheng is valid in the case where T
0 is a semi-Fredholm operator but not in general. 相似文献
6.
Stephen H. Hechler 《Israel Journal of Mathematics》1973,15(4):384-395
For any topological spaceT, S. Mrówka has defined Exp (T) to be the smallest cardinal κ (if any such cardinals exist) such thatT can be embedded as a closed subset of the productN
κ of κ copies ofN (the discrete space of cardinality ℵ0). We prove that forQ, the space of the rationals with the inherited topology, Exp (Q) is equal to a certain covering number, and we show that by modifying some earlier work of ours it can be seen that it is
consistent with the usual axioms of set theory including the choice that this number equal any uncountable regular cardinal
less than or equal to 2ℵ
0. Mrówka has also defined and studied the class ℳ={κ: Exp (N
κ)=κ} whereN
κ is the discrete space of cardinality κ. It is known that the first cardinal not in ℳ must not only be inaccessible but cannot
even belong to any of the first ω Mahlo classes. However, it is not known whether every cardinal below 2ℵ
0 is contained in ℳ. We prove that if there exists a maximal family of almost-disjoint subsets ofN of cardinality κ, then κ∈ℳ, and we then use earlier work to prove that if it is consistent that there exist cardinals which
are not in the first ω Mahlo classes, then it is consistent that there exist such cardinals below 2ℵ
0 and that ℳ nevertheless contain all cardinals no greater than 2ℵ
0. Finally, we consider the relationship between ℳ and certain “large cardinals”, and we prove, for example, that if μ is any
normal measure on a measurable cardinal, then μ(ℳ)=0. 相似文献
7.
Eli Glasner 《Journal d'Analyse Mathématique》1994,64(1):241-262
For a minimal distal flow (X, T) and a positive integern, let be the largest distal factor of ordern. The existence of a denseG
δ subset ω ofX is shown, such that forx ∈ ω the orbit closure of (x,x,...,x) ∈ X
n+1 under τ =T ×T
2 ... ×T
n+1 is π-saturated. In fact, an analogous statement for a general minimal flow is proved in terms of its PI-tower. On the way
we get some topological “ergodic” decomposition theorems. 相似文献
8.
Let E be a row-finite directed graph, let G be a locally compact abelian group with dual group Ĝ = Γ, let ω be a labeling map from E* to Γ, and let (C*(E), G, α
ω
) be the C*-dynamical system defined by ω. Some mappings concerning the AF-embedding construction of C*(E) ×aw GC*(E) \times _{\alpha ^\omega } G are studied in more detail. Several necessary conditions of AF-embedding and some properties of almost proper labeling map
are obtained. Moreover it is proved that if E is constructed by attaching some 1-loops to a directed graph T consisting of some rooted directed trees and G is compact, then ω is almost proper, that is a sufficient condition for AF-embedding, if and only if Σ
j=1
k
wgj 1 1G\omega _{\gamma _j } \ne 1_\Gamma for any loop γ
i
, γ
2, ..., γ
k
attached to one path in T. 相似文献
9.
Richard Haydon 《Israel Journal of Mathematics》1977,28(4):313-324
Two closely related results are presented, one of them concerned with the connection between topological and measure-theoretic
properties of compact spaces, the other being a non-separable analogue of a result of Peŀczyński's about Banach spaces containingL
1. Let τ be a regular cardinal satisfying the hypothesis that κω<τ whenever κ<τ. The following are proved: 1) A compact spaceT carries a Radon measure which is homogeneous of type τ, if and only if there exists a continuous surjection ofT onto [0, 1]τ. 2) A Banach spaceX has a subspace isomorphic tol
1(τ) if and only ifX
∗ has a subspace isomorphic toL
1({0, 1}τ). An example is given to show that a more recent result of Rosenthal's about Banach spaces containingl
1 does not have an obvious transfinite analogue. A second example (answering a question of Rosenthal's) shows that there is
a Banach spaceX which contains no copy ofl
1 (ω1), while the unit ball ofX
∗ is not weakly∗ sequentially compact. 相似文献
10.
E. G. Straus 《Israel Journal of Mathematics》1963,1(4):221-223
For any two positive integersk, l and anyɛ>0 there exists anN(k, l, ɛ) so that given anyl convex bodiesC
1, …,C
l symmetric about the origin inE
n withn≧N there exists a subspaceE
k so that eachC
i intersectsE
k, or has a projection intoE
k, in a set which is nearly spherical (asphericity <ɛ). The measure of the totality ofE
k which intersect a given body inE
n in a nearly ellipsoidal set is considered and an affine invariant measure is introduced for that purpose. 相似文献
11.
M. Rudelson 《Israel Journal of Mathematics》1995,89(1-3):189-204
We prove a variant of a theorem of N. Alon and V. D. Milman. Using it we construct for everyn-dimensional Banach spacesX andY a measure space Ω and two operator-valued functionsT: Ω→L(X, Y),S: Ω→L(Y, X) so that ∫Ω
S(ω)oT(ω)dω is the identity operator inX and ∫Ω||S(ω)||·||T(ω)||dω=O(n
α
) for some absolute constantα<1.
We prove also that any subset of the unitn-cube which is convex, symmetric with respect to the origin and has a sufficiently large volume possesses a section of big
dimension isomorphic to ak-cube.
Research supported in part by a grant of the Israel Academy of Sciences. 相似文献
12.
We prove a version of Furstenberg’s ergodic theorem with restrictions on return times. More specifically, for a measure preserving
system (X, B, μ,T), integers 0 ≤j <k, andE ⊂X with μ(E) > 0, we show that there existsn ≡ j (modk) with ώ(E ∩T
-nE ∩T
-2nE ∩T
-3nE) > 0, so long asT
k is ergodic. This result requires a deeper understanding of the limit of some nonconventional ergodic averages and the introduction
of a new class of systems, the ‘Quasi-Affine Systems’.
This work was partially carried out while the second author was visiting the Université de Marne la Vallée, supported by NSF
grant 9804651. 相似文献
13.
Let X be a locally compact topological space and (X, E, Xω) be any triple consisting of a hyperfinite set X in a sufficiently saturated nonstandard universe, a monadic equivalence relation E on X, and an E-closed galactic set Xω ⊆ X, such that all internal subsets of Xω are relatively compact in the induced topology and X is homeomorphic to the quotient Xω/E. We will show that each regular complex Borel measure on X can be obtained by pushing down the Loeb measure induced by some internal function
X ? *\Bbb CX \rightarrow {}{^{\ast}{\Bbb C}}
. The construction gives rise to an isometric isomorphism of the Banach space M(X) of all regular complex Borel measures on X, normed by total variation, and the quotient
Mw(X)/M0(X){\cal M}_{\omega}(X)/{\cal M}_0(X)
, for certain external subspaces
M0(X), Mw(X){\cal M}_0(X), {\cal M}_{\omega}(X)
of the hyperfinite dimensional Banach space
*\Bbb CX{}{^{\ast}{\Bbb C}}^X
, with the norm ‖f‖1 = ∑x ∈ X |f(x)|. If additionally X = G is a hyperfinite group, Xω = Gω is a galactic subgroup of G, E is the equivalence corresponding to a normal monadic subgroup G0 of Gω, and G is isomorphic to the locally compact group Gω/G0, then the above Banach space isomorphism preserves the convolution, as well, i.e., M(G) and
Mw(G)/M0(G){\cal M}_{\omega}(G)/{\cal M}_0(G)
are isometrically isomorphic as Banach algebras. 相似文献
14.
This work contains an improvement of earlier results of Boggess and Dwilewicz regarding global approximation of CR functions
by entire functions in the case of hypersurface graphs. In this work, we show that if ω, an open subset of a real hypersurface in ℂ
n
, can be graphed over a convex subset in ℝ2n−1, then ω is CR-Runge in the sense that continuous CR functions on ω can be approximated by entire functions on ℂ
n
in the compact open topology of ω. Examples are presented to show that this approximation result does not hold for graphed CR submanifolds in higher codimension.
R. Dwilewicz is partially supported by the Polish Science Foundation (KBN) grant N201 019 32/805. 相似文献
15.
M. E. Palistrant 《Theoretical and Mathematical Physics》1999,119(3):761-777
We obtain the basic system of equations for a superconductivity theory of a system with a chaotically distributed paramagnetic
substitution impurity in which the Migdal theorem is violated (the condition ωD ≪E
F cannot be assumed). The electron-phonon and impurity diagrams and also the additional diagrams corresponding to intersections
of the electron-phonon and electron-impurity lines are taken into account. In the weak electron-phonon coupling limit, we
obtain an equation for the superconducting transition temperature TC that differs from the corresponding equation for the usual superconductors by renormalizations of TC0 and of the impurity scattering parameter, ρ. These quantities depend essentially on the Migdal parameter ωD/E
F and on the transferred momentum qc. We show that the decrease of TC with the increase of the impurity concentration is slowed, as compared with usual superconductors, to an extent determined
by m and qc. We also evaluate the isotopic coefficient α, whose behavior as a function of the impurity concentration depends on m and
qc.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 119, No. 3, pp 455–474, June, 1999 相似文献
16.
Homogeneous graded metrics over split ℤ2-graded manifolds whose Levi-Civita connection is adapted to a given splitting, in the sense recently introduced by Koszul,
are completely described. A subclass of such is singled out by the vanishing of certain components of the graded curvature
tensor, a condition that plays a role similar to the closedness of a graded symplectic form in graded symplectic geometry:
It amounts to determining a graded metric by the data {g, ω, Δ′}, whereg is a metric tensor onM, ω 0 is a fibered nondegenerate skewsymmetric bilinear form on the
Batchelor bundleE → M, and Δ′ is a connection onE satisfying Δ′ω = 0. Odd metrics are also studied under the same criterion and they are specified by the data {κ, Δ′}, with
κ ∈ Hom (TM, E) invertible, and Δ′κ = 0. It is shown in general that even graded metrics of constant graded curvature can be supported only
over a Riemannian manifold of constant curvature, and the curvature of Δ′ onE satisfiesR
Δ′ (X,Y)2 = 0. It is shown that graded Ricci flat even metrics are supported over Ricci flat manifolds and the curvature of the connection
Δ′ satisfies a specific set of equations. 0 Finally,
graded Einstein even metrics can be supported only over Ricci flat Riemannian manifolds. Related results for graded metrics
on Ω(M) are also discussed.
Partially supported by DGICYT grants #PB94-0972, and SAB94-0311; IVEI grant 95-031; CONACyT grant #3189-E9307. 相似文献
17.
Two invertible dynamical systems (X, gA, μ, T) and (Y, ℬ, ν, S), where X, Y are metrizable spaces and T, S are homeomorphisms on X and Y, are said to be finitarily orbit equivalent if there exists an invertible measure preserving mapping ϕ from a subset X
0 of X of full measure to a subset Y
0 of Y of full measure such that ϕ|x
0 is continuous in the relative topology on X
0, ϕ
−1|Y
0 is continuous in the relative topology on Y
0 and ϕ(Orb
T
(x)) = Orb
Sϕ
(x) for μ-a.e. x ∈ X. In this article a finitary orbit equivalence mapping is shown to exist between any two irreducible Markov chains. 相似文献
18.
D. M. Israfilov 《Constructive Approximation》2001,17(3):335-351
Let G\subset C be a finite domain with a regular Jordan boundary L . In this work, the approximation properties of a p -Faber polynomial series of functions in the weighted Smirnov class E
p
(G,ω) are studied and the rate of polynomial approximation, for f∈ E
p
( G,ω) by the weighted integral modulus of continuity, is estimated. Some application of this result to the uniform convergence
of the Bieberbach polynomials π
n
in a closed domain \overline G with a smooth boundary L is given.
February 25, 1999. Date revised: October 20, 1999. Date accepted: May 26, 2000. 相似文献
19.
Let E be an arbitrary measurable set, E ⊂ T
N
= [−π, π)N, N ≥ 1, μE > 0, and let μ be a measure. In this paper, a weak generalized almost everywhere localization is studied, i.e., for given subsets E
1 ⊂ E, μE
1 > 0 we study the almost everywhere convergence of multiple trigonometric Fourier series of functions that are zero on E. We obtain sufficient conditions for the almost everywhere convergence of multiple Fourier series (summable over rectangles)
of functions from {ie031-01}, as δ → 0 on E
1. These conditions are given in terms of the structure and geometry of the sets E
1 and E and are related to certain orthogonal projections of the sets; they are called the {ie031-02} property of the set E. Previously, one of the authors had introduced the {ie031-03}, k = 1, 2, properties of the set E, which are related to one-dimensional and two-dimensional projections of the sets E and E
1 respectively, as sufficient conditions for the almost everywhere convergence of Fourier series of functions from L
1(T
N
) and L
p
(T
N
), p > 1. The results presented generalize these ideas.
__________
Translated from Sovremennaya Matematika. Fundamental'nye Napravleniya (Contemporary Mathematics. Fundamental Directions),
Vol. 25, Theory of Functions, 2007. 相似文献
20.
It is shown that ifT is a measure preserving automorphism on a probability space (Ω,B, m) which admits a random variable X0 with mean zero such that the stochastic sequence X0 o Tn,n ε ℤ is orthonormal and spans L0
2(Ω,B,m), then for any integerk ≠ 0, the random variablesX o Tnk,n ε ℤ generateB modulom. 相似文献