共查询到20条相似文献,搜索用时 78 毫秒
1.
H. Martini K. J. Swanepoel P. Oloff de Wet 《Journal of Optimization Theory and Applications》2009,143(1):149-157
We give a new proof that a star {op
i
:i=1,…,k} in a normed plane is a Steiner minimal tree of vertices {o,p
1,…,p
k
} if and only if all angles formed by the edges at o are absorbing (Swanepoel in Networks 36: 104–113, 2000). The proof is simpler and yet more conceptual than the original one.
We also find a new sufficient condition for higher-dimensional normed spaces to share this characterization. In particular,
a star {op
i
:i=1,…,k} in any CL-space is a Steiner minimal tree of vertices {o,p
1,…,p
k
} if and only if all angles are absorbing, which in turn holds if and only if all distances between the normalizations
\frac1||pi||pi\frac{1}{\Vert p_{i}\Vert}p_{i}
equal 2. CL-spaces include the mixed ℓ
1 and ℓ
∞ sum of finitely many copies of ℝ. 相似文献
2.
This paper presents a property of geometric and topological nature of Gateaux differentiability points and Fréchet differentiability points of almost CL-spaces. More precisely, if we denote by a maximal convex set of the unit sphere of a CL-space , and by the cone generated by , then all Gateaux differentiability points of are just n-s, and all Fréchet differentiability points of are (where n-s denotes the non-support points set of ).
3.
Lixin Cheng 《Journal of Mathematical Analysis and Applications》2011,377(2):464-470
We call a Banach space X admitting the Mazur-Ulam property (MUP) provided that for any Banach space Y, if f is an onto isometry between the two unit spheres of X and Y, then it is the restriction of a linear isometry between the two spaces. A generalized Mazur-Ulam question is whether every Banach space admits the MUP. In this paper, we show first that the question has an affirmative answer for a general class of Banach spaces, namely, somewhere-flat spaces. As their immediate consequences, we obtain on the one hand that the question has an approximately positive answer: Given ε>0, every Banach space X admits a (1+ε)-equivalent norm such that X has the MUP; on the other hand, polyhedral spaces, CL-spaces admitting a smooth point (in particular, separable CL-spaces) have the MUP. 相似文献
4.
Jean-François Le Gall 《Inventiones Mathematicae》2007,169(3):621-670
We discuss scaling limits of large bipartite planar maps. If p≥2 is a fixed integer, we consider, for every integer n≥2, a random planar map M
n
which is uniformly distributed over the set of all rooted 2p-angulations with n faces. Then, at least along a suitable subsequence, the metric space consisting of the set of vertices of M
n
, equipped with the graph distance rescaled by the factor n
-1/4, converges in distribution as n→∞ towards a limiting random compact metric space, in the sense of the Gromov–Hausdorff distance. We prove that the topology
of the limiting space is uniquely determined independently of p and of the subsequence, and that this space can be obtained as the quotient of the Continuum Random Tree for an equivalence
relation which is defined from Brownian labels attached to the vertices. We also verify that the Hausdorff dimension of the
limit is almost surely equal to 4. 相似文献
5.
Mahmoud Baroun Lahcen Maniar Roland Schnaubelt 《Integral Equations and Operator Theory》2009,65(2):169-193
We show the existence and uniqueness of the (asymptotically) almost periodic solution to parabolic evolution equations with
inhomogeneous boundary values on
\mathbbR{\mathbb{R}} and
\mathbbR±\mathbb{R}_{\pm}, if the data are (asymptotically) almost periodic. We assume that the underlying homogeneous problem satisfies the ‘Acquistapace–Terreni’
conditions and has an exponential dichotomy. If there is an exponential dichotomy only on half intervals ( − ∞, − T] and [T, ∞), then we obtain a Fredholm alternative of the equation on
\mathbbR{\mathbb{R}} in the space of functions being asymptotically almost periodic on
\mathbbR+{\mathbb{R}}_{+} and
\mathbbR-\mathbb{R}_{-}. 相似文献
6.
We give sufficient conditions for the interchange of the operations of limit and the Birkhoff integral for a sequence (f
n
) of functions from a measure space to a Banach space. In one result the equi-integrability of f
n
’s is involved and we assume f
n
→ f almost everywhere. The other result resembles the Lebesgue dominated convergence theorem where the almost uniform convergence
of (f
n
) to f is assumed. 相似文献
7.
In the present paper we prove a Korovkin type approximation theorem for a sequence of positive linear operators acting from
a weighted space Cρ1 into a weighted space Bρ2 with the use of a matrix summability method which includes both convergence and almost convergence. We also study the rates
of convergence of these operators. 相似文献
8.
I. G. Nikolaev 《Commentarii Mathematici Helvetici》1995,70(1):210-234
Schur's theorem states that an isotropic Riemannian manifold of dimension greater than two has constant curvature. It is natural
to guess that compact almost isotropic Riemannian manifolds of dimension greater than two are close to spaces of almost constant
curvature. We take the curvature anisotropy as the discrepancy of the sectional curvatures at a point. The main result of
this paper is that Riemannian manifolds in Cheeger's class ℜ(n,d,V,A) withL
1-small integral anisotropy haveL
p-small change of the sectional curvature over the manifold. We also estimate the deviation of the metric tensor from that
of constant curvature in theW
p
2
-norm, and prove that compact almost isotropic spaces inherit the differential structure of a space form. These stability
results are based on the generalization of Schur' theorem to metric spaces. 相似文献
9.
LetS be a topological semigroup andAP(S) the space of continous complex almost periodic functions onS. We obtain characterizations of compact and weakly compact operators from a Banach spaceX into AP(S). For this we use the almost periodic compactification ofS obtained through uniform spaces. For a bounded linear operatorT fromX into AP(S), letT
5, be the translate ofT bys inS defined byT
5(x)=(Tx)
5
. We define topologies on the space of bounded linear operators fromX into AP(S) and obtain the necessary and sufficient conditions for an operatorT to be compact or weakly compact in terms of the uniform continuity of the maps→T
5. IfS is a Hausdorff topological semigroup, we also obtain characterizations of compact and weakly compact multipliers on AP(S) in terms of the uniform continuity of the map S→μs, where μs denotes the unique vector measure corresponding to the operatorT
5. 相似文献
10.
Uroš Kuzman 《Journal of Geometric Analysis》2010,20(1):168-176
We study the deformation space of an embedded J-holomorphic disc D in an almost complex surface (X,J). Every such J is shown to be equivalent to a small deformation of a certain model structure J
β
along D, where β
:
D→ℂ is a complex valued function whose modulus |β| is a biholomorphic invariant. Furthermore, we find a nonlinear invertible operator mapping the space of all small J-holomorphic deformations of the given J-holomorphic disc onto the space of small holomorphic deformations of the standard disc in ℂ2. 相似文献
11.
Shixin Gan 《数学学报(英文版)》1999,15(2):187-196
In this paper, we prove that under theF
4 conditions, anyL log+
L bounded two-parameter Banach spece valued martingale converges almost surely to an integrable Banach space valued random
variable if and only if the Banach space has the Radon-Nikodym property. We further prove that the above conclusion remains
true if theF
4 condition is replaced by the weaker localF
4 condition.
Project supported by the National Natural Science Foundation of China and the State Education Commission Ph. D. Station Foundation 相似文献
12.
Primariness of a Banach space is almost always obtained through the use of the Pelczynski decomposition method. In this paper
we show that it is possible to directly construct UFDD’s in many cases from which the primariness can be deduced. We give
applications tol
p andX
p.
Research supported in part by NSF grant DMS-8602395. 相似文献
13.
A common way to produce a convex relaxation of a Mixed Integer Quadratically Constrained Program (MIQCP) is to lift the problem
into a higher-dimensional space by introducing variables Y
ij
to represent each of the products x
i
x
j
of variables appearing in a quadratic form. One advantage of such extended relaxations is that they can be efficiently strengthened
by using the (convex) SDP constraint
Y - x xT \succeq 0{Y - x x^T \succeq 0} and disjunctive programming. On the other hand, the main drawback of such an extended formulation is its huge size, even
for problems for which the number of x
i
variables is moderate. In this paper, we study methods to build low-dimensional relaxations of MIQCP that capture the strength
of the extended formulations. To do so, we use projection techniques pioneered in the context of the lift-and-project methodology.
We show how the extended formulation can be algorithmically projected to the original space by solving linear programs. Furthermore,
we extend the technique to project the SDP relaxation by solving SDPs. In the case of an MIQCP with a single quadratic constraint,
we propose a subgradient-based heuristic to efficiently solve these SDPs. We also propose a new eigen-reformulation for MIQCP, and a cut generation technique to strengthen this reformulation using polarity. We present extensive computational
results to illustrate the efficiency of the proposed techniques. Our computational results have two highlights. First, on
the GLOBALLib instances, we are able to generate relaxations that are almost as strong as those proposed in our companion
paper even though our computing times are about 100 times smaller, on average. Second, on box-QP instances, the strengthened
relaxations generated by our code are almost as strong as the well-studied SDP+RLT relaxations and can be solved in less than
2 s, even for large instances with 100 variables; the SDP+RLT relaxations for the same set of instances can take up to a couple
of hours to solve using a state-of-the-art SDP solver. 相似文献
14.
We show that if (S(t))
t≧0 is a contraction semigroup on a closed convex subset of a uniformly convex Banach space, then every bounded and “asymptotically
isometric” almost-orbit of (S(t))
t≧0 is weakly almost periodic in the sense of Eberlein. As one consequence, results on the existence of almost periodic solutions
to the abstract Cauchy problem are obtained without the need fora priori compactness assumptions. As a further consequence, the known strong ergodic limit theorems for (almost-) orbits of nonlinear
contraction semigroups turn out to be special cases of Eberlein’s classical ergodic theorem for weakly almost periodic functions. 相似文献
15.
The purpose of this paper is to introduce a new class of almost complex structures J on a Riemannian manifold M by using a certain identity for the relationship between the tensor F
i
j
of J and the Riemann curvature tensor R
hijk
of M. This class contains the Kählerian structures, and its relationship with some known classes of almost Hermitian structures defined by similar identities is discussed. For convenience we call each structure of this new class an almost C-structure, and a manifold with an almost C-structure an almost C-manifold. We obtain an analogue of F. Schur's theorem concerning the holomorphic sectional curvature of an almost Hermitian C-manifold, and some sufficient conditions for an almost Hermitian C-manifold to be Kählerian. We show that these results are also true for a manifold with a complex structure. 相似文献
16.
J. Borsík 《Acta Mathematica Hungarica》2007,115(4):319-332
Let X be a topological space and (Y,d) be a metric space. If f: X → Y is a function then there is a function a
f
: X → [0, ∞] such that f is almost continuous at x if and only if a
f
(x) = 0. Some properties of this function are investigated.
Supported by grant VEGA 2/6087/26 and APVT-51-006904. 相似文献
17.
George Androulakis Alexey I. Popov Adi Tcaciuc Vladimir G. Troitsky 《Integral Equations and Operator Theory》2009,65(4):473-484
We introduce and study the following modified version of the Invariant Subspace Problem: whether every operator T on an infinite-dimensional Banach space has an almost invariant half-space, that is, a subspace Y of infinite dimension and infinite codimension such that Y is of finite codimension in T(Y). We solve this problem in the affirmative for a large class of operators which includes quasinilpotent weighted shift operators
on ℓp (1 ≤ p < ∞) or c0. 相似文献
18.
Volker Runde 《Archiv der Mathematik》2011,97(4):325-331
Using the notion of complete compactness introduced by H. Saar, we define completely almost periodic functionals on completely
contractive Banach algebras. We show that, if (M, Γ) is a Hopf–von Neumann algebra with M injective, then the space of completely almost periodic functionals on M
* is a C*-subalgebra of M. 相似文献
19.
We analyze the connection between two ideas of apparently different nature.
On one hand, the existence of an extended Chebyshev basis, which means that
the Hermite interpolation problem has always a unique solution. On the other
hand, the existence of a normalized totally positive basis, which means that
the space is suitable for design purposes. We prove that the intervals where
the existence of a normalized totally positive basis is guaranteed are those intervals where
the existence of an extended Chebyshev basis of the space of derivatives can be ensured.
We apply our results to the spaces C
n
generated by 1,t, , t
n-2, cos t, sin t.
In particular, C
5 is a space suitable for design which permits the exact reproduction of
remarkable parametric curves, including lines and circles with a single control polygon.
We prove that this space has the minimal dimension for this purpose. 相似文献
20.
V. V. Savchuk 《Ukrainian Mathematical Journal》2008,60(6):910-926
We construct a linear method {ie910-01} for the approximation (in the unit disk) of classes of holomorphic functions {ie910-02}
that are the Hadamard convolutions of the unit balls of the Bergman space A
p
with reproducing kernels {ie910-03}. We give conditions for ψ under which the method {ie910-04} approximates the class {ie910-05}
in the metrics of the Hardy space H
s
and the Bergman space A
s
, 1 ≤ s ≤ p, with an error that coincides in order with the value of the best approximation by algebraic polynomials.
Translated from in Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 6, pp. 783–795, June, 2008. 相似文献