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1.
2.
E. Naraghirad 《Optimization Letters》2009,3(1):89-100
In this paper, we consider a problem of best approximation (simultaneous farthest point) for bounded sets in a real normed
linear space X. We study simultaneous farthest point in X by elements of bounded sets, and present various characterizations of simultaneous farthest point of elements by bounded
sets in terms of the extremal points of the closed unit ball of X
*, where X
* is the dual space of X. We establish the characterizations of simultaneous farthest points for bounded sets in , the space of all real-valued continuous functions on a compact topological space Q endowed with the usual operations and with the norm . It is important to state clearly that the contribution of this paper in relation with the previous works (see, for example,
[9, Theorem 1.13]) is a technical method to represent the distance from a bounded set to a compact convex set in X which specifically concentrates on the Hahn-Banach Theorem in X. 相似文献
3.
Antonio Cossidente 《Designs, Codes and Cryptography》2009,51(2):123-129
In the geometric setting of commuting orthogonal and unitary polarities we construct an infinite family of complete (q + 1)2–spans of the Hermitian surface , q odd. A construction of an infinite family of minimal blocking sets of , q odd, admitting PSL
2(q), is also provided.
相似文献
4.
The multiplicative spectrum of a complex Banach space X is the class
(X) of all (automatically compact and Hausdorff) topological spaces appearing as spectra of Banach algebras (X, *) for all possible continuous multiplications on X turning X into a commutative associative complex algebra with unity. Properties of multiplicative spectra are studied. In particular,
we show that
(X
n
) consists of countable compact spaces with at most n nonisolated points for any separable, hereditarily indecomposable Banach space X. We prove that
(C[0, 1]) coincides with the class of all metrizable compact spaces.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 14, Algebra,
2004. 相似文献
5.
John Polhill 《Designs, Codes and Cryptography》2009,52(2):163-169
By modifying a construction for Hadamard (Menon) difference sets we construct two infinite families of negative Latin square
type partial difference sets in groups of the form where p is any odd prime. One of these families has the well-known Paley parameters, which had previously only been constructed in
p-groups. This provides new constructions of Hadamard matrices and implies the existence of many new strongly regular graphs
including some that are conference graphs. As a corollary, we are able to construct Paley–Hadamard difference sets of the
Stanton-Sprott family in groups of the form when is a prime power. These are new parameters for such difference sets.
相似文献
6.
Vladimir Pestov 《Israel Journal of Mathematics》2002,127(1):317-357
In this paper we further study links between concentration of measure in topological transformation groups, existence of fixed
points, and Ramsey-type theorems for metric spaces. We prove that whenever the group Iso
of isometries of Urysohn’s universal complete separable metric space
, equipped with the compact-open topology, acts upon an arbitrary compact space, it has a fixed point. The same is true if
is replaced with any generalized Urysohn metric spaceU that is sufficiently homogeneous. Modulo a recent theorem by Uspenskij that every topological group embeds into a topological
group of the form Iso(U), our result implies that every topological group embeds into an extremely amenable group (one admitting an invariant multiplicative
mean on bounded right uniformly continuous functions). By way of the proof, we show that every topological group is approximated
by finite groups in a certain weak sense. Our technique also results in a new proof of the extreme amenability (fixed point
on compacta property) for infinite orthogonal groups. Going in the opposite direction, we deduce some Ramsey-type theorems
for metric subspaces of Hilbert spaces and for spherical metric spaces from existing results on extreme amenability of infinite
unitary groups and groups of isometries of Hilbert spaces. 相似文献
7.
In this paper we define partially ordered quasi-uniform spaces (X,
, ≤) (PO-quasi-uniform spaces) as those space with a biconvex quasi-uniformity
on the poset (X, ≤) and give a construction of a (transitive) biconvex compatible quasi-uniformity on a partially ordered topological space
when its topology satisfies certain natural conditions. We also show that under certain conditions on the topology
of a PO-quasi-uniform space (X,
, ≤), the bicompletion
of (X,
) is also a PO-quasi-uniform space (
, ⪯) with a partial order ⪯ on
that extends ≤ in a natural way.
相似文献
8.
Christer Borell 《Probability Theory and Related Fields》2008,140(1-2):195-205
Let be an integer, let γ be the standard Gaussian measure on , and let . Given this paper gives a necessary and sufficient condition such that the inequality is true for all Borel sets A
1,...,A
m
in of strictly positive γ-measure or all convex Borel sets A
1,...,A
m
in of strictly positive γ-measure, respectively. In particular, the paper exhibits inequalities of the Brunn–Minkowski type
for γ which are true for all convex sets but not for all measurable sets.
相似文献
9.
Sehie PARK 《数学学报(英文版)》2007,23(8):1509-1526
Let B be the class of 'better' admissible multimaps due to the author. We introduce new concepts of admissibility (in the sense of Klee) and of Klee approximability for subsets of G-convex uniform spaces and show that any compact closed multimap in B from a G-convex space into itself with the Klee approximable range has a fixed point. This new theorem contains a large number of known results on topological vector spaces or on various subclasses of the class of admissible G-convex spaces. Such subclasses are those of O-spaces, sets of the Zima-Hadzic type, locally G-convex spaces, and LG-spaces. Mutual relations among those subclasses and some related results are added. 相似文献
10.
John F. Toland 《Arkiv f?r Matematik》2001,39(2):383-394
Let
denote the Hardy space of real-valued functions on the unit circle with weak derivatives in the usual real Hardy space
. It is shown that when the weak derivative of a locally Lipschitz continuous functionf has bounded variation on compact sets the Nemytskii operatorF, defined byF(u)=f·u, maps
continuously into itself. A further condition sufficient for the continuous Fréchet differentiability ofF is then added. 相似文献
11.
In this paper we examine whether the number of pairwise non-isomorphic minimal blocking sets in PG(2, q) of a certain size is larger than polynomial. Our main result is that there are more than polynomial pairwise non-isomorphic
minimal blocking sets for any size in the intervals [2q−1, 3q−4] for q odd and for q square. We can also prove a similar result for certain values of the intervals and .
相似文献
12.
We consider several kinds of partition relations on the set of real numbers and its powers, as well as their parameterizations with the set of all infinite sets of natural numbers, and show that they hold in some models of set theory. The proofs use generic absoluteness,
that is, absoluteness under the required forcing extensions. We show that Solovay models are absolute under those forcing
extensions, which yields, for instance, that in these models for every well ordered partition of there is a sequence of perfect sets whose product lies in one piece of the partition. Moreover, for every finite partition
of there is and a sequence of perfect sets such that the product lies in one piece of the partition, where is the set of all infinite subsets of X. The proofs yield the same results for Borel partitions in ZFC, and for more complex partitions in any model satisfying a certain degree of generic absoluteness.
This work was supported by the research projects MTM 2005-01025 of the Spanish Ministry of Science and Education and 2005SGR-00738
of the Generalitat de Catalunya. A substantial part of the work was carried out while the second-named author was ICREA Visiting
Professor at the Centre de Recerca Matemàtica in Bellaterra (Barcelona), and also during the first-named author’s stays at
the Instituto Venezolano de Investigaciones Científicas and the California Institute of Technology. The authors gratefully
acknowledge the support provided by these institutions. 相似文献
13.
We present a new distance characterization of Aleksandrov spaces of non-positive curvature. By introducing a quasilinearization
for abstract metric spaces we draw an analogy between characterization of Aleksandrov spaces and inner product spaces; the
quasi-inner product is defined by means of the quadrilateral cosine—a metric substitute for the angular measure between two
directions at different points. Our main result states that a geodesically connected metric space is an Aleksandrov domain (also known as a CAT(0) space) if and only if the quadrilateral cosine does not exceed one for every two pairs of
distinct points in . We also observe that a geodesically connected metric space is an domain if and only if, for every quadruple of points in , the quadrilateral inequality (known as Euler’s inequality in ) holds. As a corollary of our main result we give necessary and sufficient conditions for a semimetric space to be an domain. Our results provide a complete solution to the Curvature Problem posed by Gromov in the context of metric spaces
of non-positive curvature.
相似文献
14.
We construct a nonarchimedean (or p-adic) analogue of the classical ternary Cantor set
. In particular, we show that this nonarchimedean Cantor set
is self-similar. Furthermore, we characterize
as the subset of 3-adic integers whose elements contain only 0’s and 2’s in their 3-adic expansions and prove that
is naturally homeomorphic to
. Finally, from the point of view of the theory of fractal strings and their complex fractal dimensions [7, 8], the corresponding
nonarchimedean Cantor string resembles the standard archimedean (or real) Cantor string perfectly.
Dedicated to Vladimir Arnold, on the occasion of his jubilee 相似文献
15.
In this paper we have proved several approximation theorems for the family of minimal surfaces in that imply, among other things, that complete minimal surfaces are dense in the space of all minimal surfaces endowed with
the topology of C
k
convergence on compact sets, for any .
As a consequence of the above density result, we have been able to produce the first example of a complete proper minimal
surface in with uncountably many ends.
This research is partially supported by MEC-FEDER Grant no. MTM2004 - 00160. 相似文献
16.
Vasily A. Prokhorov Edward B. Saff Maxim Yattselev 《Complex Analysis and Operator Theory》2009,3(2):501-524
Let be a bounded simply connected domain with boundary Γ and let be a regular compact set with connected complement. In this paper we investigate asymptotics of the extremal constants:
where is the supremum norm on a compact set K, is the set of all algebraic polynomials of degree at most m, and as . Subsequently, we obtain asymptotic behavior of the Kolmogorov k-widths, , of the unit ball An∞ of restricted to E in C(E), where H∞ is the Hardy space of bounded analytic functions on G and C(E) is the space of continuous functions on E.
Received: April 24, 2008. Accepted: May 15, 2008. 相似文献
17.
In this paper, we characterize the dynamic of every Abelian subgroups
of
,
or
. We show that there exists a
-invariant, dense open set U in
saturated by minimal orbits with
a union of at most n
-invariant vector subspaces of
of dimension n−1 or n−2 over
. As a consequence,
has height at most n and in particular it admits a minimal set in
.
This work is supported by the research unit: systèmes dynamiques et combinatoire: 99UR15-15 相似文献
18.
Philip Kremer 《Archive for Mathematical Logic》2006,45(8):1021-1032
Let
be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality
and a temporal modality
, understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language
by interpreting
in dynamic topological systems, i.e. ordered pairs
, where X is a topological space and f is a continuous function on X. Artemov, Davoren and Nerode have axiomatized a logic S4C, and have shown that S4C is sound and complete for this semantics. Zhang and Mints have shown that S4C is complete relative to a particular topological space, Cantor space. The current paper produces an alternate proof of the Zhang-Mints result. 相似文献
19.
A singular riemannian foliation on a complete riemannian manifold M is said to admit sections if each regular point of M is contained in a complete totally geodesic immersed submanifold Σ that meets every leaf of orthogonally and whose dimension is the codimension of the regular leaves of . We prove that the algebra of basic forms of M relative to is isomorphic to the algebra of those differential forms on Σ that are invariant under the generalized Weyl pseudogroup of
Σ. This extends a result of Michor for polar actions. It follows from this result that the algebra of basic function is finitely
generated if the sections are compact. We also prove that the leaves of coincide with the level sets of a transnormal map (generalization of isoparametric map) if M is simply connected, the sections are flat and the leaves of are compact. This result extends previous results due to Carter and West, Terng, and Heintze, Liu and Olmos.
Marcos M. Alexandrino and Claudio Gorodski have been partially supported by FAPESP and CNPq. 相似文献
20.
Valentina S. Harizanov Carl G. JockuschJr. Julia F. Knight 《Archive for Mathematical Logic》2009,48(1):39-53
We study the complexity of infinite chains and antichains in computable partial orderings. We show that there is a computable
partial ordering which has an infinite chain but none that is or , and also obtain the analogous result for antichains. On the other hand, we show that every computable partial ordering
which has an infinite chain must have an infinite chain that is the difference of two sets. Our main result is that there is a computably axiomatizable theory K of partial orderings such that K has a computable model with arbitrarily long finite chains but no computable model with an infinite chain. We also prove
the corresponding result for antichains. Finally, we prove that if a computable partial ordering has the feature that for every , there is an infinite chain or antichain that is relative to , then we have uniform dichotomy: either for all copies of , there is an infinite chain that is relative to , or for all copies of , there is an infinite antichain that is relative to . 相似文献