共查询到20条相似文献,搜索用时 31 毫秒
1.
Tijani Pakhrou 《Mathematische Nachrichten》2008,281(3):396-401
Let Y be a reflexive subspace of the Banach space X, let (Ω, Σ, μ) be a finite measure space, and let L∞(μ, X) be the Banach space of all essentially bounded μ ‐Bochner integrable functions on Ω with values in X, endowed with its usual norm. Let us suppose that Σ0 is a sub‐σ ‐algebra of Σ, and let μ0 be the restriction of μ to Σ0. Given a natural number n, let N be a monotonous norm in ?n . We prove that L∞(μ, Y) is N ‐simultaneously proximinal in L∞(μ,X), and that if X is reflexive then L∞(μ0, X) is N ‐simultaneously proximinal in L∞(μ, X) in the sense of Fathi, Hussein, and Khalil [3]. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
2.
Victor Alexandru Angel Popescu Elena Liliana Popescu Sobia Sultana 《Monatshefte für Mathematik》2009,38(3):223-233
Let (K, v) be a perfect rank one valued field and let ([`(Kv)],[`(v)]){(\overline{K_{v}},\overline{v})} be the canonical valued field obtained from (K, v) by the unique extension of the valuation [(v)\tilde]{\widetilde{v}} of K
v
, the completion of K relative to v, to a fixed algebraic closure [`(Kv)]{\overline{K_{v}}} of K
v
. Let [`(K)]{\overline{K}} be the algebraic closure of K in [`(Kv)]{\overline {K_{v}}}. An algebraic extension L of K, L ì [`(K)]{L\subset\overline{K}}, is said to be a v-adic maximal extension, if [`(v)] | L{\overline{v}\mid_{L}} is the only extension of v to L and L is maximal with this property. In this paper we describe some basic properties of such extensions and we consider them in
connection with the v-adic spectral norm on [`(K)]{\overline{K}} and with the absolute Galois groups Gal([`(K)]/K){(\overline{K}/K)} and Gal([`(Kv)] /Kv){(\overline{K_{v}} /K_{v})}. Some other auxiliary results are given, which may be useful for other purposes. 相似文献
3.
Zhi-jian QIU Department of Economic Mathematics Southwestern University of Finance Economics Chengdu China 《中国科学A辑(英文版)》2007,50(3):305-312
For a compact subset K in the complex plane, let Rat(K) denote the set of the rational functions with poles off K. Given a finite positive measure with support contained in K, let R2(K,v) denote the closure of Rat(K) in L2(v) and let Sv denote the operator of multiplication by the independent variable z on R2(K, v), that is, Svf = zf for every f∈R2(K, v). SupposeΩis a bounded open subset in the complex plane whose complement has finitely many components and suppose Rat(Ω) is dense in the Hardy space H2(Ω). Letσdenote a harmonic measure forΩ. In this work, we characterize all subnormal operators quasi-similar to Sσ, the operators of the multiplication by z on R2(Ω,σ). We show that for a given v supported onΩ, Sv is quasi-similar to Sσif and only if v/■Ω■σ and log(dv/dσ)∈L1(σ). Our result extends a well-known result of Clary on the unit disk. 相似文献
4.
A. S. Asratian H. J. Broersma J. Van den Heuvel H. J. Veldman 《Journal of Graph Theory》1996,21(1):1-10
For an integer i, a graph is called an Li-graph if, for each triple of vertices u, v, w with d(u, v) = 2 and w (element of) N(u) (intersection) N(v), d(u) + d(v) ≥ | N(u) (union) N(v) (union) N(w)| —i. Asratian and Khachatrian proved that connected Lo-graphs of order at least 3 are hamiltonian, thus improving Ore's Theorem. All K1,3-free graphs are L1-graphs, whence recognizing hamiltonian L1-graphs is an NP-complete problem. The following results about L1-graphs, unifying known results of Ore-type and known results on K1,3-free graphs, are obtained. Set K = lcub;G|Kp,p+1 (contained within) G (contained within) Kp V Kp+1 for some ρ ≥ } (v denotes join). If G is a 2-connected L1-graph, then G is 1-tough unless G (element of) K. Furthermore, if G is as connected L1-graph of order at least 3 such that |N(u) (intersection) N(v)| ≥ 2 for every pair of vertices u, v with d(u, v) = 2, then G is hamiltonian unless G ϵ K, and every pair of vertices x, y with d(x, y) ≥ 3 is connected by a Hamilton path. This result implies that of Asratian and Khachatrian. Finally, if G is a connected L1-graph of even order, then G has a perfect matching. © 1996 John Wiley & Sons, Inc. 相似文献
5.
G. Griffith Elder 《Archiv der Mathematik》2010,94(1):43-47
Let K be a complete local field of characteristic p with perfect residue field, and let L/K be a finite, totally ramified, Galois p-extension with G = Gal(L/K). Let v L be the normalized valuation with ${v_L(L^{\times})=\mathbb{Z} }Let K be a complete local field of characteristic p with perfect residue field, and let L/K be a finite, totally ramified, Galois p-extension with G = Gal(L/K). Let v
L
be the normalized valuation with
vL(L×)=\mathbbZ {v_L(L^{\times})=\mathbb{Z} }. Let pL ? L{\pi_L\in L} be a prime element, and let p′ (x) be the derivative of the minimal polynomial for π
L
over K. We show that any element r ? L{\rho\in L} with vL(r) o -vL(p¢(pL))-1 mod [L:K]{v_L(\rho)\equiv -v_L(p'(\pi_L))-1\bmod[L:K]} generates a normal basis: K[G]ρ = L. This criterion is tight: Given any integer i with
i\not o -vL(p¢(pL))-1 mod [L:K]{i\not\equiv -v_L(p'(\pi_L))-1\bmod[L:K]}, there is a ri ? L{\rho_i\in L} with v
L
(ρ
i
) = i such that
K[G]ri\subsetneq L{K[G]\rho_i\subsetneq L}. 相似文献
6.
We consider the following type of problems. Given a graph G = (V, E) and lists L(v) of allowed colors for its vertices v ∈ V such that |L(v)| = p for all v ∈ V and |L(u) ∩ L(v)| ≤ c for all uv ∈ E, is it possible to find a “list coloring,” i.e., a color f(v) ∈ L(v) for each v ∈ V, so that f(u) ≠ f(v) for all uv ∈ E? We prove that every of maximum degree Δ admits a list coloring for every such list assignment, provided p ≥ . Apart from a multiplicative constant, the result is tight, as lists of length may be necessary. Moreover, for G = Kn (the complete graph on n vertices) and c = 1 (i.e., almost disjoint lists), the smallest value of p is shown to have asymptotics (1 + o(1)) . For planar graphs and c = 1, lists of length 4 suffice. ˜© 1998 John Wiley & Sons, Inc. J Graph Theory 27: 43–49, 1998 相似文献
7.
The object of this paper is to prove the following theorem: Let Y be a closed subspace of the Banach space X, (S,Σ,μ) a σ-finite measure space, L(S,Y) (respectively, L(S, X)) the space of all strongly measurable functions from S to Y (respectively, X), and p a positive number. Then L(S,Y) is pointwise proximinal in L(S,X) if and only if Lp(μ,Y) is proximinal in Lp(μ,X). As an application of the theorem stated above, we prove that if Y is a separable closed subspace of the Banach space X, p is a positive number, then Lp(μ,Y) is proximinal in Lp(μ,X) if and only if Y is proximinal in X. Finally, several other interesting results on pointwise best approximation are also obtained. 相似文献
8.
It is shown that every probability measure on the interval [0, 1] gives rise
to a unique infinite random graph g on vertices
{v1,
v2, . . .}
and a sequence of random graphs gn on vertices
{v1, . . . ,
vn}
such that
.
In particular,
for Bernoulli graphs with
stable property Q,
can be strengthened to: probability space (, F, P),
set of infinite graphs
G(Q) ,
F with property Q such
that
.AMS Subject Classification: 05C80, 05C62. 相似文献
9.
Two-side inequalities for the modified Bessel functionI
v(x), Kv(x) of the first and third kind and of order v, are established. The chief tool is the monotonocity of the functionsI
v+1(x)/I
v(x),K
v+1(x)/K
v(x). 相似文献
10.
《Quaestiones Mathematicae》2013,36(3-4):269-288
Abstract Using a lifting of £∞ (μ, X) ([5],[6]), we construct a lifting ρ x of the seminormed vector space £∞ (μ, X) of measurable, essentially bounded X-valued functions. We show that in a certain sense such a lifting always exists. If μ is Lebesgue measure on (0, 1) we show that ρ x exists as map from £∞ ((O, 1), X) → £∞,((0, l), X) if and only if X is reflexive. In general the lifted function takes its values in X **. Therefore we investigate the question, when f ε £∞ (μ, X) is strictly liftable in the sense that the lifted function is a map with values even in X. As an application we introduce the space £∞ strong (μ, L (X, Y**)), a subspace of the space of strongly measurable, essentially bounded L (X, Y, **)-valued functions, and the associated quotient space £∞ strong (μ, L (X,Y**)). We show that this space is a Banach space because there is a kind of a Dunford-Pettis Theorem for a subspace of L (X, £∞(μ Y**)). Finally we investigate the measurability property of functions in £∞(μ Y**)) und see that there exists a connection to the Radon-Nikodym property of the space L (X, Y). 相似文献
11.
Carl Johan Casselgren 《Discrete Mathematics》2011,(13):168
Let Ks×m be the complete multipartite graph with s parts and m vertices in each part. Assign to each vertex v of Ks×m a list L(v) of colors, by choosing each list uniformly at random from all 2-subsets of a color set C of size σ(m). In this paper we determine, for all fixed s and growing m, the asymptotic probability of the existence of a proper coloring φ, such that φ(v)∈L(v) for all v∈V(Ks×m). We show that this property exhibits a sharp threshold at σ(m)=2(s−1)m. 相似文献
12.
Liliana Pavel 《Mediterranean Journal of Mathematics》2008,5(3):341-356
Let K be a compact hypergroup.We investigate Trig(K), the linear span of coordinate functions of the irreducible representations of K. Contrary to the group case, Trig(K) endowed with the usual multiplication does not bear an algebra structure, but it has a natural normed algebra structure
when it inherits the convolution from , the algebra of all bounded Radon measures. We characterize the center of the algebras , L
p
(K) and Trig(K) respectively, and consequently we obtain, for a certain class of hypergroups, the correspondence between the structure space
of the center of L
1(K) and the center of Trig(K). As an application we study the existence of a finite universal Korovkin set w.r.t. positive operators in the center of
L
1(K), in particular in L
1(K), whenever K is commutative.
The author was partially supported by the Romanian Academy under the grant No. 22/2007. 相似文献
13.
The object of this paper is to prove the following theorem: If Y is a closed subspace of the Banach space X, then L1(μ, Y) is proximinal in L1(μ, X) if and only if Lp(μ, Y) is proximinal in Lp(μ, Y) for every p, 1 < p < ∞. As an application of this result we prove that if Y is either reflexive or Y is a separable proximinal dual space, then L1(μ, Y) is proximinal in L1(μ, X). 相似文献
14.
Let U := L\G be a homogeneous variety defined over a number field K, where G is a connected semisimple K-group and L is a connected maximal semisimple K-subgroup of G with finite index in its normalizer. Assuming that G(K
v
) acts transitively on U(K
v
) for almost all places v of K, we obtain an asymptotic for the number of rational points U(K) with height bounded by T as T → ∞, and settle new cases of Manin’s conjecture for many wonderful varieties. The main ingredient of our approach is the
equidistribution of semisimple adelic periods, which is established using the theory of unipotent flows. 相似文献
15.
Martin Fuchs 《Mathematical Methods in the Applied Sciences》1996,19(15):1225-1232
We discuss certain classes of quasi-static non-Newtonian fluids for which a power-law of the form σD=∇ϕ(ℰv) holds. Here σD is the stress deviator, v the velocity field, ℰv its symmetric derivative and ϕ is the function \[ \phi ({\cal E}v)=\frac 12\mu _\infty \left| {\cal E}v\right| ⁁2+\frac 1p\mu _0\left\{ \begin{array}{c} \left( 1+\left| {\cal E}v\right| ⁁2\right) ⁁{p/2} \\ \text{or} \\ \left| {\cal E}v\right| ⁁p \end{array} \right\}, \] ϕ(ℰv)=1 2 μ∞∣ℰv∣2+1 p μ0 (1+∣ℰv∣2)p/2 or ∣ℰv∣p, μ∞⩾0, μ0⩾0, μ∞+μ0>0, 1<p<∞. We then prove various regularity results for the velocity field v, for example differentiability almost everywhere and local boundedness of the tensor ℰv. 相似文献
16.
Let v, k be positive integers and k ≥ 3, then Kk = : {v: v ≥ k} is a 3‐BD closed set. Two finite generating sets of 3‐BD closed sets K4 and K5 are obtained by H. Hanani [5] and Qiurong Wu [12] respectively. In this article we show that if v ≥ 6, then v ∈ B3(K,1), where K = {6,7,…,41,45,46,47,51,52,53,83,84}\{22,26}; that is, we show that K is a generating set for K6. Finally we show that v ∈ B3(6,20) for all v ∈ K\{35,39,40,45}. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 128–136, 2008 相似文献
17.
For 1 ≤ i < j < d, a j-dimensional subspace L of
and a convex body K in
, we consider the projection K|L of K onto L. The directed projection function v
i,j
(K;L,u) is defined to be the i-dimensional size of the part of K|L which is illuminated in direction u ∈ L. This involves the i-th surface area measure of K|L and is motivated by Groemer’s [17] notion of semi-girth of bodies in
. It is well-known that centrally symmetric bodies are determined (up to translation) by their projection functions, we extend
this by showing that an arbitrary body is determined by any one of its directed projection functions. We also obtain a corresponding
stability result. Groemer [17] addressed the case i = 1, j = 2, d = 3. For j > 1, we then consider the average of v
1,j
(K;L,u) over all spaces L containing u and investigate whether the resulting function
determines K. We will find pairs (d,j) for which this is the case and some pairs for which it is false. The latter situation will be seen to be related to some
classical results from number theory. We will also consider more general averages for the case of centrally symmetric bodies.
The research of the first author was supported in part by NSF Grant DMS-9971202 and that of the second author by a grant from
the Volkswagen Foundation. 相似文献
18.
We characterize the proper t-wise balanced designs t-(v,K,1) for t ≥ 3, λ = 1 and v ≤ 16 with at least two block sizes. While we do not examine extensions of S(3,4,16)'s, we do determine all other possible extensions of S(3,K,v)'s for v ≤ 16. One very interesting extension is an S(4, {5,6}, 17) design.©1995 John Wiley & Sons, Inc. 相似文献
19.
Richard A Alò André de Korvin Vo Van Tho 《Journal of Mathematical Analysis and Applications》1978,63(3):563-590
For a Banach space E and for 1 ? p < ∞ let ?p<∞ let LEp(μ) = LEp(S,B,μ) denote all Bochner p-integrable E-valued functions on a measure space (S,B,μ). Under study are convergence theorems for integrals of functions in LEp(μ) with respect to Nemytskii measures. Weak integrals are then denoted to Hammerstein operators, and a study of topologies generated by vector measures leads to a characterization of compact Hammerstein operators. 相似文献
20.
《Indagationes Mathematicae (Proceedings)》1988,91(3):225-230
It is known that Lr(E, C(K)), the space of all regular operators from E into C(K), is a Riesz space for all Riesz spaces E if and only if K is Stonian. We prove that this statement holds if E is replaced by C(K), where K is a compact space, the cardinal number of which satisfies a certain condition. 相似文献