共查询到20条相似文献,搜索用时 515 毫秒
1.
Amine El Sahili 《Journal of Graph Theory》2003,44(4):296-303
Consider two maps f and g from a set E into a set F such that f(x) ≠ g(x) for every x in E. Suppose that there exists a positive integer n such that for any element z in F either f?1(z) or g?1(z) has at most n elements. Then, E can be partitioned into 2n + 1 subsets E1, E2,…,E2n + 1 such that f(Ei)∩ g(Ei) = ?, 1 ≤ i ≤ 2n + 1. © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 296–303, 2003 相似文献
2.
Valeria Marraffa 《Journal of Theoretical Probability》1988,1(3):255-261
It is shown here that for any Banach spaceE-valued amart (X
n) of classB, almost sure convergence off(Xn) tof(X) for eachf in a total subset ofE
* implies scalar convergence toX. 相似文献
3.
XIAJIANGUO 《高校应用数学学报(英文版)》1998,13(1):109-116
Let E be a compact Lie group, G a closed subgroup of E, and H a closed normal sub-group of G. For principal fibre bundle (E,p, E,/G;G) tmd (E/H,p‘,E/G;G/H), the relation between auta(E) (resp. autce (E)) and autG/H(E/H) (resp. autGe/H(E/H)) is investigated by using bundle map theory and transformation group theory. It will enable us to compute the group JG(E) (resp. SG(E)) while the group J G/u(E/H) is known. 相似文献
4.
For n -dimensional subspaces E
n
, F
n
of L
1
(-1,1) with E
n
spanned by Chebyshev polynomials of the second kind and F
n
the set of Müntz polynomials with , , it is shown that the relative projection constants satisfy
(E
n
, L
1
(-1,1))
C log n and
(F
n
, L
1
(-1,1)) = O(1) , . The spaces L
1
w(α,β)
, where w
α,β
is the weight function of the Jacobi polynomials and , are also studied. The Jacobi partial sum projections, which are used in connection with E
n
, are not minimal.
September 26, 1996. 相似文献
5.
6.
Let E be a closed set with inf E = a and sup E = b, and k be a positive integer. Let f : E Rbe such that the k-th Peano derivative of f relative to E, f
(k) (x, E), exists. It is proved under certain condition on the function f, that an extension F : [a, b] Rof f exists such that the ordinary derivative of F of order k, F
<k> (x) exists on [a, b] and is continuous on [a, b], and f
<> (x, E) = F
<i> (x) on E, for i = 1, 2, &, k. 相似文献
7.
《Quaestiones Mathematicae》2013,36(3-4):303-309
Abstract For a completely regular space X and a normed space E let Ck (x, E) (resp., Cp (x, E)) be the set of all E-valued continuous maps on X endowed with the compact-open (resp., pointwise convergence) topology. It is shown that the set of all F-valued linear continuous maps on Ck (x, E) when equipped with the topology of uniform convergence on the members of some families of bounded subsets of Ck (x, E) is a complete uniform space if F is a Band space and X is Dieudonné complete. This result is applied to prove that Dieudonné completeness is preserved by linear quotient surjections from Ck (x, E) onto Ck (Y, E) (resp., from Cp (x, E) onto Cp (x, E)) provided E, F are Band spaces and Y is a k-space. 相似文献
8.
Let E,F be two Banach spaces,B(E,F),B+(E,F),Φ(E,F),SΦ(E,F) and R(E,F) be bounded linear,double splitting,Fredholm,semi-Frdholm and finite rank operators from E into F,respectively. Let Σ be any one of the following sets:{T ∈Φ(E,F):Index T=constant and dim N(T)=constant},{T ∈ SΦ(E,F):either dim N(T)=constant< ∞ or codim R(T)=constant< ∞} and {T ∈ R(E,F):Rank T=constant< ∞}. Then it is known that Σ is a smooth submanifold of B(E,F) with the tangent space TAΣ={B ∈ B(E,F):BN(A)-R(A) } for any A ∈Σ. However,for ... 相似文献
9.
We consider two person zero-sum stochastic games. The recursive formula for the valuesvλ (resp.v
n) of the discounted (resp. finitely repeated) version can be written in terms of a single basic operator Φ(α,f) where α is the weight on the present payoff andf the future payoff. We give sufficient conditions in terms of Φ(α,f) and its derivative at 0 for limv
n and limvλ to exist and to be equal.
We apply these results to obtain such convergence properties for absorbing games with compact action spaces and incomplete
information games. 相似文献
10.
V. É. Geit 《Mathematical Notes》1971,10(5):768-776
We prove the following: for every sequence {Fv}, Fv ? 0, Fv > 0 there exists a functionf such that
- En(f)?Fn (n=0, 1, 2, ...) and
- Akn?k? v=1 n vk?1 Fv?1?Ωk (f, n?1) (n=1, 2, ...).
11.
Yehoram Gordon 《Israel Journal of Mathematics》1966,4(3):177-188
GivenF(z),f
1(z), ..,f
n(z) defined on a finite point setE, and givenB — the set of generalised polynomials Σ
k
=1/n
a
kfk(z) — the definition of a juxtapolynomial is extended in the following manner: for a fixedλ(0<λ≦1),f(z) εB is called a generalizedλ-weak juxtapolynomial toF(z) onE if and only if there exists nog(z) εB for whichg(z)=F(z) wheneverf(z)=F(z) and |g(z)−F(z) |<λ|f(z)−F(z)| wheneverf(z)≠F(z). The properties of suchf(z) are investigated with particular attention given to the real case.
This note is an extension of a part of the author’s M.Sc. Thesis under the supervision of Prof. B. Grünbaum to whom the author
wishes to express his sincerest appreciation. The author also wishes to thank Dr. J. Lindenstrauss for his valuable remarks
in the preparation of this paper. 相似文献
12.
Complete convergence of weighted sums of martingale differences 总被引:2,自引:0,他引:2
Kai Fun Yu 《Journal of Theoretical Probability》1990,3(2):339-347
LetF
oF
1 ... be an increasing family of -algebras. For eachn1,X
n isF
n-measurable, andE(X
n|Fn–1) is zero almost surely, andE(|En|p|Fn–1) is bounded by a finite constant almost surely for somep2. Leta
n1,...,a
nn be constants. Conditions are given to establish the complete convergence of (a
n1
X
1+...+a
nnXn)/n
1/p
, thereby obtaining an extension of Chow's (1966) result for the case of independent and identically distributed random variables. Whenp>2, the conditions are an improvement on existing results for the case of independence and identical distribution. 相似文献
13.
Edge-Colorings with No Large Polychromatic Stars 总被引:1,自引:0,他引:1
Tao Jiang 《Graphs and Combinatorics》2002,18(2):303-308
Given a graph G and a positive integer r, let f
r
(G) denote the largest number of colors that can be used in a coloring of E(G) such that each vertex is incident to at most r colors. For all positive integers n and r, we determine f
r
(K
n,n
) exactly and f
r
(K
n
) within 1. In doing so, we disprove a conjecture by Manoussakis, Spyratos, Tuza and Voigt in [4].
Received: May 17, 1999 Final version received: January 12, 2000 相似文献
14.
S. P. Zhou 《Israel Journal of Mathematics》1992,78(1):75-83
The present paper gives a converse result by showing that there exists a functionf ∈C
[−1,1], which satisfies that sgn(x)f(x) ≥ 0 forx ∈ [−1, 1], such that {fx75-1} whereE
n
(0)
(f, 1) is the best approximation of degreen tof by polynomials which are copositive with it, that is, polynomialsP withP(x(f(x) ≥ 0 for allx ∈ [−1, 1],E
n(f) is the ordinary best polynomial approximation off of degreen. 相似文献
15.
This paper contains some theorems related to the best approximation ρn(f;E) to a function f in the uniform metric on a compact set by rational functions of degree at most n. We obtain results characterizing the relationship between ρn(f;K) and ρn(f;E) in the case when complements of compact sets K and E are connected, K is a subset of the interior Ω of E, and f is analytic in Ω and continuous on E. 相似文献
16.
Jilong Zhang 《Journal of Mathematical Analysis and Applications》2010,367(2):401-490
We investigate value distribution and uniqueness problems of difference polynomials of meromorphic functions. In particular, we show that for a finite order transcendental meromorphic function f with λ(1/f)<ρ(f) and a non-zero complex constant c, if n?2, then fn(z)f(z+c) assumes every non-zero value a∈C infinitely often. This research also shows that there exist two sets S1 with 9 (resp. 5) elements and S2 with 1 element, such that for a finite order nonconstant meromorphic (resp. entire) function f and a non-zero complex constant c, Ef(z)(Sj)=Ef(z+c)(Sj)(j=1,2) imply f(z)≡f(z+c). This gives an answer to a question of Gross concerning a finite order meromorphic function f and its shift. 相似文献
17.
Hans-Peter Blatt Ren Grothmann Ralitza Kovacheva 《Journal of Approximation Theory》2004,126(2):157-170
Let E be a compact set in
with connected complement and positive logarithmic capacity. For any f continuous on E and analytic in the interior of E, we consider the distribution of extreme points of the error of best uniform polynomial approximation on E. Let Λ=(nj) be a subsequence of
such that nj+1/nj→1. If, for nΛ, An( f)∂E denotes the set of extreme points of the error function, we prove that there is a subsequence Λ′ of Λ such that the distribution of any (n+2)th Fekete point set
of An( f) tends weakly to the equilibrium distribution on E as n→∞ in Λ′. Furthermore, we prove a discrepancy result for the distribution of the point sets
if the boundary of E is smooth enough. 相似文献
18.
Stability of Doob—Meyer Decomposition Under Extended Convergence 总被引:1,自引:0,他引:1
JeanMemin 《应用数学学报(英文版)》2003,19(2):177-190
In what follows, we consider the relation between Aldous‘s extended convergence and weak convergence of filtrations. We prove that, for a sequence (X^n) of Ft^n )-special semimartingales, with canonical decomposition X^n =M^n A^n, if the extended convergence (X^n,F.^n)→(X,T. ) holds with a quasi-left continuous (Ft)-special semimartingale X = M A, then, under an additional assumption of uniform integrability,we get the convergence in probability under the Skorokhod topology: M^n↑P→M and A^n↑P→ A. 相似文献
19.
Simple graphs are considered. Let G be a graph andg(x) andf(x) integer-valued functions defined on V(G) withg(x)⩽f(x) for everyxɛV(G). For a subgraphH ofG and a factorizationF=|F
1,F
2,⃛,F
1| ofG, if |E(H)∩E(F
1)|=1,1⩽i⩽j, then we say thatF orthogonal toH. It is proved that for an (mg(x)+k,mf(x) -k)-graphG, there exists a subgraphR ofG such that for any subgraphH ofG with |E(H)|=k,R has a (g,f)-factorization orthogonal toH, where 1⩽k<m andg(x)⩾1 orf(x)⩾5 for everyxɛV(G).
Project supported by the Chitia Postdoctoral Science Foundation and Chuang Xin Foundation of the Chinese Academy of Sciences. 相似文献
20.
If A : C∞E → C∞F is an elliptic operator between sections of vector bundles E, F over a closed smooth n-manifold X, Y a smooth (n – 1)-submanifold of X with trivial normal bundle, and Ψ = (ΨE, ΨF) a pair of automorphisms of E | Y and F | Y inducing a diffeomorphism f of Y and commuting with the principal symbol σ A of A over Y, then an elliptic operator AΨ is (uniquely up to operators of lower order) defined between sections of vector bundles EΨ, FΨ over a closed manifold Xf, all obtained by cutting and pasting the respective objects along Y. The difference index AΨ – index A is investigated and the relations with additivity properties of topological invariants and with classical transmission problems are explained. 相似文献