共查询到20条相似文献,搜索用时 31 毫秒
1.
孙太祥 《高校应用数学学报(英文版)》2002,17(3):313-318
Let f be a tree map,P(f) the set of periodic points of f and CR(f) the set of chain recurrent points of f. In this paper,the notion of division for invariant closed subsets of a tree map is introduced. It is proved that: (1) fhas zero topological entropy if and only if for any x∈CR(f)-P(f) and each natural number s the orbit of x under f^5 has a division; (2) If f has zero topological entropy,then for any xECR(f)--P(f) the w-limit set of x is an infinite minimal set. 相似文献
2.
3.
Notes on combinatorial set theory 总被引:1,自引:0,他引:1
Saharon Shelah 《Israel Journal of Mathematics》1973,14(3):262-277
We shall prove some unconnected theorems: (1) (G.C.H.) \omega _{\alpha + 1} \to \left( {\omega _\alpha + \xi } \right)_2^2 when ℵα is regular, │ξ│+<ωα. (2) There is a Jonsson algebra in ℵα+n, and \aleph _{a + n} \not \to \left[ {\aleph _{a + n} } \right]_{\aleph _{a + n} }^{n + 1} if 2^{\aleph _{ - - } } = \aleph
_{a + n} \cdot (3) If λ>ℵ0 is a strong limit cardinal, then among the graphs with ≦λ vertices each of valence <λ there is a universal one. (4)(G.C.H.) If f is a set mapping on \omega _{a + 1} (ℵα regular) │f(x)∩f(y│<ℵα, then there is a free subset of order-type ζ for every ζ<ωα+1. 相似文献
4.
A. K. Varma 《Israel Journal of Mathematics》1968,6(1):66-73
LetR
n(f; x) be a trigonometric polynomial of ordern satisfying Eqs. (1.1) and (1.2). The object of this note is to obtain sufficient conditions in order that thepth derivative ofR
n(f, x) converges uniformly tof
(p)(x) on the real line. The sufficient conditions turns out to bef
(p)(x) ∈ Lipα, α>0 with the restrictions of Eq. (1.3).
The author acknowledges financial support for this work from the University of Alberta, Post Doctoral Fellowship 1966–67.
The author is extremely grateful to the referee for pointing out some valuable results and suggestions. 相似文献
5.
Soon Mo JUNG 《数学学报(英文版)》2006,22(2):583-586
The stability problems of the exponential (functional) equation on a restricted domain will be investigated, and the results will be applied to the study of an asymptotic property of that equation. More precisely, the following asymptotic property is proved: Let X be a real (or complex) normed space. A mapping f : X → C is exponential if and only if f(x + y) - f(x)f(y) → 0 as ||x|| + ||y|| → ∞ under some suitable conditions. 相似文献
6.
Given a (known) function f:[0,1]→(0,1), we consider the problem of simulating a coin with probability of heads f(p) by tossing a coin with unknown heads probability p, as well as a fair coin, N times each, where N may be random. The work of Keane and O’Brien (ACM Trans. Model. Comput. Simul. 4(2):213–219, 1994) implies that such a simulation scheme with the probability ℙ
p
(N<∞) equal to 1 exists if and only if f is continuous. Nacu and Peres (Ann. Appl. Probab. 15(1A):93–115, 2005) proved that f is real analytic in an open set S⊂(0,1) if and only if such a simulation scheme exists with the probability ℙ
p
(N>n) decaying exponentially in n for every p∈S. We prove that for α>0 noninteger, f is in the space C
α
[0,1] if and only if a simulation scheme as above exists with ℙ
p
(N>n)≤C(Δ
n
(p))
α
, where
\varDelta n(x):=max{?{x(1-x)/n},1/n}\varDelta _{n}(x):=\max\{\sqrt{x(1-x)/n},1/n\}. The key to the proof is a new result in approximation theory: Let B+n\mathcal{B}^{+}_{n} be the cone of univariate polynomials with nonnegative Bernstein coefficients of degree n. We show that a function f:[0,1]→(0,1) is in C
α
[0,1] if and only if f has a series representation ?n=1¥Fn\sum_{n=1}^{\infty}F_{n} with Fn ? B+nF_{n}\in \mathcal{B}^{+}_{n} and ∑
k>n
F
k
(x)≤C(Δ
n
(x))
α
for all x∈[0,1] and n≥1. We also provide a counterexample to a theorem stated without proof by Lorentz (Math. Ann. 151:239–251, 1963), who claimed that if some jn ? B+n\varphi_{n}\in\mathcal{B}^{+}_{n} satisfy |f(x)−φ
n
(x)|≤C(Δ
n
(x))
α
for all x∈[0,1] and n≥1, then f∈C
α
[0,1]. 相似文献
7.
LetX be a real linear normed space, (G, +) be a topological group, andK be a discrete normal subgroup ofG. We prove that if a continuous at a point or measurable (in the sense specified later) functionf:X →G fulfils the condition:f(x +y) -f(x) -f(y) ∈K whenever ‖x‖ = ‖y‖, then, under some additional assumptions onG,K, andX, there esists a continuous additive functionA :X →G such thatf(x) -A(x) ∈K. 相似文献
8.
Jorge J. Betancor Juan C. Fariña Teresa Martinez Lourdes Rodríguez-Mesa 《Arkiv f?r Matematik》2008,46(2):219-250
In this paper we investigate Riesz transforms R
μ
(k) of order k≥1 related to the Bessel operator Δμ
f(x)=-f”(x)-((2μ+1)/x)f’(x) and extend the results of Muckenhoupt and Stein for the conjugate Hankel transform (a Riesz transform of order one). We
obtain that for every k≥1, R
μ
(k) is a principal value operator of strong type (p,p), p∈(1,∞), and weak type (1,1) with respect to the measure dλ(x)=x
2μ+1
dx in (0,∞). We also characterize the class of weights ω on (0,∞) for which R
μ
(k) maps L
p
(ω) into itself and L
1(ω) into L
1,∞(ω) boundedly. This class of weights is wider than the Muckenhoupt class of weights for the doubling measure dλ. These weighted results extend the ones obtained by Andersen and Kerman. 相似文献
9.
Ferenc Móricz 《Acta Mathematica Hungarica》2012,134(3):356-368
We consider complex-valued functions f∈L
1(ℝ+), where ℝ+:=[0,∞), and prove sufficient conditions under which the sine Fourier transform [^(f)]s\hat{f}_{s} and the cosine Fourier transform [^(f)]c\hat{f}_{c} belong to one of the Lipschitz classes Lip (α) and lip (α) for some 0<α≦1, or to one of the Zygmund classes Zyg (α) and zyg (α) for some 0<α≦2. These sufficient conditions are best possible in the sense that they are also necessary if f(x)≧0 almost everywhere. 相似文献
10.
E. Yu. Romanenko 《Ukrainian Mathematical Journal》2005,57(11):1792-1808
Let {I, f, Z
+} be a dynamical system induced by a continuous mapping f of a closed bounded interval I into itself. To describe the dynamics of neighborhoods of points unstable under the mapping f, we propose the concept of the εω-set ω
f, ε(x) of a point x as the ω-limit set of the ε-neighborhood of the point x. We investigate the relationship between the εω-set and the domain of influence of a point. It is also shown that the domain
of influence of an unstable point is always a cycle of intervals. The results obtained can be directly used in the theory
of difference equations with continuous time and similar equations.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 11, pp. 1534–1547, November, 2005. 相似文献
11.
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
12.
R. I. Hovsepyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2009,44(4):205-211
It is proved that any measurable, finite function f(x) has a smooth primitive F(x), i.e. there is a function F(x) such that F′(x) = f(x) almost everywhere, and particularly ω(δ; F) = o(δ ln δ). This is an improvement of N. N. Luzin’s theorem which states just the continuity of the primitive F(x). 相似文献
13.
Hui Xue Lao 《数学学报(英文版)》2009,25(4):687-692
Let Af(n) be the coefficient of the logarithmic derivative for the Hecke L-function. In this paper we study the cancellation of the function Ay(n) twisted with an additive character e(α√n), α 〉0, i.e. Ef(x) = Σx〈n〈2x Af(n)e(α√n). 相似文献
14.
Yaochen Zhu 《数学学报(英文版)》2000,16(3):395-398
Let f (x) be a continued fraction with elements a
n
x, where coefficients a
n
are positive algebraic numbers. Using the criterion of [l] for any nonzero real algebraic numbers α1,...,αs with distinct absolute values the algebraic independence of the values f(α1), ..., f(αs) is proved under certain assumption concerning only with a
n
. For some transcendental numbers ξ the algebraic independence of values f(ξj)(j∈ℤ) is also established.
Received March 27, 1998, Accepted September 28, 1998 相似文献
15.
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
16.
The transversal number, packing number, covering number and strong stability number of hypergraphs are denoted by τ, ν, ϱ
and α, respectively. A hypergraph family t is called τ-bound (ϱ-bound) if there exists a “binding function”f(x) such that τ(H)≦f(v(H)) (ϱ(H)≦f(α(H))) for allH ∈ t. Methods are presented to show that various hypergraph families are τ-bound and/or ϱ-bound. The results can be applied
to families of geometrical nature like subforests of trees, boxes, boxes of polyominoes or to families defined by hypergraph
theoretic terms like the family where every subhypergraph has the Helly-property. 相似文献
17.
Nils Svanstedt 《Applications of Mathematics》2008,53(2):143-155
Multiscale stochastic homogenization is studied for convection-diffusion problems. More specifically, we consider the asymptotic
behaviour of a sequence of realizations of the form ∂u
ɛ
ω
/ ∂t+1 / ɛ
3
C(T
3(x/ɛ
3)ω
3) · ∇u
ɛ
ω
− div(α(T
2(x/ɛ
2)ω
2, t) ∇u
ɛ
ω
) = f. It is shown, under certain structure assumptions on the random vector field C(ω
3) and the random map α(ω
1, ω
2, t), that the sequence {u
ɛ
ω
} of solutions converges in the sense of G-convergence of parabolic operators to the solution u of the homogenized problem ∂u/∂t − div (B(t)∇u= f). 相似文献
18.
Jindřich Zapletal 《Israel Journal of Mathematics》1997,97(1):101-111
Two total functionsf, g fromω
1 toω are called strongly almost disjoint if {α<ω
1:f(α)=g(α)} is finite. We show that it is consistent with ZFC to have families of pairwise strongly almost disjoint functions of arbitrary
prescribed size. 相似文献
19.
袁荣 《应用数学学报(英文版)》1998,14(1):68-73
Itiswellknownthattheexistenceofalmostperiodicsolutionsiscloselyrelatedtothestabilityofsolutions.Forfunctionaldifferentialequationswithinfinitedelay,Y.Hin.[5'6]studiedtheproblemsontheexistenceofalmostperiodicsolutionsandthestability.However,therearefewpapersll2]dealingwithneutralfunctionaldifferentialequationswithinfinitedelay.Inthepresentpaper,forneutralfunctionaldifferentialequationswithinfinitedelay,weprovetheinherencetheoremfortheuniformlystableoperatorD(t),definethestabilitywithrespecttot… 相似文献
20.
We investigate the relationships between smooth and strongly smooth points of the unit ball of an order continuous symmetric
function space E, and of the unit ball of the space of τ-measurable operators E(M,t){E(\mathcal{M},\tau)} associated to a semifinite von Neumann algebra (M, t){(\mathcal{M}, \tau)}. We prove that x is a smooth point of the unit ball in E(M, t){E(\mathcal{M}, \tau)} if and only if the decreasing rearrangement μ(x) of the operator x is a smooth point of the unit ball in E, and either μ(∞; f) = 0, for the function f ? SE×{f\in S_{E^{\times}}} supporting μ(x), or s(x
*) = 1. Under the assumption that the trace τ on M{\mathcal{M}} is σ-finite, we show that x is strongly smooth point of the unit ball in E(M, t){E(\mathcal{M}, \tau)} if and only if its decreasing rearrangement μ(x) is a strongly smooth point of the unit ball in E. Consequently, for a symmetric function space E, we obtain corresponding relations between smoothness or strong smoothness of the function f and its decreasing rearrangement μ(f). Finally, under suitable assumptions, we state results relating the global properties such as smoothness and Fréchet smoothness
of the spaces E and E(M,t){E(\mathcal{M},\tau)}. 相似文献