共查询到20条相似文献,搜索用时 343 毫秒
1.
Xiaolong Li 《Bulletin of the Brazilian Mathematical Society》2012,43(1):73-98
For a homoclinic class H(p f ) of f ?? Diff1(M), f?OH(p f ) is called R-robustly entropy-expansive if for g in a locally residual subset around f, the set ?? ? (x) = {y ?? M: dist(g n (x), g n (y)) ?? g3 (?n ?? ?)} has zero topological entropy for each x ?? H(p g ). We prove that there exists an open and dense set around f such that for every g in it, H(p g ) admits a dominated splitting of the form E ?? F 1 ?? ... ?? F k ?? G where all of F i are one-dimensional and non-hyperbolic, which extends a result of Pacifico and Vieitez for robustly entropy-expansive diffeomorphisms. Some relevant consequences are also shown. 相似文献
2.
P. van der Cruyssen 《BIT Numerical Mathematics》1982,22(4):533-537
Consider the (n+1)st order nonhomogeneous recursionX
k+n+1=b
k
X
k+n
+a
k
(n)
X
k+n-1+...+a
k
(1)
X
k
+X
k
.Leth be a particular solution, andf
(1),...,f
(n),g independent solutions of the associated homogeneous equation. It is supposed thatg dominatesf
(1),...,f
(n) andh. If we want to calculate a solutiony which is dominated byg, but dominatesf
(1),...,f
(n), then forward and backward recursion are numerically unstable. A stable algorithm is derived if we use results constituting a link between Generalised Continued Fractions and Recursion Relations. 相似文献
3.
M. A. Botto 《Journal of Approximation Theory》1976,16(4):347-365
We investigate two sequences of polynomial operators, H2n − 2(A1,f; x) and H2n − 3(A2,f; x), of degrees 2n − 2 and 2n − 3, respectively, defined by interpolatory conditions similar to those of the classical Hermite-Féjer interpolators H2n − 1(f, x). If H2n − 2(A1,f; x) and H2n − 3(A2,f; x) are based on the zeros of the jacobi polynomials Pn(α,β)(x), their convergence behaviour is similar to that of H2n − 1(f;, x). If they are based on the zeros of (1 − x2)Tn − 2(x), their convergence behaviour is better, in some sense, than that of H2n − 1(f, x). 相似文献
4.
We consider the Tikhonov regularizer fλ of a smooth function f ε H2m[0, 1], defined as the solution (see [1]) to We prove that if f(j)(0) = f(j)(1) = 0, J = m, …, k < 2m − 1, then ¦f − fλ¦j2 Rλ(2k − 2j + 3)/2m, J = 0, …, m. A detailed analysis is given of the effect of the boundary on convergence rates. 相似文献
5.
P. Erdös 《Israel Journal of Mathematics》1963,1(3):156-160
Denote byG(n; m) a graph ofn vertices andm edges. We prove that everyG(n; [n
2/4]+1) contains a circuit ofl edges for every 3 ≦l<c
2
n, also that everyG(n; [n
2/4]+1) contains ak
e(u
n, un) withu
n=[c
1 logn] (for the definition ofk
e(u
n, un) see the introduction). Finally fort>t
0 everyG(n; [tn
3/2]) contains a circuit of 2l edges for 2≦l<c
3
t
2.
This work was done while the author received support from the National Science Foundation, N.S.F. G.88. 相似文献
6.
U. Feiste 《Mathematische Nachrichten》1978,83(1):161-165
Compact metric spaces χ of such a kind, that ??f =??(X), are characterized, ??(X) is the σ-field of BOREL sets and ??f(X) is the field generated by all open subset of X. Our main result is Theorem 5: If χ is a compact metric space, then the following conditions are equivalent:
- 1 ??f(X) =??(X).
- 2 card (X) ≦x0 and there are k, m?N such that card (X(k)) = m.
- 3 There are k, m?N such that χ is homeomorphic to ωk · m + 1.
7.
Given graphs H1,…, Hk, let f(H1,…, Hk) be the minimum order of a graph G such that for each i, the induced copies of Hi in G cover V(G). We prove constructively that f(H1, H2) ≤ 2(n(H1) + n(H2) − 2); equality holds when H1 = H 2 = Kn. We prove that f(H1, K n) = n + 2√δ(H1)n + O(1) as n → ∞. We also determine f(K1, m −1, K n) exactly. © 2000 John Wiley & Sons, Inc. J Graph Theory 34: 180–190, 2000 相似文献
8.
Let Hn be the nth Hermite polynomial, i.e., the nth orthogonal on
polynomial with respect to the weight w(x)=exp(−x2). We prove the following: If f is an arbitrary polynomial of degree at most n, such that |f||Hn| at the zeros of Hn+1, then for k=1,…,n we have f(k)Hn(k), where · is the
norm. This result can be viewed as an inequality of the Duffin and Schaeffer type. As corollaries, we obtain a Markov-type inequality in the
norm, and estimates for the expansion coefficients in the basis of Hermite polynomials. 相似文献
9.
Let ??(n, m) denote the class of simple graphs on n vertices and m edges and let G ∈ ?? (n, m). There are many results in graph theory giving conditions under which G contains certain types of subgraphs, such as cycles of given lengths, complete graphs, etc. For example, Turan's theorem gives a sufficient condition for G to contain a Kk + 1 in terms of the number of edges in G. In this paper we prove that, for m = αn2, α > (k - 1)/2k, G contains a Kk + 1, each vertex of which has degree at least f(α)n and determine the best possible f(α). For m = ?n2/4? + 1 we establish that G contains cycles whose vertices have certain minimum degrees. Further, for m = αn2, α > 0 we establish that G contains a subgraph H with δ(H) ≥ f(α, n) and determine the best possible value of f(α, n). 相似文献
10.
Daniel J Madden 《Journal of Number Theory》1981,13(4):499-514
The primitive elements of a finite field are those elements of the field that generate the multiplicative group of k. If f(x) is a polynomial over k of small degree compared to the size of k, then f(x) represents at least one primitive element of k. Also f(x) represents an lth power at a primitive element of k, if l is also small. As a consequence of this, the following results holds.Theorem. Let g(x) be a square-free polynomial with integer coefficients. For all but finitely many prime numbers p, there is an integer a such that g(a) is equivalent to a primitive element modulo p.Theorem. Let l be a fixed prime number and f(x) be a square-free polynomial with integer coefficients with a non-zero constant term. For all but finitely many primes p, there exist integers a and b such that a is a primitive element and f(a) ≡ b1 modulo p. 相似文献
11.
Letf(t) = ∑a
k
e
ikt
be infinitely differentiable on R, |f(t)|<1. It is known that under these assumptions ‖n‖ converges to a finite limitl asn → ∞ (l
2 = sec(arga),a = (f′(0))2 -f″(0)). We obtain here more precise results: (i) an asymptotic series (in powers ofn
-1/2) for the Fourier coefficientsa
nk
off
n
, which holds uniformly ink asn → ∞; (ii) an asymptotic series (this time only powers ofn
-1 are present!) for ‖f
n
‖; (iii) the fact that ifi
j
f
(j)(0) is real forj = 1,2,..., 2h + 2 then ‖f
n
‖ = l + o(n
-h
),n → ∞. More generally, we obtain analogous finite asymptotic expansions whenf is assumed to be differentiable only finitely many times. 相似文献
12.
Torben Maack Bisgaard 《Mathematische Nachrichten》2000,210(1):67-83
For every a > 1, there is a function f : N20 → R, which is positive semidefinite but not a moment sequence, such that |f(m, n)| ≥ m+ na(m+n) for all (m, n). The constant 1 is the best possible. 相似文献
13.
A Hamiltonian graph G of order n is k-ordered, 2 ≤ k ≤ n, if for every sequence v1, v2, …, vk of k distinct vertices of G, there exists a Hamiltonian cycle that encounters v1, v2, …, vk in this order. Define f(k, n) as the smallest integer m for which any graph on n vertices with minimum degree at least m is a k-ordered Hamiltonian graph. In this article, answering a question of Ng and Schultz, we determine f(k, n) if n is sufficiently large in terms of k. Let g(k, n) = − 1. More precisely, we show that f(k, n) = g(k, n) if n ≥ 11k − 3. Furthermore, we show that f(k, n) ≥ g(k, n) for any n ≥ 2k. Finally we show that f(k, n) > g(k, n) if 2k ≤ n ≤ 3k − 6. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 17–25, 1999 相似文献
14.
In this paper, we study the existence of anti‐periodic solutions for the first order evolution equation in a Hilbert space H, where G : H → ? is an even function such that ?G is a mapping of class (S+) and f : ? → ? satisfies f(t + T) = –f(t) for any t ∈ ? with f(·) ∈ L2(0, T; H). (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
For the Jacobi-type Bernstein–Durrmeyer operator M
n,κ
on the simplex T
d
of ℝ
d
, we proved that for f∈L
p
(W
κ
;T
d
) with 1<p<∞,
K2,\varPhi(f,n-1)k,p £ c||f-Mn,kf||k,p £ c¢K2,\varPhi(f,n-1)k,p+c¢n-1||f||k,p,K_{2,\varPhi}\bigl(f,n^{-1}\bigr)_{\kappa,p}\leq c\|f-M_{n,\kappa}f\|_{\kappa,p}\leq c'K_{2,\varPhi}\bigl(f,n^{-1}\bigr)_{\kappa ,p}+c'n^{-1}\|f\|_{\kappa,p}, 相似文献
16.
Let Tn, n = 1,2,… be a sequence of linear contractions on the space where is a finite measure space. Let M be the subspace of L1 for which Tng → g weakly in L1 for g?M. If Tn1 → 1 strongly, then Tnf → f strongly for all f in the closed vector sublattice in L1 generated by M.This result can be applied to the determination of Korovkin sets and shadows in L1. Given a set G ? L1, its shadow S(G) is the set of all f?L1 with the property that Tnf → f strongly for any sequence of contractions Tn, n = 1, 2,… which converges strongly to the identity on G; and G is said to be a Korovkin set if S(G) = L1. For instance, if 1 ?G, then, where M is the linear hull of G and M is the sub-σ-algebra of generated by {x?X: g(x) > 0} for g?M. If the measure algebra is separable, has Korovkin sets consisting of two elements. 相似文献
17.
Toshiyasu Arai 《Mathematical Logic Quarterly》2002,48(1):125-130
For α < ε0, Nα denotes the number of occurrences of ω in the Cantor normal form of α with the base ω. For a binary number-theoretic function f let B(K; f) denote the length n of the longest descending chain (α0, …, αn–1) of ordinals <ε0 such that for all i < n, Nαi ≤ f (K, i). Simpson [2] called ε0 as slowly well ordered when B (K; f) is totally defined for f (K; i) = K · (i+ 1). Let |n| denote the binary length of the natural number n, and |n|k the k-times iterate of the logarithmic function |n|. For a unary function h let L(K; h) denote the function B (K; h0(K; i)) with h0(K, i) = K + |i| · |i|h(i). In this note we show, inspired from Weiermann [4], that, under a reasonable condition on h, the functionL (K; h) is primitive recursive in the inverse h–1 and vice versa. 相似文献
18.
P. V. Chunaev 《Proceedings of the Steklov Institute of Mathematics》2010,270(1):278-284
We study the approximation of functions f(z) that are analytic in a neighborhood of zero by finite sums of the form H
n
(z) = H
n
(h, f, {λ
k
}; z) = Σ
k=1
n
λ
k
h(λ
k
z), where h is a fixed function that is analytic in the unit disk |z| < 1 and the numbers λ
k
(which depend on h, f, and n) are calculated by a certain algorithm. An exact value of the radius of the convergence H
n
(z) → f(z), n → ∞, and an order-sharp estimate for the rate of this convergence are obtained; an application to numerical analysis is given. 相似文献
19.
Ana María Suchanek 《Journal of multivariate analysis》1978,8(4):589-597
A remarkable theorem proved by Komlòs [4] states that if {fn} is a bounded sequence in L1(R), then there exists a subsequence {fnk} and f L1(R) such that fnk (as well as any further subsequence) converges Cesaro to f almost everywhere. A similar theorem due to Révész [6] states that if {fn} is a bounded sequence in L2(R), then there is a subsequence {fnk} and f L2(R) such that Σk=1∞ ak(fnk − f) converges a.e. whenever Σk=1∞ | ak |2 < ∞. In this paper, we generalize these two theorems to functions with values in a Hilbert space (Theorems 3.1 and 3.3). 相似文献
20.
Izolda Gorgol 《Graphs and Combinatorics》2008,24(4):327-331
A subgraph of an edge-colored graph is called rainbow if all of its edges have different colors. For a graph H and a positive integer n, the anti-Ramsey number f (n, H) is the maximum number of colors in an edge-coloring of K
n
with no rainbow copy of H. The rainbow number
rb(n, H) is the minimum number of colors such that any edge-coloring of K
n
with rb(n, H) number of colors contains a rainbow copy of H. Certainly rb(n, H) = f(n, H) + 1. Anti-Ramsey numbers were introduced by Erdős et al. [4] and studied in numerous papers.
We show that for n ≥ k + 1, where C
k
+ denotes a cycle C
k
with a pendant edge. 相似文献
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