共查询到20条相似文献,搜索用时 31 毫秒
1.
Hask?z Co?kun 《Journal of Mathematical Analysis and Applications》2002,276(2):833-844
We consider Hill's equation y″+(λ−q)y=0 where q∈L1[0,π]. We show that if ln—the length of the n-th instability interval—is of order O(n−(k+2)) then the real Fourier coefficients ank,bnk of q(k)—k-th derivative of q—are of order O(n−2), which implies that q(k) is absolutely continuous almost everywhere for k=0,1,2,…. 相似文献
2.
Letl andk be positive integers, and letX={0,1,...,l k?1}. Is it true that for every coloring δ:X×X→{0,1,...} there either exist elementsx 0<x 1<...<x l ofX with δ(x 0,x 1)=δ(x 1,x 2)=...=δ(x l?1,x l), or else there exist elementsy 0<y 1<...<y k ofX with δ(y i?1,y i) ∈ δ(y j?1,y j) for all 1<-i<j≤k? We prove here that this is the case if eitherl≤2, ork≤4, orl≥(3k)2k . The general question remains open. 相似文献
3.
Paul W. Eloe Johnny Henderson 《Journal of Mathematical Analysis and Applications》2007,331(1):240-247
For the nth order differential equation, y(n)=f(x,y,y′,…,y(n−1)), we consider uniqueness implies existence results for solutions satisfying certain nonlocal (k+2)-point boundary conditions, 1?k?n−1. Uniqueness of solutions when k=n−1 is intimately related to uniqueness of solutions when 1?k?n−2. These relationships are investigated as well. 相似文献
4.
Dalibor Froncek 《Discrete Mathematics》2009,309(2):501-389
We completely solve certain case of a “two delegation negotiation” version of the Oberwolfach problem, which can be stated as follows. Let H(k,3) be a bipartite graph with bipartition X={x1,x2,…,xk},Y={y1,y2,…,yk} and edges x1y1,x1y2,xkyk−1,xkyk, and xiyi−1,xiyi,xiyi+1 for i=2,3,…,k−1. We completely characterize all complete bipartite graphs Kn,n that can be factorized into factors isomorphic to G=mH(k,3), where k is odd and mH(k,3) is the graph consisting of m disjoint copies of H(k,3). 相似文献
5.
If r(p) is the least positive integral value of x for which y2 ≡ x(x + 1) ? (x + r ? 1)(modp) has a solution, we conjecture that r(p) ≤ r2 ? r + 1 with equality for infinitely many primes p. A proof is sketched for r = 5. A further generalization to y2 ≡ (x + a1) ? (x + ar) is suggested, where the a's are fixed positive integers. 相似文献
6.
G. Sampson 《Journal of Mathematical Analysis and Applications》2007,334(1):196-205
For aj,bj?1, j=1,2,…,d, we prove that the operator maps into itself for , where , and k(x,y)=φ(x,y)eig(x,y), φ(x,y) satisfies (1.2) (e.g. φ(x,y)=|x−y|iτ,τ real) and the phase g(x,y)=xa⋅yb. We study operators with more general phases and for these operators we require that aj,bj>1, j=1,2,…,d, or al=bl?1 for some l∈{1,2,…,d}. 相似文献
7.
Chen’s Conjecture and Its Generalization 总被引:1,自引:0,他引:1
Let l1, l2, ..., lg be even integers and x be a sufficiently large number. In this paper, the authors prove that the number of positive odd integers k ≤ x such that (k +l1)^2, (k +l2)^2, ..., (k +lg)^2 can not be expressed as 2^n+p^α is at least c(g)x, where p is an odd prime and the constant c(g) depends only on g. 相似文献
8.
Bruce R. Ebanks 《Results in Mathematics》2002,42(1-2):37-41
?(x + y) - ?(x) - ?(y) = ?(x ?1 + y ?l) are identical to those of the Cauchy equation ?(xy) = ?(x) + ?(y) when ? is a function from the positive real numbers into the reals. In the present article, we prove this equivalence for functions mapping the set of nonzero elements of a field (excluding ?2) . 相似文献
9.
Manisha Kulkarni 《Indagationes Mathematicae》2003,14(1):35-44
Let g(y) ? Q[Y] be an irreducible polynomial of degree n ≥ 3. We prove that there are only finitely many rational numbers x, y with bounded denominator and an integer m ≥ 3 satisfying the equation x(x + 1) (x + 2)…(x + (m − 1) ) = g(y). We also obtain certain finiteness results when g(y) is not an irreducible polynomial. 相似文献
10.
Balázs Patkós 《Journal of Combinatorial Theory, Series A》2009,116(5):1047-1055
A family of sets F⊆X2 is defined to be l-trace k-Sperner if for any subset Y of X with size l the trace of F on Y (the restriction of F to Y) does not contain any chain of length k+1. In this paper we investigate the maximum size that an l-trace k-Sperner family (with underlying set [n]={1,2,…,n}) can have for various values of k, l and n. 相似文献
11.
Given a 2k component (column) vector z=(x′,y′)′, x′=(x1,…, xk), y′= (y1,…,yk), having a 2k variate multivariate normal distribution with mean vector zero, and an unknown 2k×2k positive definite correlation matrix Σ, Shafer and Olkin (1983) conjecture that P(x,y)=P{|x1|<c,…,|xk|<c,|y1|<c,…,|yk|<c} is minimized when Σ has a certain pattern. This conjecture is proved to be correct. A known inequality is generalized. 相似文献
12.
Boštjan Brešar Manoj Changat Prasanth G. Narasimha-Shenoi 《Discrete Mathematics》2009,309(20):6114-2609
The concept of the k-Steiner interval is a natural generalization of the geodesic (binary) interval. It is defined as a mapping S:V×?×V?2V such that S(u1,…,uk) consists of all vertices in G that lie on some Steiner tree with respect to a multiset W={u1,…,uk} of vertices from G. In this paper we obtain, for each k, a characterization of the class of graphs in which every k-Steiner interval S has the so-called union property, which says that S(u1,…,uk) coincides with the union of geodesic intervals I(ui,uj) between all pairs from W. It turns out that, as soon as k>3, this class coincides with the class of graphs in which the k-Steiner interval enjoys the monotone axiom (m), respectively (b2) axiom, the conditions from betweenness theory. Notably, S satisfies (m), if x1,…,xk∈S(u1,…,uk) implies S(x1,…,xk)⊆S(u1,…,uk), and S satisfies (b2) if x∈S(u1,u2,…,uk) implies S(x,u2,…,uk)⊆S(u1,…,uk). In the case k=3, these three classes are different, and we give structural characterizations of graphs for which their Steiner interval S satisfies the union property as well as the monotone axiom (m). We also prove several partial observations on the class of graphs in which the 3-Steiner interval satisfies (b2), which lead to the conjecture that these are precisely the graphs in which every block is a geodetic graph with diameter at most two. 相似文献
13.
De-Jun Feng 《Advances in Mathematics》2005,195(1):24-101
In this paper, we give a systematical study of the local structures and fractal indices of the limited Rademacher functions and Bernoulli convolutions associated with Pisot numbers. For a given Pisot number in the interval (1,2), we construct a finite family of non-negative matrices (maybe non-square), such that the corresponding fractal indices can be re-expressed as some limits in terms of products of these non-negative matrices. We are especially interested in the case that the associated Pisot number is a simple Pisot number, i.e., the unique positive root of the polynomial xk-xk-1-…-x-1 (k=2,3,…). In this case, the corresponding products of matrices can be decomposed into the products of scalars, based on which the precise formulas of fractal indices, as well as the multifractal formalism, are obtained. 相似文献
14.
In this paper we consider a super-Brownian motion X with branching mechanism k(x)zα, where k(x) > 0 is a bounded Holder continuous function on Rd and infx∈Rd k(x) = 0. We prove that if k(x) ≥ //x// -l(0 ≤l < ∞) for sufficiently large x, then X has compact support property, and for dimension d = 1, if k(x) ≥exp(-l‖x‖)(0≤l < ∞) for sufficiently large x, then X also has compact support property. The maximal order of k(x) for finite time extinction is different between d = 1, d = 2 and d ≥ 3: it is O(‖x‖-(α+1)) in one dimension, O(‖x‖-2(log‖x‖)-(α+1) ) in two dimensions, and O(‖x‖2) in higher dimensions. These growth orders also turn out to be the maximum order for the nonexistence of a positive solution for 1/2Δu =k(x)uα. 相似文献
15.
Noga Alon Michal Feldman Ariel D. Procaccia Moshe Tennenholtz 《Discrete Mathematics》2010,310(23):3432-3435
Consider the unit circle S1 with distance function d measured along the circle. We show that for every selection of 2n points x1,…,xn,y1,…,yn∈S1 there exists i∈{1,…,n} such that . We also discuss a game theoretic interpretation of this result. 相似文献
16.
Let N′(k) denote the number of coprime integral solutions x, y of y2 = x3 + k. It is shown that lim supk→∞N′(k) ≥ 12. 相似文献
17.
Robin J. Chapman Amit Khetan Robert J. Waters 《Journal of Combinatorial Theory, Series A》2009,116(1):205-214
There is a strikingly simple classical formula for the number of lattice paths avoiding the line x=ky when k is a positive integer. We show that the natural generalization of this simple formula continues to hold when the line x=ky is replaced by certain periodic staircase boundaries—but only under special conditions. The simple formula fails in general, and it remains an open question to what extent our results can be further generalized. 相似文献
18.
Li Qiu 《Linear algebra and its applications》2007,422(1):304-307
Let A1, … , Ak be positive semidefinite matrices and B1, … , Bk arbitrary complex matrices of order n. We show that
span{(A1x)°(A2x)°?°(Akx)|x∈Cn}=range(A1°A2°?°Ak) 相似文献
19.
Vít Jelínek 《Discrete Applied Mathematics》2010,158(7):841-2876
Rank-width is a graph width parameter introduced by Oum and Seymour. It is known that a class of graphs has bounded rank-width if, and only if, it has bounded clique-width, and that the rank-width of G is less than or equal to its branch-width.The n×nsquare grid, denoted by Gn,n, is a graph on the vertex set {1,2,…,n}×{1,2,…,n}, where a vertex (x,y) is connected by an edge to a vertex (x′,y′) if and only if |x−x′|+|y−y′|=1.We prove that the rank-width of Gn,n is equal to n−1, thus solving an open problem of Oum. 相似文献
20.
Ignacy Kotlarski 《Annali di Matematica Pura ed Applicata》1966,74(1):129-134
Summary The aim of this paper is to prove the following theorem about characterization of probability distributions in Hilbert spaces:Theorem. — Let x1, x2, …, xn be n (n≥3) independent random variables in the Hilbert spaceH, having their characteristic functionals fk(t) = E[ei(t,x
k)], (k=1, 2, …, n): let y1=x1 + xn, y2=x2 + xn, …, yn−1=xn−1 + xn.
If the characteristic functional f(t1, t2, …, tn−1) of the random variables (y1, y2, …, yn−1) does not vanish, then the joint distribution of (y1, y2, …, yn−1) determines all the distributions of x1, x2, …, xn up to change of location. 相似文献