Consider the Schrödinger equation {fx25-1}. The following estimates are proved: (A) IfV≡0 then for any 0≤α<1/2, {fx25-2}, and for α=1/2,s>1/2, {fx25-3} (B) If |V(x)|≤C(1+|x|2)?1?δ, δ>0, then (if 0 is neither an eigenvalue nor a resonance of ?Δ+V), {fx25-4}. 相似文献
We prove that a 2-connected graph G of order p is hamiltonian if for all distinct vertices u and v, dist(u,v) = 2 implies that |N(u) U N(v)| ? (2p - 1)/3. We also demonstrate hamiltonian-connected and traceability properties in graphs under similar conditions. 相似文献
Let {X,Xn;n ≥ 1} be a strictly stationary sequence of ρ-mixing random variables with mean zeros and finite variances. Set Sn =∑k=1^n Xk, Mn=maxk≤n|Sk|,n≥1.Suppose limn→∞ESn^2/n=:σ^2〉0 and ∑n^∞=1 ρ^2/d(2^n)〈∞,where d=2 if 1≤r〈2 and d〉r if r≥2.We prove that if E|X|^r 〈∞,for 1≤p〈2 and r〉p,then limε→0ε^2(r-p)/2-p ∑∞n=1 n^r/p-2 P{Mn≥εn^1/p}=2p/r-p ∑∞k=1(-1)^k/(2k+1)^2(r-p)/(2-p)E|Z|^2(r-p)/2-p,where Z has a normal distribution with mean 0 and variance σ^2. 相似文献
The paper introduces singular integral operators of a new type defined in the space Lp with the weight function on the complex plane. For these operators, norm estimates are derived. Namely, if V is a complex-valued function on the complex plane satisfying the condition |V(z) ? V(??)| ?? w|z ? ??| and F is an entire function, then we put $$P_F^* f(z) = \mathop {\sup }\limits_{\varepsilon > 0} \left| {\int\limits_{\left| {\zeta - z} \right| > \varepsilon } {F\left( {\frac{{V(\zeta ) - V(z)}} {{\zeta - z}}} \right)\frac{{f(\zeta )}} {{\left( {\zeta - z} \right)^2 }}d\sigma (\zeta )} } \right|.$$ It is shown that if the weight function ?? is a Muckenhoupt Ap weight for 1 < p < ??, then $$\left\| {P_F^* f} \right\|_{p,\omega } \leqslant C(F,w,p)\left\| f \right\|_{p,\omega } .$$. 相似文献
Suppose G is a transitive permutation group on a finite set W\mit\Omega of n points and let p be a prime divisor of |G||G|. The smallest number of points moved by a non-identity p-element is called the minimal p-degree of G and is denoted mp (G). ¶ In the article the minimal p-degrees of various 2-transitive permutation groups are calculated. Using the classification of finite 2-transitive permutation groups these results yield the main theorem, that mp(G) 3 [(p-1)/(p+1)] ·|W|m_{p}(G) \geq {{p-1} \over {p+1}} \cdot |\mit\Omega | holds, if Alt(W) \nleqq G {\rm Alt}(\mit\Omega ) \nleqq G .¶Also all groups G (and prime divisors p of |G||G|) for which mp(G) £ [(p-1)/(p)] ·|W|m_{p}(G)\le {{p-1}\over{p}} \cdot |\mit\Omega | are identified. 相似文献
The vertex linear arboricity vla(G) of a nonempty graph G is the minimum number of subsets into which the vertex set V(G) can be partitioned so that each subset induces a subgraph whose connected components are paths. This paper provides an upper bound for vla(G) of a connected nonempty graph G, namely vla(G) ≦ 1 + ?δ(G)/2? where δ(G) denotes the maximum degree of G. Moreover, if δ(G) is even, then vla(G) = 1 + ?δ(G)/2? if and only if G is either a cycle or a complete graph. 相似文献
A connected graph G is called t-tough if t · w(G - S) ? |S| for any subset S of V(G) with w(G - S) > 1, where w(G - S) is the number of connected components of G - S. We prove that every k-tough graph has a k-factor if k|G| is even and |G| ? k + 1. This result, first conjectured by Chvátal, is sharp in the following sense: For any positive integer k and for any positive real number ε, there exists a (k - ε)-tough graph G with k|G| even and |G| ? k + 1 which has no k-factor. 相似文献
Let X be an observation from a p-variate (p ≥ 3) normal random vector with unknown mean vector θ and known covariance matrix . The problem of improving upon the usual estimator of θ, δ0(X) = X, is considered. An approach is developed which can lead to improved estimators, δ, for loss functions which are polynomials in the coordinates of (δ ? θ). As an example of this approach, the loss L(δ, θ) = |δ ? θ|4 is considered, and estimators are developed which are significantly better than δ0. When is the identity matrix, these estimators are of the form . 相似文献
The concept of a (1, 2)-eulerian weight was introduced and studied in several papers recently by Seymour, Alspach, Goddyn, and Zhang. In this paper, we proved that if G is a 2-connected simple graph of order n (n ≧ 7) and w is a smallest (1, 2)-eulerian weight of graph G, then |Ew=even | n - 4, except for a family of graphs. Consequently, if G admits a nowhere-zero 4-flow and is of order at least 7, except for a family of graphs, the total length of a shortest cycle covering is at most | V(G) | + |E(G) |- 4. This result generalizes some previous results due to Bermond, Jackson, Jaeger, and Zhang. 相似文献
We determine all connected normal edge-transitive Cayley graphs on non-abelian groups with order 4p,where p is a prime number.As a consequence we prove if |G|=2δp,δ=0,1,2 and p prime,then Γ=Cay(G,S) is a connected normal 1/2 arc-transitive Cayley graph only if G=F4p,where S is an inverse closed generating subset of G which does not contain the identity element of G and F 4p is a group with presentation F4p = a,b|ap=b4=1,b-1ab=aλ,where λ2≡-1(mod p). 相似文献
We prove that max |p′(x)|, where p runs over the set of all algebraic polynomials of degree not higher than n ≥ 3 bounded in modulus by 1 on [−1, 1], is not lower than
( n - 1 ) \mathord
/
\vphantom ( n - 1 ) ?{1 - x2} ?{1 - x2} {{\left( {n - 1} \right)} \mathord{\left/{\vphantom {{\left( {n - 1} \right)} {\sqrt {1 - {x^2}} }}} \right.} {\sqrt {1 - {x^2}} }} for all x ∈ (−1, 1) such that
| x | ? èk = 0[ n \mathord
For p∈(?∞, ∞) letQp(?Δ) be the space of all complex-valued functions f on the unit circle ?Δ satisfying $\mathop {\sup }\limits_{I \subset \partial \Delta } \left| I \right|^{ - p} \int_I {\int_I {\frac{{\left| {f(z) - f(w)} \right|^2 }}{{\left| {z - w} \right|^{2 - p} }}\left| {dz} \right|\left| {dw} \right|< \infty } } $ , where the supremum is taken over all subarcs I ? ?Δ with the arclength |I|. In this paper, we consider some essential properties ofQp(?Δ). We first show that if p>1, thenQp(?Δ)=BMO(?Δ), the space of complex-valued functions with bounded mean oscillation on ?Δ. Second, we prove that a function belongs toQp(?Δ) if and only if it is Möbius bounded in the Sobolev spaceLp2(?Δ). Finally, a characterization ofQp(?Δ) is given via wavelets. 相似文献
In this paper we shall consider the critical elliptic
equation
$ -\triangle u + \lambda a(x) u = u^{(N+2)/(N-2)}, \ \ x\in \Bbb
R^N, \\ u > 0, \quad \int_{\Bbb R^N} |\nabla u|^2 \, dx < + \infty, \quad\quad (0.1)$ -\triangle u + \lambda a(x) u = u^{(N+2)/(N-2)}, \ \ x\in \Bbb
R^N, \\ u > 0, \quad \int_{\Bbb R^N} |\nabla u|^2 \, dx < + \infty, \quad\quad (0.1)
where
$\lambda >0, N > 4$\lambda >0, N > 4
and a(x)
is a real continuous, non
negative function, not identically zero. By using a local Pohozaev
identity, we show that problem (0.1) does not admit a
family of solutions
ulu_\lambda
which blows-up and concentrates as
l? +¥\lambda \to +\infty
at some zero point x0 of a(x)
if the order of flatness of the function a(x) at x0 is
b ? [2,N-4)\beta\in[2,N-4) 相似文献
where B is a ball in \({\mathbb{R}}^N\) , 1 < p < (N + 2)/(N ? 2), N ≥ 3 and the potential V is radially symmetric. We construct positive clustering solutions in an annulus having O(1/?) critical points, as well as sign changing solutions with O(1/?) zeroes concentrating near zero.
Let H : Lp ( R ) → Lp( R ), 1 < p < ∞ be the real HILBERT transform. A bounded, linear operator u:E → F (E, F BANACH spaces) is a HT-operator, if the mapping u ? H : E ? L2( R , E) → L2( R , F) has a bounded, linear extension to L2( R ) → L2( R , F). For E = F and u = idE BOURGAIN [3] and BURKHOLDER [5] have shown that this holds if and only if E ? UMD. We study these HT-operators and, in particular, we construct a HT-operator which is not UMD-factorable. Furthermore, we show that a UMD-space E is a HILBERT space if and only if |idE ? H| = 1. 相似文献
It is proved that the problem $$\mathop {\sum\nolimits_{i = 1}^v {\nabla _i (|\nabla u|^{p - 2} \nabla _i u)^ - |u|^{p * - 1} u + \lambda |u|^{p - 2} u = 0 in \Omega .} }\limits_{n = 0 on \partial \Omega .}$$ where Ω ?RN a singly-connected region with an “odd” boundary, N > p, and p* = Np/(N ? p) is a critical Sobolev exponent, has, under the appropriate conditions on λ, q, and N, no less than (2N+2) nontrivial solutions in \(\mathop W\limits^0 _{p^1 } (\Omega )\) . 相似文献
It was conjectured by Fan that if a graph G = (V,E) has a nowhere-zero 3-flow, then G can be covered by two even subgraphs of total size at most |V| + |E| - 3. This conjecture is proved in this paper. It is also proved in this paper that the optimum solution of the Chinese postman problem and the solution of minimum cycle covering problem are equivalent for any graph admitting a nowhere-zero 4-flow. 相似文献
Consider a flat two-dimensional vortex sheet perturbed initially by a small analytic disturbance. By a formal perturbation analysis, Moore derived an approximate differential equation for the evolution of the vortex sheet. We present a simplified derivation of Moore's approximate equation and analyze errors in the approximation. The result is used to prove existence of smooth solutions for long time. If the initial perturbation is of size ? and is analytic in a strip |??m γ| < ρ, existence of a smooth solution of Birkhoff's equation is shown for time t < k2p, if ? is sufficiently small, with κ → 1 as ? → 0. For the particular case of sinusoidal data of wave length π and amplitude e, Moore's analysis and independent numerical results show singularity development at time tc = |log ?| + O(log|log ?|. Our results prove existence for t < κ|log ?|, if ? is sufficiently small, with k κ → 1 as ? → 0. Thus our existence results are nearly optimal. 相似文献