GLOBAL CLASSICAL SOLUTIONS TO QUASILINEAR HYPERBOLIC SYSTEMS WITH WEAK LINEAR DEGENERACY

§1. Introduction and Main Results Consider the following ?rst order quasilinear strictly hyperbolic system ?u ?u A(u) = 0, (1.1) ?t ?xwhere u = (u1, ···,un)T is the unknown vector function of (t,x) and A(u) is an n×n matrixwith suitably smooth elements aij(u) (i,j = 1, ···,n). By the de?nition …     

积域上一类奇异积分算子的L~p有界性

本文证明,对于Ω∈(1)∩L(log~+L)~2(S~(n-1)×S~(m-1)),h(r,s)∈L~∞(R_+~1×R_+~1)和P_(N_1),P_(N_2)∈(2),带粗糙核的奇异积分算子为L~p有界。     

Almansi decomposition for Dunkl operators

Let Ωbe a G-invariant convex domain in RN including 0, where G is a Coxeter group associated with reduced root system R. We consider functions f defined in Ωwhich are Dunkl polyharmonic, i.e. (△h)nf =0 for some integer n. Here △h=∑j=1N Dj2 is the Dunkl Laplacian, and Dj is the Dunkl operator attached to the Coxeter group G, where kv is a multiplicity function on R and σv is the reflection with respect to the root v. We prove that any Dunkl polyharmonic function f has a decomposition of the form f(x)=f0(x) |x|2f1(x) … |x|2(n-1)fn-1(x),(?)x∈Ω, where fj are Dunkl harmonic functions, i.e. △hfj = 0. This generalizes the classical Almansi theorem for polyharmonic functions as well as the Fischer decomposition.     

一类解析函数类的Hankel行列式的上界估计

本文对在单位圆盘U={z∈C：l│z│〈1}内解析且满足（1-λ）f（z）/z＋λf^1（z）〈1＋Az/1＋Bz（-1≤B＜A≤1;z∈U的函数f所对应的Hankel行列式│a2a4-a^23│,利用Toeplitz行列式的性质得到了其上界估计。     

SPECTRAL GAP SOLUTIONS OF THE DISSIPATIVE KIRCHHOFF EQUATION

§1. Introduction This paper is devoted to the question of the global solvability of the dissipative Kirch-ho? equation ?t u ? m 2 | x u|2dx x u δ?tu = 0 (x ∈?, t > 0), …     

有限Diophantine逼近与Fibonacci多项式

设x为一无理数具简单的连分式展开x = [a0, a1, a2,…, an].若对无穷多个是标k有ak> n则至少有m个解p/q(p与q互素)使不等式 x - p/q 相似文献   

一个无k次幂因子D.H.Lehmer数的渐近性质

设素数p>2,对任何满足条件1 a相似文献   

On k-ordered Hamiltonian graphs

A Hamiltonian graph G of order n is k-ordered, 2 ≤ k ≤ n, if for every sequence v₁, v₂, …, v_k of k distinct vertices of G, there exists a Hamiltonian cycle that encounters v₁, v₂, …, v_k 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     

A fast parallel algorithm for finding Hamiltonian cycles in dense graphs

Suppose that 0<η<1 is given. We call a graph, G, on n vertices an η-Chvátal graph if its degree sequence d₁≤d₂≤?≤d_n satisfies: for k<n/2, d_k≤min{k+ηn,n/2} implies d_n−k−ηn≥n−k. (Thus for η=0 we get the well-known Chvátal graphs.) An -algorithm is presented which accepts as input an η-Chvátal graph and produces a Hamiltonian cycle in G as an output. This is a significant improvement on the previous best -algorithm for the problem, which finds a Hamiltonian cycle only in Dirac graphs (δ(G)≥n/2 where δ(G) is the minimum degree in G).     

完全3-一致超图K_n~((3))的哈密顿圈分解

基于王建方和李东给出的超图哈密顿圈的定义和Katona-Kierstead给出的超图哈密顿链的定义,近年来,国内外学者对一致超图的哈密顿圈分解的研究有一系列结果.特别是Bailey-Stevens和Meszka-Rosa研究了完全3-一致超图K_n~((3))的哈密顿圈分解,得到了n=6k+1,6k+2(k=1,2,3,4,5)的哈密顿圈分解.本文在吉日木图提出的边划分方法的基础上继续研究,得到了完全3-一致超图K_n~((3))的哈密顿圈分解的算法,由此得到了n=6k+2,6k+4(k=1,2,3,4,5,6,7),n=6k+5(k=1,2,3,4,5,6)时的圈分解.这一结果将Meszka-Rosa关于K_n~((3))的哈密顿圈分解结果从n≤32提高到了n≤46(n≠43).     

On the Set of Cycle Lengths in a Hamiltonian Graph with a Given Maximum Degree

Let n and be two integers such that 2n–1. We describe the set of cycle lengths occurring in any hamiltonian graph G of order n and maximum degree . We conclude that for the case this set contains all the integers belonging to the union [3,2–n+2][n–+2,+1], and for it contains every integer between 3 and +1. We also study the set of cycle lengths in a hamiltonian graph with two fixed vertices of large degree sum. Our main results imply that the stability s(P) for the property of being pancyclic satisfies      

Hamilton体系与辛正交系的完备性*

本文定义了一个Banach空间ZH,并证明了一类Hamilton体系的本征函数系(辛正交系)在ZH空间中具有完备性.还证明了如下结论ZH空间能连续嵌入到L₂[0,1]×L₂[0,1]但ZH≠L₂[0,1]×L₂[0,1].     

Hamiltonian Cycle Systems Which Are Both Cyclic and Symmetric

The notion of a symmetric Hamiltonian cycle system (HCS) of a graph Γ has been introduced and studied by J. Akiyama, M. Kobayashi, and G. Nakamura [J Combin Des 12 (2004), 39–45] for , by R. A. Brualdi and M. W. Schroeder [J Combin Des 19 (2011), 1–15] for , and then naturally extended by V. Chitra and A. Muthusamy [Discussiones Mathematicae Graph Theory, to appear] to the multigraphs and . In each case, there must be an involutory permutation ψ of the vertices fixing all the cycles of the HCS and at most one vertex. Furthermore, for , this ψ should be precisely the permutation switching all pairs of endpoints of the edges of I. An HCS is cyclic if it is invariant under some cyclic permutation of all the vertices. The existence question for a cyclic HCS of has been completely solved by Jordon and Morris [Discrete Math (2008), 2440–2449]—and we note that their cyclic construction is also symmetric for (mod 8). It is then natural to study the existence problem of an HCS of a graph or multigraph Γ as above which is both cyclic and symmetric. In this paper, we completely solve this problem: in the case of even order, the final answer is that cyclicity and symmetry can always cohabit when a cyclic solution exists. On the other hand, imposing that a cyclic HCS of odd order is also symmetric is very restrictive; we prove in fact that an HCS of with both properties exists if and only if is a prime.     

Long cycles and paths in distance graphs

For n∈N and D⊆N, the distance graph has vertex set {0,1,…,n−1} and edge set {ij∣0≤i,j≤n−1,|j−i|∈D}. Note that the important and very well-studied circulant graphs coincide with the regular distance graphs.A fundamental result concerning circulant graphs is that for these graphs, a simple greatest common divisor condition, their connectivity, and the existence of a Hamiltonian cycle are all equivalent. Our main result suitably extends this equivalence to distance graphs. We prove that for a finite set D of order at least 2, there is a constant c_D such that the greatest common divisor of the integers in D is 1 if and only if for every n, has a component of order at least n−c_D if and only if for every n≥c_D+3, has a cycle of order at least n−c_D. Furthermore, we discuss some consequences and variants of this result.     

Neighborhood unions and cyclability of graphs

A graph G is said to be cyclable if for each orientation of G, there exists a set S of vertices such that reversing all the arcs of with one end in S results in a hamiltonian digraph. Let G be a 3-connected graph of order n36. In this paper, we show that if for any three independent vertices x₁, x₂ and x₃, |N(x₁)N(x₂)|+|N(x₂)N(x₃)|+|N(x₃)N(x₁)|2n+1, then G is cyclable.     

Averaging for Hamiltonian Systems with One Fast Phase and Small Amplitudes

In this paper we consider an analytic Hamiltonian system differing from an integrable system by a small perturbation of order . The corresponding unperturbed integrable system is degenerate with proper and limit degeneracy: all variables, except two, are at rest and there is an elliptic singular point in the plane of these two variables. It is shown that by an analytic symplectic change of the variable, which is -close to the identity substitution, the Hamiltonian can be reduced to a form differing only by exponentially small ( ) terms from the Hamiltonian possessing the following properties: all variables, except two, change slowly at a rate of order and for the two remaining variables the origin is the point of equilibrium; moreover, the Hamiltonian depends only on the action of the system linearized about this equilibrium.     

一类孤立子系统的Hamilton结构及Liouville可积性

本文给出了一个2×2谱问题及其相应的孤子族,并利用此孤子族的Lenard算子对的性质,证明了该系统是具有Bi-Hamilton结构和Multi-Hamilton结构的广义Hamilton系统,进一步给出其Liouville可积性的证明.此外,值得提出的是此系统可约化为广义TD族、TD族和广义C-KdV族、C-KdV族等,并得到了该孤子族的Hamilton泛函与守恒密度之问的一一对应关系.     

一些数学物理问题中的Hamilton方程

讨论了新的一系列在数学物理方程中微分方程的Hamilton正则表示,其中包括变系数2阶对称方程的Hamilton系统,关于常系数的4阶对称方程新的非齐次Hamilton表示,MKdV方程以及KP方程的正则表示.     

Hamiltonian cycles in n-factor-critical graphs

A graph G is said to be n-factor-critical if G−S has a 1-factor for any SV(G) with |S|=n. In this paper, we prove that if G is a 2-connected n-factor-critical graph of order p with , then G is hamiltonian with some exceptions. To extend this theorem, we define a (k,n)-factor-critical graph to be a graph G such that G−S has a k-factor for any SV(G) with |S|=n. We conjecture that if G is a 2-connected (k,n)-factor-critical graph of order p with , then G is hamiltonian with some exceptions. In this paper, we characterize all such graphs that satisfy the assumption, but are not 1-tough. Using this, we verify the conjecture for k2.