共查询到20条相似文献,搜索用时 31 毫秒
1.
Let H be a multigraph, possibly containing loops. An H-subdivision is any simple graph obtained by replacing the edges of H with paths of arbitrary length. Let H be an arbitrary multigraph of order k, size m, n
0(H) isolated vertices and n
1(H) vertices of degree one. In Gould and Whalen (Graphs Comb. 23:165–182, 2007) it was shown that if G is a simple graph of order n containing an H-subdivision H{\mathcal{H}} and
d(G) 3 \fracn+m-k+n1(H)+2n0(H)2{\delta(G) \ge \frac{n+m-k+n_1(H)+2n_0(H)}{2}}, then G contains a spanning H-subdivision with the same ground set as H{\mathcal{H}} . As a corollary to this result, the authors were able to obtain Dirac’s famed theorem on hamiltonian graphs; namely that
if G is a graph of order n ≥ 3 with
d(G) 3 \fracn2{\delta(G)\ge\frac{n}{2}} , then G is hamiltonian. Bondy (J. Comb. Theory Ser. B 11:80–84, 1971) extended Dirac’s theorem by showing that if G satisfied the condition
d(G) 3 \fracn2{\delta(G) \ge \frac{n}{2}} then G was either pancyclic or a complete bipartite graph. In this paper, we extend the result from Gould and Whalen (Graphs Comb.
23:165–182, 2007) in a similar manner. An H-subdivision H{\mathcal{H}} in G is 1-extendible if there exists an H-subdivision H*{\mathcal{H}^{*}} with the same ground set as H{\mathcal{H}} and |H*| = |H| + 1{|\mathcal{H}^{*}| = |\mathcal{H}| + 1} . If every H-subdivision in G is 1-extendible, then G is pan-H-linked. We demonstrate that if H is sufficiently dense and G is a graph of large enough order n such that
d(G) 3 \fracn+m-k+n1(H)+2n0(H)2{\delta(G) \ge \frac{n+m-k+n_1(H)+2n_0(H)}{2}} , then G is pan-H-linked. This result is sharp. 相似文献
2.
Hassen Ben Mohamed 《The Ramanujan Journal》2010,21(2):145-171
In this work, we consider the Jacobi-Dunkl operator Λ
α,β
,
a 3 b 3 \frac-12\alpha\geq\beta\geq\frac{-1}{2}
,
a 1 \frac-12\alpha\neq\frac{-1}{2}
, on ℝ. The eigenfunction
Yla,b\Psi_{\lambda}^{\alpha,\beta}
of this operator permits to define the Jacobi-Dunkl transform. The main idea in this paper is to introduce and study the Jacobi-Dunkl
transform and the Jacobi-Dunkl convolution product on new spaces of distributions 相似文献
3.
Kengo Matsumoto 《Mathematische Zeitschrift》2010,265(4):735-760
A C*-symbolic dynamical system ${(\mathcal{A}, \rho, \Sigma)}A C*-symbolic dynamical system (A, r, S){(\mathcal{A}, \rho, \Sigma)} consists of a unital C*-algebra A{\mathcal{A}} and a finite family { ra }a ? S{\{ \rho_\alpha \}_{\alpha \in \Sigma}} of endomorphisms ρ
α
of A{\mathcal{A}} indexed by symbols α of Σ satisfying some conditions. The endomorphisms ra, a ? S{\rho_\alpha, \alpha \in \Sigma } yield both a subshift Λ and a C*-algebra of a Hilbert C*-bimodule. The obtained C*-algebra is regarded as a crossed product of A{\mathcal{A}} by the subshift Λ. We will study simplicity condition of these C*-algebras. Some examples such as irrational rotation Cuntz–Krieger algebras will be studied. 相似文献
4.
Alessio Martini 《Mathematische Zeitschrift》2010,265(4):831-848
The Heisenberg–Pauli–Weyl (HPW) uncertainty inequality on
\mathbbRn{\mathbb{R}^n} says that
|| f ||2 £ Ca,b|| |x|a f||2\fracba+b|| (-D)b/2f||2\fracaa+b.\| f \|_2 \leq C_{\alpha,\beta}\| |x|^\alpha f\|_2^\frac{\beta}{\alpha+\beta}\| (-\Delta)^{\beta/2}f\|_2^\frac{\alpha}{\alpha+\beta}. 相似文献
5.
Martin Reiris 《Annales Henri Poincare》2010,10(8):1559-1604
Let (g, K)(k) be a CMC (vacuum) Einstein flow over a compact three-manifold Σ with non-positive Yamabe invariant (Y(Σ)). As noted by Fischer and Moncrief, the reduced volume ${\mathcal{V}(k)=\left(\frac{-k}{3}\right)^{3}{\rm Vol}_{g(k)}(\Sigma)}
6.
Recently, Girstmair and Schoissengeier studied the asymptotic behavior of the arithmetic mean of Dedekind sums
\frac1j(N) ? 0 £ m < Ngcd(m,N)=1 |S(m,N)|\frac{1}{\varphi(N)} \sum_{\mathop{\mathop{ 0 \le m< N}}\limits_{\gcd(m,N)=1}} \vert S(m,N)\vert
, as N → ∞. In this paper we consider the arithmetic mean of weighted differences of Dedekind sums in the form
Ah(Q)=\frac1?\fracaq ? FQh(\fracaq) ×?\fracaq ? FQh(\fracaq) |s(a¢,q¢)-s(a,q)|A_{h}(Q)=\frac{1}{\sum_{\frac{a}{q} \in {\cal F}_{Q}}h\left(\frac{a}{q}\right)} \times \sum_{\frac{a}{q} \in {\cal F}_{\!Q}}h\left(\frac{a}{q}\right) \vert s(a^{\prime},q^{\prime})-s(a,q)\vert
, where
h:[0,1] ? \Bbb Ch:[0,1] \rightarrow {\Bbb C}
is a continuous function with
ò01 h(t) d t 1 0\int_0^1 h(t) \, {\rm d} t \ne 0
,
\fracaq{\frac{a}{q}}
runs over
FQ{\cal F}_{\!Q}
, the set of Farey fractions of order Q in the unit interval [0,1] and
\fracaq < \fraca¢q¢{\frac{a}{q}}<\frac{a^{\prime}}{q^{\prime}}
are consecutive elements of
FQ{\cal F}_{\!Q}
. We show that the limit lim
Q→∞
A
h
(Q) exists and is independent of h. 相似文献
7.
We construct an explicit intertwining operator L{\mathcal L} between the Schr?dinger group eit \frac\triangle2{e^{it \frac\triangle2}} and the geodesic flow on certain Hilbert spaces of symbols on the cotangent bundle T*X Γ of a compact hyperbolic surface X Γ = Γ\D. We also define Γ-invariant eigendistributions of the geodesic flow PSj, k, nj,-nk{PS_{j, k, \nu_j,-\nu_k}} (Patterson-Sullivan distributions) out of pairs of \triangle{\triangle} -eigenfunctions, generalizing the diagonal case j = k treated in Anantharaman and Zelditch (Ann. Henri Poincaré 8(2):361–426, 2007). The operator L{\mathcal L} maps PSj, k, nj,-nk{PS_{j, k, \nu_j,-\nu_k}} to the Wigner distribution WGj,k{W^{\Gamma}_{j,k}} studied in quantum chaos. We define Hilbert spaces HPS{\mathcal H_{PS}} (whose dual is spanned by {PSj, k, nj,-nk{PS_{j, k, \nu_j,-\nu_k}}}), resp. HW{\mathcal H_W} (whose dual is spanned by {WGj,k}{\{W^{\Gamma}_{j,k}\}}), and show that L{\mathcal L} is a unitary isomorphism from HW ? HPS.{\mathcal H_{W} \to \mathcal H_{PS}.} 相似文献
8.
A variety ${\mathbb{V}}${\mathbb{V}} is var-relatively universal if it contains a subvariety
\mathbbW{\mathbb{W}} such that the class of all homomorphisms that do not factorize through any algebra in
\mathbbW{\mathbb{W}} is algebraically universal. And
\mathbbV{\mathbb{V}} has an algebraically universal α-expansion
a\mathbbV{\alpha\mathbb{V}} if adding α nullary operations to all algebras in
\mathbbV{\mathbb{V}} gives rise to a class
a\mathbbV{\alpha\mathbb{V}} of algebras that is algebraically universal. The first two authors have conjectured that any varrelative universal variety
\mathbbV{\mathbb{V}} has an algebraically universal α-expansion
a\mathbbV{\alpha\mathbb{V}} . This note contains a more general result that proves this conjecture. 相似文献
9.
Ponnusamy Saminathan Vasudevarao Allu M. Vuorinen 《Complex Analysis and Operator Theory》2011,5(3):955-966
For ${\alpha\in\mathbb C{\setminus}\{0\}}
|