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1.
Let and be graphs where the set of vertices is the set of points of the integer lattice and the set of edges consists of all pairs of vertices whose city block and chessboard distances, respectively, are 1.In this paper it is shown that the partition dimensions of these graphs are 3 and 4, respectively, while their metric dimensions are not finite. Also, for every n3 there exists an induced subgraph of of order 3n-1 with metric dimension n and partition dimension 3. These examples will answer a question raised by Chartrand, Salehi and Zhang. Furthermore, graphs of order n9 having partition dimension n-2 are characterized, thus completing the characterization of graphs of order n having partition dimension 2, n, or n-1 given by Chartrand, Salehi and Zhang. The list of these graphs includes 23 members. 相似文献
2.
Let n3 and let F be a 2-regular graph of order n. The Oberwolfach problem OP(F) asks for a 2-factorisation of Kn if n is odd, or of Kn−I if n is even, in which each 2-factor is isomorphic to F. We show that there is an infinite set of primes congruent to such that OP(F) has a solution for any 2-regular graph F of order . We also show that for each of the infinitely many with prime, OP(F) has a solution for any 2-regular graph F of order n. 相似文献
3.
We give new examples of FA presentable torsion-free abelian groups. Namely, for every n2, we construct a rank n indecomposable torsion-free abelian group which has an FA presentation. We also construct an FA presentation of the group in which every nontrivial cyclic subgroup is not FA recognizable. 相似文献
4.
Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data 总被引:2,自引:0,他引:2
We consider the defocusing, -critical Hartree equation for the radial data in all dimensions (n5). We show the global well-posedness and scattering results in the energy space. The new ingredient in this paper is that we first take advantage of the term in the localized Morawetz identity to rule out the possibility of energy concentration, instead of the classical Morawetz estimate dependent of the nonlinearity. 相似文献
5.
Let Γ denote a d-bounded distance-regular graph with diameter d2. A regular strongly closed subgraph of Γ is said to be a subspace of Γ. Define the empty set to be the subspace with diameter -1 in Γ. For 0ii+sd-1, let denote the set of all subspaces in Γ with diameters i,i+1,…,i+s including Γ and . If we define the partial order on by ordinary inclusion (resp. reverse inclusion), then is a poset, denoted by (resp. ). In the present paper we show that both and are atomic lattices, and classify their geometricity. 相似文献
6.
Let k1 be an integer and G be a graph of order n3k satisfying the condition that σ2(G)n+k-1. Let v1,…,vk be k independent vertices of G, and suppose that G has k vertex-disjoint triangles C1,…,Ck with viV(Ci) for all 1ik.Then G has k vertex-disjoint cycles such that
- (i) for all 1ik.
- (ii) , and
- (iii) At least k-1 of the k cycles are triangles.
Keywords: Degree sum condition; Independent vertices; Vertex-disjoint cycles 相似文献
7.
We explore the extent to which a variant of a celebrated formula due to Jost and Pais, which reduces the Fredholm perturbation determinant associated with the Schrödinger operator on a half-line to a simple Wronski determinant of appropriate distributional solutions of the underlying Schrödinger equation, generalizes to higher dimensions. In this multi-dimensional extension the half-line is replaced by an open set , , n2, where Ω has a compact, nonempty boundary ∂Ω satisfying certain regularity conditions. Our variant involves ratios of perturbation determinants corresponding to Dirichlet and Neumann boundary conditions on ∂Ω and invokes the corresponding Dirichlet-to-Neumann map. As a result, we succeed in reducing a certain ratio of modified Fredholm perturbation determinants associated with operators in L2(Ω;dnx), , to modified Fredholm determinants associated with operators in L2(∂Ω;dn−1σ), n2. Applications involving the Birman–Schwinger principle and eigenvalue counting functions are discussed. 相似文献
8.
We study a new Liouville-type phenomenon for entire weak supersolutions of elliptic partial differential equations of the form A(u)=0 on , n2. Typical examples of the operator A(u) are the p-Laplacian for p>1, the mean curvature operator, and their well-known modifications. 相似文献
9.
Let χ be the Dirichlet character modulo q3 and L(s,χ) denote the corresponding Dirichlet L-function. The mean value of is studied and a few asymptotic formulae are given. Hybrid mean value of , general Kloosterman sums and general quadratic Gauss sums are considered. 相似文献
10.
Let mp be the minimum of the product under the conditions that and . In our previous paper [J. Kaneko, On an extremal problem of Selberg, J. Approx. Theory 142 (2006) 129–137], we showed that the following estimates hold. provided p255. In this note, we prove that the limit of as p→∞ exists and is expressed by the (unique) solution of some simultaneous transcendental equations. By using this expression we obtain numerically. 相似文献
11.
Raffaella Cilia Joaquín M. Gutirrez 《Journal of Mathematical Analysis and Applications》2009,360(2):609-623
It is well known that a (linear) operator between Banach spaces is completely continuous if and only if its adjoint takes bounded subsets of Y* into uniformly completely continuous subsets, often called (L)-subsets, of X*. We give similar results for differentiable mappings. More precisely, if UX is an open convex subset, let be a differentiable mapping whose derivative is uniformly continuous on U-bounded subsets. We prove that f takes weak Cauchy U-bounded sequences into convergent sequences if and only if f′ takes Rosenthal U-bounded subsets of U into uniformly completely continuous subsets of . As a consequence, we extend a result of P. Hájek and answer a question raised by R. Deville and E. Matheron. We derive differentiable characterizations of Banach spaces not containing ℓ1 and of Banach spaces without the Schur property containing a copy of ℓ1. Analogous results are given for differentiable mappings taking weakly convergent U-bounded sequences into convergent sequences. Finally, we show that if X has the hereditary Dunford–Pettis property, then every differentiable function as above is locally weakly sequentially continuous. 相似文献
12.
Let , with
-1=x0n<x1n<<xnn<xn+1,n=1