ISSN 1439-8516 CN 11-2039/O1
Let D be a finite and simple digraph with vertex set V (D). The minimum degree δ of a digraph D is defined as the minimum value of its out-degrees and its in-degrees. If D is a digraph with minimum degree δ and edge-connectivity λ, then λ ≤ δ. A digraph is maximally edge-connected if λ=δ. A digraph is called super-edge-connected if every minimum edge-cut consists of edges incident to or from a vertex of minimum degree. In this note we show that a digraph is maximally edge-connected or super-edge-connected if the number of arcs is large enough.
In this paper we give a classification of special endomorphisms of nil-manifolds:Let f:N/Γ → N/Γ be a covering map of a nil-manifold and denote by A:N/Γ → N/Γ the nil-endomorphism which is homotopic to f. If f is a special T A-map, then A is a hyperbolic nil-endomorphism and f is topologically conjugate to A.
In this paper, we construct random two-faced families of matrices with non-Gaussian entries to approximate a bi-free central limit distribution with a positive definite covariance matrix. We prove that, under modest conditions weaker than independence, a family of random two-faced families of matrices with non-Gaussian entries is asymptotically bi-free from a two-faced family of constant diagonal matrices.
We consider a fourth order nonlinear PDE involving the critical Sobolev exponent on a bounded domain of Rn, n ≥ 5 with Navier condition on the boundary. We study the lack of compactness of the problem and we provide an existence theorem through a new index formula.
In this paper, we study the complete f-moment convergence for widely orthant dependent (WOD, for short) random variables. A general result on complete f-moment convergence for arrays of rowwise WOD random variables is obtained. As applications, we present some new results on complete f-moment convergence for WOD random variables. We also give an application to nonparametric regression models based on WOD errors by using the complete convergence that we established. Finally, the choice of the fixed design points and the weight functions for the nearest neighbor estimator are proposed, and a numerical simulation is provided to verify the validity of the theoretical result.
Basing upon the recent development of the Patterson-Sullivan measures with a Hölder continuous nonzero potential function, we use tools of both dynamics of geodesic flows and geometric properties of negatively curved manifolds to present a new formula illustrating the relation between the exponential decay rate of Patterson-Sullivan measures with a Hölder continuous potential function and the corresponding critical exponent.
In this paper, we prove quasi-modularity property for the twisted Gromov-Witten theory of O(3) over P2. Meanwhile, we derive its holomorphic anomaly equation.
This paper constructs several families of self-complementary Cayley graphs of extraspecial p-groups, where p is a prime and congruent to 1 modulo 4.
0 and f(z) ≠ ∞ whenever a(z)=0. If for any f ∈ F, f'(z) -a(z)fk(z) ≠ b(z), then F is normal on D.
