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Stein open subsets with analytic complements in compact complex spaces

Jing Zhang — 2015

Annales Polonici Mathematici

Let Y be an open subset of a reduced compact complex space X such that X - Y is the support of an effective divisor D. If X is a surface and D is an effective Weil divisor, we give sufficient conditions so that Y is Stein. If X is of pure dimension d ≥ 1 and X - Y is the support of an effective Cartier divisor D, we show that Y is Stein if Y contains no compact curves, H i ( Y , Y ) = 0 for all i > 0, and for every point x₀ ∈ X-Y there is an n ∈ ℕ such that Φ | n D | - 1 ( Φ | n D | ( x ) ) Y is empty or has dimension 0, where Φ | n D | is the map from...

Gradient estimates for a nonlinear equation Δ f u + c u - α = 0 on complete noncompact manifolds

Jing ZhangBingqing Ma — 2011

Communications in Mathematics

Let ( M , g ) be a complete noncompact Riemannian manifold. We consider gradient estimates on positive solutions to the following nonlinear equation Δ f u + c u - α = 0 in M , where α , c are two real constants and α > 0 , f is a smooth real valued function on M and Δ f = Δ - f . When N is finite and the N -Bakry-Emery Ricci tensor is bounded from below, we obtain a gradient estimate for positive solutions of the above equation. Moreover, under the assumption that -Bakry-Emery Ricci tensor is bounded from below and | f | is bounded from above,...

The Minimum Spectral Radius of Signless Laplacian of Graphs with a Given Clique Number

Li SuHong-Hai LiJing Zhang — 2014

Discussiones Mathematicae Graph Theory

In this paper we observe that the minimal signless Laplacian spectral radius is obtained uniquely at the kite graph PKn−ω,ω among all connected graphs with n vertices and clique number ω. In addition, we show that the spectral radius μ of PKm,ω (m ≥ 1) satisfies [...] More precisely, for m > 1, μ satisfies the equation [...] where [...] and [...] . At last the spectral radius μ(PK∞,ω) of the infinite graph PK∞,ω is also discussed.

On The Determinant of q-Distance Matrix of a Graph

Hong-Hai LiLi SuJing Zhang — 2014

Discussiones Mathematicae Graph Theory

In this note, we show how the determinant of the q-distance matrix Dq(T) of a weighted directed graph G can be expressed in terms of the corresponding determinants for the blocks of G, and thus generalize the results obtained by Graham et al. [R.L. Graham, A.J. Hoffman and H. Hosoya, On the distance matrix of a directed graph, J. Graph Theory 1 (1977) 85-88]. Further, by means of the result, we determine the determinant of the q-distance matrix of the graph obtained from a connected weighted graph...

Some estimates for commutators of Riesz transform associated with Schrödinger type operators

Yu LiuJing ZhangJie-Lai ShengLi-Juan Wang — 2016

Czechoslovak Mathematical Journal

Let 1 = - Δ + V be a Schrödinger operator and let 2 = ( - Δ ) 2 + V 2 be a Schrödinger type operator on n ( n 5 ) , where V 0 is a nonnegative potential belonging to certain reverse Hölder class B s for s n / 2 . The Hardy type space H 2 1 is defined in terms of the maximal function with respect to the semigroup { e - t 2 } and it is identical to the Hardy space H 1 1 established by Dziubański and Zienkiewicz. In this article, we prove the L p -boundedness of the commutator b = b f - ( b f ) generated by the Riesz transform = 2 2 - 1 / 2 , where b BMO θ ( ρ ) , which is larger than the...

An efficient connected dominating set algorithm in wsns based on the induced tree of the crossed cube

Jing ZhangLi XuShu-ming ZhouWei WuXiucai Ye — 2015

International Journal of Applied Mathematics and Computer Science

The connected dominating set (CDS) has become a well-known approach for constructing a virtual backbone in wireless sensor networks. Then traffic can forwarded by the virtual backbone and other nodes turn off their radios to save energy. Furthermore, a smaller CDS incurs fewer interference problems. However, constructing a minimum CDS is an NP-hard problem, and thus most researchers concentrate on how to derive approximate algorithms. In this paper, a novel algorithm based on the induced tree of...

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