arXiv subjects

Weiyi Zhang

Publications and source records attributed to Weiyi Zhang.

61 records · Page 4Linked to original sources

arXiv2011

Symplectic forms and cohomology decomposition of almost complex 4-manifolds

For any compact almost complex manifold $(M,J)$, the last two authors defined two subgroups $H_J^+(M)$, $H_J^-(M)$ of the degree 2 real de Rham cohomology group $H^2(M, \mathbb{R})$ in arXiv:0708.2520. These are the sets of cohomology classes which can be represented by $J$-invariant, respectively, $J$-anti-invariant real $2-$forms. In this note, it is shown that in dimension 4 these subgroups induce a cohomology decomposition of $H^2(M, \mathbb{R})$. This is a specifically 4-dimensional result, as it follows from a recent work of Fino and Tomassini. Some estimates for the dimensions of these groups are also established when the almost complex structure is tamed by a symplectic form and an equivalent formulation for a question of Donaldson is given.

math.SG↗

arXiv2011

On the J-anti-invariant cohomology of almost complex 4-manifolds

For a compact almost complex 4-manifold $(M,J)$, we study the subgroups $H^{\pm}_J$ of $H^2(M, \mathbb{R})$ consisting of cohomology classes representable by $J$-invariant, respectively, $J$-anti-invariant 2-forms. If $b^+ =1$, we show that for generic almost complex structures on $M$, the subgroup $H^-_J$ is trivial. Computations of the subgroups and their dimensions $h^{\pm}_J$ are obtained for almost complex structures related to integrable ones. We also prove semi-continuity properties for $h^{\pm}_J$.

math.SG↗

arXiv2011

The band-gap structures and recovery rules of generalized n-component Fibonacci piezoelectric superlattices

The spectral evolution from periodic structure to random structure has always been an interesting topic in solid state physics, the generalized n-component Fibonacci sequences (n- CF) provide a convenient tool to investigate such process since its randomness can be controlled via the parameter n. In this letter, the band-gap structures of n-CF piezoelectric superlattices have been calculated using the transfer-matrix-method, the self-similarity behavior and recovery rule have been systematically analyzed. Consistent with the rigorous mathematical proof by Hu et al.[A. Hu et al. Phys. Rev. B. 48, 829 (1993)], we find that the n-CF sequences with 2 \leq n \leq 4 are identified as quasiperiodic. The imaginary wave numbers are characterized by the self-similar spectrum, their major peaks can all be properly indexed. In addition, we find that the n = 5 sequence belongs to a critical case which lies at the border between quasiperiodic to aperiodic structures. The frequency range of self-similarity pattern approaches to zero and a unique indexing of imaginary wave numbers becomes impossible. Our study offers the information on the critical 5-CF superlattice which was not available before. The classification of band-gap structures and the scaling laws around fixed points are also given.

cond-mat.mtrl-sci↗

arXiv2010

QoS Routing in Smart Grid

Smart grid is an emerging technology which is able to control the power load via price signaling. The communication between the power supplier and power customers is a key issue in smart grid. Performance degradation like delay or outage may cause significant impact on the stability of the pricing based control and thus the reward of smart grid. Therefore, a QoS mechanism is proposed for the communication system in smart grid, which incorporates the derivation of QoS requirement and applies QoS routing in the communication network. For deriving the QoS requirement, the dynamics of power load and the load-price mapping are studied. The corresponding impacts of different QoS metrics like delay are analyzed. Then, the QoS is derived via an optimization problem that maximizes the total revenue. Based on the derived QoS requirement, a simple greedy QoS routing algorithm is proposed for the requirement of high speed routing in smart grid. It is also proven that the proposed greedy algorithm is a $K$-approximation. Numerical simulation shows that the proposed mechanism and algorithm can effectively derive and secure the communication QoS in smart grid.

cs.IT↗

arXiv2009

The Kodaira Dimension of Lefschetz Fibrations

In this note, we verify that the complex Kodaira dimension $κ^h$ equals the symplectic Kodaira dimension $κ^s$ for smooth 4-manifolds with complex and symplectic structures. We also calculate the Kodaira dimension for many Lefschetz fibrations.

math.SG↗

arXiv2009

Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds

We introduce certain homology and cohomology subgroups for any almost complex structure and study their pureness, fullness and duality properties. Motivated by a question of Donaldson, we use these groups to relate J-tamed symplectic cones and J-compatible symplectic cones over a large class of almost complex manifolds, including all Kahler manifolds, almost Kahler 4-manifolds and complex surfaces.

math.SG↗

arXiv2009

Additivity and Relative Kodaira Dimensions

In this paper we introduce the notion of relative Kodaira dimension for a symplectic 4-manifold M with a possibly disconnected embedded symplectic surface F. One notable feature is that the sphere components of F have to be discarded, which resembles the definition of Thurston norm of 3-manifolds. To define it we need to establish several homological properties of embedded symplectic surfaces. We also formulate the notion of relative minimal model, and prove the existence and the somewhat surprising uniqueness.

math.SG↗