Berezin transform and Toeplitz operators on harmonic Bergman spaces

For an operator which is a finite sum of products of finitely many Toeplitz operators on the harmonic Bergman space over the half-space, we study the problem: Does the boundary vanishing property of the Berezin transform imply compactness? This is motivated by the Axler-Zheng theorem for analytic Bergman spaces, but the answer would not be yes in general, because the Berezin transform annihilates the commutator of any pair of Toeplitz operators. Nevertheless we show that the answer is yes for certain subclasses of operators. In order to do so, we first find a sufficient condition on general operators and use it to reduce the problem to whether the Berezin transform is one-to-one on related subclasses.     

Average distance and maximum induced forest

With the help of the Graffiti system, Fajtlowicz conjectured around 1992 that the average distance between two vertices of a connected graph G is at most half the maximum order of an induced bipartite subgraph of G, denoted α₂(G). We prove a strengthening of this conjecture by showing that the average distance between two vertices of a connected graph G is at most half the maximum order of an induced forest, denoted F(G). Moreover, we characterize the graphs maximizing the average distance among all graphs G having a fixed number of vertices and a fixed value of F(G) or α₂(G). Finally, we conjecture that the average distance between two vertices of a connected graph is at most half the maximum order of an induced linear forest (where a linear forest is a union of paths). © 2008 Wiley Periodicals, Inc. J Graph Theory 60: 31–54, 2009     

Simulation study of ghost image phenomenon induced by contrast enhancement film in plasma display panels

We have performed simulations of the ghost image phenomenon induced by a contrast enhancement film used for plasma display panels (PDPs). An optical imaging system was designed in order to investigate the ghost image qualitatively and quantitatively. We report on and discuss the effects of the material parameters and film orientation on the relative illuminance of the ghost image for a conventional louver-type contrast enhancement film adopting a trapezoidal black-stripe structure. The ghost image phenomenon is strongly affected by the film orientation relative to the PDP module and the difference between the refractive index of the ultraviolet curable urethane acrylate layer and that of the black stripes. We show that when the top side of the black stripes faces the PDP module and the refractive index difference is small, the ghost image phenomenon is weakened.     

ESIPT-Inspired Dual-Mode Photoswitches with Fast Molecular Isomerization in the Solid State

Photoswitchable materials have attracted considerable attention in various fields. Developing excellent solid-state dual-mode photoswitches is an important but challenging task. Herein, we propose a new strategy to construct an excited-state intramolecular proton transfer (ESIPT) inspired photoswitch ( DiAH-pht ) that possesses aggregation-induced emission (AIE) features and displays a fast molecular isomerization process characterized by dual-mode behavior in the solid state. Mechanistic studies indicate that introduction of a bulky group can create a folded molecular conformation that provides adequate volume to facilitate photoisomerization and the enhanced ESIPT effect can boost the isomerization process. The feasibility of our strategy was further demonstrated by the activated photoisomerization performance of the Schiff base derivatives. Furthermore, DiAH-pht shows good performance in the fields of dual-mode information encryption and high-density data storage.