Compactly Supported Tensor Product Complex Tight Framelets with Directionality

Although tensor product real-valued wavelets have been successfully applied to many high-dimensional problems, they can only capture well edge singularities along the coordinate axis directions. As an alternative and improvement of tensor product real-valued wavelets and dual tree complex wavelet transform, recently tensor product complex tight framelets with increasing directionality have been introduced in [8] and applied to image denoising in [13]. Despite several desirable properties, the directional tensor product complex tight framelets constructed in [8,13] are bandlimited and do not have compact support in the space/time domain. Since compactly supported wavelets and framelets are of great interest and importance in both theory and application, it remains as an unsolved problem whether there exist compactly supported tensor product complex tight framelets with directionality. In this paper, we shall satisfactorily answer this question by proving a theoretical result on directionality of tight framelets and by introducing an algorithm to construct compactly supported complex tight framelets with directionality. Our examples show that compactly supported complex tight framelets with directionality can be easily derived from any given eligible low-pass filters and refinable functions. Several examples of compactly supported tensor product complex tight framelets with directionality have been presented

Synthesis of Distributed Longitudinal Control Protocols for a Platoon of Autonomous Vehicles

We develop a framework for control protocol synthesis for a platoon of autonomous vehicles subject to temporal logic specifications. We describe the desired behavior of the platoon in a set of linear temporal logic formulas, such as collision avoidance, close spacing or comfortability. The problem of decomposing a global specification for the platoon into distributed specification for each pair of adjacent vehicles is hard to solve. We use the invariant specifications to tackle this problem and the decomposition is proved to be scalable.. Based on the specifications in Assumption/Guarantee form, we can construct a two-player game (between the vehicle and its closest leader) locally to automatically synthesize a controller protocol for each vehicle. Simulation example for a distributed vehicles control problem is also shown

Gothic Writing Technique and Yin-Yang Theory in The Fall of the House of Usher

In both theoretical and practical senses, Gothic writing techniques and Yin-Yang theory share many similarities. To some extent, Gothic writing techniques can be explained by Yin-Yang theory and their application in Gothic fictions can be transferred to corresponding regulations in Yin-Yang theory. This paper mainly looks into the similarities and dissimilarities of them, specifically in Edgar Allen Poe’s The Fall of the House of Usher. This paper studies this two terms from a philosophical perspective

Stability of Phase-modulated Quantum Key Distribution System

Phase drift and random fluctuation of interference visibility in double unbalanced M-Z QKD system are observed and distinguished. It has been found that the interference visibilities are influenced deeply by the disturbance of transmission fiber. Theory analysis shows that the fluctuation is derived from the envioronmental disturbance on polarization characteristic of fiber, especially including transmission fiber. Finally, stability conditions of one-way anti-disturbed M-Z QKD system are given out, which provides a theoretical guide in pragmatic anti-disturbed QKD.Comment: 9 pages, 3 figue

Electron transfer theory revisit: Quantum solvation effect

The effect of solvation on the electron transfer (ET) rate processes is investigated on the basis of the exact theory constructed in J. Phys. Chem. B Vol. 110, (2006); quant-ph/0604071. The nature of solvation is studied in a close relation with the mechanism of ET processes. The resulting Kramers' turnover and Marcus' inversion characteristics are analyzed accordingly. The classical picture of solvation is found to be invalid when the solvent longitudinal relaxation time is short compared with the inverse temperature.Comment: 5 pages, 3 figures. J. Theo. & Comput. Chem., accepte