On the Triality Theory for a Quartic Polynomial Optimization Problem

This paper presents a detailed proof of the triality theorem for a class of fourth-order polynomial optimization problems. The method is based on linear algebra but it solves an open problem on the double-min duality left in 2003. Results show that the triality theory holds strongly in a tri-duality form if the primal problem and its canonical dual have the same dimension; otherwise, both the canonical min-max duality and the double-max duality still hold strongly, but the double-min duality holds weakly in a symmetrical form. Four numerical examples are presented to illustrate that this theory can be used to identify not only the global minimum, but also the largest local minimum and local maximum.Comment: 16 pages, 1 figure; J. Industrial and Management Optimization, 2011. arXiv admin note: substantial text overlap with arXiv:1104.297

Innovation Institution and Spatial Transfer of Energy Industry: The Case of Jiangsu Province, China

This study aims to explore the effect of innovation institution on spatial transfer of energy industry in Jiangsu, China. We focus on the disparity of innovation and energy industry, and analyze the spatial transfer difference in different types of energy industry, rather than view energy industry as a whole. The study demonstrates the spatial change of energy industry at regional level and maps the spatial pattern at city level. The study chooses intellectual property rights (IPRs) protection intensity, authorization patents and local research and development (R&D) investment as the proxy of innovation. Using official data and employing panel fixed-effect model at city-industry level, we conclude (a) innovation abilities significantly influence the spatial transfer of energy industry in Jiangsu. Especially, due to the different time, IPRs protection, patent counts, and R&D investment have different effects on different regions in Jiangsu; (b) 2010 is an important turning point for energy industry development in Jiangsu, and after 2010, the energy industry begins to shift to the middle and northern Jiangsu, whereas the spatial pattern of energy industry in coastal cities is basically unchanged; (c) there is a great difference between the regions in Jiangsu Province, and industrial upgrading has not been achieved in northern Jiangsu

Optimal Controlled Teleportation

We give the analytic expressions of maximal probabilities of successfully controlled teleportating an unknown qubit via every kind of tripartite states. Besides, another kind of localizable entanglement is also determined. Furthermore, we give the sufficient and necessary condition that a three-qubit state can be collapsed to an EPR pair by a measurement on one qubit, and characterize the three-qubit states that can be used as quantum channel for controlled teleporting a qubit of unknown information with unit probability and with unit fidelity.Comment: 4 page

Effect of disorder with long-range correlation on transport in graphene nanoribbon

Transport in disordered armchair graphene nanoribbons (AGR) with long-range correlation between quantum wire contact is investigated by transfer matrix combined with Landauer's formula. Metal-insulator transition is induced by disorder in neutral AGR. Thereinto, the conductance is one conductance quantum for metallic phase and exponentially decays otherwise when the length of AGR is infinity and far longer than its width. Similar to the case of long-range disorder, the conductance of neutral AGR first increases and then decreases while the conductance of doped AGR monotonically decreases, as the disorder strength increases. In the presence of strong disorder, the conductivity depends monotonically and non-monotonically on the aspect ratio for heavily doped and slightly doped AGR respectively.Comment: 6 pages, 8 figures; J. Phys: Condensed Matter (May 2012

Robust H∞ feedback control for uncertain stochastic delayed genetic regulatory networks with additive and multiplicative noise

The official published version can found at the link below.Noises are ubiquitous in genetic regulatory networks (GRNs). Gene regulation is inherently a stochastic process because of intrinsic and extrinsic noises that cause kinetic parameter variations and basal rate disturbance. Time delays are usually inevitable due to different biochemical reactions in such GRNs. In this paper, a delayed stochastic model with additive and multiplicative noises is utilized to describe stochastic GRNs. A feedback gene controller design scheme is proposed to guarantee that the GRN is mean-square asymptotically stable with noise attenuation, where the structure of the controllers can be specified according to engineering requirements. By applying control theory and mathematical tools, the analytical solution to the control design problem is given, which helps to provide some insight into synthetic biology and systems biology. The control scheme is employed in a three-gene network to illustrate the applicability and usefulness of the design.This work was funded by Royal Society of the U.K.; Foundation for the Author of National Excellent Doctoral Dissertation of China. Grant Number: 2007E4; Heilongjiang Outstanding Youth Science Fund of China. Grant Number: JC200809; Fok Ying Tung Education Foundation. Grant Number: 111064; International Science and Technology Cooperation Project of China. Grant Number: 2009DFA32050; University of Science and Technology of China Graduate Innovative Foundation