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

Gravitational Lensing and Anisotropies of CBR on the Small Angular Scales

We investigate the effect of gravitational lensing, produced by linear density perturbations, for anisotropies of the Cosmic Background Radiation (CBR) on scales of arcminutes. In calculations, a flat universe ($\Omega=1$) and the Harrison-Zel'dovich spectrum ($n=1$) are assumed. The numerical results show that on scales of a few arcminutes, gravitational lensing produces only negligible anisotropies in the temperature of the CBR. Our conclusion disagrees with that of Cay\'{o}n {\it et al.} who argue that the amplification of $\Delta T/T$ on scales $\le 3'$ may even be larger than 100\%.Comment: Accepted by MNRAS. 16 pages, 2 figures, tarred, compressed and uuencoded Postscript file

On the sine-Gordon--Thirring equivalence in the presence of a boundary

In this paper, the relationship between the sine-Gordon model with an integrable boundary condition and the Thirring model with boundary is discussed and the reflection $R$-matrix for the massive Thirring model, which is related to the physical boundary parameters of the sine-Gordon model, is given. The relationship between the the boundary parameters and the two formal parameters appearing in the work of Ghoshal and Zamolodchikov is discussed.Comment: 14 pages, Latex, to be published in Int. J. Mod. Phys. A. Two references adde

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

Quantifier Elimination over Finite Fields Using Gr\"obner Bases

We give an algebraic quantifier elimination algorithm for the first-order theory over any given finite field using Gr\"obner basis methods. The algorithm relies on the strong Nullstellensatz and properties of elimination ideals over finite fields. We analyze the theoretical complexity of the algorithm and show its application in the formal analysis of a biological controller model.Comment: A shorter version is to appear in International Conference on Algebraic Informatics 201

Can gravitational dynamics be obtained by diffeomorphism invariance of action?

It has recently been suggested that the gravitational dynamics could be obtained by requiring the action to be invariant under diffeomorphism transformations. We argue that the action constructed in usual way is automatically diffeomorphism invariant in nature, which thus invalidates this alternative perspective to obtain gravitational dynamics. Especially, we also show what is wrong with the technical derivation of gravitational dynamics in the alternative approach.Comment: version published in PR