Holography, chiral Lagrangian and form factor relations

We perform a detailed study of mesonic properties in a class of holographic models of QCD, which is described by the Yang-Mills plus Chern-Simons action. By decomposing the 5 dimensional gauge field into resonances and integrating out the massive ones, we reproduce the Chiral Perturbative Theory Lagrangian up to ${\cal O}(p^6)$ and obtain all the relevant low energy constants (LECs). The numerical predictions of the LECs show minor model dependence, and agree reasonably with the determinations from other approaches. Interestingly, various model-independent relations appear among them. Some of these relations are found to be the large-distance limits of universal relations between form factors of the anomalous and even-parity sectors of QCD.Comment: Typo corrected; 8 pages, 1 figure; Proceedings of the Xth Quark Confinement and the Hadron Spectrum, October 8-12, 2012, TUM Campus Garching, Munich, German

A new solution approach to polynomial LPV system analysis and synthesis

Based on sum-of-squares (SOS) decomposition, we propose a new solution approach for polynomial LPV system analysis and control synthesis problems. Instead of solving matrix variables over a positive definite cone, the SOS approach tries to find a suitable decomposition to verify the positiveness of given polynomials. The complexity of the SOS-based numerical method is polynomial of the problem size. This approach also leads to more accurate solutions to LPV systems than most existing relaxation methods. Several examples have been used to demonstrate benefits of the SOS-based solution approach

A mathematical model for contingent claim pricing in a preannounced policy

This paper presents a mathematical model for contingent claim pricing in a preannounced policy. There are some properties in the model. First, one can distinguish the preannouncement effects on the mean and volatility of asset returns. Second, the European call option pricing solution in the model can reduce to the Black-Sholes (1973) formula as no preannouncement effects occur before maturity.Preannounced policy, Preannouncement effect, Fat tails, Discontinuity, Option pricing.

Li-Yorke chaos in hybrid systems on a time scale

By using the reduction technique to impulsive differential equations [1], we rigorously prove the presence of chaos in dynamic equations on time scales (DETS). The results of the present study are based on the Li-Yorke definition of chaos. This is the first time in the literature that chaos is obtained for DETS. An illustrative example is presented by means of a Duffing equation on a time scale.Comment: 16 pages, 2 figure

Unpredictable Points and Chaos

It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. The existing definitions of chaos are formulated in sets of motions. This is the first time that description of chaos is initiated from a single motion. The theoretical results are exemplified by means of the symbolic dynamics.Comment: 9 page