Equilibrium states of the pressure function for products of matrices

Let $\{M_i\}_{i=1}^\ell$ be a non-trivial family of $d\times d$ complex matrices, in the sense that for any $n\in \N$, there exists $i_1... i_n\in \{1,..., \ell\}^n$ such that $M_{i_1}... M_{i_n}\neq {\bf 0}$. Let $P \colon (0,\infty)\to \R$ be the pressure function of $\{M_i\}_{i=1}^\ell$. We show that for each $q>0$, there are at most $d$ ergodic $q$-equilibrium states of $P$, and each of them satisfies certain Gibbs property.Comment: 12 pages. To appear in DCD

Omnidirectionally Bending to the Normal in epsilon-near-Zero Metamaterials

Contrary to conventional wisdom that light bends away from the normal at the interface when it passes from high to low refractive index media, here we demonstrate an exotic phenomenon that the direction of electromagnetic power bends towards the normal when light is incident from arbitrary high refractive index medium to \epsilon-near-zero metamaterial. Moreover, the direction of the transmitted beam is close to the normal for all angles of incidence. In other words, the electromagnetic power coming from different directions in air or arbitrary high refractive index medium can be redirected to the direction almost parallel to the normal upon entering the \epsilon-near-zero metamaterial. This phenomenon is counterintuitive to the behavior described by conventional Snell's law and resulted from the interplay between \epsilon-near-zero and material loss. This property has potential applications in communications to increase acceptance angle and energy delivery without using optical lenses and mechanical gimbals

Jump risk, time-varying risk premia, and technical trading profits

In this paper we investigate the recently documented trading profits based on technical trading rules in an asset pricing framework that incorporates jump risk and time-varying risk premia. Following Brock, Lakonishok, and LeBaron (1992), we apply popular technical trading rules to the daily S&P 500 index over a long period of time. Trading profits are examined using bootstrap simulation to address distributional anomalies. We estimate a variety of asset pricing models, including the random walk, autoregressive models, a combined jump diffusion model, and a combined model of jump-diffusion and autoregressive conditional heteroskedasticity. Technical trading profits are shown to be statistically significant for the pure diffusion models and autoregressive models, yet become less significant when jump risk is incorporated into the model and virtually disappear for an asset pricing model that incorporates both jump risk and time-varying risk premia. The empirical evidence suggests that technical trading profits could be fair compensation for the risk of price discontinuity as well as time-varying risk premia of asset returns. Alternatively, technical trading profits provide a test of specification of asset pricing models; in this vein the evidence provides support for the incorporation of jump risk into asset pricing models.Financial markets ; Prices