Strong laws of large numbers for sub-linear expectations

We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities.Comment: 10 page

The Tychonoff uniqueness theorem for the G-heat equation

In this paper, we obtain the Tychonoff uniqueness theorem for the G-heat equation

An Invariance Principle of G-Brownian Motion for the Law of the Iterated Logarithm under G-expectation

The classical law of the iterated logarithm (LIL for short)as fundamental limit theorems in probability theory play an important role in the development of probability theory and its applications. Strassen (1964) extended LIL to large classes of functional random variables, it is well known as the invariance principle for LIL which provide an extremely powerful tool in probability and statistical inference. But recently many phenomena show that the linearity of probability is a limit for applications, for example in finance, statistics. As while a nonlinear expectation--- G-expectation has attracted extensive attentions of mathematicians and economists, more and more people began to study the nature of the G-expectation space. A natural question is: Can the classical invariance principle for LIL be generalized under G-expectation space? This paper gives a positive answer. We present the invariance principle of G-Brownian motion for the law of the iterated logarithm under G-expectation

Inf-convolution of G-expectations

In this paper we will discuss the optimal risk transfer problems when risk measures are generated by G-expectations, and we present the relationship between inf-convolution of G-expectations and the inf-convolution of drivers G.Comment: 23 page

Mesons and Nucleons in Soft-Wall AdS/QCD with Constrained Infrared Background

The purpose of this paper is to further study the soft-wall AdS/QCD model with constrained IR background. By including a quartic bulk scalar potential we study various meson and nucleon spectra. This model naturally realizes the asymptotical linearity of these mass spectra simultaneously, together with correctly pattern of explicit and dynamical chiral symmetry breaking. The agreement between the theoretical calculations and the experimental data is good.Comment: 17 pages,5 table

Nonclassical photon pairs generated from a room-temperature atomic ensemble

We report experimental generation of non-classically correlated photon pairs from collective emission in a room-temperature atomic vapor cell. The nonclassical feature of the emission is demonstrated by observing a violation of the Cauchy-Schwarz inequality. Each pair of correlated photons are separated by a controllable time delay up to 2 microseconds. This experiment demonstrates an important step towards the realization of the Duan-Lukin-Cirac-Zoller scheme for scalable long-distance quantum communication.Comment: 4 pages, 2 figure

Pupillometry, a bioengineering overview

The pupillary control system is examined using a microprocessor based integrative pupillometer. The real time software functions of the microprocessor include: data collection, stimulus generation and area to diameter conversion. Results of an analysis of linear and nonlinear phenomena are presented