Abstract:
We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as a finite linear combination of geometric terms and present conditions on the structure of these linear combinations such that the resulting measure may yield an invariant measure of a random walk. We demonstrate that each geometric term must individually satisfy the balance equations in the interior of the state space and further show that the geometric terms in an invariant measure must have a pairwise-coupled structure. Finally, we show that at least one of the coefficients in the linear combination must be negative.

Abstract:
We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as an infinite sum of geometric terms. We present necessary conditions for the invariant measure to be a sum of geometric terms. We demonstrate that, under a mild regularity condition, each geometric term must individually satisfy the balance equations in the interior of the state space. We show that the geometric terms in an invariant measure must be the union of finitely many pairwise-coupled sets of infinite cardinality. We further show that for the invariant measure to be a sum of geometric terms, the random walk cannot have transitions to the north, northeast or east. Finally, we show that for an infinite weighted sum of geometric terms to be an invariant measure at least one of the weights must be negative.

Abstract:
We consider two-node queue with finite buffers modeled as a two-dimensional random walk on a finite state space. We develop an approximation scheme based on the Markov reward approach to error bounds in order to bound performance measures of a two-dimensional finite random walk in terms of a perturbed random walk in which only the transitions along the boundaries are different from those in the original model. The invariant measure of the perturbed random walk is of product-form. We first apply this approximation scheme to a tandem queue with finite buffers and some variants of this model. Then, we show that our approximation scheme is sufficiently general by applying it to a coupled-queue with finite buffers and processor sharing.

Abstract:
We consider homogeneous random walks in the quarter-plane. The necessary conditions which characterize random walks of which the invariant measure is a sum of geometric terms are provided in [2,3]. Based on these results, we first develop an algorithm to check whether the invariant measure of a given random walk is a sum of geometric terms. We also provide the explicit form of the invariant measure if it is a sum of geometric terms. Secondly, for random walks of which the invariant measure is not a sum of geometric terms, we provide an approximation scheme to obtain error bounds for the performance measures. Finally, some numerical examples are provided.

Abstract:
We consider the invariant measure of a homogeneous continuous- time Markov process in the quarter-plane. The basic solutions of the global balance equation are the geometric distributions. We first show that the invariant measure can not be a finite linear combination of basic geometric distributions, unless it consists of a single basic geo- metric distribution. Second, we show that a countable linear combina- tion of geometric terms can be an invariant measure only if it consists of pairwise-coupled terms. As a consequence, we obtain a complete characterization of all countable linear combinations of geometric dis- tributions that may yield an invariant measure for a homogeneous continuous-time Markov process in the quarter-plane.

Designing and developing computer-assisted image processing techniques to help doctors improve their diagnosis has received considerable interests over the past years. In this paper, we used the kolmogorov complexity model to analyze the CT images of the healthy liver and multiple daughter hydatid cysts. Before the complexity characteristic calculating, the image preprocessing methods had been used for image standardization. From the kolmogorov complexity model, complexity characteristic were calculated in order to quantify the complexity, between healthy liver and multiple daughter hydatid cysts. Then we use statistical method to analyze the complexity characteristic of those two types of images. Our preliminary results show that the complexity characteristic has statistically significant (p<0.05) to analyze these two types CT images, between the healthy liver and the multiple daughter hydatid cysts. Furthermore, the result leads us to the conclusion that the kolmogorov complexity model could use for analyze the hydatid disease and will also extend the analysis the other lesions of liver.

Abstract:
Grid-connected wind turbines are fluctuating power sources that may produce flicker during continuous operation. This paper presents a simulation model of a MW-level variable speed wind turbine with a full-scale back-to-back power converter and permanent magnet synchronous generator (PMSG) developed in the simulation tool of PSCAD/EMTDC. Flicker emission of this system is investigated. The 3p (three times per revolution) power oscillation due to wind shear and tower shadow effects is the significant part in the flicker emission of variable speed wind turbines with PMSG during continuous operation. A new method of flicker mitigation by controlling the rotational speed is proposed. It smoothes the 3p active power oscillations from wind shear and tower shadow effects of the wind turbine by varying the rotational speed of the PMSG. Simulation results show that damping the 3p active power oscillation by using the flicker mitigation speed controller is an effective means for flicker mitigation of variable speed wind turbines with full-scale back-to-back power converters and PMSG during continuous operation.

Abstract:
Three types of macromolecular organic matters (MOMs), i.e. humic acid (HA), kerogen+black carbon (KB), and black carbon (BC) were extracted from marine sediments of Xiamen Gulf, southeast of China. The chemical composition, morphological property and source of the three extractions were characterized by elemental analyzer/isotope ratio mass spectrometry (EA/IRMS) and scanning electron microscope (SEM). The results showed that KB was the predominant fraction in MOMs, which accounted for 61.79%－89.15% of the total organic content (TOC), while HA consisted less than 5%. The relative high contents of kerogen and BC, and low contents of HA in the samples indicated that anthropogenic input might be the major source of organic matter in marine sediments near the industrial regions. The characterization of SEM, not only revealed morphological properties of the three fractions, but also allowed a better understanding of the source of MOMs. The δ13C values of the three fractions suggested that materials from terrestrial C3 plants were predominant. Furthermore, the anthropogenic activities, such as the discharge of sewage, coal and biomass combustion from industry nearby and agricultural practices within drainage basin of the Jiulong River, were remarkably contributed to the variations in δ13C values of MOMs in the offshore marine sediments.

Abstract:
Here I define soft matter as materials working in the vicinity of a moderate point, at which the system has balanced entropy and enthalpy contributions and the order parameter fluctuation maximizes. Moreover, the maximization of the associated response function explains their sensitivity to thermal conditions.

Abstract:
Alkali-earth atoms have a long-lived electronic excited state, which can be localized in the Fermi sea of ground state atoms by an external potential and serve as magnetic impurities, due to the spin-exchange interaction between the excited and the ground state atoms. This can give rise to the Kondo effect. However, in order to achieve this effect in current atomic gas experiment, it requires the Kondo temperature to be increased to a sizable portion of the Fermi temperature. In this letter we propose that the spin-exchange interaction can be strongly enhanced by utilizing the confinement-induced resonance (CIR). We analyze this system by the renormalization group approach, and we show that nearby a CIR, the Kondo temperature can indeed be increased to the regime attainable by current experiments.