We give a new description of the fundamental double four-spiral semigroup. The fundamental four-spiral semigroup Sp4 and the fundamental double fourspiral semigroup DSp4 were introduced in [1], [3], and [4]. These semigroups are interesting examples of fundamental regular semigroups, and are indispensable building blocks of bisimple, idempotent-generated regular semigroups. Their basic properti...

With the development of RS technology, the evaluation of DOM becomes more important. Multi-level fuzzy comprehensive evaluation is the traditional method for DOM evaluation. But in the process of traditional multi-Level Fuzzy Comprehensive Assessment, the weight of evaluation factor which are subjective is always ascertained by experts. The method can cause evaluation bias because of the subjec...

A new methodology to measure coded image/video quality using the just-noticeable-difference (JND) idea was proposed in [1]. Several small JND-based image/video quality datasets were released by the Media Communications Lab at the University of Southern California in [2,3]. In this work, we present an effort to build a large-scale JND-based coded video quality dataset. The dataset consists of 22...

In this paper we introduce a large class of subordinators called special subordinators and study their potential theory. Then we study the potential theory of processes obtained by subordinating a killed symmetric stable process in a bounded open set D with special subordinators. We establish a one-to-one correspondence between the nonnegative harmonic functions of the killed symmetric stable p...

For any α ∈ (0, 2), a truncated symmetric α-stable process in R is a symmetric Lévy process in R with no diffusion part and with a Lévy density given by c|x| 1{|x|<1} for some constant c. In [24] we have studied the potential theory of truncated symmetric stable processes. Among other things, we proved that the boundary Harnack principle is valid for the positive harmonic functions of this proc...

In this paper we study the Martin boundary of open sets with respect to a large class of purely discontinuous symmetric Lévy processes in R. We show that, if D ⊂ R is an open set which is κ-fat at a boundary point Q ∈ ∂D, then there is exactly one Martin boundary point associated with Q and this Martin boundary point is minimal. AMS 2010 Mathematics Subject Classification: Primary 60J50, 31C40;...

The unexpected faintness of high-redshift Type Ia supernovae (SNe Ia), as measured by two teams, has been interpreted as evidence that the expansion of the Universe is accelerating. We review the current challenges to this interpretation and seek to answer whether the cosmological implications are compelling. We discuss future observations of SNe Ia which could offer extraordinary evidence to t...

We use the sample covariation to develop asymptotic tests for independence for data in the normal domain of attraction of a stable law. The tests can be used for finite or infinite variance processes. In a simulation study we compare the finite sample performance of the proposed tests to the Portmanteau test commonly used in time series modeling. The null convergence of the test statistics to t...

Recently it was shown in Kim [26] that Fatou’s theorem for transient censored α-stable processes in a bounded C open set is true. Here we give a probabilistic proof of relative Fatou’s theorem for (−∆)-harmonic functions (equivalently for symmetric α-stable processes) in bounded κ-fat open set where α ∈ (0, 2). That is, if u is positive (−∆)-harmonic function in a bounded κ-fat open set D and h...