External perturbation manifested system size resonance in a mesoscopic hormone signaling model

In mesoscopic reaction systems that contain only finite number of reactants, molecular fluctuation (or the so called internal noise), which can be characterized by the system size, plays an important role in nonlinear systems. In this work, the effect of internal noise is studied in a mesoscopic hormone signaling model with the presence of external perturbations (noise or signal). Simulation results reveal that the internal noise can play a constructive role to optimize the regularity of the noise induced internal signal only when external perturbation is present. This is a novel external perturbations induced system size resonance, which indicates that in complex mesoscopic systems, the system can automatically avoid the destructive environmental effects by tuning its size. Such kind of nontrivial cooperative effect may attribute to the fact that external perturbations broadened the regulation scope of the key mutual feedback. Therefore, current finding is of practical significance for similar physiological systems where the intercellular regulation plays the dominate role for signaling.     

On some types of covering rough sets from topological points of view

The concept of coverings is one of the fundamental concepts in topological spaces and plays a big part in the study of topological problems. This motivates the research of covering rough sets from topological points of view. From topological points of view, we can get a good insight into the essence of covering rough sets and make our discussions concise and profound. In this paper, we first construct a type of topology called the topology induced by the covering on a covering approximation space. This notion is indeed in the core of this paper. Then we use it to define the concepts of neighborhoods, closures, connected spaces, and components. Drawing on these concepts, we define several pairs of approximation operators. We not only investigate the relationships among them, but also give clear explanations of the concepts discussed in this paper. For a given covering approximation space, we can use the topology induced by the covering to investigate the topological properties of the space such as separation, connectedness, etc. Finally, a diagram is presented to show that the collection of all the lower and upper approximations considered in this paper constructs a lattice in terms of the inclusion relation ⊆.     

The Bergman kernel functions on Hua domains

We get the Bergman kernel functions in explicit formulas on four types of Hua domain.There are two key steps: First, we give the holomorphic automorphism groups of four types of Hua domain; second, we introduce the concept of semi-Reinhardt domain and give their complete orthonormal systems. Based on these two aspects we obtain the Bergman kernel function in explicit formulas on Hua domains.     

On some congruence properties of elliptic curves

In this paper, as a consequence of a theorem of Serre on congruence properties of elliptic curves, a complete solution (see Theorem 2.1) is given for an open question (i.e., the KKP question) presented recently by Kim, Koo, and Park. Some partial results for the KKP question of S-type are obtained (see Theorem 3.1 and Corollary 3.2). Several further related questions are also presented and discussed.     

Orientably-regular embeddings of a class of multipartite graphs

The orientably-regular embeddings of complete multipartite graphs have been determined by the contributions of several papers. After that, a natural question can be asked: How about the regular embeddings of the multipartite graphs with m parts, while each part contains n vertices(not necessarily complete multipartite). In this paper, we classify all the orientably-regular embeddings of these graphs when m is a prime q and n is a prime power pe.