Abstract:
Let A be a finite dimensional symmetric cllular algebras. We construct a nilpotent ideal in A. The ideal connects the radicals of cell modules with the radical of the algebra. It also reveals some information on the dimensions of simple modules of A.

Abstract:
Let R be an integral domain and A a cellular algebra. Suppose that A is equipped with a family of Jucys-Murphy elements which satisfy the separation condition. Let K be the field of fractions of R. We give a necessary and sufficient condition under which the center of $A_{K}$ consists of the symmetric polynomials in Jucys-Murphy elements.

Abstract:
Let $R$ be an integral domain and $A$ a symmetric cellular algebra over $R$ with a cellular basis $\{C_{S,T}^\lam \mid \lam\in\Lambda, S,T\in M(\lam)\}$. We will construct an ideal $L(A)$ of the center of $A$ and prove that $L(A)$ contains the so-called Higman ideal. When $R$ is a field, we prove that the dimension of $L(A)$ is not less than the number of non-isomorphic simple $A$-modules.

Abstract:
For a Frobenius cellular algebra, we prove that if the left (right) dual basis of a cellular basis is again cellular, then the algebra is symmetric. Moreover, some ideals of the center are constructed by using the so-called Nakayama twisted center.

Abstract:
In recent years, the narrow bandgap antimonide based compound semiconductors (ABCS) are widely regarded as the first candidate materials for fabrication of the third generation infrared photon detectors and integrated circuits with ultra-high speed and ultra-low power consumption. Due to their unique bandgap structure and physical properties, it makes a vast space to develop various novel devices, and becomes a hot research area in many developed countries such as USA, Japan, Germany and Israel etc. Research progress in the preparation and application of ABCS materials, existing problems and some latest results are briefly introduced.

Abstract:
The complexity of natural resource management is increasingly recognized and requires adaptive governance at multiple levels. It is particularly significant to explore the impacts of government interventions on the management practices of local communities and on target social-ecological systems. The Inner Mongolian rangeland was traditionally managed by indigenous people using their own institutions that were adapted to the highly variable local climate and were able to maintain the resilience of the social-ecological system for more than 1000 years. However, external interventions have significantly affected the rangeland social-ecological system in recent decades. In this paper, using livestock breed improvement as an example, we track government interventions from the traditional era through the collective period to the present market economy period based on a review of historical documents and case studies. Using the concept of social-ecological system resilience, we diagnose the impacts of interventions on livestock breed management in the rangeland social-ecological system, and discuss how these interventions occur. We found that government interventions in livestock breeding have gradually decoupled the pastoral society from its supporting ecological system. During this process, external powers have increasingly displaced the local community in defining the nature of rangeland management. Power asymmetry and discourse have contributed to this displacement.

Abstract:
This paper is devoted to investigating mean square stability of a class of stochastic reaction-diffusion systems with Markovian switching and impulsive perturbations. Based on Lyapunov functions and stochastic analysis method, some new criteria are established. Moreover, a class of semilinear stochastic impulsive reaction-diffusion differential equations with Markovian switching is discussed and a numerical example is presented to show the effectiveness of the obtained results.

Abstract:
In this paper, we mainly study Jordan derivations of dual extension algebras and those of generalized one-point extension algebras. It is shown that every Jordan derivation of dual extension algebras is a derivation. As applications, we obtain that every Jordan generalized derivation and every generalized Jordan derivation on dual extension algebras are both generalized derivations. For generalized one-point extension algebras, it is proved that under certain conditions, each Jordan derivation of them is the sum of a derivation and an anti-derivation.

Abstract:
Let $K$ be a field and $\Gamma$ a finite quiver without oriented cycles. Let $\Lambda$ be the path algebra $K(\Gamma, \rho)$ and let $\mathscr{D}(\Lambda)$ be the dual extension of $\Lambda$. In this paper, we prove that each Lie derivation of $\mathscr{D}(\Lambda)$ is of the standard form.

Abstract:
For a finite dimensional Frobenius cellular algebra, a sufficient and necessary condition for a simple cell module to be projective is given. A special case that dual bases of the cellular basis satisfying a certain condition is also considered. The result is similar to that in symmetric case.