Approximation for Dominating Set Problem with Measure Functions

In this paper, we study the Dominating Set problem with measure functions, which is extended from the general Dominating Set problem. We study the correspondnig problems on complexity, approximation and inapproximability for Dominating Set problem with measure functions. In addition, we extend our results to the weighted graphs

The Non-Perturbative Quantum Nature of the Dislocation-Phonon Interaction

Despite the long history of dislocation-phonon interaction studies, there are many problems that have not been fully resolved during this development. These include an incompatibility between a perturbative approach and the long-range nature of a dislocation, the relation between static and dynamic scattering, and the nature of dislocation-phonon resonance. Here by introducing a fully quantized dislocation field, the "dislon"[1], a phonon is renormalized as a quasi-phonon, with shifted quasi-phonon energy, and accompanied by a finite quasi-phonon lifetime that is reducible to classical results. A series of outstanding legacy issues including those above can be directly explained within this unified phonon renormalization approach. In particular, a renormalized phonon naturally resolves the decades-long debate between dynamic and static dislocation-phonon scattering approaches.Comment: 5 pages main text, 3 figures, 10 pages supplemental material

Empirical study on clique-degree distribution of networks

The community structure and motif-modular-network hierarchy are of great importance for understanding the relationship between structures and functions. In this paper, we investigate the distribution of clique-degree, which is an extension of degree and can be used to measure the density of cliques in networks. The empirical studies indicate the extensive existence of power-law clique-degree distributions in various real networks, and the power-law exponent decreases with the increasing of clique size.Comment: 9 figures, 4 page

Educational policy process on local government in contemporary China : focusing on the privatization experiment of the public school after 1990

Educational policy process in China is becoming a main subject in educational administration. Preceding researches had focus to the problems in the policy implementation. In other word, although decentralization had been advancing and it had been criticized about the relationship between central-local that the issues that needs to be address was left behind. And it was the main research purposes to offer solutions in solving the real issues between centralization and decentralization. As the analysis approach, there is little what analyzed an educational policy in the analysis framework of policy process. The paper focusing on the decision-making and the process of implementation in educational administration, and enlighten the structure and the feature of educational policy process in China. Furthermore, the paper adds the viewpoint of the relationship between central-local analyzing the task that cannot be solved only by the structure and policy pertaining in the policy process environment. This research focuses the sructure of educational policy process and the grade of the local authority discretionary rights in policy process, and the mechanism that made it possible. The following are concrete work subject. (1) Does the local authority have any power to implement it. (2) Why implementing the privatization policy what stops them from practicing it. (3) Whether the system works or not. From a privatization experiment policy, we can find that there are still possibilities of discretion in local authority. The policy process of top-down control is changed. The educational policy-making and implementation process in local authority have broad latitude in policy process. A local forms a policy is made by the local to fit actual condition in the local area. Hence jurisdiction to a compulsory education was transferred to the local authority. However, the central government set forth the opposite plan to public schools choice. The central government directed local to regulate approval and license for setting up privatization experiment schools. However, the central government did not take a decisive control action in the privatization experiment schools. Central government did not oppose school choice in privatization experiment school. Furthermore, the local authority has power over the public schools because it contributes immensely to its finances