The Harnack distance on space  and its conformal invariance were constructed and studied by Herron. In this paper, we obtain the Harnack distance on domains  in . Then, we use this concept to investigate some properties of the positive harmonic function class. These results are obtained in the complex plane, so it is advantageous to take some tools of the complex analysis. The main result of this paper is the property of the local uniform convergence of the positive harmonic sequences on a domain in the complex plane.

Evaluating the socioeconomic efficiency of scientific and technological topics/projects after acceptance is very difficult because it is not easy to find common ground on the criteria for evaluating the socioeconomic efficiency of topics/ projects of different research fields. Hence, depending on researchers' views, the evaluation criteria or the weight of evaluating the socioeconomic efficiency of each topic/project should be different. This study uses the expert method and the Analytic Hierarchy Process (AHP) method to determine the criteria and to calculate weights for criteria on five scientific fields according to scientific sub-disciplines in Binh Dinh province, including agricultural science, natural science, social sciences and humanities, medical science, engineering and technological sciences. Our research shows that the evaluation of the socioeconomic efficiency of the provincial topics/projects should be based on eight aspects, including science, technology, economics, environment, culturesociety, information-management, and education. At the same time, the results also identified a set of common criteria for evaluating the socioeconomic efficiency of topics/projects and suggested how to calculate points and to rank the effectiveness of topics/projects. However, the weight of the criteria and the composition of each criterion is different.