弱广义向量拟似变分不等式解的存在性

研究拓扑向量空间上弱广义向量拟似变分不等式解的存在性问题.与Khaliq和Rashid等在单调或伪单调假设条件下,利用KKM定理证明解的存在性不同,在集值映射是非空凸值映射并且有开下截口的条件下,利用Fan-Browder不动点原理证明解的存在性.     

Multifractal analysis of the software evolution in software networks

As the scale and complexity have been increased in software systems, developers place more emphases on software engineering and system designs. Software architecture is evolved with update of softwares, and it plays a fundamental role in determining quality of software systems. Multifractal characteristics of software networks can reflect software quality. In this paper, we construct a software network from the dependencies between object classes, and gain a deep understanding of software through network analysis. To be specific, multifractal analysis of the software network is performed based on a modified box-covering algorithm that yields fewer boxes. We verify that software with different functions and dependencies is multifractal. Further, different versions of the software are compared to discover the evolution of the software architecture. The results show that the singularity of class dependencies decreases as the software is updated. This trend leads to a more specific division of functions between software modules. One of the visible advantages of our work is that it allows the characterization of software structures at the code level. The methodology and results of this paper provide new insights into the evaluation and design of large-scale software systems.