This paper begins to study the limiting behavior of a family of Hermitian Yang-Mills(HYM for brevity) metrics on a class of rank two slope stable vector bundles over a product of two elliptic curves with K?hler metri...This paper begins to study the limiting behavior of a family of Hermitian Yang-Mills(HYM for brevity) metrics on a class of rank two slope stable vector bundles over a product of two elliptic curves with K?hler metrics ωε when ε → 0. Here, ωε are flat and have areas ε and ε-1 on the two elliptic curves, respectively.A family of Hermitian metrics on the vector bundle are explicitly constructed and with respect to them, the HYM metrics are normalized. We then compare the family of normalized HYM metrics with the family of constructed Hermitian metrics by doing estimates. We get the higher order estimates as long as the C^0-estimate is provided. We also get the estimate of the lower bound of the C^0-norm. If the desired estimate of the upper bound of the C^0-norm can be obtained, then it would be shown that these two families of metrics are close to arbitrary order in ε in any Cknorms.展开更多
System analysts often use software fault prediction models to identify fault-prone modules during the design phase of the software development life cycle. The models help predict faulty modules based on the software m...System analysts often use software fault prediction models to identify fault-prone modules during the design phase of the software development life cycle. The models help predict faulty modules based on the software metrics that are input to the models. In this study, we consider 20 types of metrics to develop a model using an extreme learning machine associated with various kernel methods. We evaluate the effectiveness of the mode using a proposed framework based on the cost and efficiency in the testing phases. The evaluation process is carried out by considering case studies for 30 object-oriented software systems. Experimental results demonstrate that the application of a fault prediction model is suitable for projects with the percentage of faulty classes below a certain threshold, which depends on the efficiency of fault identification(low: 47.28%; median: 39.24%; high: 25.72%). We consider nine feature selection techniques to remove the irrelevant metrics and to select the best set of source code metrics for fault prediction.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11871016, 11421061 and 11025103)
文摘This paper begins to study the limiting behavior of a family of Hermitian Yang-Mills(HYM for brevity) metrics on a class of rank two slope stable vector bundles over a product of two elliptic curves with K?hler metrics ωε when ε → 0. Here, ωε are flat and have areas ε and ε-1 on the two elliptic curves, respectively.A family of Hermitian metrics on the vector bundle are explicitly constructed and with respect to them, the HYM metrics are normalized. We then compare the family of normalized HYM metrics with the family of constructed Hermitian metrics by doing estimates. We get the higher order estimates as long as the C^0-estimate is provided. We also get the estimate of the lower bound of the C^0-norm. If the desired estimate of the upper bound of the C^0-norm can be obtained, then it would be shown that these two families of metrics are close to arbitrary order in ε in any Cknorms.
基金the FIST project,of DST, government of India for sponsoring the work on web engineering and cloud based computing
文摘System analysts often use software fault prediction models to identify fault-prone modules during the design phase of the software development life cycle. The models help predict faulty modules based on the software metrics that are input to the models. In this study, we consider 20 types of metrics to develop a model using an extreme learning machine associated with various kernel methods. We evaluate the effectiveness of the mode using a proposed framework based on the cost and efficiency in the testing phases. The evaluation process is carried out by considering case studies for 30 object-oriented software systems. Experimental results demonstrate that the application of a fault prediction model is suitable for projects with the percentage of faulty classes below a certain threshold, which depends on the efficiency of fault identification(low: 47.28%; median: 39.24%; high: 25.72%). We consider nine feature selection techniques to remove the irrelevant metrics and to select the best set of source code metrics for fault prediction.