Matrix analysis is one of the appropriate mathematical methods used in engineering sciences. In methods based on matrix analysis special inverse matrix , properties of matrices are used in linear algebra problems. For the first time, the structure of matrix converters was presented by gyagy and pully under the purely theoretical concept with the motivation of optimizing the fundamental performance of cyclo-converters, in order to obtain output voltage with unlimited frequency and direct conversion using controllable two-way switches. Considering the essential role of inverse matrices in engineering sciences and considering the class of matrices inverses. Now, We introduce a new class of generalized inverse which is called n−strongly Drazin inverse and some elementary properties of the n−strongly Drazin inverse are obtained. Certain multiplicative and additive results for the n−strongly Drazin inverse in a Banach algebra are presented. We then apply some conditions under which a 2×2 block operator matrix has n−strongly Drazin inverse over Banach spaces. Manuscript profile

The present research was conducted with the aim of comparing the effectiveness of virtual education based on positive psychology on the resilience of students of Tehran's gifted schools. This research is a semi-experimental type with a pre-test-post-test design with a control group. The statistical population of the research included all the students of the gifted schools, who were studying in the first secondary schools. In order to select subjects from one of the schools accessible to Tehran's brilliant talents in the first year of high school, 45 people were randomly selected and replaced in two experimental groups (n) and a control group. The pre-test was conducted for both groups. The first experimental group was During 14 sessions of 90 minutes, they were trained based on positive psychology, and the second group was trained based on cognitive-behavioral methods. During this period, the control group did not receive any training in these fields.Conclusion: The results showed that there is a significant difference between the performance of the two groups in the resilience post-test. While, as expected, the resilience of the control group did not have significant changes, but training based on positive psychology improved the resilience index by 9.67% and changed their resilience performance. The effect of education based on cognitive-behavioral method, although it is less than the positive method, but it is with a significant amount of 6.27%, which can create relative changes in the resilience of students. Manuscript profile