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Aquib, Mohd,Shahid, Mohammad Hasan Department of Mathematics 2018 Kyungpook mathematical journal Vol.58 No.1
In this paper, we prove the optimal inequalities for the generalized normalized ${\delta}$-Casorati curvature and the normalized scalar curvature for different submanifolds in generalized (${\kappa},{\mu}$)-space forms. The proof is based on an optimization procedure involving a quadratic polynomial in the components of the second fundamental form. We also characterize the submanifolds on which equalities hold.
Mathematics learning inequality among children of private and public schools
Parvez, Aquib,Laxminarayana, K. 서울대학교 교육연구소 2022 Asia Pacific Education Review Vol.23 No.2
In this study, we research the gap in average mathematics learning between the children of private and public schools at two points. We have divided them into two groups on the basis of the type of school they are attending or last attended. We first skim through their various background characteristics at these two points. We then explore these background characteristics and using the threefold Blinder–Oaxaca decomposition, we find that it is the difference in the average endowments between the two which consistently explains the gap in average performance between them. We also find the role of differential impact of the background characteristics on the average learning outcome of children on the first point. The most important and consistent contributor to the endowment effect is the schooling cost and the time allocation on studies. One striking result is the now significant contribution of the gap in average years of schooling which is worrying because these children are from the same age group. We conclude that with the average features and returns of the private school children, the gap in learning between them would have been removed. Moreover, the public school children would have performed better than the private school children.
GEOMETRIC INEQUALITIES FOR WARPED PRODUCTS SUBMANIFOLDS IN GENERALIZED COMPLEX SPACE FORMS
Mohd Aquib,Mohd Aslam,Michel Nguiffo Boyom,Mohammad Hasan Shahid Korean Mathematical Society 2023 대한수학회논문집 Vol.38 No.1
In this article, we derived Chen's inequality for warped product bi-slant submanifolds in generalized complex space forms using semisymmetric metric connections and discuss the equality case of the inequality. Further, we discuss non-existence of such minimal immersion. We also provide various applications of the obtained inequalities.