We study how the geometry of a projective variety X is reflected in the positivity properties of the diagonal ∆X considered as a cycle on X ×X. We analyze when the diagonal is big, when it is nef, and when it is rigid. In each case, we give several implications for the geometric properties of X. For example, when the cohomology class of ∆X is big, we prove that the Hodge groups H(X) vanish for ...

Tuberculosis of the tonsils is by no means a common condition, Mullin (1923), for example, in analysing 400 tonsillectomies found only 4.25 per cent cases of tuberculous tonsils. The present study is based on 2,477 tonsillectomies in the Madras General Hospital. This series covers a period of five years from January 1928 to December 1932. We, however, feel that this investigation is incomplete ...

the work  addressed in this paper is a comparative study between convergence of the  acceleration techniques, diagonal pad'{e} approximants and shanks transforms, on homotopy analysis method  and adomian decomposition method for solving  differential equations of integer and fractional orders.