For a general normed vector space,a special optimal value function called a maximal time function is considered.This covers the farthest distance function as a special case,and has a close relationship with the smalle...For a general normed vector space,a special optimal value function called a maximal time function is considered.This covers the farthest distance function as a special case,and has a close relationship with the smallest enclosing ball problem.Some properties of the maximal time function are proven,including the convexity,the lower semicontinuity,and the exact characterizations of its subdifferential formulas.展开更多
This paper considered the Noether normalization of a finitely generated algebra over an algebraically closed field. It gives a necessary and sufficient condition as well as an algorithm for the identification of those...This paper considered the Noether normalization of a finitely generated algebra over an algebraically closed field. It gives a necessary and sufficient condition as well as an algorithm for the identification of those algebraically independent variables, then uses these elements to construct the Noether normalization of this algebra.展开更多
Let G be a finite group of Lie type E6 over Fq (adjoint or simply connected) and W be the Weyl group of G. We describe maximal tori T such that T has a complement in its algebraic normalizer N(G, T). It is well known ...Let G be a finite group of Lie type E6 over Fq (adjoint or simply connected) and W be the Weyl group of G. We describe maximal tori T such that T has a complement in its algebraic normalizer N(G, T). It is well known that for each maximal torus T of G there exists an element w ∈ W such that N(G, T )/T ■ CW(w). When T does not have a complement isomorphic to CW(w), we show that w has a lift in N(G, T) of the same order.展开更多
基金supported by the National Natural Science Foundation of China(11201324)the Fok Ying Tuny Education Foundation(141114)the Sichuan Technology Program(2022ZYD0011,2022NFSC1852).
文摘For a general normed vector space,a special optimal value function called a maximal time function is considered.This covers the farthest distance function as a special case,and has a close relationship with the smallest enclosing ball problem.Some properties of the maximal time function are proven,including the convexity,the lower semicontinuity,and the exact characterizations of its subdifferential formulas.
文摘This paper considered the Noether normalization of a finitely generated algebra over an algebraically closed field. It gives a necessary and sufficient condition as well as an algorithm for the identification of those algebraically independent variables, then uses these elements to construct the Noether normalization of this algebra.
基金Russian Science Foundation (project no. 14-21-00065).
文摘Let G be a finite group of Lie type E6 over Fq (adjoint or simply connected) and W be the Weyl group of G. We describe maximal tori T such that T has a complement in its algebraic normalizer N(G, T). It is well known that for each maximal torus T of G there exists an element w ∈ W such that N(G, T )/T ■ CW(w). When T does not have a complement isomorphic to CW(w), we show that w has a lift in N(G, T) of the same order.
