This paper considers the differentiability of C 0 semigroups with respect to (w.r.t.) parameters contained in their infinitesimal generators.It is proved that the generalized continuity and strong differentiability ...This paper considers the differentiability of C 0 semigroups with respect to (w.r.t.) parameters contained in their infinitesimal generators.It is proved that the generalized continuity and strong differentiability of their infinitesimal generators w.r.t.parameters imply the differentiability of the C 0 semigroups.The results are applied to the differentiability of the solution of a linear delay differential equation w.r.t.its delays.展开更多
This paper considers the necessary condition of the parameter identification problem dudt=(A+B(q))u u(0)=x x∈X with the cost functional J(q)≡12∫ T 0‖Cu(t;q)-y(t)‖ 2 H d t It is proved that the optimal...This paper considers the necessary condition of the parameter identification problem dudt=(A+B(q))u u(0)=x x∈X with the cost functional J(q)≡12∫ T 0‖Cu(t;q)-y(t)‖ 2 H d t It is proved that the optimal estimate q 0 is determined by the optimal system which consists of the sate equation,the adjoint equation and the optimal condition.展开更多
This article proposes a few tangent cones,which are relative to the constraint qualifications of optimization problems.With the upper and lower directional derivatives of an objective function,the characteristics of c...This article proposes a few tangent cones,which are relative to the constraint qualifications of optimization problems.With the upper and lower directional derivatives of an objective function,the characteristics of cones on the constraint qualifications are presented.The interrelations among the constraint qualifications,a few cones involved, and level sets of upper and lower directional derivatives are derived.展开更多
Strong and weak limits as well as strong and weak differentials of multi-variable indeterminate forms are discussed based on the thorough exploration of differentiation to solve the strong and weak limits and differen...Strong and weak limits as well as strong and weak differentials of multi-variable indeterminate forms are discussed based on the thorough exploration of differentiation to solve the strong and weak limits and differentials of unitary indeterminate forms. The fruit of this work is going to be reported in three parts. The first part presents the standard analysis on this subject which supplements, systematizes and advances L. Hospital抯 principles on differential calculus by applying special ,general, and limit guaranteeing theories together with K(t) and XhK0 theories. The combination of theoretical analysis and geometric signification makes the derivation intuitional, visual and easy to perceive.展开更多
文摘This paper considers the differentiability of C 0 semigroups with respect to (w.r.t.) parameters contained in their infinitesimal generators.It is proved that the generalized continuity and strong differentiability of their infinitesimal generators w.r.t.parameters imply the differentiability of the C 0 semigroups.The results are applied to the differentiability of the solution of a linear delay differential equation w.r.t.its delays.
基金Supported by the National Natural Science Foundation of China(No.697740 1 2 )
文摘This paper considers the necessary condition of the parameter identification problem dudt=(A+B(q))u u(0)=x x∈X with the cost functional J(q)≡12∫ T 0‖Cu(t;q)-y(t)‖ 2 H d t It is proved that the optimal estimate q 0 is determined by the optimal system which consists of the sate equation,the adjoint equation and the optimal condition.
基金the Natural Science Foundation ofFujian Province of China(S0650021,2006J0215)the National Natural Science Foundation of China(10771086)
文摘This article proposes a few tangent cones,which are relative to the constraint qualifications of optimization problems.With the upper and lower directional derivatives of an objective function,the characteristics of cones on the constraint qualifications are presented.The interrelations among the constraint qualifications,a few cones involved, and level sets of upper and lower directional derivatives are derived.
文摘Strong and weak limits as well as strong and weak differentials of multi-variable indeterminate forms are discussed based on the thorough exploration of differentiation to solve the strong and weak limits and differentials of unitary indeterminate forms. The fruit of this work is going to be reported in three parts. The first part presents the standard analysis on this subject which supplements, systematizes and advances L. Hospital抯 principles on differential calculus by applying special ,general, and limit guaranteeing theories together with K(t) and XhK0 theories. The combination of theoretical analysis and geometric signification makes the derivation intuitional, visual and easy to perceive.
