The main goal of this paper is to introduce necessary efficiency conditionsfor a class of multi-time vector fractional variational problems with nonlinear equal-ity and inequality constraints involving higher-order pa...The main goal of this paper is to introduce necessary efficiency conditionsfor a class of multi-time vector fractional variational problems with nonlinear equal-ity and inequality constraints involving higher-order partial derivatives.We considerthe multi-time multiobjective variational problem(MFP)of minimizing a vector ofpath-independent curvilinear integral functionals quotients subject to PDE and/or PDIconstraints,developing an optimization theory on the higher-order jet bundles.展开更多
In this paper, we construct a category of short exact sequences of vector bundles and prove that it is equivalent to the category of double vector bundles. Moreover, operations on double vector bundles can be transfer...In this paper, we construct a category of short exact sequences of vector bundles and prove that it is equivalent to the category of double vector bundles. Moreover, operations on double vector bundles can be transferred to operations on the corresponding short exact sequences. In particular, we study the duality theory of double vector bundles in term of the corresponding short exact sequences. Examples including the jet bundle and the Atiyah algebroid are discussed.展开更多
文摘The main goal of this paper is to introduce necessary efficiency conditionsfor a class of multi-time vector fractional variational problems with nonlinear equal-ity and inequality constraints involving higher-order partial derivatives.We considerthe multi-time multiobjective variational problem(MFP)of minimizing a vector ofpath-independent curvilinear integral functionals quotients subject to PDE and/or PDIconstraints,developing an optimization theory on the higher-order jet bundles.
基金Supported by National Natural Science Foundation of China(Grant Nos.11001146,11101179)the Beijing Higher Education Young Elite Teacher Project
文摘In this paper, we construct a category of short exact sequences of vector bundles and prove that it is equivalent to the category of double vector bundles. Moreover, operations on double vector bundles can be transferred to operations on the corresponding short exact sequences. In particular, we study the duality theory of double vector bundles in term of the corresponding short exact sequences. Examples including the jet bundle and the Atiyah algebroid are discussed.
