Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized complex algebraic differential equations and obtain...Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized complex algebraic differential equations and obtain some results.展开更多
The space-fractional telegraph equation is analyzed and the Fourier transform of its funda-mental solution is obtained and discussed.A symmetric process with discontinuous trajectories, whose transition function satis...The space-fractional telegraph equation is analyzed and the Fourier transform of its funda-mental solution is obtained and discussed.A symmetric process with discontinuous trajectories, whose transition function satisfies thespace-fractional telegraph equation, is presented. Its limiting behaviour and the connectionwith symmetric stable processes is also examined.展开更多
The sparse nonlinear programming （SNP） is to minimize a general continuously differentiable func- tion subject to sparsity, nonlinear equality and inequality constraints. We first define two restricted constraint qu...The sparse nonlinear programming （SNP） is to minimize a general continuously differentiable func- tion subject to sparsity, nonlinear equality and inequality constraints. We first define two restricted constraint qualifications and show how these constraint qualifications can be applied to obtain the decomposition properties of the Frechet, Mordukhovich and Clarke normal cones to the sparsity constrained feasible set. Based on the decomposition properties of the normal cones, we then present and analyze three classes of Karush-Kuhn- Tucker （KKT） conditions for the SNP. At last, we establish the second-order necessary optimality condition and sufficient optimality condition for the SNP.展开更多
In this paper, by means of Sadovskii fixed point theorem, the authors establish a result concerning the controllability for a class of abstract neutral functional differential systems where the linear part is non-dens...In this paper, by means of Sadovskii fixed point theorem, the authors establish a result concerning the controllability for a class of abstract neutral functional differential systems where the linear part is non-densely defined and satisfies the Hille-Yosida condition. As an application, an example is provided to illustrate the obtained result.展开更多
文摘Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized complex algebraic differential equations and obtain some results.
基金Project supported by the National Natural Science Foundation of China (No. 10071014).
文摘The space-fractional telegraph equation is analyzed and the Fourier transform of its funda-mental solution is obtained and discussed.A symmetric process with discontinuous trajectories, whose transition function satisfies thespace-fractional telegraph equation, is presented. Its limiting behaviour and the connectionwith symmetric stable processes is also examined.
基金supported by National Natural Science Foundation of China(Grant No.11431002)Shandong Province Natural Science Foundation(Grant No.ZR2016AM07)
文摘The sparse nonlinear programming （SNP） is to minimize a general continuously differentiable func- tion subject to sparsity, nonlinear equality and inequality constraints. We first define two restricted constraint qualifications and show how these constraint qualifications can be applied to obtain the decomposition properties of the Frechet, Mordukhovich and Clarke normal cones to the sparsity constrained feasible set. Based on the decomposition properties of the normal cones, we then present and analyze three classes of Karush-Kuhn- Tucker （KKT） conditions for the SNP. At last, we establish the second-order necessary optimality condition and sufficient optimality condition for the SNP.
基金Project supported by the Tianyuan Foundation of Mathematics (No. A0324624)the National Natural Science Founcation of China (No. 10371040)the Shanghai Priority Academic Discipline.
文摘In this paper, by means of Sadovskii fixed point theorem, the authors establish a result concerning the controllability for a class of abstract neutral functional differential systems where the linear part is non-densely defined and satisfies the Hille-Yosida condition. As an application, an example is provided to illustrate the obtained result.
