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This paper is devoted to parabolic fractional boundary value problems involving fractional derivative of Sturm-Liouville type. We investigate the existence and uniqueness results on an open bounded real interval, prove the existence of solutions to a quadratic boundary optimal control problem and provide a characterization via optimality system. We then investigate the analogous problems for a parabolic fractional Sturm-Liouville problem on a star graph with mixed Dirichlet and Neumann boundary controls.
In this paper various conditions under which a weighted composition operator Wψ,ϕ on the weighted Hardy space H2(β) becomes complex symmetric with respect to some special conjugation have been explored. We also investigate some important properties of the complex symmetric operator Wψ,ϕ such as hermiticity and isometry.
In this paper, we present a variant of Krasnoselskii’s fixed point theorem in the case of ordered Banach spaces, where the order is generated by a normal and minihedral cone. In such a structure, there is a possibility to give a new sence to the concept of contraction.
We study the linear dependence of disjoint unions of double points of an integral and non-degenerate variety X\subset ℙ^r. Such sets are called Terracini loci. Our main results are for Segre-Veronese embeddings and a few other homogeneous spaces. To study the minimal number of such double points which are linearly dependent, it is useful to study the minimal degree curves contained in X. We give an example (the Segre embedding of ℙ1\times ℙ1) in which these curves are not suffcient to describe these Terracini loci.
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