Registered users receive a variety of benefits including the ability to customize email alerts, create favorite journals list, and save searches.
Please note that a Project Euclid web account does not automatically grant access to full-text content. An institutional or society member subscription is required to view non-Open Access content.
Contact firstname.lastname@example.org with any questions.
We discuss the existence of an orthogonal basis consisting of decomposable vectors for some symmetry classes of tensors associated with certain subgroups of the full symmetric group. The dimensions of these symmetry classes of tensors are also computed.
A large class of special Finsler manifolds can be endowed with Finsler connections whose “-part” does not depend on the directions. We call these Finsler connections -basic and present a systematic treatment of them, using (in a simplified form) the Frölicher-Nijenhuis calculus. We provide an axiomatic description of a distinguished class of -basic Finsler connections, the class of Ichijyō connections. With the help of an Ichijyō connection we present new characterizations of generalized Berwald manifolds, as well as – in particular – of Berwald manifolds and locally Minkowski manifolds.
We consider the initial value problem of a partial differential equation in some function spaces on the interval of the real line. By using the representation formula of the solution to the equation, we define a -semigroup of bounded linear operators on . When and is or , we give sufficient conditions for the semigroup to be chaotic by using the spectral property of its infinitesimal generator. When and , we also give sufficient conditions for the semigroup to be chaotic by using the property of an admissible weight function.