Multi-operator colligations and multivariate characteristic functions

In the spectral theory of non-self-adjoint operators there is a well-known operation of product of operator colligations. Many similar operations appear in the theory of infinite-dimensional groups as multiplications of double cosets. We construct characteristic functions for such double cosets and get semigroups of matrix-valued functions in matrix balls.Comment: 15p

Radicals of 0-regular algebras

We consider a generalisation of the Kurosh--Amitsur radical theory for rings (and more generally multi-operator groups) which applies to 0-regular varieties in which all operations preserve 0. We obtain results for subvarieties, quasivarieties and element-wise equationally defined classes. A number of examples of radical and semisimple classes in particular varieties are given, including hoops, loops and similar structures. In the first section, we introduce 0-normal varieties (0-regular varieties in which all operations preserve 0), and show that a key isomorphism theorem holds in a 0-normal variety if it is subtractive, a property more general than congruence permutability. We then define our notion of a radical class in the second section. A number of basic results and characterisations of radical and semisimple classes are then obtained, largely based on the more general categorical framework of L. M\'arki, R. Mlitz and R. Wiegandt as in [13]. We consider the subtractive case separately. In the third section, we obtain results concerning subvarieties and quasivarieties based on the results of the previous section, and also generalise to subtractive varieties some results for multi-operator group radicals defined by simple equational rules. Several examples of radical and semisimple classes are given for a range of fairly natural 0-normal varieties of algebras, most of which are subtractive

Energy sharing and trading in multi-operator heterogeneous network deployments

© 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.With a view to the expected increased data traffic volume and energy consumption of the fifth generation networks, the use of renewable energy (RE) sources and infrastructure sharing have been embraced as energy and cost-saving technologies. Aiming at reducing cost and grid energy consumption, in the present paper, we study RE exchange (REE) possibilities in late-trend network deployments of energy harvesting (EH) macrocell and small cell base stations (EH-MBSs, EH-SBSs) that use an EH system, an energy storage system, and the smart grid as energy procurement sources. On this basis, we study a two-tier network composed of EH-MBSs that are passively shared among a set of mobile network operators (MNOs), and EH-SBSs that are provided to MNOs by an infrastructure provider (InP). Taking into consideration the infrastructure location and the variety of stakeholders involved in the network deployment, we propose as REE approaches 1) a cooperative RE sharing, based on bankruptcy theory, for the shared EH-MBSs and 2) a non-cooperative, aggregator-assisted RE trading, which uses double auctions to describe the REE acts among the InP provided EH-SBSs managed by different MNOs, after an initial internal REE among the ones managed by a single MNO. Our results display that our proposals outperform baseline approaches, providing a considerable reduction in SG energy utilization and costs, with satisfaction of the participant parties.Peer ReviewedPostprint (author's final draft