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The largest class of multi-valued systems satisfying the module-like axioms are the hyper modules. The main tools concerning the class of Hv -- (R -- S)-bi-modules are fundamental relations. First we define Hv -- (R -- S)-hyper-bi-modules and investigate exact secqenses in this field and find equivalent conditions of exactness. [ABSTRACT FROM AUTHOR]

In this paper, we study an excision theorem of the dihedral and reflexive (co)homology theory of associative algebras. That is, for such an extension, we obtain a six-term exact sequence in the dihedral cohomology. Also, we present and prove the relation between cyclic and dihedral cohomology of algebras and some examples. [ABSTRACT FROM AUTHOR]

In this paper we provide an axiomatic analysis of the classical diagram chasing method of Mac Lane, that relies on duality and chasing elements of pointed sets, which allows one to generalize this method from abelian categories to non-abelian ones. Among the examples where the generalized method can be used are all modular semiexact categories in the sense of Grandis (which include all Puppe-Mitchell exact categories) and sequentiable categories in the sense of Bourn (which include all semi-abelian categories, and in particular, the categories of group-like structures). The method turns out to be closely related to the essential features of these categories. At the same time, in some sense, it simplifies the usual proofs of some of the standard diagram lemmas in them. [ABSTRACT FROM AUTHOR]

In this paper, we offer a systematic development of state representation theory for singular linear systems in the behavioural setting of Willems. [ABSTRACT FROM PUBLISHER]

Abstract: Fuhrmann’s state-space construction (in its generalized form) is used to obtain a general theory of first order representations of Fliess models defined over an arbitrary noetherian commutative ring. The case of arbitrary linear delay differential equations is involved. [Copyright &y& Elsevier]