Chordal graphs are important in the structural and algorithmic graph theory. A digraph analogue of chordal was introduced by Haskin Rose 1973 but has not been subject active studies until recently when a characterization semicomplete digraphs terms forbidden subdigraphs found Meister Telle. Locally digraphs, quasi-transitive extended amongst most popular generalizations digraphs. We extend subd...

Let G be a Lie group and g its algebra. We develop theory of quasi Poisson structures relative to not necessarily non-degenerate Ad-invariant symmetric 2-tensor in the tensor square one general Hamiltonian bilinear form on g, structure being given by skew bracket two variables such that suitable data defined terms as symmetry involving measure how fails satisfy Jacobi identity. The present appr...

Let A be a finite alphabet and let L ⊂ (A∗)n be an n-variable language over A. We say that L is regular if it is the language accepted by a synchronous n-tape finite state automaton, it is quasi-regular if it is accepted by an asynchronous n-tape automaton, and it is weakly regular if it is accepted by a non-deterministic asynchronous n-tape automaton. We investigate the closure properties of t...

Let A be a finite alphabet and let L ⊂ (A∗)n be an n-variable language over A. We say that L is regular if it is the language accepted by a synchronous n-tape finite state automaton, it is quasi-regular if it is accepted by an asynchronous n-tape automaton, and it is weakly regular if it is accepted by a non-deterministic asynchronous n-tape automaton. We investigate the closure properties of t...

The notion of a quasi-free Hilbert module over a function algebra A consisting of holomorphic functions on a bounded domain Ω in complex m space is introduced. It is shown that quasi-free Hilbert modules correspond to the completion of the direct sum of a certain number of copies of the algebra A. A Hilbert module is said to be weakly regular (respectively, regular) if there exists a module map...

We show how to construct secret-key functional encryption (SKFE) supporting unbounded polynomially many functional decryption keys, that is, collusion-resistant SKFE solely from SKFE supporting only one functional decryption key. The underlying single-key SKFE needs to be weakly succinct, that is, the size of its encryption circuit is sub-linear in the size of functions. We show we can transfor...

We show that every word hyperbolic, surface-by-(noncyclic) free group Γ is as rigid as possible: the quasi-isometry group of Γ equals the abstract commensurator group Comm(Γ), which in turn contains Γ as a finite index subgroup. As a corollary, two such groups are quasi-isometric if and only if they are commensurable, and any finitely generated group quasi-isometric to Γ must be weakly commensu...