We give a new proof of the vanishing of H1(X, V ) for negative vector bundles V on normal projective varieties X satisfying rank V < dim X. Our proof is geometric, it uses a topological characterization of the affine bundles associated with non-trivial cocycles α ∈ H1(X, V ) of negative vector bundles. Following the same circle of ideas, we use the analytic characteristics of affine bundles to ...

We discuss some aspects of the extension to continuous systems of a statistical measure of complexity introduced by López-Ruiz, Mancini, and Calbet [Phys. Lett. A 209, 321 (1995)]. In general, the extension of a magnitude from the discrete to the continuous case is not a trivial process and requires some kind of choice. In the present study, several possibilities appear available. One of them i...

In this paper, we prove that the Nakayama automorphism of a graded skew PBW extension over finitely presented Koszul Auslander-regular algebra has trivial homological determinant. For A = ?(R)&lt;x1, x2&gt; connected R, compute its P-determinant and inverse ?. particular case quasi-commutative extensions Artin-Schelter regular algebras, show explicitly connection between ring coefficients exten...

In this paper we present a transformation of propositional default theories into so-called propositional argumentation systems. This transformation allows to characterize all notions of Reiter’s default logic in the framework of argumentation systems. This means that computing extension, or determining if a given formula belongs to one extension or all extensions can be answered without leaving...

An extension to finite state transducers is presented, in which atomic symbols are replaced by arbitrary predicates over symbols. The extension is motivated by applications in natural language processing (but may be more widely applicable) as well as by the observation that transducers with predicates generally have fewer states and fewer transitions. Although the extension is fairly trivial fo...

The second central extension of the planar Galilei group has been alleged to have its origin in the spin variable. This idea is explored here by considering local Galilean covariant field theory for free fields of arbitrary spin. It is shown that such systems generally display only a trivial realization of the second central extension. While it is possible to realize any desired value of the ex...

Let C be an algebraically closed field with trivial derivation and let F denote the differential rational field C〈Y1, . . . , Y5〉, with Y1, . . . , Y5 differentially independent over C. We show that there is a Picard-Vessiot extension E ⊃ F for a matrix equation X ′ = XA(Yi), with differential Galois group SO3, with the property that if F is any differential field with field of constants C then...

Let ̃ SL(2, F) be the metaplectic two-fold cover of SL(2, F), the special linear group in two variables over a local field F of characteristic 0. The inverse image T̃ of a maximal torus T in ̃ SL(2, F) is an abelian extension of T by ±1. We consider the question of whether this extension is trivial. More generally we find the minimal subgroup A of the circle for which the extension is split when c...

We analyze the well-known equivalence between quadratic Kontsevich-Penner and Hermitian matrix models from point of view superintegrability relations, i.e. explicit formulas for character averages. This is not that trivial on Kontsevich side, seems important further studies various deformations models. In particular, Brezin-Hikami extension above becomes straightforward.