Search results for " Algebra"

Triple planes with $p_g=q=0$

2019

We show that general triple planes with p_g=q=0 belong to at most 12 families, that we call surfaces of type I,..., XII, and we prove that the corresponding Tschirnhausen bundle is direct sum of two line bundles in cases I, II, III, whereas is a rank 2 Steiner bundle in the remaining cases. We also provide existence results and explicit constructions for surfaces of type I,..., VII, recovering all classical examples and discovering several new ones. In particular, triple planes of type VII provide counterexamples to a wrong claim made in 1942 by Bronowski.

Transformations by diagonal matrices in a normed space

1962

The cup product of Hilbert schemes for K3 surfaces

2003

To any graded Frobenius algebra A we associate a sequence of graded Frobenius algebras A [n] so that there is canonical isomorphism of rings (H *(X;ℚ)[2]) [n] ≅H *(X [n] ;ℚ)[2n] for the Hilbert scheme X [n] of generalised n-tuples of any smooth projective surface X with numerically trivial canonical bundle.

Polynomial identities for the Jordan algebra of a degenerate symmetric bilinear form

2013

Let J(n) be the Jordan algebra of a degenerate symmetric bilinear form. In the first section we classify all possible G-gradings on J(n) where G is any group, while in the second part we restrict our attention to a degenerate symmetric bilinear form of rank n - 1, where n is the dimension of the vector space V defining J(n). We prove that in this case the algebra J(n) is PI-equivalent to the Jordan algebra of a nondegenerate bilinear form.

On i-topological spaces: generalization of the concept of a topological space via ideals

2006

[EN] The aim of this paper is to generalize the structure of a topological space, preserving its certain topological properties. The main idea is to consider the union and intersection of sets modulo “small” sets which are defined via ideals. Developing the concept of an i-topological space and studying structures with compatible ideals, we are concerned to clarify the necessary and sufficient conditions for a new space to be homeomorphic, in some certain sense, to a topological space.

Probabilistic Interpretations of Predicates

2016

In classical logic, any m-ary predicate is interpreted as an m-argument two-valued relation defined on a non-empty universe. In probability theory, m-ary predicates are interpreted as probability measures on the mth power of a probability space. m-ary probabilistic predicates are equivalently semantically characterized as m-dimensional cumulative distribution functions defined on \(\mathbb {R}^m\). The paper is mainly concerned with probabilistic interpretations of unary predicates in the algebra of cumulative distribution functions defined on \(\mathbb {R}\). This algebra, enriched with two constants, forms a bounded De Morgan algebra. Two logical systems based on the algebra of cumulative…

A note on the closed graph theorem

1977

Interpolating sequences on uniform algebras

2009

Abstract We consider the problem of whether a given interpolating sequence for a uniform algebra yields linear interpolation. A positive answer is obtained when we deal with dual uniform algebras. Further we prove that if the Carleson generalized condition is sufficient for a sequence to be interpolating on the algebra of bounded analytic functions on the unit ball of c 0 , then it is sufficient for any dual uniform algebra.

Timed Sets, Functional Complexity, and Computability

2012

AbstractThe construction of various categories of “timed sets” is described in which the timing of maps is considered modulo a “complexity order”. The properties of these categories are developed: under appropriate conditions they form discrete, distributive restriction categories with an iteration. They provide a categorical basis for modeling functional complexity classes and allow the development of computability within these settings. Indeed, by considering “program objects” and the functions they compute, one can obtain models of computability – i.e. Turing categories – in which the total maps belong to specific complexity classes. Two examples of this are introduced in some detail whi…

Elements with square roots in compact groups

2010

The probability that a randomly chosen element has a square root is studied in [1, 2, 8] in the finite case. Here we deal with the infinite case.