Search results for "filtered"

Automated diffraction tomography combined with electron precession: a new tool forab initionanostructure analysis

2009

AbstractThree-dimensional electron diffraction data was collected with our recently developed module for automated diffraction tomography and used to solve inorganic as well as organic crystal structuresab initio. The diffraction data, which covers nearly the full relevant reciprocal space, was collected in the standard nano electron diffraction mode as well as in combination with the precession technique and was subsequently processed with a newly developed automated diffraction analysis and processing software package. Non-precessed data turned out to be sufficient forab initiostructure solution by direct methods for simple crystal structures only, while precessed data allowed structure s…

Structure analysis of titanate nanorods by automated electron diffraction tomography

2011

A hitherto unknown phase of sodium titanate, NaTi3O6(OH)·2H2O, was identified as the intermediate species in the synthesis of TiO2 nanorods. This new phase, prepared as nanorods, was investigated by electron diffraction, X-ray powder diffraction, thermogravimetric analysis and high-resolution transmission electron microscopy. The structure was determined ab initio using electron diffraction data collected by the recently developed automated diffraction tomography technique. NaTi3O6(OH)·2H2O crystallizes in the monoclinic space group C2/m. Corrugated layers of corner- and edge-sharing distorted TiO6 octahedra are intercalated with Na+ and water of crystallization. The nanorods are typically …

Some geometric properties of disk algebras

2014

Abstract In this paper we study some geometrical properties of certain classes of uniform algebras, in particular the ball algebra A u ( B X ) of all uniformly continuous functions on the closed unit ball and holomorphic on the open unit ball of a complex Banach space X . We prove that A u ( B X ) has k -numerical index 1 for every k , the lushness and also the AHSP. Moreover, the disk algebra A ( D ) , and more in general any uniform algebra whose Choquet boundary has no isolated points, is proved to have the polynomial Daugavet property. Most of those properties are extended to the vector valued version A X of a uniform algebra A .

Identities of PI-Algebras Graded by a Finite Abelian Group

2011

We consider associative PI-algebras over an algebraically closed field of zero characteristic graded by a finite abelian group G. It is proved that in this case the ideal of graded identities of a G-graded finitely generated PI-algebra coincides with the ideal of graded identities of some finite dimensional G-graded algebra. This implies that the ideal of G-graded identities of any (not necessary finitely generated) G-graded PI-algebra coincides with the ideal of G-graded identities of the Grassmann envelope of a finite dimensional (G × ℤ2)-graded algebra, and is finitely generated as GT-ideal. Similar results take place for ideals of identities with automorphisms.

Multialternating graded polynomials and growth of polynomial identities

2012

Let G be a finite group and A a finite dimensional G-graded algebra over a field of characteristic zero. When A is simple as a G-graded algebra, by mean of Regev central polynomials we construct multialternating graded polynomials of arbitrarily large degree non vanishing on A. As a consequence we compute the exponential rate of growth of the sequence of graded codimensions of an arbitrary G-graded algebra satisfying an ordinary polynomial identity. In particular we show it is an integer. The result was proviously known in case G is abelian.

Bootstrap validation of links of a minimum spanning tree

2018

We describe two different bootstrap methods applied to the detection of a minimum spanning tree obtained from a set of multivariate variables. We show that two different bootstrap procedures provide partly distinct information that can be highly informative about the investigated complex system. Our case study, based on the investigation of daily returns of a portfolio of stocks traded in the US equity markets, shows the degree of robustness and completeness of the information extracted with popular information filtering methods such as the minimum spanning tree and the planar maximally filtered graph. The first method performs a "row bootstrap" whereas the second method performs a "pair bo…

On the canonical algebra of smoothings of sandwiched singularities

2004

Integral curves of derivations

1988

We integrate, by a constructive method, derivations of even degree on the sections of an exterior bundle by families of Z 2-graded algebra automorphisms, dependent on a real parameter, and which satisfy a flow condition. We also study the case of local endomorphisms when their components of degree zero and derivations and with no component of negative degree, but then we have integral families of R-linear automorphisms. This integration method can be applied to the Frolicher—Nijenhuis derivations on the Cartan algebra of differential forms, and to the integration of superfields on graded manifolds.

An Introduction to Geometric Algebra and Conics

2016

This chapter introduces the conics and characterizes them from an algebraic perspective. While in depth geometrical aspects of the conics lie outside the scopes of this chapter, this chapter is an opportunity to revisit concepts studied in other chapters such as matrix and determinant and assign a new geometric characterization to them.

Affine varieties and lie algebras of vector fields

1993

In this article, we associate to affine algebraic or local analytic varieties their tangent algebra. This is the Lie algebra of all vector fields on the ambient space which are tangent to the variety. Properties of the relation between varieties and tangent algebras are studied. Being the tangent algebra of some variety is shown to be equivalent to a purely Lie algebra theoretic property of subalgebras of the Lie algebra of all vector fields on the ambient space. This allows to prove that the isomorphism type of the variety is determinde by its tangent algebra.