Search results for "Orff"

The Daugavet equation for polynomials

2007

In this paper we study when the Daugavet equation is satisfied for weakly compact polynomials on a Banach space X, i.e. when the equality ‖Id + P‖ = 1 + ‖P‖ is satisfied for all weakly compact polynomials P : X −→ X. We show that this is the case when X = C(K), the real or complex space of continuous functions on a compact space K without isolated points. We also study the alternative Daugavet equation max |ω|=1 ‖Id + ω P‖ = 1 + ‖P‖ for polynomials P : X −→ X. We show that this equation holds for every polynomial on the complex space X = C(K) (K arbitrary) with values in X. The result is not true in the real case. Finally, we study the Daugavet and the alternative Daugavet equations for k-h…

Relatively weakly open convex combinations of slices

2018

We show that c 0 c_0 and, in fact, C ( K ) C(K) for any scattered compact Hausdorff space K K have the property that finite convex combinations of slices of the unit ball are relatively weakly open.

Banach spaces where convex combinations of relatively weakly open subsets of the unit ball are relatively weakly open

2018

We introduce and study Banach spaces which have property CWO, i.e., every finite convex combination of relatively weakly open subsets of their unit ball is open in the relative weak topology of the unit ball. Stability results of such spaces are established, and we introduce and discuss a geometric condition---property (co)---on a Banach space. Property (co) essentially says that the operation of taking convex combinations of elements of the unit ball is, in a sense, an open map. We show that if a finite dimensional Banach space $X$ has property (co), then for any scattered locally compact Hausdorff space $K$, the space $C_0(K,X)$ of continuous $X$-valued functions vanishing at infinity has…

Boundary blow-up under Sobolev mappings

2014

We prove that for mappings $W^{1,n}(B^n, \R^n),$ continuous up to the boundary, with modulus of continuity satisfying certain divergence condition, the image of the boundary of the unit ball has zero $n$-Hausdorff measure. For H\"older continuous mappings we also prove an essentially sharp generalized Hausdorff dimension estimate.

Free vs. Locally Free Kleinian Groups

2015

Abstract We prove that Kleinian groups whose limit sets are Cantor sets of Hausdorff dimension < < 1 are free. On the other hand we construct for any ε > > 0 an example of a non-free purely hyperbolic Kleinian group whose limit set is a Cantor set of Hausdorff dimension < < 1 + + ε.

Compressed Drinfeld associators

2004

Drinfeld associator is a key tool in computing the Kontsevich integral of knots. A Drinfeld associator is a series in two non-commuting variables, satisfying highly complicated algebraic equations - hexagon and pentagon. The logarithm of a Drinfeld associator lives in the Lie algbera L generated by the symbols a,b,c modulo [a,b]=[b,c]=[c,a]. The main result is a description of compressed associators that satisfy the compressed pentagon and hexagon in the quotient L/[[L,L],[L,L]]. The key ingredient is an explicit form of Campbell-Baker-Hausdorff formula in the case when all commutators commute.

Generalized dimension distortion under Sobolev mappings

2011

Edukacja historyczna: Polska – Europa – świat.Jak przedstawiać historię Polski, by Europa i świat chciały ją poznawać?

2020

This publication has been prepared by a group of doctoral studens at the Institute of History of the University of Opole, as a result of discussions on the prospects for the development of historical education in Poland, Europe and the world, undertaken during the course: Historical education: Poland – Europe – the World. The result of these considerations is this article, which proposes some possibilities of presenting the history of Poland in an objective manner, at the same time one that may arouse interest outside Poland. The content of the article is a proposal to promote prominent figures associated with Poland over the cen- turies, people of different sexes, professions and fields of…

Oikeudenmukaisuus sisäsyntyisinä oikeuksina ja kasvatus oikeudenmukaisuuteen dialogisen pluralismin kontekstissa : näkökulmia ja tulkintoja Nicholas …

2017

The study offers a philosophical analysis of Nicholas Wolterstorff’s theory of justice and education for justice. Crucial aspects of Wolterstorff’s theory are his understanding of justice as inherent rights and justice as inherent worth. Interrelated to this are the concepts of life-goods, well-being and the good life. Within this framework of rights grounded in worth, the notions of natural human rights and human dignity occupy a special position. These notions in turn form the philosophical foundation and implications for education for justice. The study is divided into two parts. The first part delves into the notion of justice as inherent rights. The key aspects addressed in this sectio…

Ledrappier-Young formula and exact dimensionality of self-affine measures

2017

In this paper, we solve the long standing open problem on exact dimensionality of self-affine measures on the plane. We show that every self-affine measure on the plane is exact dimensional regardless of the choice of the defining iterated function system. In higher dimensions, under certain assumptions, we prove that self-affine and quasi self-affine measures are exact dimensional. In both cases, the measures satisfy the Ledrappier-Young formula. peerReviewed