Search results for "continuity"
showing 8 items of 378 documents
Mappings of Lp-integrable distortion: regularity of the inverse
2016
Let be an open set in ℝn and suppose that is a Sobolev homeomorphism. We study the regularity of f–1 under the Lp-integrability assumption on the distortion function Kf. First, if is the unit ball and p > n – 1, then the optimal local modulus of continuity of f–1 is attained by a radially symmetric mapping. We show that this is not the case when p ⩽ n – 1 and n ⩾ 3, and answer a question raised by S. Hencl and P. Koskela. Second, we obtain the optimal integrability results for ∣Df–1∣ in terms of the Lp-integrability assumptions of Kf.
Regularity and modulus of continuity of space-filling curves
2019
We study critical regularity assumptions on space-filling curves that possess certain modulus of continuity. The bounds we obtain are essentially sharp, as demonstrated by an example. peerReviewed
Primitives extraction based on structured-light images
2013
International audience; Geometric attributes such as curvature or surface orientation are additional information of the 3D points obtained after the scanning of an object. In the classic 3D chain, characterized by a sequential structure, these information are determined from the dense point cloud (from a 3D scanner). Then, they are used to reduce the amount of information and allows to obtain a simplified model. In this paper, we investigate the possibility to extract some geometric attributes, directly from 2D images obtained by the camera of a structured-light system.
Retoryka ciągłości: o dziedzictwie prawnym II Rzeczpospolitej i rządów komunistycznych
2017
The aim of the article is to establish whether the continuity between the Second and Third Polish Republics officially declared by the Polish elites is based on facts. The authors analyse the question with regard to three areas: symbolic events (handing over of the presidential insignia in 1990 and the 1998 resolution of the Senate of the Republic of Poland on legal continuity), judgements of ordinary courts and the Constitutional Court as well as legal scholarship. In their conclusion they point out that the rhetoric of continuity between the Second and the Third Polish Republics on the legal level hides real continuity between the communist regime and the normative system in force in Pol…
A Stieltjes Approach to Static Hedges
2014
Static hedging of complicated payoff structures by standard instruments becomes increasingly popular in finance. The classical approach is developed for quite regular functions, while for less regular cases, generalized functions and approximation arguments are used. In this note, we discuss the regularity conditions in the classical decomposition formula due to P. Carr and D. Madan (in Jarrow ed, Volatility, pp. 417–427, Risk Publ., London, 1998) if the integrals in this formula are interpreted as Lebesgue integrals with respect to the Lebesgue measure. Furthermore, we show that if we replace these integrals by Lebesgue–Stieltjes integrals, the family of representable functions can be exte…
Isometries between spaces of multiple Dirichlet series
2019
Abstract In this paper we study spaces of multiple Dirichlet series and their properties. We set the ground of the theory of multiple Dirichlet series and define the spaces H ∞ ( C + k ) , k ∈ N , of convergent and bounded multiple Dirichlet series on C + k . We give a representation for these Banach spaces and prove that they are all isometrically isomorphic, independently of the dimension. The analogous result for A ( C + k ) , k ∈ N , which are the spaces of multiple Dirichlet series that are convergent on C + k and define uniformly continuous functions, is obtained.
Fostering Heuristic Strategies in Mathematics Teacher Education
2018
International audience; The “double discontinuity” stated by Felix Klein 1908 is still relevant in the mathematics teacher education at German universities. We are developing a course approach, which is intended to bridge the double discontinuity in a didactic dimension. We offer additional learning opportunities for teacher students, which are characterized by clarifications of mathematical methods that are fundamental to the regular lecture contents. We focus especially on reflections on heuristic strategies, which are the core part of mathematical methods according to George Pólya. Feedback shows that students consider our approach as helpful in the transition from school to university.
Continuidad de las innovaciones tecnológicas: el reto de las intervenciones biomédicas de mejora humana
2013
One of the most recent debates among ethicists concerning the course of technological innovation is the human enhancement debate, which has been generated by the possibility of pushing human limits further by using the power of science. Many philosophers have warned us about the dangers of modifying human nature in a technical way. However, others argue that there are no morally salient differences between enhancing technical interventions and other kinds of technologies that human beings have taken to be usual for them. This paper shall critically analyze this argument. The main aim of this critical analysis is twofold, first, to show that people who make this argument are biased in severa…