scholarly journals Escaping a Neighborhood Along a Prescribed Sequence in Lie Groups and Banach Algebras

2019 ◽  
Vol 63 (3) ◽  
pp. 484-505
Author(s):  
Catalin Badea ◽  
Vincent Devinck ◽  
Sophie Grivaux
Keyword(s):  
Lie Groups ◽  
Common Core ◽  
Banach Algebras ◽  
Small Neighborhood ◽  
Positive Operators ◽  
Normed Algebra ◽  
Topological Groups ◽  
The Common ◽  
The Given ◽  
Spectral Characterizations

AbstractIt is shown that Jamison sequences, introduced in 2007 by Badea and Grivaux, arise naturally in the study of topological groups with no small subgroups, of Banach or normed algebra elements whose powers are close to identity along subsequences, and in characterizations of (self-adjoint) positive operators by the accretiveness of some of their powers. The common core of these results is a description of those sequences for which non-identity elements in Lie groups or normed algebras escape an arbitrary small neighborhood of the identity in a number of steps belonging to the given sequence. Several spectral characterizations of Jamison sequences are given, and other related results are proved.

scholarly journals Completeness of Infinite-dimensional Lie Groups in Their Left Uniformity

2019 ◽  
Vol 71 (1) ◽  
pp. 131-152 ◽  
Author(s):  
Helge Glöckner
Keyword(s):  
Lie Groups ◽  
Direct Limit ◽  
Topological Groups ◽  
Test Function ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Function Group ◽  
The Given ◽  
Locally Convex ◽  
Infinite Dimensional Lie Groups

AbstractWe prove completeness for the main examples of infinite-dimensional Lie groups and some related topological groups. Consider a sequence $G_{1}\subseteq G_{2}\subseteq \cdots \,$ of topological groups $G_{n}$ n such that $G_{n}$ is a subgroup of $G_{n+1}$ and the latter induces the given topology on $G_{n}$, for each $n\in \mathbb{N}$. Let $G$ be the direct limit of the sequence in the category of topological groups. We show that $G$ induces the given topology on each $G_{n}$ whenever $\cup _{n\in \mathbb{N}}V_{1}V_{2}\cdots V_{n}$ is an identity neighbourhood in $G$ for all identity neighbourhoods $V_{n}\subseteq G_{n}$. If, moreover, each $G_{n}$ is complete, then $G$ is complete. We also show that the weak direct product $\oplus _{j\in J}G_{j}$ is complete for each family $(G_{j})_{j\in J}$ of complete Lie groups $G_{j}$. As a consequence, every strict direct limit $G=\cup _{n\in \mathbb{N}}G_{n}$ of finite-dimensional Lie groups is complete, as well as the diffeomorphism group $\text{Diff}_{c}(M)$ of a paracompact finite-dimensional smooth manifold $M$ and the test function group $C_{c}^{k}(M,H)$, for each $k\in \mathbb{N}_{0}\cup \{\infty \}$ and complete Lie group $H$ modelled on a complete locally convex space.

THE EU SUGAR MARKET PROFILE AND ITS MAIN DRIVERS

2015 ◽  
Author(s):  
Lubos SMUTKA ◽  
Irena BENEŠOVÁ ◽  
Patrik ROVNÝ ◽  
Renata MATYSIK-PEJAS
Keyword(s):  
Market Failure ◽  
Current System ◽  
Quota System ◽  
Considerable Debate ◽  
Sugar Market ◽  
The Common ◽  
The One ◽  
Production Capacities ◽  
The Given ◽  
The Eu

Sugar is one of the most important elements in human nutrition. The Common Market Organisation for sugar has been a subject of considerable debate since its establishment in 1968. The European agricultural market has been criticized for its heavy regulations and subsidization. The sugar market is one of the most regulated ones; however, this will change radically in 2017 when the current system of production quotas will end. The current EU sugar market changed is structure during the last several decades. The significant number of companies left the market and EU internal sugar market became more concentrated. The aim of this paper is presentation characteristics of sugar market with respect to the supposed market failure – reduction in competition. The analysis also identifies the main drivers and determinants of the EU especially quota sugar market. In relation to paper’s aim the following results are important. The present conditions of the European sugar market have led to market failure when nearly 75 % (10 million tonnes) of the quota is controlled by five multinational companies only. These multinational alliances (especially German and French one) are also taking control over the production capacities of their subsidiaries. In most countries, this causes serious problems as the given quota is controlled by one or two producers only. This is a significant indicator of market imperfection. The quota system cannot overcome the problem of production quotas on the one hand and the demand on the other; furthermore, it also leads to economic inefficiency. The current EU sugar market is under the control of only Sudzucker, Nordzucker, Pfeifer and Langen, Tereos and ABF.

O ENSINO RELIGIOSO EM QUESTÃO

2018 ◽  
Vol 9 (21) ◽  
pp. 459
Author(s):  
Mauro Rocha Baptista
Keyword(s):  
Supreme Court ◽  
Religious Education ◽  
Common Core ◽  
Historical Perspective ◽  
National Curriculum ◽  
The Other ◽  
Federal Constitution ◽  
The Supreme Court ◽  
The Common

Neste artigo analisamos a relação do Ensino Religioso com a sua evolução ao longo do contexto recente do Brasil para compreender a posição do Supremo Tribunal Federal ao considerar a possibilidade do Ensino Religioso confessional. Inicialmente apresentaremos a perspectiva legislativa criada com a constituição de 1988 e seus desdobramentos nas indicações curriculares. Neste contexto é frisado a intenção de incluir o Ensino Religioso na Base Nacional Curricular Comum, o que acabou não acontecendo. A tendência manifesta nas duas primeiras versões da BNCC era de um Ensino Religioso não-confessional. Uma tendência que demarcava a função do Ensino Religioso em debater a religião, mas que não permitia o direcionamento por uma vertente religioso qualquer. Esta posição se mostrava uma evolução da primeira perspectiva histórica mais associada à catequese confessional. Assim como também ultrapassava a interpretação posterior de um ecumenismo interconfessional, que mantinha a superioridade do cristianismo ante as demais religiões. Sendo assim, neste artigo, adotaremos o argumento de que a decisão do STF, de seis votos contra cinco, acaba retrocedendo ante o que nos parecia um caminho muito mais frutífero.Palavras-chave: Ensino Religioso. Supremo Tribunal Federal. Confessional. Interconfessional. Não-confessional.Abstract: On this article, we analyze the relation between Religious education and its evolution along the currently Brazilian context in order to understand the position of the Supreme Court in considering the possibility of a confessional Religious education. Firstly, we are going to present the legislative perspective created with the 1988 Federal Constitution and its impacts in the curricular lines. On this context it was highlighted the intention to include the Religious Education on the Common Core National Curriculum (CCNC), which did not really happened. The tendency manifested in the first two versions of the CCNC was of a non-confessional Religious Education. A tendency that delineated the function of the Religious Education as debating religion, but not giving direction on any religious side. This position was an evolution of the first historical perspective more associated to the confessional catechesis. It also went beyond the former interpretation of an inter-confessional ecumenism, which kept the superiority of the Christianity over the other religions. As such, in this paper we adopt the argument that the decision of the Supreme Court, of six votes against five, is a reversal of what seemed to be a much more productive path on the Religious Education.Keywords: Religious Education. Brazilian Supreme Court. Confessional. Inter-confessional. Non- confessional.Enviado: 23-01-2018 - Aprovado e publicado: 12-2018

The Still Life of Objects – Heidegger, Schapiro, and Derrida reconsidered

2015 ◽  
Vol 60 (1) ◽  
pp. 81-102
Author(s):  
KErstin Thomas
Keyword(s):  
Still Life ◽  
Work Of Art ◽  
Concrete Material ◽  
Vincent Van Gogh ◽  
Starting Point ◽  
Specific Object ◽  
Truth Claims ◽  
The Common ◽  
Critical Intervention ◽  
The Given

Kerstin Thomas revaluates the famous dispute between Martin Heidegger, Meyer Schapiro, and Jacques Derrida, concerning a painting of shoes by Vincent Van Gogh. The starting point for this dispute was the description and analysis of things and artworks developed in his essay, “The Origin of the Work of Art”. In discussing Heidegger’s account, the art historian Meyer Schapiro’s main point of critique concerned Heidegger’s claim that the artwork reveals the truth of equipment in depicting shoes of a peasant woman and thereby showing her world. Schapiro sees a striking paradox in Heidegger’s claim for truth, based on a specific object in a specific artwork while at the same time following a rather metaphysical idea of the artwork. Kerstin Thomas proposes an interpretation, which exceeds the common confrontation of philosophy versus art history by focussing on the respective notion of facticity at stake in the theoretical accounts of both thinkers. Schapiro accuses Heidegger of a lack of concreteness, which he sees as the basis for every truth claim on objects. Thomas understands Schapiro’s objections as motivated by this demand for a facticity, which not only includes the work of art, but also investigator in his concrete historical perspective. Truth claims under such conditions of facticity are always relative to historical knowledge, and open to critical intervention and therefore necessarily contingent. Following Thomas, Schapiro’s critique shows that despite his intention of giving the work of art back its autonomy, Heidegger could be accused of achieving quite the opposite: through the abstraction of the concrete, the factual, and the given to the type, he actually sets the self and the realm of knowledge of the creator as absolute and not the object of his knowledge. Instead, she argues for a revaluation of Schapiro’s position with recognition of the arbitrariness of the artwork, by introducing the notion of factuality as formulated by Quentin Meillassoux. Understood as exchange between artist and object in its concrete material quality as well as with the beholder, the truth of painting could only be shown as radically contingent. Thomas argues that the critical intervention of Derrida who discusses both positions anew is exactly motivated by a recognition of the contingent character of object, artwork and interpretation. His deconstructive analysis can be understood as recognition of the dynamic character of things and hence this could be shown with Meillassoux to be exactly its character of facticity – or factuality.

scholarly journals On the Difficulty of Budget Allocation in Claims Problems with Indivisible Items and Prices

2021 ◽  
Author(s):  
Teresa Estañ ◽  
Natividad Llorca ◽  
Ricardo Martínez ◽  
Joaquín Sánchez-Soriano
Keyword(s):  
Budget Allocation ◽  
Pareto Efficiency ◽  
Claims Problems ◽  
The Common ◽  
The Given

AbstractIn this paper we study the class of claims problems where the amount to be divided is perfectly divisible and claims are made on indivisible units of several items. Each item has a price, and the available amount falls short to be able to cover all the claims at the given prices. We propose several properties that may be of interest in this particular framework. These properties represent the common principles of fairness, efficiency, and non-manipulability by merging or splitting. Efficiency is our focal principle, which is formalized by means of two axioms: non-wastefulness and Pareto efficiency. We show that some combinations of the properties we consider are compatible, others are not.

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