Examples of asymptotically \ell_^1 Banach spaces

Two examples of asymptotic $\ell_{1}$ Banach spaces are given. The first, $X_{u}$, has an unconditional basis and is arbitrarily distortable. The second, $X$, does not contain any unconditional basic sequence. Both are spaces of the type of Tsirelson. We thus answer a question raised by W.T.Gowers

Banach Spaces Of The Type Of Tsirelson

To any pair ( M , theta ) where M is a family of finite subsets of N compact in the pointwise topology, and 0<theta < 1 , we associate a Tsirelson-type Banach space T_M^theta . It is shown that if the Cantor-Bendixson index of M is greater than n and theta >{1/n} then T_M^theta is reflexive. Moreover, if the Cantor-Bendixson index of M is greater than omega then T_M^theta does not contain any l^p, while if the Cantor-Bendixson index of M is finite thenT_M^theta contains some l^p or c_o . In particular, if M ={ A subset N : |A| leq n } and {1/n}<theta <1 then T_M^theta is isomorphic to some l^p

Modified mixed Tsirelson spaces

We study the modified and boundedly modified mixed Tsirelson spaces $T_M[({\cal F}_{k_n},\theta_n)_{n=1}^{\infty }]$ and $T_{M(s)}[({\cal F}_{k_n},\theta_n)_{n=1}^{\infty }]$ respectively, defined by a subsequence $({\cal F}_{k_n})$ of the sequence of Schreier families $({\cal F}_n)$. These are reflexive asymptotic $\ell_1$ spaces with an unconditio- nal basis $(e_i)_i$ having the property that every sequence $\{ x_i\}_{i=1}^n$ of normalized disjointly supported vectors contained in $\langle e_i\rangle_{i=n}^{\infty }$ is equivalent to the basis of $\ell_1^n$. We show that if $\lim\theta_n^{1/n}=1$ then the space $T[({\cal F}_n,\theta_n) _{n=1}^{\infty }]$ and its modified variations are totally incomparable by proving that $c_0$ is finitely disjointly representable in every block subspace of $T[({\cal F}_n, \theta_n)_{n=1}^{\infty }]$. Next, we present an example of a boundedly modified mixed Tsirelson space $X_{M(1),u}$ which is arbitrarily distortable. Finally, we construct a variation of the space $X_{M(1),u}$ which is hereditarily indecomposable

A set of ontologies to drive tools for the control of vector-borne diseases

We are developing a set of ontologies that deal with vector-borne diseases and the arthropod vectors that transmit them. For practical reasons (application priorities), we initiated this project with an ontology of insecticide resistance followed by a series of ontologies that describe malaria as well as physiological processes of mosquitoes that are relevant to, and involved in, disease transmission. These will be expanded to encompass other vector-borne diseases as well as non-mosquito vectors. The aim of the whole undertaking, which is worked out in the frame of the international IDO (Infectious Disease Ontology) project, is to provide the community with a set of ontological tools that can be used both in the development of specific databases and, most importantly, in the construction of decision support systems to control these diseases

Hereditarily Indecomposable Banach algebras of diagonal operators

We provide a characterization of the Banach spaces $X$ with a Schauder basis $(e_n)_{n\in\mathbb{N}}$ which have the property that the dual space $X^*$ is naturally isomorphic to the space $\mathcal{L}_{diag}(X)$ of diagonal operators with respect to $(e_n)_{n\in\mathbb{N}}$ . We also construct a Hereditarily Indecomposable Banach space ${\mathfrak X}_D$ with a Schauder basis $(e_n)_{n\in\mathbb{N}}$ such that ${\mathfrak X}^*_D$ is isometric to $\mathcal{L}_{diag}({\mathfrak X}_D)$ with these Banach algebras being Hereditarily Indecomposable. Finally, we show that every $T\in \mathcal{L}_{diag}({\mathfrak X}_D)$ is of the form $T=\lambda I+K$, where $K$ is a compact operator.Comment: 35 pages, submitted for publication to Israel J. Mat

Strictly singular non-compact diagonal operators on HI spaces

We construct a Hereditarily Indecomposable Banach space \eqs_d with a Schauder basis \seq{e}{n} on which there exist strictly singular non-compact diagonal operators. Moreover, the space \mc{L}_{\diag}(\eqs_d) of diagonal operators with respect to the basis \seq{e}{n} contains an isomorphic copy of $\ell_{\infty}(\N)$

LES TRANSFORMATIONS DU DROIT DU TRΑVAIL ET LA CRISE: LES RÉPONSES DU DROIT GREC

La présente étude examine les transformations  du droit grec du travail  survenues à la suite des mesures d’austérité adoptées  par  les  gouvernements helléniques en réponse à la  crise. Elle se divise pour cette raison en trois parties. La première partie aborde la physionomie du système grec des relations de travail, avant la crise de la dette. La deuxième partie examine  le contenu des mesures d’austérité grecques et  les répercussions de celles-ci au droit et à la pratique des relations du travail La  troisième partie  traite  le problème de la compatibilité entre ces mesures et les règles constitutionnelles, internationales et supranationales qui garantissent les droits sociaux. Elle examine  notamment comment les juridictions helléniques et internationales ont abordé les problèmes d’inconstitutionnalité et de non-conventionalité posés par ces mesures----------------------------------------------------------------------------The present essay examines the transformations that occurred in Greek labour law as a result of the austerity measures adopted by Greek governments in response to the debt crisis. It is divided into three parts: the first part outlines the particularities/characteristics/featuresof the Greek system of labour relations before the crisis, while the second part examines the content of the Greek austerity measures and their impact on Greek labour law and labour relations. The third part addresses the issue of compliance between these measures and the international and supranational constitutional rules pertaining to social rights. In particular, it examines the rulings of Greek and European Courts addressing the problem of the constitutionality and conventionality of these measures as well as the reception of these rulings.

L'effet horizontal des droits sociaux selon la jurisprudence de la CJUE et la pratique des juridictions nationales

La présente  étude examine l¿effet horizontal des droits sociaux consacrés par la Charte des Droits  Fondamentaux de l¿UE  ,  Partant  de  l¿arrêt  C-176/12 Association de médiation sociale v. CGT de l¿ CJUE qui  refusa d¿attribuer un tel effet à l¿article  27 de la Charte  garantissant le droit des travailleurs  à l¿information et a la consultation  au sein de l¿entreprise     l¿auteur  met en lumière le contexte juridique et politique de cet arrêt.  Elle  répond  ainsi à la question de savoir   si  le refus précité de la Cour  se justifie des particularités de la Charte  et du Droit de l¿Union ou bien  s¿il constitue une manifestation nouvelle de la politique restrictive que suit  traditionnellement     la Cour  en matière  des droits sociaux.  ------------------------------------------------------------------------------This study examines the horizontal effect of social rights enshrined in the Charter of Fundamental Rights of the EU. Its starting point is the Case C-176/12 Association for Social Mediation v. CGT in which the ECJ refused to recognize such an effect to Article 27 of the Charter, guaranteeing workers' right to information and consultation within the undertaking. The author sheds light on the legal and political background of this judgment. It thus answers to the question whether the refusal of the Court is justified by the peculiarities of the Charter and of the EU law, or whether it expresses the restrictive policy that follows last years the Court in the area of social rights.Artículo revisado por pare

LES TRANSFORMATIONS DU DROIT DU TR¿VAIL ET LA CRISE: LES RÉPONSES DU DROIT GREC

La présente étude examine les transformations  du droit grec du travail  survenues à la suite des mesures d¿austérité adoptées  par  les  gouvernements helléniques en réponse à la  crise. Elle se divise pour cette raison en trois parties. La première partie aborde la physionomie du système grec des relations de travail, avant la crise de la dette. La deuxième partie examine  le contenu des mesures d¿austérité grecques et  les répercussions de celles-ci au droit et à la pratique des relations du travail La  troisième partie  traite  le problème de la compatibilité entre ces mesures et les règles constitutionnelles, internationales et supranationales qui garantissent les droits sociaux. Elle examine  notamment comment les juridictions helléniques et internationales ont abordé les problèmes d¿inconstitutionnalité et de non-conventionalité posés par ces mesures----------------------------------------------------------------------------The present essay examines the transformations that occurred in Greek labour law as a result of the austerity measures adopted by Greek governments in response to the debt crisis. It is divided into three parts: the first part outlines the particularities/characteristics/featuresof the Greek system of labour relations before the crisis, while the second part examines the content of the Greek austerity measures and their impact on Greek labour law and labour relations. The third part addresses the issue of compliance between these measures and the international and supranational constitutional rules pertaining to social rights. In particular, it examines the rulings of Greek and European Courts addressing the problem of the constitutionality and conventionality of these measures as well as the reception of these rulings. Artículo revisado por pare