Search results for "SETS"

Some Applications of the Poincaré-Bendixson Theorem

2021

We consider a C 1 vector field X defined on an open subset U of the plane, with compact closure. If X has no singular points and if U is simply connected, a weak version of the Poincaré-Bendixson Theorem says that the limit sets of X in U are empty but that one can defined non empty extended limit sets contained into the boundary of U. We give an elementary proof of this result, independent of the classical Poincaré-Bendixson Theorem. A trapping triangle T based at p, for a C 1 vector field X defined on an open subset U of the plane, is a topological triangle with a corner at a point p located on the boundary ∂U and a good control of the tranversality of X along the sides. The principal app…

Integrability of orthogonal projections, and applications to Furstenberg sets

2022

Let $\mathcal{G}(d,n)$ be the Grassmannian manifold of $n$-dimensional subspaces of $\mathbb{R}^{d}$, and let $\pi_{V} \colon \mathbb{R}^{d} \to V$ be the orthogonal projection. We prove that if $\mu$ is a compactly supported Radon measure on $\mathbb{R}^{d}$ satisfying the $s$-dimensional Frostman condition $\mu(B(x,r)) \leq Cr^{s}$ for all $x \in \mathbb{R}^{d}$ and $r > 0$, then $$\int_{\mathcal{G}(d,n)} \|\pi_{V}\mu\|_{L^{p}(V)}^{p} \, d\gamma_{d,n}(V) \tfrac{1}{2}$ and $t \geq 1 + \epsilon$ for a small absolute constant $\epsilon > 0$. We also prove a higher dimensional analogue of this estimate for codimension-1 Furstenberg sets in $\mathbb{R}^{d}$. As another corollary of our method,…

Sharp capacity estimates for annuli in weighted R^n and in metric spaces

2017

We obtain estimates for the nonlinear variational capacity of annuli in weighted R^n and in metric spaces. We introduce four different (pointwise) exponent sets, show that they all play fundamental roles for capacity estimates, and also demonstrate that whether an end point of an exponent set is attained or not is important. As a consequence of our estimates we obtain, for instance, criteria for points to have zero (resp. positive) capacity. Our discussion holds in rather general metric spaces, including Carnot groups and many manifolds, but it is just as relevant on weighted R^n. Indeed, to illustrate the sharpness of our estimates, we give several examples of radially weighted R^n, which …

Financial assets and patrimonial issues in international families

2021

: The paper deals with patrimonial issues in International families and with the European Regulations 1103 and 1104/ 2016 together with regulation 650/2012. The paper particularly focuses on financial assets: Bank Account; Share of Investments Funds; Life Insurance; Virtual assets like criptovalutes; real estate wealth. This perspective implies the need to find the rule governing the succession or the families? patrimonial issues, also taking into account the different rules in the different states concerned of the contracts that govern the circulation of such goods.

Getting married or entering into a partnership : the patrimonial issues of choice in french law

2021

In French law, there are only two models of couples between which a choice is really possible to organize their patrimonial relationships: partnership or marriage. But, if the couple intends to organize a transfer of assets between companions both during the union and in case of death, it is definitely marriage that offers more possibilities than partnership. Often, young French couples, who do not wish to marry, either not at the begining of their relationship or not at all, have the idea that, if marriage organizes a legal protection of the couple, the partners have the possibility to provide conventionally equivalent protection. In fact, this idea is wrong.

Основы теории нечетких топологических пространств

1991

Strategic analysis of transit service quality using fuzzy AHP methodology

2013

Customer satisfaction analyses are deeply based on customers' judgments and as consequence, they can be characterized by a certain degree of uncertainty generally ascribed to coexistence of three relevant aspects: vagueness, imprecision and subjectivity. In the present paper, a methodology able to handle such uncertainty, based on the ServQual discrepancy paradigm and that uses in combined manner the AHP method and the Fuzzy Sets Theory is proposed in order to overcome limitations of the traditional service evaluation approaches. Subsequently, by considering the Italian public transit service sector, a service quality analysis is conducted and the overall transit service quality structure i…

Induction of B-cell development in adult mice reveals the ability of bone marrow to produce B-1a cells

2009

AbstractTo study B-cell development from bone marrow (BM), we generated recombination-activating gene 1 (Rag1)–targeted mice lacking mature lymphocytes. B-cell development can be induced in such mice by B cell–specific restoration of a functional Rag1 transcription unit. Follicular and marginal zone B cells populated the spleen when Rag1 expression was permitted. Notably, the peritoneal cavity was dominated by bona fide B-1a cells, as judged by surface markers and functional properties. These BM-derived B-1a cells exhibited a polyclonal VDJ repertoire with substantial N nucleotide insertions. Nevertheless, physiologic frequencies of phosphatidylcholine-specific B cells were detected. Import…

Genetic proof for the transient nature of the Th17 phenotype

2010

IL-17-producing CD4(+) T cells (Th17) have been classified as a new T helper cell subset. Using an IL-17 fate mapping mouse strain, which genetically fixes the memory of IL-17 expression, we demonstrate that IL-17A/F-expressing T helper cells generated either in vitro or in vivo are not a stable T-cell subset. Upon adoptive transfer of IL-17F-reporter-positive Th17 cells to RAG-deficient or WT animals, encephalitogenic Th17 cells partially lose IL-17 expression and upregulate IFN-γ. Additionally, we show that Th1 cells can convert in vivo to IL-17A/IFN-γ-coexpressing cells in the mesenteric lymph nodes (mLN). Our data classify IL-17A and IL-17F as cytokines produced transiently in response …

Contribution of IL-17-producing {gamma}{delta} T cells to the efficacy of anticancer chemotherapy.

2011

IL-17 production by γδ T cells is required for tumor cell infiltration by IFN-γ–producing CD8+ T cells and inhibition of tumor growth in response to anthracyclines.