Basic properties of nonsmooth Hormander's vector fields and Poincare's inequality

We consider a family of vector fields defined in some bounded domain of R^p, and we assume that they satisfy Hormander's rank condition of some step r, and that their coefficients have r-1 continuous derivatives. We extend to this nonsmooth context some results which are well-known for smooth Hormander's vector fields, namely: some basic properties of the distance induced by the vector fields, the doubling condition, Chow's connectivity theorem, and, under the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare's inequality. By known results, these facts also imply a Sobolev embedding. All these tools allow to draw some consequences about second order differential operators modeled on these nonsmooth Hormander's vector fields.Comment: 60 pages, LaTeX; Section 6 added and Section 7 (6 in the previous version) changed. Some references adde

Gendered sphere of traditional knowledge in Morocco

Indigenous knowledge (IK) and its various definitions—Indigenous and Local Knowledge (ILK), Traditional Knowledge (TK), Traditional Ecological Knowledge (TEK), Indigenous Ecological Knowledge (IEK), Local Ecological Knowledge (LEK)—is a cumulative body of knowledge, practice, experience, and beliefs, evolving through adaptive processes and culturally transmitted through generations. It is about the relationship that living beings maintain with one another and with all living things in their environment. In rural Morocco as other parts of the world, IK has allowed rural communities to sustain livelihoods, buffer for extreme climatic conditions, maintain resource availability and food security. For all its virtues, IK is increasingly recognized for its contribution to sustainable resource management, sustainable agriculture, climate change adaptation, and food security. It has not, however, been recognized for the promotion of women’s social enterprise. As the central authorities in Morocco struggle to integrate rural women into development initiatives, it has failed to take into account women’s traditional knowledge. This is coupled with the stigmatized image that many rural illiterate women are “backwards,” reinforced by the perception that women who have left the countryside to live in urban areas are more successful. This book chapter is about the need to acknowledge and record women’s Indigenous/traditional knowledge practices and skills as a powerful educational tool to reconcile and lift rural women out of poverty through social enterprise.info:eu-repo/semantics/publishedVersio

"Soggetto umano - Soggetto giuridico". II diritto nella prospettiva ontologico-esistenziale di Sergio Cotta.

La reflexion sobre el pensamiento de Sergio Cotta se expone teniendo como texto-guia Soggetto umano - Soggetto giuridico (Giuffre, Milano 1997), obra en la que definia, exactamente diez afios antes de su fallecimiento, las lineas de su pensamiento en torno al hombre y al derecho costruidas en sus anos de docencia romana. El pensamiento de Cotta se perfila, en primer lugar, a traves de dos lineas fundamentales: la del historicismo hegeliano y la logica dialectica, sobre el piano filosofico; y la de Kelsen sobre el piano de la teoria del derecho. En segundo lugar, a traves de la recepcion de los materiales epistemicos ofrecidos por las filosofias y las investigaciones empiricas del novecientos; desde la fenomenologia a la antropologia y a la logica, hasta el psicoandlisis y la fonologia. Montanari muestra como Cotta llega a construir su tesis filosdfica fundamental: la "giuridicita intrinseca del vivere umano", entendida como perspectiva capaz de dotar de significado prdctico a la existencia humana en cuanto strutturalmente relazionale. En particular, es el ligamen entre la fenomenologia y las investigaciones antropologicas, lo que permite a Cotta determinar los "invarianti" o "residui" (en sentido precisamente fenomenologico) que connotan el existir en el mundo del hombre y que se especifican, existencialmente, en dos necesidades fundamentales: "esser se stesso e non esser solo". Tales necesidades individuan la condicion que el derecho debe respetar para no violar la universalidad del ser sujeto humano. Sobre el alcance fdosofico de esta ultima tesis se centra la parte conclusiva del texto, en la que el autor da paso a un didlogo ideal con su maestro. Las reflexiones sobre el concepto de finitezza, propuesto por Cotta, y sobre el, en parte diverso, de finitudine, titilizado por Montanari, subrayan en particular el valor di una linea tedrica radicada en la hermeneutica del dato existencial. El "problema" de la dimensidn finita del ser humano es asi comprendido como limite racional y conscientemente abierto a lo infinito

K/T age for the popigai impact event

The multi-ringed POPIGAI structure, with an outer ring diameter of over 100 km, is the largest impact feature currently recognized on Earth with an Phanerozoic age. The target rocks in this relatively unglaciated region consist of upper Proterozoic through Mesozoic platform sediments and igneous rocks overlying Precambrian crystalline basement. The reported absolute age of the Popigai impact event ranges from 30.5 to 39 Ma. With the intent of refining this age estimate, a melt-breccia (suevite) sample from the inner regions of the Popigai structure was prepared for total fusion and step-wise heating Ar-40/Ar-39 analysis. Although the total fusion and step-heating experiments suggest some degree of age heterogeneity, the recurring theme is an age of around 64 to 66 Ma

Long-range frustration in T=0 first-step replica-symmetry-broken solutions of finite-connectivity spin glasses

In a finite-connectivity spin-glass at the zero-temperature limit, long-range correlations exist among the unfrozen vertices (whose spin values being non-fixed). Such long-range frustrations are partially removed through the first-step replica-symmetry-broken (1RSB) cavity theory, but residual long-range frustrations may still persist in this mean-field solution. By way of population dynamics, here we perform a perturbation-percolation analysis to calculate the magnitude of long-range frustrations in the 1RSB solution of a given spin-glass system. We study two well-studied model systems, the minimal vertex-cover problem and the maximal 2-satisfiability problem. This work points to a possible way of improving the zero-temperature 1RSB mean-field theory of spin-glasses.Comment: 5 pages, two figures. To be published in JSTA

Evidence for a long duration component in the prompt emission of short Gamma-Ray Bursts detected with BeppoSAX

A statistical study on the light curves of all the short Gamma-Ray Bursts detected with the Gamma Ray Burst Monitor (GRBM) aboard BeppoSAX is reported. Evidence for a very weak and long duration component associated with these events in the two 1 s counters of the GRBM (40-700 keV and >100 keV) is found. It starts a few tens of seconds before the burst and continues for about 30 s after the burst. The overall hardness of this component is comparable with that of the event itself. The detection of a signal before the onset time and the similar hardness are consistent with an interpretation of the long duration component in terms of prompt emission associated with short GRBs.Comment: 12 pages, 6 figures, accepted for publication in ApJ

Generalized Jacobi identities and ball-box theorem for horizontally regular vector fields

We consider a family of vector fields and we assume a horizontal regularity on their derivatives. We discuss the notion of commutator showing that different definitions agree. We apply our results to the proof of a ball-box theorem and Poincar\'e inequality for nonsmooth H\"ormander vector fields.Comment: arXiv admin note: material from arXiv:1106.2410v1, now three separate articles arXiv:1106.2410v2, arXiv:1201.5228, arXiv:1201.520

A look at the links between drainage density and flood statistics

Abstract. We investigate the links between the drainage density of a river basin and selected flood statistics, namely, mean, standard deviation, coefficient of variation and coefficient of skewness of annual maximum series of peak flows. The investigation is carried out through a three-stage analysis. First, a numerical simulation is performed by using a spatially distributed hydrological model in order to highlight how flood statistics change with varying drainage density. Second, a conceptual hydrological model is used in order to analytically derive the dependence of flood statistics on drainage density. Third, real world data from 44 watersheds located in northern Italy were analysed. The three-level analysis seems to suggest that a critical value of the drainage density exists for which a minimum is attained in both the coefficient of variation and the absolute value of the skewness coefficient. Such minima in the flood statistics correspond to a minimum of the flood quantile for a given exceedance probability (i.e., recurrence interval). Therefore, the results of this study may provide useful indications for flood risk assessment in ungauged basins

Object migration in temporal object-oriented databases

The paper presents T-ORM (Temporal Objects with Roles Model), an object-oriented data model based on the concepts of class and role. In order to represent the evolution of real-world entities, T-ORM allows objects to change state, roles and class in their lifetime. In particular, it handles structural and behavioral changes that occur in objects when they migrate from a given class to another. First, the paper introduces the basic features of the T-ORM data model, emphasizing those related to object migration. Then, it presents the query and manipulation languages associated with T-ORM, focusing on the treatment of the temporal aspects of object evolution

Cavity method for quantum spin glasses on the Bethe lattice

We propose a generalization of the cavity method to quantum spin glasses on fixed connectivity lattices. Our work is motivated by the recent refinements of the classical technique and its potential application to quantum computational problems. We numerically solve for the phase structure of a connectivity $q=3$ transverse field Ising model on a Bethe lattice with $\pm J$ couplings, and investigate the distribution of various classical and quantum observables.Comment: 27 pages, 9 figure