Asymptotic regularity conditions for the strong convergence towards weak limit sets and weak attractors of the 3D Navier-Stokes equations

The asymptotic behavior of solutions of the three-dimensional Navier-Stokes equations is considered on bounded smooth domains with no-slip boundary conditions or on periodic domains. Asymptotic regularity conditions are presented to ensure that the convergence of a Leray-Hopf weak solution to its weak omega-limit set (weak in the sense of the weak topology of the space H of square-integrable divergence-free velocity fields) are achieved also in the strong topology of H. In particular, if a weak omega-limit set is bounded in the space V of velocity fields with square-integrable vorticity then the attraction to the set holds also in the strong topology of H. Corresponding results for the strong convergence towards the weak global attractor of Foias and Temam are also presented.Comment: 10 page

Convergence of time averages of weak solutions of the three-dimensional Navier-Stokes equations

Using the concept of stationary statistical solution, which generalizes the notion of invariant measure, it is proved that, in a suitable sense, time averages of almost every Leray-Hopf weak solution of the three-dimensional incompressible Navier-Stokes equations converge as the averaging time goes to infinity. This system of equations is not known to be globally well-posed, and the above result answers a long-standing problem, extending to this system a classical result from ergodic theory. It is also showed that, from a measure-theoretic point of view, the stationary statistical solution obtained from a generalized limit of time averages is independent of the choice of the generalized limit. Finally, any Borel subset of the phase space with positive measure with respect to a stationary statistical solution is such that for almost all initial conditions in that Borel set and for at least one Leray-Hopf weak solution starting with that initial condition, the corresponding orbit is recurrent to that Borel subset and its mean sojourn time within that Borel subset is strictly positive.Comment: Version 2: fixed some typos; added some references; and expanded some sentences and some remarks for the sake of clarit

Cape Verdean Counter Cultural Hip-Hop(s) & the Mobilization of the Culture of Radical Memory: Public Pedagogy for Liberation or Continued Colonial Enslavement

The paper traces the possibilities and limitations of transnational Cape Verdean Hip-Hop’s mobilization of the culture of radical memory for the disruption of racialized transnational capitalism and neocolonialism. One of the most common reference points, both in the symbolic formations of popular culture and emerging scholarly texts is the focus on CV Hip-Hop’s embrace of the life and work of Amilcar Cabral. Undoubtedly, Cape Verdean Hip-Hop Culture(s) & Cape Verdean youth counter-culture(s), more broadly, continues to serve as the most vital space for the (re)mobilization and (re)invigoration of Cabral’s thought, yet, much more is unfolding in these spaces. The paper argues that we must maintain a broader analysis on the intersection of the art form and the culture of memory. It also argues that our analysis must perpetually name regressive forces even as progressive projects unfold so as not to re-inscribe negative relations of power. Although the paper is primarily conceptual/theoretical, the tools of ethnography (rather than a full blown ethnography) are intersected to centralize artistic voices and for purposes of reflexivity. Observations of CV Hip-Hop music videos take centrality as it allows one to comprehend emerging elements of hip-hop beyond rap lyrics. Transcripts of interviews with hip-hop heads are integrated throughout

Socioepistemología y matemáticas

En esta ponencia se discutió el estado que guarda la investigación en Matemática Educativa en distintos planos y con el empleo de ejemplos, se puso especial énfasis en las Tesis de base de la teoría y en el papel que juega la noción de práctica social en la construcción y difusión institucional del conocimiento matemático. Ahora ampliamos esto con un par de ejemplos

A systematic revision of the South American freshwater stingrays (chondrichthyes: potamotrygonidae) (batoidei, myliobatiformes, phylogeny, biogeography)

Three genera are recognized in the family Potamotrygonidae of neotropical freshwater stingrays: Potamotrygon, Paratrygon, and Plesiotrygon, the latter being described as a new genus. Potamotrygon is polytypic, and both Paratrygon and Plesiotrygon are monotypic, as far as known. The family name Potamotrygonidae has priority over Paratrygonidae Gill. Nineteen previously described species of Potamotrygonidae are recognized: Paratrygon aiereba, Potamotrygon brachyura, P. castexi, P. constellata, P. dumerilii, P. falkneri, P. henlei, P. histrix, P. humerosa, P. leopoldi, P. magdalenae, P. motoro, P. ocellata, P. orbignyi, P. schroederi, P. schuemacheri, P. scobina, P. signata, and P. yepezi. One additional specific name is established as new (Plesiotrygon iwamae). Three of the eighteen recognized species of Potamotrygon are resurrected from synonymy (P. dumerilii, P. henlei, and P. orbignyi), one previously overlooked subspecific name (Trygon histrix ocellata) is erected to specific rank, and one previously overlooked specific name (Taeniura constellata) is placed in the genus Potamotrygon, and treated as a senior synonym of P. circularis. The remaining names previously assigned to the Potamotrygonidae include: eight junior synonyms (Disceus thayeri, Potamotrygon brumi, P. circularis, P. laticeps, P. menchacai, Trygon mulleri, T. reticulatus, and T. strogylopterus), five doubtful names (Elipesurus spinicauda, Potamotrygon africana, P. alba, P. humboldtii, and Trygon garrapa), two invalid names (Potamotrygon labratoris and P. pauckei), two doubtful names corresponding to one unidentified marine species of the family Dasyatididae (Raja ajereba and R. orbicularis), and one freshwater species of Dasyatis (D. garouaensis) originally described in the genus Potamotrygon. Potamotrygon and Paratrygon are regarded as sister groups, and Plesiotrygon as the primitive potamotrygonid genus, based on a cladistic analysis of stingray characters. Plesiotrygon is restricted to the upper Amazon drainage, and Paratrygon is known from most of the Amazon drainage, occurring also in Rio Orinoco. Eleven species of Potamotrygon have Amazonian distribution (including Rio Tocantins), four of which occur also in other drainages. Four species of Potamotrygon are apparently endemic to Rio Paraguay and lower Rio Parana drainages (P. brachyura, P. falkneri, P. histrix, and P. schuemacheri); P. yepezi is endemic to the Maracaibo basin in Venezuela; P. magdalenae is endemic to Rio Magdalena and Rio Atrato drainages in Colombia, and P. signata is apparently endemic to Rio Parna(\u27)iba drainage in Brazil

The effect of work related mechanical stress on the peripheral temperature of the hand

The evolution and developments in modern industry have resulted a wide range of occupational activities, some of which can lead to industrial injuries. Due to the activities of occupational medicine, much progress has been made in transforming the way that operatives perform their tasks. However there are still many occupations where manual tasks have become more repetitive, contributing to the development of conditions that affect the upper limbs. Repetitive Strain Injury is one classification of those conditions which is related to overuse of repetitive movement. Hand Arm Vibration Syndrome is a subtype of this classification directly related to the operation of instruments and machinery which involves vibration. These conditions affect a large number of individuals, and are costly in terms of work absence, loss of income and compensation. While such conditions can be difficult to avoid, they can be monitored and controlled, with prevention usually the least expensive solution. In medico-legal situations it may be difficult to determine the location or the degree of injury, and therefore determining the relevant compensation due is complicated by the absence of objective and quantifiable methods. This research is an investigation into the development of an objective, quantitative and reproducible diagnostic procedure for work related upper limb disorders. A set of objective mechanical provocation tests for the hands have been developed that are associated with vascular challenge. Infrared thermal imaging was used to monitor the temperature changes using a well defined capture protocol. Normal reference values have been measured and a computational tool used to facilitate the process and standardise image processing. These objective tests have demonstrated good discrimination between groups of healthy controls and subjects with work related injuries but not individuals, p<0.05, and are reproducible. A maximum value for thermal symmetry of 0.5±0.3ºC for the whole upper limbs has been established for use as a reference. The tests can be used to monitor occupations at risk, aiming to reduce the impact of these conditions, reducing work related injury costs, and providing early detection. In a medico-legal setting this can also provide important objective information in proof of injury and ultimately in objectively establishing whether or not there is a case for compensation

Los organismos perforantes de las costas argentinas

El presente trabajo trata sobre el hallazgo en Mar del Plata de Lyrodus pedícellatus (Quatrefages, 1849), nueva cita para la malacofauna argentina, con lo que se amplía el rango de distribución geográfica de la misma. Observaciones en el medio natural y en acuario han demostrado que se trata de una especie muy frecuente, perfectamente adaptada a las condiciones ecológicas de esta nueva área. Con los datos bibliográficos existentes se ha confeccionado una tabla donde se incluyen los nombres válidos y las localidades en las que se encontraron Teredínidos en Sud América, y una clave para su identificación taxonómica.In the present study, Lyrodus pedicellatus (Quatrefages, 1849) is mentioned to be found for the first time in Argentine coasts. This species, recently collected at the port of Mar del Plata and surrounding areas, vas previously known for Brasil, as its southern limit of distribution in America. Observations in natural environment and in aquarium demonstrates that this wood-borer is perfectly adapted to the ecological conditions of this new area. This work also includes a table with the valid names and localities of the 17 species actually known for South American coasts, and a key for its taxonomic identification