Young Measures Generated by Ideal Incompressible Fluid Flows

In their seminal paper "Oscillations and concentrations in weak solutions of the incompressible fluid equations", R. DiPerna and A. Majda introduced the notion of measure-valued solution for the incompressible Euler equations in order to capture complex phenomena present in limits of approximate solutions, such as persistence of oscillation and development of concentrations. Furthermore, they gave several explicit examples exhibiting such phenomena. In this paper we show that any measure-valued solution can be generated by a sequence of exact weak solutions. In particular this gives rise to a very large, arguably too large, set of weak solutions of the incompressible Euler equations.Comment: 35 pages. Final revised version. To appear in Arch. Ration. Mech. Ana

Censored Bayesian models for genetic evaluation of age at first calving in Brazilian Brahman cattle

We compared different Bayesian models to handle censored data for genetic parameters estimation of age at first calving (AFC) in Brazilian Brahman cattle. Data from females with AFC above 1825 days of age were assumed to have failed to calve and were considered as censored records. Data including information of 53, 703 cows were analyzed through the following methods: conventional linear model method (LM), which consider only uncensored records; simulation method (SM), in which the data were augmented by drawing random samples from positive truncated normal distributions; penalty method (PM), in which a constant of 21 days was added to censored records; and the bivariate threshold-linear method (TLcens). The LM was the most suited for genetic evaluation of AFC in Brazilian Brahman cattle based on the predictive ability evaluation through cross-validation analysis. The similar results for LM and PM regarding Spearman correlations, and the higher percentages of selected animals in common, indicated that there was not relevant reranking of animals when censored records were used. In summary, the heritability estimates for AFC ranged from 0.09 (TLcens) to 0.20 (LM). Given its poor predictive performance, the SM is not recommended for handling censored records for genetic evaluation of AFC

A Mach-Zehnder Interferometer for a Two-Photon Wave Packet

We propose an experiment that permits observation of the de Broglie two-photon wave packet behavior for a pair of photons, using a Mach-Zehnder interferometer. It is based on the use of pulsed lasers to generate pairs of photons via spontaneous parametric down-conversion and the post-selection of events. It differs from previous realizations by the use of a third time-correlated photon to engineer the state of the photons. The same technique can give us which-path information via an ``interaction-free'' experiment and can be used in other experiments on the foundations of quantum mechanics related to wave-particle duality and to nonlocality.Comment: Submmited for publication in Physical Review

AVALIAÇÃO DOS EFEITOS DE DIFERENTES CONCENTRAÇÕES DE CLORO NA DESCAPSULAÇÃO E ECLOSÃO DE LARVAS DE ARTEMIA (Artemia sp.)

This paper was prepared in the Aquaculture Laboratory of the Federal University of the State of Parana, Brazil, with the purpose of determining the best sodium hypochloride (NaClO with 6% active ingredient) dosage to be employed in the artemia oocysts hatching process.The artemia oocysts were hydrated for 1 hour, filtered and submitted to a 10-minute chlorine treatment. The chlorine dosages tested were the following (NaClO - 6% sodium hypochloride): 0.38g, 0.75g, 1.50g, 3.00g and 6.00g of active ingredient per liter of water. Soon after chlorine application the oocysts were rinsed to eliminate the chlorine and immediately the oocysts were put into transparent plastic vials with water in the constant aeration and luminosity, where they remained for 53 hours. For the nauplii count one mililiter of the vial was put into a test tube with an interconnected aeration. Three counts were made for all repetitions and the threshold analysed was the number of hatched larvae per mililiter of hatching solution. The results were submitted to a normality test and it was determined that the hatching results did not show a normal pattern, therefore, it was not possible to use those averages as a comparison basis between treatments. Subsequently non-parametric tests were performed using the overall average as a comparison basis between treatments.Techically one can see the superiority of treatment with 1.50g of active chlorine, which resulted in the highest hatching-out counts, with 50% of the observed data presented 140 larvae hatched per milimiter.O presente trabalho foi realizado no Laboratório de Aqüicultura da Universidade Federal do Paraná (UFPR), com o objetivo de determinar a melhor dose de hipoclorito de sódio (NaClO com 6% de ingrediente ativo) a ser empregada na descapsulação de oocistos de artemia. Os oocistos de artemia foram hidratados durante 1 hora, filtrados e submetidos aos tratamentos com cloro durante 10 minutos. As dosagens de cloro testadas foram as seguintes (NaClO - hipoclorito de sódio 6%): 0,38g, 0,75g, 1,50g, 3,00g e 6,00g de ingrediente ativo por litro de água. Depois da aplicação do cloro fez-se a lavagem dos oocistos para eliminar o cloro aplicado e logo após os oocistos foram colocados na água em frascos plásticos transparentes com aeração e luminosidade constante onde ficaram durante 53 horas. Para contagem dos náuplios foi pipetado um mililitro do frasco com aeração ligada. Para todas as repetições foram feitas três contagens e o parâmetro analisado foi o número de larvas eclodidas por mililitro da solução de eclosão. Os resultados foram submetidos a um teste de normalidade e foi verificado que os resultados de eclosão não tinham distribuição normal, portanto as médias não puderam ser usadas como termo de comparação entre os tratamentos. Então foram realizados testes não-paramétricos que usam a mediana como parâmetro de comparação entre os tratamentos. Tecnicamente observa-se a superioridade do tratamento de 1,50g de cloro ativo que apresentou o ponto máximo de eclosão, tendo 50% dos dados de eclosão ao redor de 140 larvas eclodidas por mililitro

Diffeomorphic approximation of Sobolev homeomorphisms

Every homeomorphism h : X -> Y between planar open sets that belongs to the Sobolev class W^{1,p}(X,Y), 1<p<\infty, can be approximated in the Sobolev norm by diffeomorphisms.Comment: 21 pages, 5 figure

Whirl mappings on generalised annuli and the incompressible symmetric equilibria of the dirichlet energy

In this paper we show a striking contrast in the symmetries of equilibria and extremisers of the total elastic energy of a hyperelastic incompressible annulus subject to pure displacement boundary conditions.Indeed upon considering the equilibrium equations, here, the nonlinear second order elliptic system formulated for the deformation u=(u1,…,uN) : EL[u,X]=⎧⎩⎨⎪⎪Δu=div(P(x)cof∇u)det∇u=1u≡φinX,inX,on∂X, where X is a finite, open, symmetric N -annulus (with N≥2 ), P=P(x) is an unknown hydrostatic pressure field and φ is the identity mapping, we prove that, despite the inherent rotational symmetry in the system, when N=3 , the problem possesses no non-trivial symmetric equilibria whereas in sharp contrast, when N=2 , the problem possesses an infinite family of symmetric and topologically distinct equilibria. We extend and prove the counterparts of these results in higher dimensions by way of showing that a similar dichotomy persists between all odd vs. even dimensions N≥4 and discuss a number of closely related issues