Curl free pressure gradients over orography in a solution of the fully compressible Euler equations with implicit treatment of acoustic and gravity waves

Steep orography can cause noisy solutions and instability in models of the atmosphere. A new technique for modelling flow over orography is introduced which guarantees curl free gradients on arbitrary grids, implying that the pressure gradient term is not a spurious source of vorticity. This mimetic property leads to better hydrostatic balance and better energy conservation on test cases using terrain following grids. Curl-free gradients are achieved by using the co-variant components of velocity over orography rather than the usual horizontal and vertical components. In addition, gravity and acoustic waves are treated implicitly without the need for mean and perturbation variables or a hydrostatic reference profile. This enables a straightforward description of the implicit treatment of gravity waves. Results are presented of a resting atmosphere over orography and the curl-free pressure gradient formulation is advantageous. Results of gravity waves over orography are insensitive to the placement of terrain-following layers. The model with implicit gravity waves is stable in strongly stratified conditions, with N∆t up to at least 10 (where N is the Brunt-V ̈ais ̈al ̈a frequency). A warm bubble rising over orography is simulated and the curl free pressure gradient formulation gives much more accurate results for this test case than a model without this mimetic property.

N-acetylcysteine protects against renal injury following bilateral ureteral obstruction

Background. Obstructive nephropathy decreases renal blood flow (RBF) and glomerular filtration rate (GFR), causing tubular abnormalities, such as urinary concentrating defect, as well as increasing oxidative stress. This study aimed to evaluate the effects of N-acetylcysteine (NAC) on renal function, as well as on the protein expression of aquaporin 2 (AQP2) and endothelial nitric oxide synthase (eNOS), after the relief of bilateral ureteral obstruction (BUO). Methods. Adult male Wistar rats were divided into four groups: sham (sham operated); sham operated + 440 mg/kg body weight (BW) of NAC daily in drinking water, started 2 days before and maintained until 48 h after the surgery; BUO (24-h BUO only); BUO + NAC-pre (24-h BUO plus 440 mg/kg BW of NAC daily in drinking water started 2 days before BUO); and BUO + NAC-post (24-h BUO plus 440 mg/kg BW of NAC daily in drinking water started on the day of BUO relief). Experiments were conducted 48 h after BUO relief. Results. Serum levels of thiobarbituric reactive substances, which are markers of lipid peroxidation, were significantly lower in NAC-treated rats than in the BUO group rats. The administration of NAC provided significant protection against post-BUO GFR drops and reductions in RBF. Renal cortices and BUO rats presented decreased eNOS protein expression of eNOS in the renal cortex of BUO group rats, whereas it was partially recovered in BUO + NAC-pre group rats. Urine osmolality was significantly lower in BUO rats than in sham group rats or NAC-treated rats, the last also presenting less interstitial fibrosis. Post-BUO downregulation of AQP2 protein expression was averted in the BUO + NAC-pre group rats. Conclusions. This study demonstrates that NAC administration ameliorates the renal function impairment observed 48 h after the relief of 24-h BUO. Oxidative stress is important for the suppression of GFR, RBF, tissue AQP2 and eNOS in the polyuric phase after the release of BUO.

ABELIANIZED OBSTRUCTION FOR FIXED POINTS OF FIBER-PRESERVING MAPS OF SURFACE BUNDLES

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

Interface de cálculo modal e visualização para estruturas flexíveis tipo Euler-Bernoulli

Neste trabalho, foram analisadas, implementadas e mostradas as características de uma interface com estrutura de programação genérica para o ambiente Windows, criando facilidades de rapidez, confiabilidade e a apresentação de resultados aos usuários do sistema matemático Maple na criação e uso de aplicações matemáticas. A interface utilizou como modelo de implementação cálculos modais de vigas clássicas de Euler-Bernoulli. O usuário encontra, em um único sistema, cálculo para vigas clássicas, terá uma entrada de dados facilitada de variáveis que serão substituídas automaticamente no programa fonte da viga e a geração de resultados em um ambiente amigável com dados e gráficos mostrados de forma organizados.

A equação de Euler e a IS: estimações para o Brasil

Neste artigo estudamos a relação entre a taxa de juros e o hiato do produto no Brasil através da estimação de modelos Novo-Keynesianos. Para tanto, estimamos os modelos por três métodos: (1) método generalizados dos momentos, (2) máxima verossimilhança utilizando dados de expectativa divulgados pelo Banco Central do Brasil e (3) máxima verossimilhança utilizando variáveis de expectativa estimadas por um modelo VAR. As conclusões são altamente dependentes do método de estimação. Ao utilizar (1), os resultados indicam uma relação espúria entre a taxa de juros real e o hiato. Entretanto, as conclusões originadas de (2) indicam que somente o hiato defasado seria uma variável relevante para a nossa especificação. Ao estimar o modelo por (3), as estimativas corroboram os resultados obtidos com o método generalizados dos momentos.

A contractive method for computing the stationary solution of the euler equation

A contractive method for computing stationary solutions of intertemporal equilibrium models is provide. The method is is implemented using a contraction mapping derived from the first-order conditions. The deterministic dynamic programming problem is used to illustrate the method. Some numerical examples are performed.

Histopathology findings in common marmosets (Callithrix jacchus Linnaeus, 1758) with chronic weight loss associated with bile tract obstruction by infestation with Platynosomum (Loos, 1907)

Chronic weight loss in marmosets is often associated with wasting marmoset syndrome (WMS), an important disease that occurs in callitrichid colonies around the world. Even though its etiology is very difficult to determine, particular variables, such as weight loss, diarrhea and alopecia, associated or not with infestation in the pancreatic ducts with Trichospirura leptossoma (Nematoda: Thelazioidea), seem to be linked with the syndrome. This study investigated the histopathology of the lungs, duodenum, liver, gallbladder, extrahepatic bile ducts and pancreatic ducts of six common marmosets (Callithrix jacchus) suffering from severe non-diarrheic weight loss. Three individuals died naturally and the other three were euthanized. Microscopic findings showed the presence of adult flukes (Platynosomum) in the liver. These flukes, which provoke common infection in cats, were also observed inside the gallbladder as well as in the intra and extrahepatic bile ducts in common marmosets. Portal fibrosis was observed in two animals, which developed chronic fibrosing hepatopathy (biliary pattern, grade 3). The disease progresses without diarrhea and without pancreatic lesions or infestation. With the rogression, the animals presented with ascending cholangitis, cholestasis and portal fibrosis, sometimes culminating in secondary biliary cirrhosis. Therefore, this nfirmity, associated with chronic weight loss in common marmosets, could be another tiological factor linked with WMS

Morphological abnormalities and apoptosis in lamellar tissue of equines after intestinal obstruction and treatment with hydrocortisone

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

De solutione problematum diophanteorum per números integros : o primeiro trabalho de Euler sobre equações diofantinas

The present dissertation analyses Leonhard Euler´s early mathematical work as Diophantine Equations, De solutione problematum diophanteorum per números íntegros (On the solution of Diophantine problems in integers). It was published in 1738, although it had been presented to the St Petersburg Academy of Science five years earlier. Euler solves the problem of making the general second degree expression a perfect square, i.e., he seeks the whole number solutions to the equation ax2+bx+c = y2. For this purpose, he shows how to generate new solutions from those already obtained. Accordingly, he makes a succession of substitutions equating terms and eliminating variables until the problem reduces to finding the solution of the Pell Equation. Euler erroneously assigns this type of equation to Pell. He also makes a number of restrictions to the equation ax2+bx+c = y and works on several subthemes, from incomplete equations to polygonal numbers

Euler e os números pentagonais

The present investigation includes a study of Leonhard Euler and the pentagonal numbers is his article Mirabilibus Proprietatibus Numerorum Pentagonalium - E524. After a brief review of the life and work of Euler, we analyze the mathematical concepts covered in that article as well as its historical context. For this purpose, we explain the concept of figurate numbers, showing its mode of generation, as well as its geometric and algebraic representations. Then, we present a brief history of the search for the Eulerian pentagonal number theorem, based on his correspondence on the subject with Daniel Bernoulli, Nikolaus Bernoulli, Christian Goldbach and Jean Le Rond d'Alembert. At first, Euler states the theorem, but admits that he doesn t know to prove it. Finally, in a letter to Goldbach in 1750, he presents a demonstration, which is published in E541, along with an alternative proof. The expansion of the concept of pentagonal number is then explained and justified by compare the geometric and algebraic representations of the new pentagonal numbers pentagonal numbers with those of traditional pentagonal numbers. Then we explain to the pentagonal number theorem, that is, the fact that the infinite product(1 x)(1 xx)(1 x3)(1 x4)(1 x5)(1 x6)(1 x7)... is equal to the infinite series 1 x1 x2+x5+x7 x12 x15+x22+x26 ..., where the exponents are given by the pentagonal numbers (expanded) and the sign is determined by whether as more or less as the exponent is pentagonal number (traditional or expanded). We also mention that Euler relates the pentagonal number theorem to other parts of mathematics, such as the concept of partitions, generating functions, the theory of infinite products and the sum of divisors. We end with an explanation of Euler s demonstration pentagonal number theorem

Os artigos de Euler sobre os números amigáveis

Among the many methodological resources that the mathematics teacher can use in the classroom, we can cite the History of Mathematics which has contributed to the development of activities that promotes students curiosity about mathematics and its history. In this regard, the present dissertation aims to translate and analyze, mathematically and historically, the three works of Euler about amicable numbers that were writed during the Eighteenth century with the same title: De numeris amicabilibus. These works, despite being written in 1747 when Euler lived in Berlin, were published in different times and places. The first, published in 1747 in Nova Acta Eruditorum and which received the number E100 in the Eneström index, summarizes the historical context of amicable numbers, mentions the formula 2nxy & 2nz used by his precursors and presents a table containing thirty pairs of amicable numbers. The second work, E152, was published in 1750 in Opuscula varii argument. It is the result of a comprehensive review of Euler s research on amicable numbers which resulted in a catalog containing 61 pairs, a quantity which had never been achieved by any mathematician before Euler. Finally, the third work, E798, which was published in 1849 at the Opera postuma, was probably the first among the three works, to be written by Euler

Notes on Newton-Euler formulation of robotic manipulators

The equations corresponding to Newton-Euler iterative method for the determination of forces and moments acting on the rigid links of a robotic manipulator are given a new treatment using composed vectors for the representation of both kinematical and dynamical quantities. It is shown that Lagrange equations for the motion of a holonomic system are easily found from the composed vectors defined in this note. Application to a simple model of an industrial robot shows that the method developed in these notes is efficient in solving the dynamics of a robotic manipulator. An example is developed, where it is seen that with the application of appropriate control moments applied to each arm of the robot, starting from a given initial position, it is possible to reach equilibrium in a final pre-assigned position.

Unscented Kalman Filter Applied to the Spacecraft Attitude Estimation with Euler Angles

The aim of this work is to test an algorithm to estimate, in real time, the attitude of an artificial satellite using real data supplied by attitude sensors that are on board of the CBERS-2 satellite (China Brazil Earth Resources Satellite). The real-time estimator used in this work for attitude determination is the Unscented Kalman Filter. This filter is a new alternative to the extended Kalman filter usually applied to the estimation and control problems of attitude and orbit. This algorithm is capable of carrying out estimation of the states of nonlinear systems, without the necessity of linearization of the nonlinear functions present in the model. This estimation is possible due to a transformation that generates a set of vectors that, suffering a nonlinear transformation, preserves the same mean and covariance of the random variables before the transformation. The performance will be evaluated and analyzed through the comparison between the Unscented Kalman filter and the extended Kalman filter results, by using real onboard data.