Nonlinear porous medium flow with fractional potential pressure

We study a porous medium equation, with nonlocal diffusion effects given by an inverse fractional Laplacian operator. We pose the problem in n-dimensional space for all t>0 with bounded and compactly supported initial data, and prove existence of a weak and bounded solution that propagates with finite speed, a property that is nor shared by other fractional diffusion models.Comment: 32 pages, Late

Research on mathematical competencies in engineering education: Where are we now?

In tertiary mathematics education for engineers (hereafter called service mathematics education, SME), there is a long-lasting controversy on what and how to teach. The goal of SME is to provide a base for engineering-specific courses and to develop mathematical competencies needed for academic success and professional practice. A leading question in engineering education is how to take mathematical competencies into account when designing content. Mathematical competencies are employed to understand, judge, do, and use mathematics in a variety of mathematical contexts and situations in which mathematics could play a role [1]. Although mathematical competencies have been introduced for about two decades, Alpers [2] noted that research in engineering higher education had focused chiefly on the modelling competency and less on other competencies. By means of a scoping review, the current study aims to examine how mathematical competencies are investigated in higher education research. The main research question is “To what extent and in what ways have mathematical competencies been examined in higher engineering education research?” Papers were retrieved and qualitatively reviewed using the Preferred Reporting Items for Systematic Reviews and Meta- Analyses (PRISMA) guidelines. A systematic search yielded 166 records, of which, 65 unique records were relevant to engineering education and screened for eligibility. A synthesis of 23 studies reviewed showed that problem-solving and modelling were the most investigated mathematical competencies and were often investigated together or with other mathematical competencies. The inconsistencies in the terminologies used suggest a need for clearer conceptualizations to advance research and inform practice on mathematical competencies

Aspectos clínicos, epidemiológicos e patológicos da infecção natural em bovinos por Trypanosoma vivax na Paraíba Clinical, epidemiological and pathological signs of natural infection in cattle by Trypanosoma vivax in Paraíba, Brazil

Descrevem-se dois surtos de tripanossomíase por Trypanosoma vivax em bovinos, ocorridos em dois estabelecimentos do alto sertão da Paraíba. Os sinais clínicos, a patologia e a epidemiologia da doença foram estudados no período de maio de 2005 a novembro de 2006.T. vivax foi identificado em esfregaços da capa leucocitária e mediante a reação em cadeia da polimerase (PCR). Os animais afetados apresentaram anorexia, depressão, febre, anemia, perda de peso, redução da produção leiteira, cegueira transitória, aborto e sinais nervosos caracterizados por incoordenação motora, salivação, opistótono, nistagno, tetania e bruxismo. Todos os animais que apresentaram sintomatologia nervosa morreram. As alterações macroscópicas observadas em um bovino submetido à necropsia foram aumento de volume dos linfonodos, atrofia serosa dos depósitos de gordura, aumento de volume do baço com evidência da polpa branca, hidropericárdio, além de petéquias e equimoses no epicárdio. Histologicamente havia meningoencefalite. O controle da doença na propriedade com tratamento específico dos casos clínicos com aceturato de diminazene foi eficiente, pois após o tratamento não se verificou mais a presença do parasita em esfregaços sanguíneos nem evidência clínica da enfermidade em até 2 meses após o início do surto. Os fatores epidemiológicos favoráveis à ocorrência dos surtos foram a abundância de vetores mecânicos, como tabanídeos e Stomozys spp., e a entrada, no rebanho, de animais oriundos de propriedades onde ocorreu a doença em questão. Sugere-se que o semi-árido do Nordeste, devido a períodos prolongados de secas e altas temperaturas, é região de instabilidade enzoótica para a tripanossomíase, em conseqüência, provavelmente, ao ambiente desfavorável para o desenvolvimento de vetores durante a maior parte do ano.<br>Two outbreaks of trypanosomiasis by Trypanosoma vivax, reported in cattle, occurred on two farms located in the state of Paraíba, northeastern Brazil. The epidemiology, clinical signs and pathology of the disease were studied from May 2005 to November 2006. T. vivax was identified morphologically and by polymerase chain reaction test (PCR). The affected cattle presented anorexia, depression, fever, anemia, weight loss, reduction in milk production, transitory blindness, abortion and some nervous signs as nystagmus, tetany and bruxism. All cattle that presented nervous signs died. Necropsy findings were enlarged lymph and spleen, serous atrophy of the fat depots, proeminence of the splenic white pulp, hydropericardium and pericardial petechiae and ecchymoses on the epicardium. Histologically there was meningoencephalitis. The treatment of the clinical cases with diminazena aceturate was efficient with clearance of the parasite from the blood or disappearance of clinical signs in up to 2 months after the beginning of the outbreak on the two farms studied. The epidemiologic factors favoring the occurrence of the outbreak were the abundance of mechanical vectors, as tabanids and Stomoxys sp., and the introduction into the herd of cattle from farms where the disease occurred. It is suggested that the semiarid of the Brazilian Northeast is an enzootic instability region for trypanosomiasis due to its prolonged periods of drought and high temperatures, constituting during most part of the year an unfavorable environment for the development of vectors