Polymer indentation with mesoscopic molecular dynamics

Indentation tests are used to determine the hardness of a material, e.g., Rockwell, Vickers, or Knoop. The indentation process is empirically observed in the laboratory during these tests; the mechanics of indentation is insufficiently understood. We have performed first molecular dynamics computer simulations of indentation resistance of polymers with a chain structure similar to that of high density polyethylene (HDPE). A coarse grain model of HDPE is used to simulate how the interconnected segments respond to an external force imposed by an indenter. Results include the time-dependent measurement of penetration depth, recovery depth, and recovery percentage, with respect to indenter force, indenter size, and indentation time parameters. The simulations provide results that are inaccessible experimentally, including continuous evolution of the pertinent tribological parameters during the entire indentation process.

On universal central extensions of Hom-Leibniz algebras

In the category of Hom-Leibniz algebras we introduce the notion of Hom-corepresentation as adequate coefficients to construct the chain complex from which we compute the Leibniz homology of Hom-Leibniz algebras. We study universal central extensions of Hom-Leibniz algebras and generalize some classical results, nevertheless it is necessary to introduce new notions of α-central extension, universal α-central extension and α-perfect Hom-Leibniz algebra due to the fact that the composition of two central extensions of Hom-Leibniz algebras is not central. We also provide the recognition criteria for these kind of universal central extensions. We prove that an α-perfect Hom-Lie algebra admits a universal α-central extension in the categories of Hom-Lie and Hom-Leibniz algebras and we obtain the relationships between both of them. In case α = Id we recover the corresponding results on universal central extensions of Leibniz algebras.

Estrutura fatorial do questionário de morbidade psiquiátrica de adultos aplicado em amostras populacionais de cidades brasileiras

A análise de componentes principais é uma técnica de estatística multivariada utilizada para examinar a interdependência entre variáveis. A sua principal característica é a capacidade de reduzir dados, e tem sido usada para o desenvolvimento de instrumentos de pesquisas psiquiátricas e na classificação dos transtornos psiquiátricos. Esta técnica foi utilizada para estudar a estrutura fatorial do Questionário de Morbidade Psiquiátrica do Adulto (QMPA). O questionário foi composto de 45 questões de resposta sim/não que identificam sintomas psiquiátricos, uso de serviço e de drogas psicotrópicas. O questionário foi aplicado em 6.470 indivíduos maiores de 15 anos, em amostras representativas da população de três cidades brasileiras (Brasília, São Paulo e Porto Alegre). O estudo teve como objetivo comparar a estrutura fatorial do questionário nas três regiões urbanas brasileiras. Sete fatores foram encontrados que explicam 42,7% da variância total da amostra. O fator 1, Ansiedade/Somatização ("eigenvalue" (EV) = 3.812 e variância explicada (VE) = 10,9%); O fator 2, Irritabilidade/Depressão (EV = 2.412 e VE = 6,9%); O fator 3, Deficiência Mental (EV= 2.014 e VE = 5,8%); O fator 4, Alcoolismo (EV = 1.903 e VE = 5,4%); O fator 5, Exaltação do Humor (EV = 1.621 e VE = 4,6%); O fator 6, Transtorno de Percepção (EV = 1.599 e VE = 4,6%) e o fator 7, Tratamento (EV = 1.592 e VE = 4,5%).O QMPA apresentou estruturas fatoriais semelhantes nas três cidades. Baseados nos achados, são feitas sugestões para que algumas questões sejam modificadas e para a exclusão de outras em uma futura versão do questionário.

Método de captura e recaptura: nova metodologia para pesquisas epidemiológicas

O método de captura e recaptura, embora não seja novo, tem sido pouco usado em estudos epidemiológicos. Trata-se de método bem adaptável e adequado para estudar populações incomuns ou esquivas, como usuários de drogas endovenosas. Tem sido usado para estudar populações diversas como prostitutas que trabalham na rua ou volume de células vermelhas no homem. Permite ainda estimar a incidência e a prevalência de doenças de forma mais precisa do que os métodos tradicionais e com uma melhor relação custo-benefício. Devido à sua relevância dentro do campo da epidemiologia, decidiu-se realizar uma revisão sobre esse método, enfocando a história, as principais aplicações e apontando as suposições teóricas que o fundamentam. Seu potencial para futuras pesquisas epidemiológicas é promissor.

Completion problems for real matrices, II

Thirty years ago, G.N. de Oliveira has proposed the following completion problems: Describe the possible characteristic polynomials of [C-ij], i,j is an element of {1, 2}, where C-1,C-1 and C-2,C-2 are square submatrices, when some of the blocks C-ij are fixed and the others vary. Several of these problems remain unsolved. This paper gives the solution, over the field of real numbers, of Oliveira's problem where the blocks C-1,C-1, C-2,C-2 are fixed and the others vary.

Assessing the effects of global warming and local social and economic conditions on the malaria transmission

OBJECTIVE: To show how a mathematical model can be used to describe and to understand the malaria transmission. METHODS: The effects on malaria transmission due to the impact of the global temperature changes and prevailing social and economic conditions in a community were assessed based on a previously presented compartmental model, which describes the overall transmission of malaria. RESULTS/CONCLUSIONS: The assessments were made from the scenarios produced by the model both in steady state and dynamic analyses. Depending on the risk level of malaria, the effects on malaria transmission can be predicted by the temperature ambient or local social and-economic conditions.

Malaria transmission model for different levels of acquired immunity and temperature-dependent parameters (vector)

OBJECTIVE: Describe the overall transmission of malaria through a compartmental model, considering the human host and mosquito vector. METHODS: A mathematical model was developed based on the following parameters: human host immunity, assuming the existence of acquired immunity and immunological memory, which boosts the protective response upon reinfection; mosquito vector, taking into account that the average period of development from egg to adult mosquito and the extrinsic incubation period of parasites (transformation of infected but non-infectious mosquitoes into infectious mosquitoes) are dependent on the ambient temperature. RESULTS: The steady state equilibrium values obtained with the model allowed the calculation of the basic reproduction ratio in terms of the model's parameters. CONCLUSIONS: The model allowed the calculation of the basic reproduction ratio, one of the most important epidemiological variables.

A mathematical model for malaria transmission relating global warming and local socioeconomic conditions

OBJECTIVE: Sensitivity analysis was applied to a mathematical model describing malaria transmission relating global warming and local socioeconomic conditions. METHODS: A previous compartment model was proposed to describe the overall transmission of malaria. This model was built up on several parameters and the prevalence of malaria in a community was characterized by the values assigned to them. To assess the control efforts, the model parameters can vary on broad intervals. RESULTS: By performing the sensitivity analysis on equilibrium points, which represent the level of malaria infection in a community, the different possible scenarios are obtained when the parameters are changed. CONCLUSIONS: Depending on malaria risk, the efforts to control its transmission can be guided by a subset of parameters used in the mathematical model.

Lanczos algorithm on the grassmann manifold

5th. European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008) 8th. World Congress on Computational Mechanics (WCCM8)

Teaching and learning mathematics using moodle

This paper summarizes a project that is contributing to a change in the way of teaching and learning Mathematics. Mathematics is a subject of the Accounting and Administration course. In this subject we teach: Functions and Algebra. The aim is that the student understand the basic concepts and is able to apply them in other issues, when possible, establishing a bridge between the issues that they have studied and their application in Accounting. As from this year, the Accounting course falls under in Bologna Process. The teacher and the student roles have changed. The time for theoretical and practical classes has been reduced, so it was necessary to modify the way of teaching and learning. In the theoretical classes we use systems of multimedia projection to present the concepts, and in the practical classes we solve exercises. We also use the Excel and the mathematical open source software wxMaxima. To supplement our theoretical and practical classes we have developed a project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio Online (Online Support Project). With the creation of this new project we wanted to take advantage already obtained results with the previous experiences, giving to the students opportunities to complement their study in Mathematics. One of the great objectives is to motivate students, encourage them to overcome theirs difficulties through an auto-study giving them more confidence. In the MatActiva project the students have a big collection of information about the way of the subject works, which includes the objectives, the program, recommended bibliography, evaluation method and summaries. It works as material support for the practical and theoretical classes, the slides of the theoretical classes are available, the sheets with exercises for the students to do in the classroom and complementary exercises, as well as the exams of previous years. Students can also do diagnostic tests and evaluation tests online. Our approach is a reflexive one, based on the professional experience of the teachers that explore and incorporate new tools of Moodle with their students and coordinate the project MatActiva.

The active mathematics project at ISCAP

This paper summarizes a project that is contributing to a change in the way of teaching and learning Mathematics. Mathematics is a subject of the Accounting and Administration course. In this subject we teach: Functions and Algebra. The aim is that the students understand the basic concepts and is able to apply them in other issues, when possible, establishing a bridge between the issues that they have studied and their application in Accounting. As from this year, the Accounting course falls under in Bologna Process. The teacher and the student roles have changed. The time for theoretical and practical classes has been reduced, so it was necessary to modify the way of teaching and learning. In the theoretical classes we use systems of multimedia projection to present the concepts, and in the practical classes we solve exercises. To supplement our theoretical and practical classes we have developed an active mathematics project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio Online (Online Support Project). In the last versions of Moodle, it is possible use the TeX language to create math questions. Using this tool we created a set of interactive materials. With the creation of this new project we wanted to take advantage already obtained results with the previous experiences, giving to the students opportunities to complement their study in Mathematics. One of the great objectives is to motivate students, encourage them to overcome theirs difficulties through an auto-study, giving them more confidence and the opportunity to seeing others perspectives of the mathematics subjects. In the MatActiva project the students have a big collection of information about the way of the subject works, which includes the objectives, the program, recommended bibliography, evaluation method and summaries. It works as material support for the practical and theoretical classes, the slides of the theoretical classes are available, the sheets with exercises for the students to do in the classroom and complementary exercises, as well as the exams of previous years. Students can also do diagnostic tests and evaluation tests online. Our approach is a reflexive one, based on the professional experience of the teachers that explore and incorporate new tools of Moodle with their students and coordinate the project MatActiva.

On the monoids of transformations that preserve the order and a uniform partition

In this article we consider the monoid O(mxn) of all order-preserving full transformations on a chain with mn elements that preserve a uniformm-partition and its submonoids O(mxn)(+) and O(mxn)(-) of all extensive transformations and of all co-extensive transformations, respectively. We determine their ranks and construct a bilateral semidirect product decomposition of O(mxn) in terms of O(mxn)(-) and O(mxn)(+).

Unified min-max and interlacing theorems for linear operators

There exist striking analogies in the behaviour of eigenvalues of Hermitian compact operators, singular values of compact operators and invariant factors of homomorphisms of modules over principal ideal domains, namely diagonalization theorems, interlacing inequalities and Courant-Fischer type formulae. Carlson and Sa [D. Carlson and E.M. Sa, Generalized minimax and interlacing inequalities, Linear Multilinear Algebra 15 (1984) pp. 77-103.] introduced an abstract structure, the s-space, where they proved unified versions of these theorems in the finite-dimensional case. We show that this unification can be done using modular lattices with Goldie dimension, which have a natural structure of s-space in the finite-dimensional case, and extend the unification to the countable-dimensional case.

Rotações no espaço tridimensional por meio de produtos quaterniônicos

Pós-graduação em Matemática Universitária - IGCE