ABSTRACT A mathematical model was developed to describe the dynamics of the primary infection of dengue virus in infants who were born to a mother immune to some serotype of the dengue virus. The model is given by a system of nonlinear ordinary differential equations with time-dependent variables for the number of dengue virus antibodies of the infant transferred from their immune, uninfected, and infected monocytes and dengue virus. The mathematical analysis was carried out where the conditions for the existence of the disease-free equilibrium and the endemic equilibrium were established. The numerical simulations were performed considering different scenarios for a basic reproductive number, R 0, illustrating the global convergence of the numerical results for the equilibrium points. The results are in agreement with our derived global stability analysis. It can be concluded that dengue hemorrhagic fever in infants could occur in the peaks observed for the infected monocytes and dengue virus.

Resumo Este trabalho consiste na obtenção de curvas de correlação entre ensaios mecânicos e testes de esclerometria a partir de um programa experimental extenso realizado em 630 corpos de prova de concreto. empregando materiais e métodos disponíveis no Brasil. Os concretos, com resistências a compressão variando de 20 MPa a 50 MPa, foram submetidos a ensaios de esclerometria e a testes mecânicos de compressão, cujos resultados foram empregados na obtenção de curvas de correlação. Tais curvas foram adotadas em medições de elementos estruturais moldados em um canteiro de obras, indicando que as curvas fornecidas pelo fabricante do equipamento não são adequadas para o material em estudo. Trata-se da primeira etapa de um amplo estudo visando contribuir para o aprimoramento das normas brasileiras que estabelecem os procedimentos para a aplicação da esclerometria para medir a resistência a compressão de concreto.

Abstract The present work consists in obtaining correlation curves between compressive tests and sclerometry tests from an extensive experimental program comprising 630 concrete cylindrical samples cast in laboratory, employing materials and methods available in Brazil. The concretes, with compressive strengths ranging from 20~MPa to 50~MPa, were submitted to sclerometry tests and mechanical compressive tests. The results were used to obtain correlation curves. which were adopted in measurements of structural elements molded in a construction site, indicating that the curves provided by the equipment manufacturer are not suitable for the material in study. This is the first stage of a broader study aiming to contribute to the improvement of the Brazilian code regulating the application of the sclerometry to obtain concrete compressive strength.

In the present paper we consider the vortex lattice properties of a square superconductor such as the vortex patterns, the Gibbs free energy, the magnetization, and the depairing critical current density. We show that this last quantity shows a matching effect, that is, it shows a discontinuous behavior as a function of the applied magnetic field.