Colombeau's theory and shock wave solutions for systems of PDEs

In this article we study the existence of shock wave solutions for systems of partial differential equations of hydrodynamics with viscosity in one space dimension in the context of Colombeau's theory of generalized functions. This study uses the equality in the strict sense and the association of generalized functions (that is the weak equality). The shock wave solutions are given in terms of generalized functions that have the classical Heaviside step function as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function that have to satisfy part of the equations in the strict sense and part of the equations in the sense of association.

Heaviside generalized functions and shock waves for a Burger kind equation

The purpose of the work is to study the existence and nonexistence of shock wave solutions for the Burger equations. The study is developed in the context of Colombeau's theory of generalized functions (GFs). This study uses the equality in the strict sense and the weak equality of GFs. The shock wave solutions are given in terms of GFs that have the Heaviside function, in x and ( x, t) variables, as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function, in R-n and R-n x R, in the distributional limit sense.

Composition and invertibility for a class of generalized functions in the Colombeau's theory

In this work we define the composite function for a special class of generalized mappings and we study the invertibility for a certain class of generalized functions with real values.

Synthesis, characterization and catalytic properties of nanocrystaline Y2O3-coated TiO2 in the ethanol dehydration reaction

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

VOICES FROM THE SOUTH: DIALOGICAL RELATIONSHIPS AND COLLABORATION IN MATHEMATICS EDUCATION

This chapter presents a collaborative experience between two neighbouring countries from South America: Argentina and Brazil. Our purpose is to share a model of international collaboration that we consider to be an alternative to the classical movement of early mathematical and scientific knowledge between East and West and between North and South. We start our chapter with a general discussion about the phenomenon of globalization considering some local examples. We characterize our collaboration exploring the tensions and difficulties we faced along our own professional development at the local as well as the international level. We describe the development of our prior collaborative work that established the foundation for our international collaboration portraying the local mathematics education communities. We refer to some balances that were created among our relationships, the expansion of our collaborative network, and how this particular collaboration allows us to contribute to the regional field and inform the international one. We discuss the way that the search for balance and symmetry, or at least a complementary asymmetry in our collaborative relationships, has led us to generate a genuine and equitable collaboration.

GENERALIZED HEAVISIDE FUNCTIONS IN THE COLOMBEAU THEORY CONTEXT

We defined generalized Heaviside functions for a variable x in R-n, and for variables (x, t) in R-n x R-m. Then study properties such as: composition, invertibility, and association relation (the weak equality). This work is developed in the Colombeau generalized functions context.

Composition for a class of generalized functions in Colombeau's theory

In Colombeau's theory, given an open subset Ω of ℝn, there is a differential algebra G(Ω) of generalized functions which contains in a natural way the space D′(Ω) of distributions as a vector subspace. There is also a simpler version of the algebra G,(Ω). Although this subalgebra does not contain, in canonical way, the space D′(Ω) is enough for most applications. This work is developed in the simplified generalized functions framework. In several applications it is necessary to compute higher intrinsic derivatives of generalized functions, and since these derivatives are multilinear maps, it is necessary to define the space of generalized functions in Banach spaces. In this article we introduce the composite function for a special class of generalized mappings (defined in open subsets of Banach spaces with values in Banach spaces) and we compute the higher intrinsic derivative of this composite function.

Collectives of humans-with-media in mathematics education: Notebooks, blackboards, calculators, computers and ... notebooks throughout 100 years of ICMI

The main aim of this study was to present evidence of the ways in which different media have conditioned and dramatically reorganized education, in general, and mathematics education, in particular. After an introduction of the theme, we discuss the epistemological perspective that provides the foundation for our analysis: the notion of humans-with-media. Then, we briefly illustrate how the medium is related to the scientific production of mathematical knowledge. We take a detour into the world of art to examine how devices and instruments have historically been associated with the production of mathematical knowledge. Then, we review studies on the history of education to show how traditional media were introduced into schools and have influenced education. In particular, we examine how devices such as blackboards and notebooks, which were novelties a 100 years ago, came to be accepted in schools and the mathematical activities that were promoted with their use. Finally, we discuss how information technology has changed education and how the Internet may have an impact on mathematics education comparable to that of the notebook over a century ago. © FIZ Karlsruhe 2009.

Wavelets in a problem of signal processing

In this work a new method is proposed for noise reduction in speech signals in the wavelet domain. The method for signal processing makes use of a transfer function, obtained as a polynomial combination of three processings, denominated operators. The proposed method has the objective of overcoming the deficiencies of the thresholding methods and the effective processing of speech corrupted by real noises. Using the method, two speech signals are processed, contaminated by white noise and colored noises. To verify the quality of the processed signals, two evaluation measures are used: signal to noise ratio (SNR) and perceptual evaluation of speech quality (PESQ).

Lactobacillus acidophilus CRL 1014 improved gut health in the SHIME® reactor

Background: How to maintain gut health is a goal for scientists throughout the world. Therefore, microbiota management models for testing probiotics, prebiotics, and synbiotics have been developed.Methods: The SHIME® model was used to study the effect of Lactobacillus acidophilus 1014 on the fermentation pattern of the colon microbiota. Initially, an inoculum prepared from human feces was introduced into the reactor vessels and stabilized over 2-wk using a culture medium. This stabilization period was followed by a 2-wk control period during which the microbiota was monitored. The microbiota was then subjected to a 4-wk treatment period by adding 5 mL of sterile peptone water with L. acidophilus CRL1014 at the concentration of 108 CFU/mL to vessel one (the stomach compartment). Plate counts, Denaturing Gradient Gel Electrophoresis (DGGE), short-chain fatty acid (SCFA) and ammonium analyses were carried out for monitoring of the microbial community from the colon compartments.Results: A significant increase (p < 0.01) in the Lactobacillus spp. and Bifidobacterium spp. populations was observed during the treatment period. The DGGE obtained showed changes in the lactobacilli community from the colon compartments of the SHIME® reactor. The (SCFA) concentration increased (p < 0.01) during the treatment period, due mainly to significant increased levels of acetic, butyric, and propionic acids. However, ammonium concentrations decreased during the same period (p < 0.01).Conclusions: This study showed the beneficial influence of L. acidophilus CRL 1014 on microbial metabolism and lactobacilli community composition for improving human health. © 2013 Sivieri et al.; licensee BioMed Central Ltd.

A comunicação em uma disciplina de Introdução a Estatística: um olhar sob a formação inicial de professores de matemática a distância

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A produção matemática em um ambiente virtual de aprendizagem: o caso da geometria euclidiana espacial

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Uma abordagem pedagógica baseada na análise de modelos para alunos de biologia: qual o papel do software?

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Prebiotic Effect of Fructooligosaccharide in the Simulator of the Human Intestinal Microbial Ecosystem (SHIME (R) Model)

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