Differential calculus and integration of generalized functions over membranes

In this paper we continue the development of the differential calculus started in Aragona et al. (Monatsh. Math. 144: 13-29, 2005). Guided by the so-called sharp topology and the interpretation of Colombeau generalized functions as point functions on generalized point sets, we introduce the notion of membranes and extend the definition of integrals, given in Aragona et al. (Monatsh. Math. 144: 13-29, 2005), to integrals defined on membranes. We use this to prove a generalized version of the Cauchy formula and to obtain the Goursat Theorem for generalized holomorphic functions. A number of results from classical differential and integral calculus, like the inverse and implicit function theorems and Green's theorem, are transferred to the generalized setting. Further, we indicate that solution formulas for transport and wave equations with generalized initial data can be obtained as well.

The lexical approach: collocability, fluency and implications for teaching

[EN] [EN] The lexical approach identifies lexis as the basis of language and focuses on the principle that language consists of grammaticalised lexis. in second language acquisition, over the past few years, this approach has generated great interest as an alternative to traditional grammar-based teaching methods. From a psycholinguistic point of view, the lexical approach consists of the capacity of understanding and producing lexical phrases as non-analysed entities (chunks). A growing body of literature concerning spoken fluency is in favour of integrating automaticity and formulaic language units into classroom practice. in line with the latest theories on SlA, we recommend the inclusion of a language awareness component as an integral part of this approach. The purpose is to induce what Schmidt (1990) calls noticing , i.e., registering forms in the input so as to store themin memory. This paper, which is in keeping with the interuniversity Research Project “Evidentialityin a multidisciplinary corpus of English research papers” of the University of las Palmas de Gran Canaria, provides a theoretical overview on theresearch of this approach taking into account both the methodological foundationson the subject and its pedagogical implications for SLA

Examples on the integral calculus /

Mode of access: Internet.

Introduction to nonlinear differential and integral equations.

First published in 1960 by the U. S. Atomic Energy Commission.

Integral calculus,

Mode of access: Internet.

Matrix-Variate Statistical Distributions and Fractional Calculus

MSC 2010: 15A15, 15A52, 33C60, 33E12, 44A20, 62E15 Dedicated to Professor R. Gorenflo on the occasion of his 80th birthday

Trajetórias de vida : lembranças, caminhos e constituições dos saberes docentes de professores de Educação Física = Paths and trajectories of life : memories, paths and establishment of teaching knowledge of Physical Education Professors

Universidade Estadual de Campinas . Faculdade de Educação Física

Becoming a teacher: student teachers´ experiences and perceptions about teaching practice

In an attempt to build a more comprehensive and holistic understanding of the complexity, dynamics and idiosyncrasies involved in becoming a teacher, this study focussed on the experiences of 295 student teachers. Their feelings, cognitions and perceptions regarding teaching practice were analysed using the short version of the Inventory of Experiences and Perceptions of the Teaching Practice. Results emphasise some of the difficulties experienced during this period (e.g., stress, sense of weariness and ‘vulnerability’), as well the positive perceptions of these student teachers regarding their growing knowledge and skilfulness, as well as their sense of efficacy, flexibility and spontaneity in their performance and interactions. Their perception of their accomplishments in achieving reasonable levels of acceptance and recognition within the school community and their positive evaluation of the guidance and support provided by their supervisors are also emphasised. Differences were found – in terms of gender and graduate course background – in the way these student teachers experienced some aspects of teaching practice.

A Review of Definitions for Fractional Derivatives and Integral

This paper presents a review of definitions of fractional order derivatives and integrals that appear in mathematics, physics, and engineering.

Pseudo Phase Plane and Fractional Calculus Modelling of Western Global Economic Downturn

This paper applies Pseudo Phase Plane (PPP) and Fractional Calculus (FC) mathematical tools for modeling world economies. A challenging global rivalry among the largest international economies began in the early 1970s, when the post-war prosperity declined. It went on, up to now. If some worrying threatens may exist actually in terms of possible ambitious military aggression, invasion, or hegemony, countries’ PPP relative positions can tell something on the current global peaceful equilibrium. A global political downturn of the USA on global hegemony in favor of Asian partners is possible, but can still be not accomplished in the next decades. If the 1973 oil chock has represented the beginning of a long-run recession, the PPP analysis of the last four decades (1972–2012) does not conclude for other partners’ global dominance (Russian, Brazil, Japan, and Germany) in reaching high degrees of similarity with the most developed world countries. The synergies of the proposed mathematical tools lead to a better understanding of the dynamics underlying world economies and point towards the estimation of future states based on the memory of each time series.

Analysis of Natural and Artificial Phenomena Using Signal Processing and Fractional Calculus

In this paper we study several natural and man-made complex phenomena in the perspective of dynamical systems. For each class of phenomena, the system outputs are time-series records obtained in identical conditions. The time-series are viewed as manifestations of the system behavior and are processed for analyzing the system dynamics. First, we use the Fourier transform to process the data and we approximate the amplitude spectra by means of power law functions. We interpret the power law parameters as a phenomenological signature of the system dynamics. Second, we adopt the techniques of non-hierarchical clustering and multidimensional scaling to visualize hidden relationships between the complex phenomena. Third, we propose a vector field based analogy to interpret the patterns unveiled by the PL parameters.

Da modelação matemática à simulação computacional: a experimentação matemática no ensino

Tese de Doutoramento em Ciências (área de especialização em Matemática).

Da modelação matemática à simulação computacional: a experimentação matemática no ensino

Tese de Doutoramento em Ciências (área de especialização em Matemática).

L'aportació de Tomàs Cerdà en la introducció del càlcul diferencial i integral a l'Espanya del segle XVIII

El desenvolupament del càlcul diferencial i integral com a disciplina científica a Europa durant el segle XVIII no és un tema nou. Però s’ha acostumat a enfocar la visió d’aquesta formació molt sovint des del “centre” i a partir de les grans figures com Isaac Newton o Gottfried Wilhelm Leibniz. En el present treball el protagonista potser, per a molts, no és una figura de primera línia; Tomàs Cerdà, és un ensenyant a Barcelona i a Madrid durant la segona meitat del segle XVIII, que “tradueix” al castellà autors anglesos, però que amb la seva pràctica està realment introduint el nou càlcul a Espanya i donant, de fet, una orientació d’aquesta nova disciplina als seus deixebles. El com i per què Cerdà decideix quin serà el seu guia en la introducció del càlcul diferencial i integral i quines seran les seves pròpies aportacions en aquesta labor seran els temes centrals del nostre treball. La nostra tasca ha anat, així doncs, a entendre millor, el procés de divulgació del coneixement científic, veient-lo en tot moment com formant part activa del mateix procés de construcció d’aquest coneixement.

Bridging the Gap: establishing the necessary infrastructure and knowledge for teaching and research in neuroscience in Africa.

Advances in neuroscience research over the last few decades have increased our understanding of how individual neurons acquire their specific properties and assemble into complex circuits, and how these circuits are affected in disease. One of the important motives driving neuroscience research is the development of new scientific techniques and interdisciplinary cooperation. Compared to developed countries, many countries on the African continent are confronted with poor facilities, lack of funding or career development programs for neuroscientists, all of which deter young scientists from taking up neuroscience as a career choice. This article highlights some steps that are being taken to promote neuroscience education and research in Africa.