Search results for "algebra"

The Bernstein Basis and its applications in solving geometric constraint systems

2012

International audience; This article reviews the properties of Tensorial Bernstein Basis (TBB) and its usage, with interval analysis, for solving systems of nonlinear, univariate or multivariate equations resulting from geometric constraints. TBB are routinely used in computerized geometry for geometric modelling in CAD-CAM, or in computer graphics. They provide sharp enclosures of polynomials and their derivatives. They are used to reduce domains while preserving roots of polynomial systems, to prove that domains do not contain roots, and to make existence and uniqueness tests. They are compatible with standard preconditioning methods and fit linear program- ming techniques. However, curre…

Algebraic thinking and generalization of patterns: a didactical experience with Italian and Chinese students

2009

Processi cognitivi e soluzioni di problemi matematici con studenti italiani e cinesi

2012

To compare cognitive processes adopted by students with different cultures in solving mathematical problems we have to focus on the Math epistemology through a cultural analysis concerning the fundamental elements of the students different cultural traditions and the philosophical, logic and linguistic bases subtended to the mathematical thought and its historical evolution. The paper describes this theoretical framework, emphasizing a possible comparison between different cognitive styles and mathematical problem solutions in the context of arithmetic and Algebraic thought of Italian and Chinese students in multicultural classes.

Ontogenesis and phylogenesis in the passage from arithmetic to algebraic thought

2012

With this work we retrace some of the fundamental historical and historical epistemological steps of the evolution of algebraic thought. Given the accepted parallelism between ontogenesis and phylogenesis we believe such a research to be a useful approach to the interpretation of obstacles and difficulties that students encounter during the acquisition of algebraic thought.

A Teaching proposal for the study of eigenvectors and eigenvalues

2017

[EN] In this work, we present a teaching proposal which emphasizes on visualization and physical applications in the study of eigenvectors and eigenvalues. These concepts are introduced using the notion of the moment of inertia of a rigid body and the GeoGebra software. The proposal was motivated after observing students¿ difficulties when treating eigenvectors and eigenvalues from a geometric point of view. It was designed following a particular sequence of activities with the schema: exploration, introduction of concepts, structuring of knowledge and application, and considering the three worlds of mathematical thinking provided by Tall: embodied, symbolic and formal.

An improved algorithm for thermal dynamic simulation of walls using Z-transform coefficients

2003

The Transfer Function Method (TFM), recommended by American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE), is one of the most modern tools available to solve heat transfer problems in building envelopes and environments. TFM utilises Z-transform to solve the equations system that describes the heat transfer in a multi-layered wall. Due to an analogy with an electric circuit, it is possible to write the equations system in a matrix suitable to be solved by computer. Authors carried out an analysis on an historical building placed in the south of Italy to test the reliability and the quality of the thermal dynamic simulation using TFM. The analysis is performed usi…

Sequential formula translation

1983

The syntax of an algorithmic language such as ALGOL is conveniently described as a sequence of states indicated by an element called cellar. Transitions are controlled by admissible state- s ymbol pairs which may be represented by a transition matrix. This description of syntax furnishes at the same time an extremely simple rule for translating into machine programs statements in the algorithmic language. Sequential treatment, however, is not feasible in the case of certain optimizing processes such as recursive address calculation.

Cover Feature: Total Synthesis of a Partial Structure from Arabinogalactan and Its Application for Allergy Prevention (Chem. Eur. J. 3/2021)

2020

Cover Picture: A Versatile Approach to CF3-Containing 2-Pyrrolidones by Tandem Michael Addition-Cyclization: Exemplification in the Synthesis of Amid…

2015

Identification of a specific type of PD from acoustic emission frequency spectra

2001

The paper presents an attempt to apply spectral analysis tools in processing acoustic emission (AE) pulses generated by partial discharge (FD). The experimental part of the paper describes spark gaps generating four types of PD and specifies parameters of measured acoustic signals and recalls the system used for measurement and analysis of the frequency spectra. Also, a spectral analysis procedure is presented, and frequency-domain descriptors characterizing AE pulses are defined. The results of the analysis are given both as time plots and amplitude and energy density spectra, related to values of the associated descriptors. The spectral analysis results cover AE pulses generated in system…