Search results for "Mathematica"
showing 10 items of 7971 documents
Gradation of Fuzzy Preconcept Lattices
2021
Noticing certain limitations of concept lattices in the fuzzy context, especially in view of their practical applications, in this paper, we propose a more general approach based on what we call graded fuzzy preconcept lattices. We believe that this approach is more adequate for dealing with fuzzy information then the one based on fuzzy concept lattices. We consider two possible gradation methods of fuzzy preconcept lattice—an inner one, called D-gradation and an outer one, called M-gradation, study their properties, and illustrate by a series of examples, in particular, of practical nature.
MAD+. Introducing Misconceptions in the Temporal Analysis of the Mathematical Modelling Process of a Fermi Problem
2021
This work describes how the combination of the mistakes committed by a group of pre-service teachers when solving a Fermi problem, with the representation of the temporal analysis of their resolutions, can offer more in-depth information about their conceptual misconceptions regarding mathematical and modelling concepts. The combined representation allows knowing when mistakes occur and provides a powerful tool for instructors to adapt the teaching–learning processes of mathematics at all levels of education. Our study is based on a recent categorisation of students’ mistakes, together with the creation of a new representation tool, called MAD+, that can combine all this information. The ma…
Algorithmics for the Life Sciences
2013
The life sciences, in particular molecular biology and medicine, have wit- nessed fundamental progress since the discovery of the “the Double Helix”. A rele- vant part of such an incredible advancement in knowledge has been possible thanks to synergies with the mathematical sciences, on the one hand, and computer science, on the other. Here we review some of the most relevant aspects of this cooperation focusing on contributions given by the design, analysis and engineering of fast al- gorithms for the life sciences.
Conjunction, Disjunction and Iterated Conditioning of Conditional Events
2013
Starting from a recent paper by S. Kaufmann, we introduce a notion of conjunction of two conditional events and then we analyze it in the setting of coherence. We give a representation of the conjoined conditional and we show that this new object is a conditional random quantity, whose set of possible values normally contains the probabilities assessed for the two conditional events. We examine some cases of logical dependencies, where the conjunction is a conditional event; moreover, we give the lower and upper bounds on the conjunction. We also examine an apparent paradox concerning stochastic independence which can actually be explained in terms of uncorrelation. We briefly introduce the…
Diagrammatic approach to cellular automata and the emergence of form with inner structure
2018
We present a diagrammatic method to build up sophisticated cellular automata (CAs) as models of complex physical systems. The diagrams complement the mathematical approach to CA modeling, whose details are also presented here, and allow CAs in rule space to be classified according to their hierarchy of layers. Since the method is valid for any discrete operator and only depends on the alphabet size, the resulting conclusions, of general validity, apply to CAs in any dimension or order in time, arbitrary neighborhood ranges and topology. We provide several examples of the method, illustrating how it can be applied to the mathematical modeling of the emergence of order out of disorder. Specif…
New Representations for Multidimensional Functions Based on Kolmogorov Superposition Theorem. Applications on Image Processing
2012
Mastering the sorting of the data in signal (nD) can lead to multiple applications like new compression, transmission, watermarking, encryption methods and even new processing methods for image. Some authors in the past decades have proposed to use these approaches for image compression, indexing, median filtering, mathematical morphology, encryption. A mathematical rigorous way for doing such a study has been introduced by Andrei Nikolaievitch Kolmogorov (1903-1987) in 1957 and recent results have provided constructive ways and practical algorithms for implementing the Kolmogorov theorem. We propose in this paper to present those algorithms and some preliminary results obtained by our team…
On essential spectra of operator-matrices and their Feshbach maps
2004
Abstract A connection between the essential spectrum of certain operator-matrices and essential spectra of the corresponding “Feshbach maps” is discussed and applied to some concrete rational operator-valued functions.
Quantum Field Theory
2018
Quantum field theory (QFT) shares many of its philosophical problems with quantum mechanics. This applies in particular to the quantum measurement process and the connected interpretive problems, to which QFT contributes hardly any new aspects, let alone solutions. The question as to how the objects described by the theory are spatially embedded was already also discussed for quantum mechanics. However, the new mathematical structure of QFT promises new answers, which renders the spatiotemporal interpretation of QFT the pivotal question. In this chapter, we sketch the mathematical characteristics of QFT and show that a particle as well as a field interpretation breaks down.
Pseudo-Bosons, So Far
2011
In the past years several extensions of the canonical commutation relations have been proposed by different people in different contexts and some interesting physics and mathematics have been deduced. Here, we review some recent results on the so-called {\em pseudo-bosons}. They arise from a special deformation of the canonical commutation relation $[a,a^\dagger]=\1$, which is replaced by $[a,b]=\1$, with $b$ not necessarily equal to $a^\dagger$. We start discussing some of their mathematical properties and then we discuss several examples.
Multi-rogue waves solutions: from the NLS to the KP-I equation
2013
Our discovery of multi-rogue wave (MRW) solutions in 2010 completely changed the viewpoint on the links between the theory of rogue waves and integrable systems, and helped explain many phenomena which were never understood before. It is enough to mention the famous Three Sister waves observed in oceans, the creation of a regular approach to studying higher Peregrine breathers, and the new understanding of 2 + 1 dimensional rogue waves via the NLS-KP correspondence. This article continues the study of the MRW solutions of the NLS equation and their links with the KP-I equation started in a previous series of articles (Dubard et al 2010 Eur. Phys. J. 185 247–58, Dubard and Matveev 2011 Natur…