Search results for " Geometry"
showing 10 items of 2294 documents
Generalized wave propagation problems and discrete exterior calculus
2018
We introduce a general class of second-order boundary value problems unifying application areas such as acoustics, electromagnetism, elastodynamics, quantum mechanics, and so on, into a single framework. This also enables us to solve wave propagation problems very efficiently with a single software system. The solution method precisely follows the conservation laws in finite-dimensional systems, whereas the constitutive relations are imposed approximately. We employ discrete exterior calculus for the spatial discretization, use natural crystal structures for three-dimensional meshing, and derive a “discrete Hodge” adapted to harmonic wave. The numerical experiments indicate that the cumulat…
Topological canal foliations
2019
Regular canal surfaces of $\mathbb{R}^3$ or $\mathbb{S}^3$ admit foliations by circles: the characteristic circles of the envelope. In order to build a foliation of $\mathbb{S}^3$ with leaves being canal surfaces, one has to relax the condition “canal” a little (“weak canal condition”) in order to accept isolated umbilics. Here, we define a topological condition which generalizes this “weak canal” condition imposed on leaves, and classify the foliations of compact orientable 3-manifolds we can obtain this way.
Introduction to Mathematical Logic, Edition 2021
2021
Textbook for students in mathematical logic. First order languages. Axioms of constructive and classical logic. Proving formulas in propositional and predicate logic. Glivenko's theorem and constructive embedding. Axiom independence. Interpretations, models and completeness theorems. Normal forms. Tableaux and resolution methods. Herbrand's theorem. Sections 1, 2, 3 represent an extended translation of the corresponding chapters of the book: V. Detlovs, Elements of Mathematical Logic, Riga, University of Latvia, 1964, 252 pp. (in Latvian).
Sur la réductibilité des graphes de contraintes géométriques
2017
La modélisation géométrique par contraintes dont les applications intéressent des communautés issues de divers domaines tels l'ingénierie mécanique, la conception assistée par ordinateur, le calcul symbolique ou la chimie moléculaire est maintenant intégré dans les outils standards de modélisation. Dans cette discipline une forme géométrique est spécifiée par les relations que doivent vérifier les composants de cette forme au lieu de spécifier explicitement ces composants. Le but de la résolution est de déduire la forme répondant à toutes ces contraintes. Diverses méthodes ont été proposées pour résoudre ce problème. Nous nous intéresserons spécifiquement aux méthodes dites graphiques ou ba…
Formation, Structural Characterization, and Calculated NMR Chemical Shifts of Selenium-Nitrogen Compounds from SeCl4 and ArNHLi (Ar = supermesityl, m…
2004
Supermesityl selenium diimide [Se{N(C6H2tBu3-2, 4, 6)}2; Se{N(mes*)}2] can be prepared in a good yield from the reaction of SeCl4 and (mes*)NHLi. The molecule adopts an unprecedented anti, anti-conformation, as deduced by DFT calculations at PBE0/TZVP level of theory and supported by 77Se NMR spectroscopy and a crystal structure determination. An analogous reaction involving (C6H2Me3-2, 4, 6)NHLi [(mes)NHLi] unexpectedly lead to the reduction of selenium and afforded the selenium diamide Se{NH(mes)}2 that was characterized by X-ray crystallography and 77Se NMR spectroscopy. The Se-N bonds of 1.847(3) and 1.852(3) A show normal single bond lengths. The <NSeN bond angle of 109.9(1)° also indi…
I poligoni stellati: origini storiche ed implicazioni didattiche
2019
The genesis of mathematical concepts in the evolutionary line of human thought in the long story and the genesis in individual optics possess evident analogies. Starting from this assumption, we describe an activity presented to 15-year-old students; the aim was to consolidate fundamental concepts of Euclidean geometry related to regular polygons. The experimentation has used a didactic approach based on the historical evolution of the formal definition of regular star polygon through the centuries. The activity and the results obtained in terms of internalization of the concepts in the students are showed.
On arithmetic sums of Ahlfors-regular sets
2021
Let $A,B \subset \mathbb{R}$ be closed Ahlfors-regular sets with dimensions $\dim_{\mathrm{H}} A =: \alpha$ and $\dim_{\mathrm{H}} B =: \beta$. I prove that $$\dim_{\mathrm{H}} [A + \theta B] \geq \alpha + \beta \cdot \tfrac{1 - \alpha}{2 - \alpha}$$ for all $\theta \in \mathbb{R} \, \setminus \, E$, where $\dim_{\mathrm{H}} E = 0$.
A multifractal approach of central place theory for sustainable planning
2013
International audience
The Poisson Point Process
2020
Poisson point processes can be used as a cornerstone in the construction of very different stochastic objects such as, for example, infinitely divisible distributions, Markov processes with complex dynamics, objects of stochastic geometry and so forth.
Complex objects classified by morphological shape analysis and elliptical Fourier descriptors
2005
This chapter deals with the classification of complex objects by morphological shape analysis and elliptical Fourier descriptors. An unsupervised method has been proposed to identify components with specific shapes by a simple edge detector and to classify them via the description of their contours. A particular application has been arranged in order to evaluate the goodness of this approach when discriminating between normal and pathological human megakaryocytes. Alterations in these cells can occur in many pathological processes and in such cases the pattern, size and shape of the cytoplasm and/or of the nucleus are extremely varied.