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Polynomials: special polynomials and number-theoretical applications / Ákos Pintér (2021)  

Public Titre : Polynomials: special polynomials and number-theoretical applications Type de document : Monographie Auteurs : Ákos Pintér, Éditeur scientifique Editeur : Bâle [Suisse] : Multidisciplinary Digital Publishing Institute MDPI Année de publication : 2021 Importance : 154 p. Format : 17 x 25 cm ISBN/ISSN/EAN : 978-3-0365-0819-1 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Mathématique [Termes IGN] distribution binomiale [Termes IGN] équation polynomiale [Termes IGN] fonction de base radiale [Termes IGN] formule d'Euler [Termes IGN] interpolation polynomiale [Termes IGN] théorème de Bernstein [Termes IGN] trigonométrie Résumé : (éditeur) Polynomials play a crucial role in many areas of mathematics including algebra, analysis, number theory, and probability theory. They also appear in physics, chemistry, and economics. Especially extensively studied are certain infinite families of polynomials. Here, we only mention some examples: Bernoulli, Euler, Gegenbauer, trigonometric, and orthogonal polynomials and their generalizations. There are several approaches to these classical mathematical objects. This Special Issue presents nine high quality research papers by leading researchers in this field. I hope the reading of this work will be useful for the new generation of mathematicians and for experienced researchers as well. Note de contenu : 1- Two variables Shivley’s matrix polynomial 2- Some symmetric identities for degenerate Carlitz-type (p, q)-Euler numbers and polynomials 3- Symmetric identities for Carlitz-type higher-order degenerate (p, q)-Euler numbers and polynomials 4- Durrmeyer-type generalization of parametric Bernstein operators 5- A collocation method using radial polynomials for solving partial differential equations 6- On the decomposability of the linear combinations of Euler polynomials with odd degrees 7- Structure of approximate roots based on symmetric properties of (p, q)-cosine and (p, q)-sine Bernoulli polynomials 8- Explicit properties of q-cosine and q-sine Euler polynomials containing symmetric structures 9- Certain results for the twice-iterated 2D q-Appell polynomials Numéro de notice : 28632 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Recueil / ouvrage collectif DOI : 10.3390/books978-3-0365-0819-1 En ligne : https://doi.org/10.3390/books978-3-0365-0819-1 Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=99635

A novel nonlinear hyperspectral unmixing approach for images of oil spills at sea / Ying Li in International Journal of Remote Sensing IJRS, vol 41 n° 12 (20 - 30 March 2020)  

Public [article]  inInternational Journal of Remote Sensing IJRS > vol 41 n° 12 (20 - 30 March 2020) . - pp 4684 - 4701 Titre : A novel nonlinear hyperspectral unmixing approach for images of oil spills at sea Type de document : Article/Communication Auteurs : Ying Li, Auteur ; Huimin Lu, Auteur ; Zhenduo Zhang, Auteur ; et al., Auteur Année de publication : 2020 Article en page(s) : pp 4684 - 4701 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Traitement d'image optique [Termes IGN] analyse des mélanges spectraux [Termes IGN] équation polynomiale [Termes IGN] hydrocarbure [Termes IGN] image hyperspectrale [Termes IGN] marée noire [Termes IGN] modèle non linéaire [Termes IGN] pollution des mers [Termes IGN] trigonométrie Résumé : (auteur) Hyperspectral remote sensing is currently being used to detect and monitor marine oil spills that cause damage to the environment. However, nonlinear interactions of oil and water make it difficult to extract their fractional abundances from the spectral response. Improving the modelling of nonlinear hyperspectral mixtures, which is required for a thorough and reliable characterization of the materials in an image, remains a challenging yet fundamental task. This study proposes a new model that combines polynomial and trigonometric systems to understand the nonlinear effects of oil and water spectral response. Although the model is nonlinear, unmixing is performed by solving a linear problem, thus allowing fast computation. Compared to classic polynomial models, the details of nonlinear interactions are better expressed and quantified, and the reconstruction accuracy and endmember abundance estimation are improved for both synthetic and real datasets. Both the polynomial and trigonometric parts of the model play important roles in characterizing nonlinearities, with statistically linear dependence areas covering more than 90% and 30%, respectively, in oil spill images sampled after the Deepwater Horizon explosion. Analysis of the experimental results suggests that the proposed model provides an efficient and accurate unmixing method that can be used to help design oil spill response plans. Numéro de notice : A2020-452 Affiliation des auteurs : non IGN Thématique : IMAGERIE Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1080/01431161.2020.1723179 Date de publication en ligne : 27/02/2020 En ligne : https://doi.org/10.1080/01431161.2020.1723179 Format de la ressource électronique : url article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=95540 [article]

Introduction to scientific programming with Python / Joakim Sundnes (2020)  

Public Titre : Introduction to scientific programming with Python Type de document : Guide/Manuel Auteurs : Joakim Sundnes, Auteur Editeur : Springer Nature Année de publication : 2020 Importance : 157 p. Format : 16 x 24 cm ISBN/ISSN/EAN : 978-3-030-50356-7 Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Langages informatiques [Termes IGN] équation polynomiale [Termes IGN] interface graphique [Termes IGN] programmation adaptée à l'objet [Termes IGN] Python (langage de programmation) Résumé : (éditeur) This open access book offers an initial introduction to programming for scientific and computational applications using the Python programming language. The presentation style is compact and example-based, making it suitable for students and researchers with little or no prior experience in programming. The book uses relevant examples from mathematics and the natural sciences to present programming as a practical toolbox that can quickly enable readers to write their own programs for data processing and mathematical modeling. These tools include file reading, plotting, simple text analysis, and using NumPy for numerical computations, which are fundamental building blocks of all programs in data science and computational science. At the same time, readers are introduced to the fundamental concepts of programming, including variables, functions, loops, classes, and object-oriented programming. Accordingly, the book provides a sound basis for further computer science and programming studies. Note de contenu : 1- Getting started with Python 2- Computing with formulas 3- Loops and lists 4- Functions and branching 5- User input and error handling 6- Arrays and plotting 7- Dictionaries and strings 8- Classes 9- Object-oriented programming Numéro de notice : 28555 Affiliation des auteurs : non IGN Thématique : GEOMATIQUE/INFORMATIQUE Nature : Manuel informatique DOI : 10.1007/978-3-030-50356-7 En ligne : https://doi.org/10.1007/978-3-030-50356-7 Format de la ressource électronique : url Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=97444

Polynomials / Cheon-Seoung Ryoo (2020)  

Public Titre : Polynomials Type de document : Guide/Manuel Auteurs : Cheon-Seoung Ryoo, Éditeur scientifique Editeur : Bâle [Suisse] : Multidisciplinary Digital Publishing Institute MDPI Année de publication : 2020 Importance : 152 p. Format : 16 x 24 cm ISBN/ISSN/EAN : 978-3-03943-315-5 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Mathématique [Termes IGN] équation différentielle [Termes IGN] équation polynomiale [Termes IGN] formule d'Euler [Termes IGN] interpolation polynomiale [Termes IGN] Ploynôme [Termes IGN] polynôme d'Hermite [Termes IGN] transformation polynomiale Résumé : (éditeur) Polynomial and its applications are well known for their proven properties and excellent applicability in interdisciplinary fields of science. Until now, research on polynomial and its applications has been done in mathematics, applied mathematics, and sciences. This book is based on recent results in all areas related to polynomial and its applications. This book provides an overview of the current research in the field of polynomials and its applications. The following papers have been published in this volume: ‘A Parametric Kind of the Degenerate Fubini Numbers and Polynomials’; ‘On 2-Variables Konhauser Matrix Polynomials and Their Fractional Integrals’; ‘Fractional Supersymmetric Hermite Polynomials’; ‘Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation’; ‘Iterating the Sum of Möbius Divisor Function and Euler Totient Function’; ‘Differential Equations Arising from the Generating Function of the (r, β)-Bell Polynomials and Distribution of Zeros of Equations’; ‘Truncated Fubini Polynomials’; ‘On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five Weights’; ‘Ground State Solutions for Fractional Choquard Equations with Potential Vanishing at Infinity’; ‘Some Identities on Degenerate Bernstein and Degenerate Euler Polynomials’; ‘Some Identities Involving Hermite Kampé de Fériet Polynomials Arising from Differential Equations and Location of Their Zeros.’ Note de contenu : 1- A parametric kind of the degenerate fubini numbers and polynomials 2- On 2-variables konhauser matrix polynomials and their fractional integrals 3- Fractional supersymmetric hermite polynomials 4- Rational approximation for solving an implicitly given colebrook flow friction equation 5- Iterating the sum of mobius divisor function and Euler Totient function 6- Differential equations arising from the generating function of the (r, β)-bell polynomials and distribution of zeros of equations 7- Truncated Fubini polynomials 8- On positive quadratic hyponormality of a unilateral weighted shift with recursively generated by five weights 9- Ground state solutions for fractional Choquard equations with potential vanishing at infinity 10- Some identities on degenerate Bernstein and degenerate Euler polynomials 11- Some identities involving Hermite Kampé de Fériet polynomials arising from differential equations and location of their zeros Numéro de notice : 28496 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Recueil / ouvrage collectif DOI : 10.3390/books978-3-03943-315-5 En ligne : https://doi.org/10.3390/books978-3-03943-315-5 Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=99245

Extension of satellite altimetry Jason-2 sea level anomalies towards the Red Sea coast using polynomial harmonic techniques / A. M. Taqi in Marine geodesy, vol 40 n° 5 (September 2017)  

Public [article]  inMarine geodesy > vol 40 n° 5 (September 2017) . - pp 315 - 328 Titre : Extension of satellite altimetry Jason-2 sea level anomalies towards the Red Sea coast using polynomial harmonic techniques Type de document : Article/Communication Auteurs : A. M. Taqi, Auteur ; A. M. Al-Subhi, Auteur ; M. A. Alsaafani, Auteur Année de publication : 2017 Article en page(s) : pp 315 - 328 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Termes IGN] altimétrie satellitaire par radar [Termes IGN] AVISO [Termes IGN] données altimétriques [Termes IGN] données Jason [Termes IGN] équation polynomiale [Termes IGN] fonction harmonique [Termes IGN] littoral [Termes IGN] niveau de la mer [Termes IGN] Rouge, mer [Termes IGN] série de Fourier [Vedettes matières IGN] Altimétrie Résumé : (Auteur) Satellite altimetry data are facing big challenges near the coasts. These challenges arise due to the fundamental difficulties of correction and land contamination in the foot print, which result in rejection of these data near the coast. Several studies have been carried out to extend these data towards the coast. Over the Red Sea, altimetry data consist of gaps, which extend to about 30–50 km from the coast. Two methods are used for processing and extending Jason-2 satellite altimetry sea level anomalies (SLAs) towards the Red Sea coast; Fourier Series Model (FSM), and the polynomial sum of sine model (SSM). FSM model technique uses Fourier series and statistical analysis reflects strong relationship with both the observation and AVISO data, with strong and positive correlation. The second prediction technique, SSM model, depends on the polynomial sum of sine, and does not reflect any relationship with the observations and AVISO data close to the coast and the correlation coefficient (CC) is weak and negative. The FSM model output results in SLA data significantly better and more accurate than the SSM model output. Numéro de notice : A2017-668 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article DOI : 10.1080/01490419.2017.1333549 En ligne : https://doi.org/10.1080/01490419.2017.1333549 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=87143 [article]

Introduction to partial differential equations / Peter J. Olver (2014)  

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3D shape histograms for similarity search and classification in spatial databases / M. Ankerst (20/07/1999)  

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Géométrie, 2. Tome 2 / Marcel Berger (1990)

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Matrices / Frank Ayres Jr (1981)

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Eléments de mathématique. Fascicule 24, Livre 2 Algèbre, chapître 9 Formes sesquilinéaires et formes quadratiques / Nicolas Bourbaki (1973)  

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Approximation quadratique du potentiel réel par un potentiel harmonique, à l'extérieur du géoïde : corrections correspondantes / Henri Marcel Dufour (1972)

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Note sur le relèvement d'un réseau de triangles sans échelle déterminée sur des points géodésiques (procédé des centres de similitude) / François Reignier (1956)

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