26 research outputs found

    Systems of Discrete Differential Equations, Constructive Algebraicity of the Solutions

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    In this article, we study systems of n≥1n \geq 1, not necessarily linear, discrete differential equations (DDEs) of order k≥1k \geq 1 with one catalytic variable. We provide a constructive and elementary proof of algebraicity of the solutions of such equations. This part of the present article can be seen as a generalization of the pioneering work by Bousquet-M\'elou and Jehanne~(2006) who settled down the case n=1n=1. Moreover, we obtain effective bounds for the algebraicity degrees of the solutions and provide an algorithm for computing annihilating polynomials of the algebraic series. Finally, we carry out a first analysis in the direction of effectivity for solving systems of DDEs in view of practical applications

    The Fifteenth Marcel Grossmann Meeting

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    The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity

    ECOS 2012

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    The 8-volume set contains the Proceedings of the 25th ECOS 2012 International Conference, Perugia, Italy, June 26th to June 29th, 2012. ECOS is an acronym for Efficiency, Cost, Optimization and Simulation (of energy conversion systems and processes), summarizing the topics covered in ECOS: Thermodynamics, Heat and Mass Transfer, Exergy and Second Law Analysis, Process Integration and Heat Exchanger Networks, Fluid Dynamics and Power Plant Components, Fuel Cells, Simulation of Energy Conversion Systems, Renewable Energies, Thermo-Economic Analysis and Optimisation, Combustion, Chemical Reactors, Carbon Capture and Sequestration, Building/Urban/Complex Energy Systems, Water Desalination and Use of Water Resources, Energy Systems- Environmental and Sustainability Issues, System Operation/ Control/Diagnosis and Prognosis, Industrial Ecology

    Collected Papers (on Neutrosophic Theory and Its Applications in Algebra), Volume IX

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    This ninth volume of Collected Papers includes 87 papers comprising 982 pages on Neutrosophic Theory and its applications in Algebra, written between 2014-2022 by the author alone or in collaboration with the following 81 co-authors (alphabetically ordered) from 19 countries: E.O. Adeleke, A.A.A. Agboola, Ahmed B. Al-Nafee, Ahmed Mostafa Khalil, Akbar Rezaei, S.A. Akinleye, Ali Hassan, Mumtaz Ali, Rajab Ali Borzooei , Assia Bakali, Cenap Özel, Victor Christianto, Chunxin Bo, Rakhal Das, Bijan Davvaz, R. Dhavaseelan, B. Elavarasan, Fahad Alsharari, T. Gharibah, Hina Gulzar, Hashem Bordbar, Le Hoang Son, Emmanuel Ilojide, Tèmítópé Gbóláhàn Jaíyéolá, M. Karthika, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Huma Khan, Madad Khan, Mohsin Khan, Hee Sik Kim, Seon Jeong Kim, Valeri Kromov, R. M. Latif, Madeleine Al-Tahan, Mehmat Ali Ozturk, Minghao Hu, S. Mirvakili, Mohammad Abobala, Mohammad Hamidi, Mohammed Abdel-Sattar, Mohammed A. Al Shumrani, Mohamed Talea, Muhammad Akram, Muhammad Aslam, Muhammad Aslam Malik, Muhammad Gulistan, Muhammad Shabir, G. Muhiuddin, Memudu Olaposi Olatinwo, Osman Anis, Choonkil Park, M. Parimala, Ping Li, K. Porselvi, D. Preethi, S. Rajareega, N. Rajesh, Udhayakumar Ramalingam, Riad K. Al-Hamido, Yaser Saber, Arsham Borumand Saeid, Saeid Jafari, Said Broumi, A.A. Salama, Ganeshsree Selvachandran, Songtao Shao, Seok-Zun Song, Tahsin Oner, M. Mohseni Takallo, Binod Chandra Tripathy, Tugce Katican, J. Vimala, Xiaohong Zhang, Xiaoyan Mao, Xiaoying Wu, Xingliang Liang, Xin Zhou, Yingcang Ma, Young Bae Jun, Juanjuan Zhang

    Generalized averaged Gaussian quadrature and applications

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    A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

    MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

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    Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

    Signal processing with Fourier analysis, novel algorithms and applications

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    Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions, also analogously known as sinusoidal modeling. The original idea of Fourier had a profound impact on mathematical analysis, physics and engineering because it diagonalizes time-invariant convolution operators. In the past signal processing was a topic that stayed almost exclusively in electrical engineering, where only the experts could cancel noise, compress and reconstruct signals. Nowadays it is almost ubiquitous, as everyone now deals with modern digital signals. Medical imaging, wireless communications and power systems of the future will experience more data processing conditions and wider range of applications requirements than the systems of today. Such systems will require more powerful, efficient and flexible signal processing algorithms that are well designed to handle such needs. No matter how advanced our hardware technology becomes we will still need intelligent and efficient algorithms to address the growing demands in signal processing. In this thesis, we investigate novel techniques to solve a suite of four fundamental problems in signal processing that have a wide range of applications. The relevant equations, literature of signal processing applications, analysis and final numerical algorithms/methods to solve them using Fourier analysis are discussed for different applications in the electrical engineering/computer science. The first four chapters cover the following topics of central importance in the field of signal processing: • Fast Phasor Estimation using Adaptive Signal Processing (Chapter 2) • Frequency Estimation from Nonuniform Samples (Chapter 3) • 2D Polar and 3D Spherical Polar Nonuniform Discrete Fourier Transform (Chapter 4) • Robust 3D registration using Spherical Polar Discrete Fourier Transform and Spherical Harmonics (Chapter 5) Even though each of these four methods discussed may seem completely disparate, the underlying motivation for more efficient processing by exploiting the Fourier domain signal structure remains the same. The main contribution of this thesis is the innovation in the analysis, synthesis, discretization of certain well known problems like phasor estimation, frequency estimation, computations of a particular non-uniform Fourier transform and signal registration on the transformed domain. We conduct propositions and evaluations of certain applications relevant algorithms such as, frequency estimation algorithm using non-uniform sampling, polar and spherical polar Fourier transform. The techniques proposed are also useful in the field of computer vision and medical imaging. From a practical perspective, the proposed algorithms are shown to improve the existing solutions in the respective fields where they are applied/evaluated. The formulation and final proposition is shown to have a variety of benefits. Future work with potentials in medical imaging, directional wavelets, volume rendering, video/3D object classifications, high dimensional registration are also discussed in the final chapter. Finally, in the spirit of reproducible research we release the implementation of these algorithms to the public using Github

    Méthodes algébriques pour l'analyse de sécurité des implantations d'algorithmes cryptographiques

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    The 10th Hilbert problem, which consists in finding integer solutions to polynomial equations is a crucial problem in cryptanalysis, which has been proven to be undecidable. However, Coppersmith published in 1996 a method based on lattice reduction, which allows to efficiently find all small solutions to some polynomial equations. Many applications of this method have risen in public key cryptanalysis, especially when the cryptosystem is executed on embedded systems and part of the secret key is revealed through physical attacks performed on the device. In this context, we propose in this thesis a physical attack on the RSA signature scheme when the CRT mode is used, where an application of Coppersmith's method allows to complete the information previously obtained by the physical attack. We also propose a new deterministic algorithm based on Coppersmith's method for factoring integers of the form N=p^{r}q^{s} in polynomial time, under the condition that r and/or s are sufficiently large. Finally, if the applications of Coppersmith's method are numerous, in practice, since the lattices to be reduced are huge, the small solutions can only be recovered until a bound which is smaller than the enounced theoretical bound. Thus, another contribution of this thesis lies in the proposition of two methods which allow to speed up the execution time of Coppersmith's algorithm. When both speedups are combined, the new algorithm performs hundreds of times faster for typical parameters, which allows to reach the theoretical bound in many cases.Le 10ème problème de Hilbert, consistant à trouver les solutions entières d'équations polynomiales est un problème crucial en cryptanalyse. Si ce dernier a été prouvé indécidable, Coppersmith publia en 1996 une méthode basée sur la réduction de réseaux permettant de trouver efficacement l'ensemble des petites solutions de certaines équations polynomiales. De nombreuses applications de cette méthode ont vu le jour dans le domaine de la cryptanalyse à clé publique, notamment lorsque le cryptosystème est exécuté sur un système embarqué et qu'une partie de la clé secrète est dévoilée par la réalisation d'attaques physiques sur le dispositif. Dans ce contexte, nous proposons une attaque physique sur le schéma de signature RSA en mode CRT où une application de la méthode de Coppersmith permet de compléter l'information obtenue par l'attaque physique. Nous proposons également un nouvel algorithme déterministe basé sur la méthode de Coppersmith pour factoriser les entiers de la forme N=p^{r}q^{s} en temps polynomial lorsque r ou s sont suffisamment grands. Enfin, si les applications de la méthode de Coppersmith sont nombreuses, en pratique, du fait que les réseaux à réduire soient gigantesques, les petites solutions ne peuvent être retrouvées que jusqu'à une borne qui est plus petite que la borne théorique annoncée. Aussi, une autre contribution de cette thèse consiste en la proposition de deux méthodes permettant une accélération du temps d'exécution de l'algorithme de Coppersmith. Lorsque les deux méthodes sont combinées, le nouvel algorithme s'effectue des centaines de fois plus rapidement pour des paramètres typiques, permettant ainsi dans de nombreux cas d'atteindre la borne théorique
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