Relevant bibliographies by topics / Weierstrass method

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  2. Dissertations / Theses
  3. Books
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Academic literature on the topic 'Weierstrass method'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Weierstrass method"

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Marcheva, Plamena I., and Stoil I. Ivanov. "Convergence Analysis of a Modified Weierstrass Method for the Simultaneous Determination of Polynomial Zeros." Symmetry 12, no. 9 (2020): 1408. http://dx.doi.org/10.3390/sym12091408.

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In 2016, Nedzhibov constructed a modification of the Weierstrass method for simultaneous computation of polynomial zeros. In this work, we obtain local and semilocal convergence theorems that improve and complement the previous results about this method. The semilocal result is of significant practical importance because of its computationally verifiable initial condition and error estimate. Numerical experiments to show the applicability of our semilocal theorem are also presented. We finish this study with a theoretical and numerical comparison between the modified Weierstrass method and the
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Goktas, Sertac, Aslı Öner, and Yusuf Gurefe. "The Extended Weierstrass Transformation Method for the Biswas–Arshed Equation with Beta Time Derivative." Fractal and Fractional 8, no. 10 (2024): 593. http://dx.doi.org/10.3390/fractalfract8100593.

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In this article, exact solutions of the Biswas–Arshed equation are obtained using the extended Weierstrass transformation method (EWTM). This method is widely used in solid-state physics, electrodynamics, and mathematical physics, and it yields exact solution functions involving trigonometric, rational trigonometric, Weierstrass elliptic, wave, and rational functions. The process involves expanding the solution functions of an elliptic differential equation into finite series by transforming them into Weierstrass functions. Furthermore, it generates parametric solutions for nonlinear algebraic
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Falcão, M. Irene, Fernando Miranda, Ricardo Severino, and M. Joana Soares. "Weierstrass method for quaternionic polynomial root-finding." Mathematical Methods in the Applied Sciences 41, no. 1 (2017): 423–37. http://dx.doi.org/10.1002/mma.4623.

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Liu, Xun, Lixin Tian, and Yuhai Wu. "Exact Solutions of the Generalized Benjamin-Bona-Mahony Equation." Mathematical Problems in Engineering 2010 (2010): 1–5. http://dx.doi.org/10.1155/2010/796398.

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We apply the theory of Weierstrass elliptic function to study exact solutions of the generalized Benjamin-Bona-Mahony equation. By using the theory of Weierstrass elliptic integration, we get some traveling wave solutions, which are expressed by the hyperbolic functions and trigonometric functions. This method is effective to find exact solutions of many other similar equations which have arbitrary-order nonlinearity.
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Marcheva, Plamena I., Ivan K. Ivanov, and Stoil I. Ivanov. "On the Q-Convergence and Dynamics of a Modified Weierstrass Method for the Simultaneous Extraction of Polynomial Zeros." Algorithms 18, no. 4 (2025): 205. https://doi.org/10.3390/a18040205.

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In the present paper, we prove a new local convergence theorem with initial conditions and error estimates that ensure the Q-quadratic convergence of a modification of the famous Weierstrass method. Afterward, we prove a semilocal convergence theorem that is of great practical importance owing to its computable initial condition. The obtained theorems improve and complement all existing such kind of convergence results about this method. At the end of the paper, we provide three numerical examples to show the applicability of our semilocal theorem to some physics problems. Within the examples,
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Shutovskyi, Arsen, and Vasyl Sakhnyuk. "Representation of Weierstrass integral via Poisson integrals." Ukrainian Mathematical Bulletin 18, no. 3 (2021): 419–27. http://dx.doi.org/10.37069/1810-3200-2021-18-3-8.

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In our research, we have presented a second-order linear partial differential equation in polar coordinates. Considering this differential equation on the unit disk, we have obtained a one-dimensional heat equation. It is well-known that the heat equation can be solved taking into account the boundary condition for the general solution on the unit circle. In our paper, the boundary-value problem is solved using the well-known method called the separation of variables. As a result, the general solution to the boundary-value problem is presented in terms of the Fourier series. Then the expressio
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Khalique, Chaudry Masood, and Karabo Plaatjie. "Symmetry Methods and Conservation Laws for the Nonlinear Generalized 2D Equal-Width Partial Differential Equation of Engineering." Mathematics 10, no. 1 (2021): 24. http://dx.doi.org/10.3390/math10010024.

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In this work, we study the generalized 2D equal-width equation which arises in various fields of science. With the aid of numerous methods which includes Lie symmetry analysis, power series expansion and Weierstrass method, we produce closed-form solutions of this model. The exact solutions obtained are the snoidal wave, cnoidal wave, Weierstrass elliptic function, Jacobi elliptic cosine function, solitary wave and exponential function solutions. Moreover, we give a graphical representation of the obtained solutions using certain parametric values. Furthermore, the conserved vectors of the und
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Fan, Lulu, and Taogetusang Bao. "Weierstrass elliptic function solutions and degenerate solutions of a variable coefficient higher-order Schrödinger equation." Physica Scripta 98, no. 9 (2023): 095238. http://dx.doi.org/10.1088/1402-4896/acec1a.

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Abstract In this paper, the auxiliary equation method is used to study the Weierstrass elliptic function solutions and degenerate solutions of the variable coefficient higher order Schrödinger equation, including Jacobian elliptic function solutions, trigonometric function solutions and hyperbolic function solutions. The types of solutions of the variable coefficient higher-order Schrödinger equation are enriched, and the method of seeking precise and accurate solutions is extended. It is concluded that the types of degenerate solutions are related to the coefficients of the equation itself wh
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Kudryashov, Nikolai A. "Nonlinear Differential Equations With Exact Solutions Expressed Via The Weierstrass Function." Zeitschrift für Naturforschung A 59, no. 7-8 (2004): 443–54. http://dx.doi.org/10.1515/zna-2004-7-807.

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A new problem is studied, that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. A method is discussed to construct nonlinear ordinary differential equations with exact solutions. The main step of our method is the assumption that nonlinear differential equations have exact solutions which are general solution of the simplest integrable equation. We use the Weierstrass elliptic equation as building block to find a number of nonlinear differential equations with exact solutions. Nonlinear differential equations of the second, third and fo
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SHI, LIANG-MA, LING-FENG ZHANG, HAO MENG, HONG-WEI ZHAO, and SHI-PING ZHOU. "A METHOD TO CONSTRUCT WEIERSTRASS ELLIPTIC FUNCTION SOLUTION FOR NONLINEAR EQUATIONS." International Journal of Modern Physics B 25, no. 14 (2011): 1931–39. http://dx.doi.org/10.1142/s0217979211100436.

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A method for constructing the solutions of nonlinear evolution equations by using the Weierstrass elliptic function and its first-order derivative was presented. This technique was then applied to Burgers and Klein–Gordon equations which showed its efficiency and validality for exactly some solving nonlinear evolution equations.
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Dissertations / Theses on the topic "Weierstrass method"

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Raujouan, Thomas. "Surfaces à courbure moyenne constante dans les espaces euclidien et hyperbolique." Thesis, Tours, 2019. http://www.theses.fr/2019TOUR4011.

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Les surfaces à courbure moyenne constante non-nulle apparaissent en physique comme solutions à certains problèmes d'interface entre deux milieux de pressions différentes. Elles sont décrites mathématiquement par des équations aux dérivées partielles et sont constructibles à partir de données holomorphes via une représentation similaire à celle de Weierstrass pour les surfaces minimales. On présente dans cette thèse deux résultats s'appuyantsur cette représentation, dite <>.Le premier indique que les données donnant naissance à un bout Delaunay de type onduloïde induisent encore un anneau
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Souza, Daniel Câmara de. "Eletrodinâmica variacional e o problema eletromagnético de dois corpos." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-26012015-213657/.

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Estudamos a Eletrodinâmica de Wheeler-Feynman usando um princípio variacional para um funcional de ação finito acoplado a um problema de valor na fronteira. Para trajetórias C2 por trechos, a condição de ponto crítico desse funcional fornece as equações de movimento de Wheeler-Feynman mais uma condição de continuidade dos momentos parciais e energias parciais, conhecida como condição de quina de Weierstrass-Erdmann. Estudamos em detalhe um sub-caso mais simples, onde os dados de fronteira têm um comprimento mínimo. Nesse caso, mostramos que a condição de extremo se reduz a um problema de valor
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Khiari, Souad. "Problèmes inverses de points sources dans les modèles de transport dispersif de contaminants : identifiabilité et observabilité." Thesis, Compiègne, 2016. http://www.theses.fr/2016COMP2301.

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La recherche et les questions abordées dans cette thèse sont de type inverse : la reconstitution d'une source ponctuelle ou la complétion d'une donnée à la limite inconnue à l'extrémité du domaine dans les modèles paraboliques de transport de contaminants. La modélisation mathématique des problèmes de pollution des eaux fait intervenir deux traceurs, l'oxygène dissous (OD) et la demande biochimique en oxygène (DBO) qui est la quantité d'oxygène nécessaire à la biodégradation de la matière organique. En effet, au cours des procédés d'autoépuration, certaines bactéries aérobies jouent un rôle pr
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Books on the topic "Weierstrass method"

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Hellman, Geoffrey, and Stewart Shapiro. Varieties of Continua. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198712749.001.0001.

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Two historical episodes form the background to the research presented here: the first is the remarkably rapid transition in the course of the nineteenth century from the ancient Aristotelian view that a true continuum cannot be composed entirely of points to the now standard, entirely punctiform frameworks for analysis and geometry found in modern texts (stemming from the work of Bolzano, Cauchy, Weierstrass, Dedekind, Cantor, et al.). The second is the mid-to-late twentieth-century revival of pre-limit methods in analysis and geometry using infinitesimals, viz. non-standard analysis due to Ab
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Book chapters on the topic "Weierstrass method"

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Falcão, Maria Irene, Fernando Miranda, Ricardo Severino, and Maria Joana Soares. "A Modified Quaternionic Weierstrass Method." In Computational Science and Its Applications – ICCSA 2022 Workshops. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-10536-4_27.

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Hristov, Vladimir, Nikolay Kyurkchiev, and Anton Iliev. "Global Convergence Properties of the SOR-Weierstrass Method." In Numerical Methods and Applications. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-18466-6_52.

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Kyurkchiev, N. "a Note on the Convergence of the SOR-like Weierstrass Method." In Computing Supplementa. Springer Vienna, 2003. http://dx.doi.org/10.1007/978-3-7091-6033-6_10.

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Rong, Yingjiao, Fei Peng, Rongqi Lv, and Shanshan Li. "Fractional Gradient Descent Algorithm for Nonlinear Additive Systems Using Weierstrass Approximation Method." In Advanced Intelligent Technologies for Information and Communication. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-5203-8_20.

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Petkovic, Miodrag S., and Dejan V. Vranic. "Euler-Like Method for the Simultaneous Inclusion of Polynomial Zeros with Weierstrass’ Correction." In Scientific Computing, Validated Numerics, Interval Methods. Springer US, 2001. http://dx.doi.org/10.1007/978-1-4757-6484-0_13.

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Bottazzini, Umberto. "The Influence of Weierstrass’s Analytical Methods in Italy." In Amphora. Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-8599-7_4.

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Franceschetti, Giorgio, and Daniele Riccio. "Scattering from Weierstrass-Mandelbrot Profiles: Extended-Boundary-Condition Method." In Scattering, Natural Surfaces, and Fractals. Elsevier, 2007. http://dx.doi.org/10.1016/b978-012265655-2/50007-6.

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Nugroho, Gunawan, Purwadi Agus Darwito, Ruri Agung Wahyuono, and Murry Raditya. "On the Generalized Simplest Equations: Toward the Solution of Nonlinear Differential Equations with Variable Coefficients." In Recent Developments in the Solution of Nonlinear Differential Equations. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.95620.

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The simplest equations with variable coefficients are considered in this research. The purpose of this study is to extend the procedure for solving the nonlinear differential equation with variable coefficients. In this case, the generalized Riccati equation is solved and becomes a basis to tackle the nonlinear differential equations with variable coefficients. The method shows that Jacobi and Weierstrass equations can be rearranged to become Riccati equation. It is also important to highlight that the solving procedure also involves the reduction of higher order polynomials with examples of K
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Ullrich, Peter. "Karl Schellbach (1804–1892) und seine Beiträge zu Mathematik, Lehrerbildung und Wissenschaftspolitik." In Exkursionen in die Geschichte der Mathematik und ihres Unterrichts. WTM-Verlag Münster, 2021. http://dx.doi.org/10.37626/ga9783959871860.0.19.

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Even though Karl Schellbach remained a high school teacher throughout his life, he left traces in mathematics, especially in the training of mathematics teachers and in science policy. Generally, he is known as teacher of Eisenstein, Hensel, and Prince Friedrich Wilhelm of Prussia, later Emperor Friedrich III, but above all as head of the “Mathematisch-pädagogische Seminar” in Berlin, which prominent mathematicians visited to prepare for school service. Schellbach published numerous journal articles and books on mathematics, both on didactics and on research topics current at his times. From 1
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Ullrich, Peter. "The concept of number by Karl Weierstraß and its first publication, viz. within a school program by Ernst Kossak." In “Dig Where You Stand” 7. Proceedings of the Seventh International Conference on the History of Mathematics Education. September 19-23, 2022, Mainz, Germany. WTM Verlag, 2023. http://dx.doi.org/10.37626/ga9783959872560.0.21.

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Karl Weierstraß (1815–1897) presented his concept of real number and its generalizations in his lectures at Berlin university, but did not publish it in printed form. Instead of this, other mathematicians wrote publications on his theory, starting off with Ernst Kossak (1839–1892) in 1872, who was a teacher at the Friedrichswerdersche Gymnasium in Berlin then. This treatise appeared within the yearly program of Kossak’s school. By choosing this way of publication, he addressed rather teachers at other secondary schools or even a generally interested public than mathematicians at universities.
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Conference papers on the topic "Weierstrass method"

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Laptiev, Oleksandr, Ivan Parkhomenko, Andrii Musienko, Andriy Makarchuk, Anton Mishchuk, and Denys Shapovalov. "Weierstrass Method of Analogue Signal Approximation." In 2023 IEEE 4th KhPI Week on Advanced Technology (KhPIWeek). IEEE, 2023. http://dx.doi.org/10.1109/khpiweek61412.2023.10311583.

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Nedzhibov, Gyurhan. "Some new properties of the Weierstrass iterative method." In “TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0100882.

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Marcheva, Plamena I., and Stoil I. Ivanov. "On the semilocal convergence of a modified weierstrass method for the simultaneous computation of polynomial zeros." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0082007.

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Nedzhibov, Gyurhan H., Milko G. Petkov, George Venkov, Vesela Pasheva, and Ralitza Kovacheva. "On Some Modifications of Weierstrass-Dochev method for simultaneous extraction of only a part of all roots of polynomials." In APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS: 36th International Conference. AIP, 2010. http://dx.doi.org/10.1063/1.3515578.

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Kovtun, Mariya, Andrew Okhrimenko, Sergiy Gnatyuk, and Vladislav Kovtun. "Development of a search method of birationally equivalent binary edwards curves for binary weierstrass curves from DSTU 4145-2002." In 2015 Second International Scientific-Practical Conference Problems of Infocommunications Science and Technology (PIC S&T). IEEE, 2015. http://dx.doi.org/10.1109/infocommst.2015.7357253.

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Bora, Can K., Michael E. Plesha, Erin E. Flater, Mark D. Street, Robert W. Carpick, and James M. Redmond. "Multiscale Roughness of MEMS Surfaces." In ASME/STLE 2004 International Joint Tribology Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/trib2004-64370.

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Investigation of contact and friction at multiple length scales is necessary for the design of surfaces in sliding microelectromechanical system (MEMS). A method is developed to investigate the geometry of asperities at different length scales. Analysis of density, height, and curvature of asperities on atomic force microscopy (AFM) images of actual silicon MEMS surfaces show these properties have a power law relationship with the sampling size used to define an asperity. This behavior and its similarity to results for fractal Weierstrass-Mandelbrot (W-M) function approximations indicate that
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Liao, Xiaoyun, and G. Gary Wang. "Variation Analysis of Non-Rigid Assembly Using FEM and Fractals." In ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/detc2004-57753.

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Many studies on the assembly of non-rigid parts suggest that the part variation affects the assembly dimensional quality. However, little is known about how the detailed microstructure of part variation influences the assembly dimensional quality. In this paper, a new method based on the finite element method (FEM) and fractal geometry is proposed to explore the influence of the part variation microstructure on the assembly dimensional variation. In the new method, a special fractal function, the Weierstrass-Mandelbrot (W-M) function, is used to extract and represent the characteristics of the
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Jaggard, Dwight L., and Y. Kim. "Scattering and Inverse scattering from bandlimited fractal slabs." In OSA Annual Meeting. Optica Publishing Group, 1987. http://dx.doi.org/10.1364/oam.1987.wx4.

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The fractal concept is useful in describing structures displaying dilation symmetry. Such structures are said to be self-similar. Physical structures, whether naturally occurring or man-made, are at best self-similar over a regime of interest between an appropriate inner and outer scale. Here we model such structures by a bandlimited Weierstrass function which incorporates these scales and possesses an identifiable fractional dimension denoted the fractal dimension. We call such structures bandlimited fractals. Of interest here is the scattering and inverse scattering of waves from 1-D bandlim
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Dawkins, Jeremy J., David M. Bevly, and Robert L. Jackson. "Multiscale Terrain Characterization Using Fourier and Wavelet Transforms for Unmanned Ground Vehicles." In ASME 2009 Dynamic Systems and Control Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/dscc2009-2718.

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This paper investigates the use of the Fourier transform and Wavelet transform as methods to supplement the more common root mean squared elevation and power spectral density methods of terrain characterization. Two dimensional terrain profiles were generated using the Weierstrass-Mandelbrot fractal equation. The Fourier and Wavelet transforms were used to decompose these terrains into a parameter set. A two degree of freedom quarter car model was used to evaluate the vehicle response before and after the terrain characterization. It was determined that the Fourier transform can be used to red
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Faz-Hernández, Armando, and Julio López. "High-Performance Elliptic Curve Cryptography: A SIMD Approach to Modern Curves." In Concurso de Teses e Dissertações. Sociedade Brasileira de Computação - SBC, 2023. http://dx.doi.org/10.5753/ctd.2023.230156.

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Cryptography based on elliptic curves is endowed with efficient methods for public-key cryptography. Recent research has shown the superiority of the Montgomery and Edwards curves over the Weierstrass curves as they require fewer arithmetic operations. Using these modern curves has, however, introduced several challenges to the cryptographic algorithm’s design, opening up new opportunities for optimization. Our main objective is to propose algorithmic optimizations and implementation techniques for cryptographic algorithms based on elliptic curves. In order to speed up the execution of these a
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