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Journal articles on the topic 'Weierstrass method'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Yang, Zonghang, and Benny Y. C. Hon. "An Improved Modified Extended tanh-Function Method." Zeitschrift für Naturforschung A 61, no. 3-4 (2006): 103–15. http://dx.doi.org/10.1515/zna-2006-3-401.

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In this paper we further improve the modified extended tanh-function method to obtain new exact solutions for nonlinear partial differential equations. Numerical applications of the proposed method are verified by solving the improved Boussinesq equation and the system of variant Boussinesq equations. The new exact solutions for these equations include Jacobi elliptic doubly periodic type,Weierstrass elliptic doubly periodic type, triangular type and solitary wave solutions

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12

COQUEREAUX, R., A. GROSSMANN, and B. E. LAUTRUP. "Iterative Method for Calculation of the Weierstrass Elliptic Function." IMA Journal of Numerical Analysis 10, no. 1 (1990): 119–28. http://dx.doi.org/10.1093/imanum/10.1.119.

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13

Smirnov, M. S., K. V. Malkov, and S. A. Rogovoy. "A Landen-type Method for Computation of Weierstrass Functions." Lobachevskii Journal of Mathematics 45, no. 6 (2024): 2941–56. http://dx.doi.org/10.1134/s1995080224602972.

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14

Kjurkchiev, N., and M. S. Petković. "The behaviour of approximations of the SOR Weierstrass method." Computers & Mathematics with Applications 32, no. 7 (1996): 117–21. http://dx.doi.org/10.1016/0898-1221(96)00160-5.

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15

Proinov, Petko D., and Milena D. Petkova. "Convergence of the two-point Weierstrass root-finding method." Japan Journal of Industrial and Applied Mathematics 31, no. 2 (2014): 279–92. http://dx.doi.org/10.1007/s13160-014-0138-4.

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16

Udo-Akpan, Udo-Akpan, Itoro Ubom, and Udoaka Otobong G. "Computational Construction of Weierstrass Sections for Semi-Invariant Polynomial Functions on Lie Algebras." Scholars Journal of Physics, Mathematics and Statistics 12, no. 04 (2024): 50–53. http://dx.doi.org/10.36347/sjpms.2024.v11i04.002.

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In this paper, we present a computational approach to construct Weierstrass sections for semi-invariant polynomial functions on Lie algebras, extending the foundational work of Bourbaki and Popov. We focus on simple Lie algebras of type B, C, or D, and their associated parabolic subalgebras, particularly those with Levi factors composed of successive blocks of size two. Our method extends the notion of Weierstrass sections introduced by Popov, enabling us to explicitly construct these sections and establish their polynomiality. Furthermore, we demonstrate how these sections facilitate the line

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17

Salas, Alvaro H., S. A. El-Tantawy, and Lorenzo J. H. Martínez. "Approximate Analytical and Numeric Solutions to a Forced Damped Gardner Equation." Scientific World Journal 2022 (May 11, 2022): 1–10. http://dx.doi.org/10.1155/2022/3240918.

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In this paper, some exact traveling wave solutions to the integrable Gardner equation are reported. The ansatz method is devoted for deriving some exact solutions in terms of Jacobi and Weierstrass elliptic functions. The obtained analytic solutions recover the solitary waves, shock waves, and cnoidal waves. Also, the relation between the Jacobi and Weierstrass elliptic functions is obtained. In the second part of this work, we derive some approximate analytic and numeric solutions to the nonintegrable forced damped Gardner equation. For the approximate analytic solutions, the ansatz method is

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18

Skuratovskii, Ruslan, and Volodymyr Osadchyy. "Elliptic and Edwards Curves Order Counting Method." International Journal of Mathematical Models and Methods in Applied Sciences 15 (April 5, 2021): 52–62. http://dx.doi.org/10.46300/9101.2021.15.8.

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We consider the algebraic affine and projective curves of Edwards over the finite field Fpn. It is well known that many modern cryptosystems can be naturally transformed into elliptic curves. In this paper, we extend our previous research into those Edwards algebraic curves over a finite field. We propose a novel effective method of point counting for both Edwards and elliptic curves. In addition to finding a specific set of coefficients with corresponding field characteristics for which these curves are supersingular, we also find a general formula by which one can determine whether or not a

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19

Wei, Long, and Yang Wang. "Infinitely Many Elliptic Solutions to a Simple Equation and Applications." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/582532.

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Based on auxiliary equation method and Bäcklund transformations, we present an idea to find infinitely many Weierstrass and Jacobi elliptic function solutions to some nonlinear problems. First, we give some nonlinear iterated formulae of solutions and some elliptic function solutions to a simple auxiliary equation, which results in infinitely many Weierstrass and Jacobi elliptic function solutions of the simple equation. Then applying auxiliary equation method to some nonlinear problems and combining the results with exact solutions of the auxiliary equation, we obtain infinitely many elliptic

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20

Petkovic, Ljiljana, Miodrag Petkovic, and Dusan Milosevic. "Inclusion Weierstrass-like root-finders with corrections." Filomat, no. 17 (2003): 143–54. http://dx.doi.org/10.2298/fil0317143p.

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In this paper we present iterative methods of Weierstrass's type for the simultaneous inclusion of all multiple zeros of a polynomial. The order of convergence of the proposed interval method is 1 + ?2 ? 2.414 or 3, depending on the type of the applied disk inversion. The criterion for the choice of a proper circular root-set is given. This criterion uses the already calculated entries which increases the computational efficiency of the presented algorithms. Numerical results are given to demonstrate the convergence behavior.

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21

Jones, Gareth, Jonathan Kirby, and Tamara Servi. "LOCAL INTERDEFINABILITY OF WEIERSTRASS ELLIPTIC FUNCTIONS." Journal of the Institute of Mathematics of Jussieu 15, no. 4 (2014): 673–91. http://dx.doi.org/10.1017/s1474748014000425.

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We explain which Weierstrass ${\wp}$-functions are locally definable from other ${\wp}$-functions and exponentiation in the context of o-minimal structures. The proofs make use of the predimension method from model theory to exploit functional transcendence theorems in a systematic way.

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22

Abdel Kader, A. H., and M. S. Abdel Latif. "New soliton solutions of the CH–DP equation using Lie symmetry method." Modern Physics Letters B 32, no. 20 (2018): 1850234. http://dx.doi.org/10.1142/s0217984918502342.

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In this paper, using Lie symmetry method, we obtain some new exact traveling wave solutions of the Camassa–Holm–Degasperis–Procesi (CH–DP) equation. Some new bright and dark soliton solutions are obtained. Also, some new doubly periodic solutions in the form of Jacobi elliptic functions and Weierstrass elliptic functions are obtained.

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23

Valchanov, Nikola, Angel Golev, and Anton Iliev. "On the Critical Points of Kyurkchiev’s Method for Solving Algebraic Equations." Serdica Journal of Computing 9, no. 1 (2015): 27–34. http://dx.doi.org/10.55630/sjc.2015.9.27-34.

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This paper is dedicated to Prof. Nikolay Kyurkchievon the occasion of his 70th anniversaryThis paper gives sufficient conditions for kth approximations ofthe zeros of polynomial f (x) under which Kyurkchiev’s method fails on thenext step. The research is linked with an attack on the global convergencehypothesis of this commonly used in practice method (as correlate hypothesisfor Weierstrass–Dochev’s method). Graphical examples are presented.

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24

Nedzhibov, Gyurhan H. "The Weierstrass iterative method as a Petrov–Galerkin method for solving eigenvalue problem." Journal of Computational and Applied Mathematics 405 (May 2022): 113961. http://dx.doi.org/10.1016/j.cam.2021.113961.

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25

Lai, Xian-Jing, Jie-Fang Zhang, and Shan-Hai Mei. "Application of the Weierstrass Elliptic Expansion Method to the Long-Wave and Short-Wave Resonance Interaction System." Zeitschrift für Naturforschung A 63, no. 5-6 (2008): 273–79. http://dx.doi.org/10.1515/zna-2008-5-606.

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With the aid of symbolic computation, nine families of new doubly periodic solutions are obtained for the (2+1)-dimensional long-wave and short-wave resonance interaction (LSRI) system in terms of the Weierstrass elliptic function method. Moreover Jacobian elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions.

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26

El Achab, Abdelfattah. "Elliptic Travelling Wave Solutions to a Generalized Boussinesq Equation." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/256019.

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Travelling wave solutions for the generalized Boussinesq wave equation are studied by using the Weierstrass elliptic function method. As a result, some previously known solutions are recovered, and at the same time some new ones are also given, as well as integrable ones.

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27

Salas, Alvaro H., Lorenzo J. Martinez H, and David L. Ocampo R. "New Solutions for the Generalized BBM Equation in terms of Jacobi and Weierstrass Elliptic Functions." Abstract and Applied Analysis 2021 (April 22, 2021): 1–10. http://dx.doi.org/10.1155/2021/5513266.

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The Jacobi elliptic function method is applied to solve the generalized Benjamin-Bona-Mahony equation (BBM). Periodic and soliton solutions are formally derived in a general form. Some particular cases are considered. A power series method is also applied in some particular cases. Some solutions are expressed in terms of the Weierstrass elliptic function.

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28

Darwish, A., H. M. Ahmed, M. Ammar, M. H. Ali, and A. H. Arnous. "SOLITONS AND OTHER SOLUTIONS FOR THE (2+1)-DIMENSIONAL HEISENBERG FERROMAGNETIC SPIN CHAIN EQUATION USING IMPROVED MODIFIED EXTENDED TANH-FUNCTION METHOD." Advances in Mathematics: Scientific Journal 10, no. 11 (2021): 3491–504. http://dx.doi.org/10.37418/amsj.10.11.9.

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This paper studies $(2 + 1)$-dimensional Heisenberg ferromagnetic spin chain model by using improved modified extended tanh-function method. Various types of solutions are extracted such as bright solitons, singular solitons, dark solitons, singular periodic solutions, Weierstrass elliptic periodic type solutions and exponential function solutions. Moreover, some of the obtained solutions are represented graphically.

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Kaczorek, Tadeusz. "Positivity and stability of fractional descriptor time–varying discrete–time linear systems." International Journal of Applied Mathematics and Computer Science 26, no. 1 (2016): 5–13. http://dx.doi.org/10.1515/amcs-2016-0001.

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Abstract The Weierstrass–Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor time-varying discrete-time linear systems. A method for computing solutions of fractional systems is proposed. Necessary and sufficient conditions for the positivity of these systems are established.

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30

Sajewski, Ł. "Descriptor fractional discrete-time linear system with two different fractional orders and its solution." Bulletin of the Polish Academy of Sciences Technical Sciences 64, no. 1 (2016): 15–20. http://dx.doi.org/10.1515/bpasts-2016-0003.

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Abstract Factional Discrete-time linear systems with fractional different orders are addressed. The Weierstrass-Kronecker decomposition theorem of the regular pencil is extended to the descriptor fractional discrete-time linear system with different fractional orders. Using the extension, method for finding the solution of the state equation is derived. Effectiveness of the method is demonstrated on a numerical example.

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31

Zayed, Elsayed M. E., Mona El-Shater, Khaled A. E. Alurrfi, Ahmed H. Arnous, Nehad Ali Shah, and Jae Dong Chung. "Dispersive optical soliton solutions with the concatenation model incorporating quintic order dispersion using three distinct schemes." AIMS Mathematics 9, no. 4 (2024): 8961–80. http://dx.doi.org/10.3934/math.2024437.

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<abstract><p>This paper addresses the new concatenation model incorporating quintic-order dispersion, incorporating four well-known nonlinear models. The concatenated models are the nonlinear Schrödinger equation, the Hirota equation, the Lakshmanan-Porsezian-Daniel equation, and the nonlinear Schrödinger equation with quintic-order dispersion. The model itself is innovative and serves as an encouragement for investigating and analyzing the extracted optical solitons. These models play a crucial role in nonlinear optics, especially in studying optical fibers. Three integration algo

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32

Ivasyk, Halyna. "The system of powers of conformal mappings and biorthogonal to them systems of the functions." Physico-mathematical modelling and informational technologies, no. 26 (December 30, 2017): 31–44. http://dx.doi.org/10.15407/fmmit2017.26.031.

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In this article we review the methods of power summation of factors. The degree of factors which are arbitrary powers of summation indices are considered. We show that using the Poisson-Abel method only those series can be summarized the order of member increase of which is proportional to the exponent depending on the summation index. At the same time the Gauss-Weierstrass method and other power factors methods can be also applied to the series the terms of which increase in proportion to the exponential dependence of the indices summation.

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33

Kaczorek, Tadeusz. "Descriptor standard and positive discrete-time nonlinear systems." Archives of Control Sciences 25, no. 2 (2015): 227–35. http://dx.doi.org/10.1515/acsc-2015-0015.

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AbstractA method of analysis of descriptor nonlinear discrete-time systems with regular pencils of linear part is proposed. The method is based on the Weierstrass-Kronecker decomposition of the pencils. Necessary and sufficient conditions for the positivity of the nonlinear systems are established. A procedure for computing the solution to the equations describing the nonlinear systems are proposed and demonstrated on numerical examples.

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Rizvi, Syed Tahir Raza, Aly R. Seadawy, Ijaz Ali, Ishrat Bibi, and Muhammad Younis. "Chirp-free optical dromions for the presence of higher order spatio-temporal dispersions and absence of self-phase modulation in birefringent fibers." Modern Physics Letters B 34, no. 35 (2020): 2050399. http://dx.doi.org/10.1142/s0217984920503996.

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In this paper, we study Biswas–Arshed (BA) model in birefringent fibers for chirp-free solitons (dromions) with the aid of sub-ordinary differential equations (ODE) method. The BA model studies the soliton transmission in optical fiber. We obtain bright, periodic, and Weierstrass elliptic function solutions with constraint conditions.

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35

Filiz, Ali, Mehmet Ekici, and Abdullah Sonmezoglu. "F-Expansion Method and New Exact Solutions of the Schrödinger-KdV Equation." Scientific World Journal 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/534063.

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F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulusmof Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful metho

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He, Yinghui. "Exact Solutions for(4+1)-Dimensional Nonlinear Fokas Equation Using ExtendedF-Expansion Method and Its Variant." Mathematical Problems in Engineering 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/972519.

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The construction of exact solution for higher-dimensional nonlinear equation plays an important role in knowing some facts that are not simply understood through common observations. In our work,(4+1)-dimensional nonlinear Fokas equation, which is an important physical model, is discussed by using the extendedF-expansion method and its variant. And some new exact solutions expressed by Jacobi elliptic function, Weierstrass elliptic function, hyperbolic function, and trigonometric function are obtained. The related results are enriched.

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BAGCHI, B., S. MALLIK, and C. QUESNE. "GENERATING COMPLEX POTENTIALS WITH REAL EIGENVALUES IN SUPERSYMMETRIC QUANTUM MECHANICS." International Journal of Modern Physics A 16, no. 16 (2001): 2859–72. http://dx.doi.org/10.1142/s0217751x01004153.

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In the framework of SUSYQM extended to deal with non-Hermitian Hamiltonians, we analyze three sets of complex potentials with real spectra, recently derived by a potential algebraic approach based upon the complex Lie algebra [Formula: see text] . This extends to the complex domain the well-known relationship between SUSYQM and potential algebras for Hermitian Hamiltonians, resulting from their common link with the factorization method and Darboux transformations. In the same framework, we also generate for the first time a pair of elliptic partner potentials of Weierstrass ℘ type, one of them

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Kaczorek, T. "Fractional descriptor standard and positive discrete-time nonlinear systems." Bulletin of the Polish Academy of Sciences Technical Sciences 63, no. 3 (2015): 651–55. http://dx.doi.org/10.1515/bpasts-2015-0076.

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AbstractA method of analysis of the fractional descriptor nonlinear discrete-time systems with regular pencils of linear part is proposed. The method is based on the Weierstrass-Kronecker decomposition of the pencils. Necessary and sufficient conditions for the positivity of the nonlinear systems are established. A procedure for computing the solution to the equations describing the nonlinear systems are proposed and demonstrated on a numerical example.

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39

Li De-Sheng and Zhang Hong-Qing. "A new method to construct Weierstrass elliptic function solutions for soliton equations." Acta Physica Sinica 54, no. 12 (2005): 5540. http://dx.doi.org/10.7498/aps.54.5540.

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40

Martynyuk, O., and V. Gorodetskyi. "THE LOCALIZATION PRINCIPLE FOR FORMAL FOURIER SERIES SUMMARIZED BY GAUSS-WEIERSTRASS METHOD." Bukovinian Mathematical Journal 7, no. 2 (2019): 30–38. http://dx.doi.org/10.31861/bmj2019.02.030.

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41

Wroń, Michał. "Faster Point Scalar Multiplication on Short Weierstrass Elliptic Curves over Fp using Twisted Hessian Curves over Fp2." Journal of Telecommunications and Information Technology, no. 3 (September 30, 2016): 98–102. http://dx.doi.org/10.26636/jtit.2016.3.753.

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This article shows how to use fast Fp2 arithmetic and twisted Hessian curves to obtain faster point scalar multiplication on elliptic curve ESW in short Weierstrass form over Fp. It is assumed that p and #ESW(Fp) are different large primes, #E(Fq) denotes number of points on curve E over field Fq and #Et SW (Fp) Fp), where Et is twist of E, is divisible by 3. For example this method is suitable for two NIST curves over Fp: NIST P-224 and NIST P-256. The presented solution may be much faster than classic approach. Presented solution should also be resistant for side channel attacks and informat

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42

Zhou, Qing-Mei. "Multiple Solutions for Nonhomogeneous Neumann Differential Inclusion Problems by thep(x)-Laplacian." Scientific World Journal 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/753262.

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A class of nonlinear Neumann problems driven byp(x)-Laplacian with a nonsmooth locally Lipschitz potential (hemivariational inequality) was considered. The approach used in this paper is the variational method for locally Lipschitz functions. More precisely, Weierstrass theorem and Mountain Pass theorem are used to prove the existence of at least two nontrivial solutions.

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43

Skuratovskii, Ruslan, and Volodymyr Osadchyy. "Criterions of Supersinguliarity and Groups of Montgomery and Edwards Curves in Cryptography." WSEAS TRANSACTIONS ON MATHEMATICS 19 (March 1, 2021): 709–22. http://dx.doi.org/10.37394/23206.2020.19.77.

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We consider the algebraic affine and projective curves of Edwards over the finite field Fpn. It is well known that many modern cryptosystems can be naturally transformed into elliptic curves. The criterions of the supersingularity of Montgomery and Edwards curves are found. In this paper, we extend our previous research into those Edwards algebraic curves over a finite field and we construct birational isomorphism of them with cubic in Weierstrass normal form. One class of twisted Edwards is researched too. We propose a novel effective method of point counting for both Edwards and elliptic cur

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Guo, Peng, Xiang Wu, and Liangbi Wang. "New Solutions of Elastic Waves in an Elastic Rod under Finite Deformation." Journal of Applied Mathematics 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/495125.

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The nonlinear wave equation of an elastic rod under finite deformation is solved by the extended mapping method. Abundant new exact traveling wave solutions for this equation are obtained, which contain trigonometric function solutions, solitary wave solutions, Jacobian elliptic function solutions, and Weierstrass elliptic function solutions. The method can be used in further works to establish more entirely new solutions for other kinds of nonlinear evolution equations arising in physics.

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Chouikha, Raouf. "Fonctions Elliptiques et Équations Différentielles Ordinaires." Canadian Mathematical Bulletin 40, no. 3 (1997): 276–84. http://dx.doi.org/10.4153/cmb-1997-034-7.

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RésuméIn this paper, we detail some results of a previous note concerning a trigonometric expansion of the Weierstrass elliptic function . In particular, this implies its classical Fourier expansion. We use a direct integration method of the ODEwhere P(u) is a polynomial of degree n = 2 or 3. In this case, the bifurcations of (E) depend on one parameter only. Moreover, this global method seems not to apply to the cases n > 3.

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Jezequel, L. "Three New Methods of Modal Identification." Journal of Vibration and Acoustics 108, no. 1 (1986): 17–25. http://dx.doi.org/10.1115/1.3269297.

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The identification of linear systems based on their dynamic responses has been the object of a great number of studies. In this work, we propose three new identification procedures which can be programmed on a microcomputer. The first of these methods uses an analytical extension of the transfer function, the second method uses a special integral transformation based on the Cauchy-Weierstrass theorem and the last method uses orthogonalization of the experimental displacement shapes by the Ritz-Galerkin procedure. These methods allow rapid detection of the modal parameters. Presented separately

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Kaczorek, Tadeusz, and Kamil Borawski. "Fractional descriptor continuous–time linear systems described by the Caputo–Fabrizio derivative." International Journal of Applied Mathematics and Computer Science 26, no. 3 (2016): 533–41. http://dx.doi.org/10.1515/amcs-2016-0037.

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Abstract The Weierstrass–Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor continuous-time linear systems described by the Caputo–Fabrizio derivative. A method for computing solutions of continuous-time systems is presented. Necessary and sufficient conditions for the positivity and stability of these systems are established. The discussion is illustrated with a numerical example.

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Zahir Hussain, Abdul Basith, and Sulthan Ibrahim Mohamed Sulaiman. "Weierstrass scale space representation and composite dilated U-net based convolution for early glaucoma diagnosis." Indonesian Journal of Electrical Engineering and Computer Science 38, no. 3 (2025): 1661. https://doi.org/10.11591/ijeecs.v38.i3.pp1661-1672.

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Glaucoma is one of the common causes of blindness in the current world. Glaucoma is a blinding optic neuropathy characterized by the degeneration of retinal ganglion cells (RGCs). Accurate diagnosis and monitoring of glaucoma are challenging task through eye examinations and additional tests. To achieve accurate diagnosis of glaucoma with higher sensitivity and specificity, novel method called Weierstrass scale space representation and composite dilated U-net based convolution (WSSR-CDC) is introduced. At first, the Weierstrass transform scale space representation is employed to enhance image

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Nedzhibov, Gyurhan H. "Convergence of the modified inverse Weierstrass method for simultaneous approximation of polynomial zeros." Communications in Numerical Analysis 2016, no. 1 (2016): 74–80. http://dx.doi.org/10.5899/2016/cna-00261.

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Petković, Miodrag S., and Lidija Z. Rančić. "On the guaranteed convergence of a cubically convergent Weierstrass-like root-finding method." International Journal of Computer Mathematics 92, no. 6 (2014): 1303–12. http://dx.doi.org/10.1080/00207160.2014.938063.

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