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Journal articles on the topic 'Elliptic method'

Author: Grafiati

Published: 28 June 2021

Last updated: 29 July 2025

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1

Yin, Zhen, Hua Li, Bang Fu Wang, and Ke Feng Song. "Study on the Design of Longitudinal-Torsional Composite Ultrasonic Elliptical Vibrator Based on FEM." Advanced Materials Research 308-310 (August 2011): 341–45. http://dx.doi.org/10.4028/www.scientific.net/amr.308-310.341.

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Based on FEM, a new type of ultrasonic elliptic vibrator design method was proposed, the ultrasonic elliptic vibration was achieved by the structural curve of the longitudinal and torsional vibrations. The impedance and vibration characteristics of the new longitudinal-torsional composite ultrasonic elliptic vibrator prototype were tested. It provides an important basis for impedance matching and longitudinal-torsional composite ultrasonic elliptical vibration application.

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2

Yin, Zhen, Hua Li, Zi Yang Cao, Ou Xie, and Yan Li. "Simulation and Experiment of New Longitudinal-Torsional Composite Ultrasonic Elliptical Vibrator." Advanced Materials Research 338 (September 2011): 79–83. http://dx.doi.org/10.4028/www.scientific.net/amr.338.79.

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A new ultrasonic elliptic vibrator design method was proposed, the ultrasonic elliptic vibration was achieved by the structural curve of the longitudinal and torsional vibrations. The model, harmonic and transient analyses of the new longitudinal-torsional composite ultrasonic elliptical vibrator were performed by using the software ANSYS, the prototype of the new vibrator was tested by using impedance analyzer and PSV-400 laser Doppler vibrometer, the correctness of the finite element simulation results and the feasibility of the new longitudinal-torsional composite ultrasonic elliptical vibr

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3

Tanaka, Naoyuki. "A New Calculation Method of Hertz Elliptical Contact Pressure." Journal of Tribology 123, no. 4 (2000): 887–89. http://dx.doi.org/10.1115/1.1352745.

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A new method for calculating elliptical Hertz contact pressure in which an elliptic integral is not necessary, has been developed. The simplest numerical integration by this method yields a Hertz contact pressure within 0.0005 percent of the theoretical spherical contact pressure. And dimensionless quantities, for calculating contact pressure, major and minor semi-axes and approach calculated by using the method agree well with those given in the references. Elliptical Hertz contact pressure can thus now be calculated by using a spreadsheet program for personal computers.

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4

Zhang, Qirui. "Factorization Method of the Elliptic Curve." Journal of Physics: Conference Series 2371, no. 1 (2022): 012005. http://dx.doi.org/10.1088/1742-6596/2371/1/012005.

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Abstract The elliptic curve is an important topic in number theory. In 1987, Lenstra discovered the elliptic-curve factorization method (ECM). [4] Nevertheless, until now, no research can have complete detailed codes in Wolfram Mathematica. This article will state the definition of the elliptic curve, analyze this ECM algorithm, and build a complete code s in Mathematica. Finally, completed factorization for 1820099 by experiment, which can prove that the code can complete ECM, but it may take much time to calculate.

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5

M., Youssef, and Baumann G. "Collocation Method to Solve Elliptic Equations Bivariate Poly-Sinc Approximation." Journal of Progressive Research in Mathematics 7, no. 3 (2016): 1079–91. https://doi.org/10.5281/zenodo.3977340.

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The paper proposes a collocation method to solve bivariate elliptic partial differential equations. The method uses Lagrange approximation based on Sinc point collocations. The proposed approximation is collocating on non-equidistant interpolation points generated by conformal maps, called Sinc points. We prove the upper bound of the error for the bivariate Lagrange approximation at these Sinc points. Then we define a collocation algorithm using this approximation to solve elliptic PDEs. We verify the Poly-Sinc technique for different elliptic equations and compare the approximate solutions wi

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6

Su, YuYang, BingXuan Yu, Ruixin Peng, and HongShu Yan. "Image Edge Analysis and Application Based on Least Squares Fitting Model." Highlights in Science, Engineering and Technology 9 (September 30, 2022): 298–309. http://dx.doi.org/10.54097/hset.v9i.1859.

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This paper presents an effective method to automatically segment and fit the edge contour curve data of a picture into straight line segments, circular arc segments or elliptical arc segments. Firstly, the curvature of each point is calculated, and the curvature change breakpoints are found to distinguish between straight lines, circular arcs and elliptical arcs; then, circular arc segments and elliptical arcs are distinguished by the change degree of curvature of adjacent points, and the automatic segmentation of contour edges is realized. Finally, the circular arc segment and elliptic arc se

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7

Dong, Changbin, Yongping Liu, and Gang Zhao. "A Method for Calculating Elliptic Gear Transmission Efficiency Based on Transmission Experiment." Strojniški vestnik – Journal of Mechanical Engineering, no. 11 (November 23, 2021): 557–69. http://dx.doi.org/10.5545/sv-jme.2021.7318.

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Transmission efficiency is an important index to evaluate the transmission performance and energy consumption of gear transmission systems. To analyse the transmission efficiency of elliptic gears, the load torque fluctuation model of elliptic gear is established to analyse the influence of load torque of an elliptic gear transmission system on the torque of input and output. The torque data of input and output under different working conditions are obtained by conducting an elliptic gear transmission test. Finally, the transmission efficiency of the elliptic gear pair is obtained through the

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8

Khalid, M., and K. A. Juhany. "An expression for the dynamic stability of blunt slender elliptic bodies in hypersonic flow." Aeronautical Journal 118, no. 1207 (2014): 1079–89. http://dx.doi.org/10.1017/s0001924000009751.

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AbstractDynamic stability data on axially symmetric pointed and blunt cones, parabolic profiles and other ogive and blunt cylindrical shapes is readily available in literature; the dynamic stability on elliptic blunt paraboloids has not been studied at any great lengths in the past. Both numerical and experimental results are scarce. The present paper uses the shock expansion method to obtain the unsteady pressure distribution on blunt elliptic conical bodies at small angles-of-attack. The resulting unsteady pressure distribution is suitably integrated over the surface of the elliptic body to

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9

ZHAO, HONG. "ANALYTICAL STUDY ON NONLINEAR DIFFERENTIAL–DIFFERENCE EQUATIONS VIA A NEW METHOD." Modern Physics Letters B 24, no. 08 (2010): 761–73. http://dx.doi.org/10.1142/s0217984910022846.

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Based on the computerized symbolic computation, a new rational expansion method using the Jacobian elliptic function was presented by means of a new general ansätz and the relations among the Jacobian elliptic functions. The results demonstrated an effective direction in terms of a uniformed construction of the new exact periodic solutions for nonlinear differential–difference equations, where two representative examples were chosen to illustrate the applications. Various periodic wave solutions, including Jacobian elliptic sine function, Jacobian elliptic cosine function and the third ellipti

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10

Huang, Jing Zhi, Teng Hui Guo, Jiu Bin Tan, and Tao Sun. "Dynamic Calibration for Measurement System of Form Measuring Instruments Based on Elliptical Standard." Applied Mechanics and Materials 870 (September 2017): 203–8. http://dx.doi.org/10.4028/www.scientific.net/amm.870.203.

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A dynamic calibration method based on elliptical standard was put forward to further improve the calibration repeatability of measurement system of form measuring instruments. In this method, the radius difference of the major axis to the minor axis of elliptic contour acts as the standard value to calibrate the measuring system, and a low pass filter is used to filter the roughness, electrical noise and high frequency vibration signal which mixed into measurement data, the elliptic contour feature can be obtained accurately based on the low order harmonic properties. Compared with the traditi

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11

Kozevnikov, V. A., and V. E. Privalov. "The laser gain under nonhomogeneous boundary conditions." Izvestiya vysshikh uchebnykh zavedenii. Fizika, no. 9 (2020): 165–71. http://dx.doi.org/10.17223/00213411/63/9/165.

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The method proposed by the authors for solving the Helmholtz equation with homogeneous boundary conditions was tested for an elliptic section. The method is generalized to the Helmholtz equation with inhomogeneous boundary conditions. The generalization is verified for circular and elliptical sections.

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12

AIKAWA, Yusuke, Koji NUIDA, and Masaaki SHIRASE. "Elliptic Curve Method Using Complex Multiplication Method." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E102.A, no. 1 (2019): 74–80. http://dx.doi.org/10.1587/transfun.e102.a.74.

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13

Zhang, Li, Guo Jun Dai, and Chang Jun Wang. "Human Tracking Method Based on Maximally Stable Extremal Regions with Multi-Cameras." Applied Mechanics and Materials 44-47 (December 2010): 3681–86. http://dx.doi.org/10.4028/www.scientific.net/amm.44-47.3681.

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With respect to the human tracking with multi-cameras in the video surveillance system, a human tracking method based on MSER (Maximally Stable Extremal Regions) was established. The approach transforms the human tracking into elliptic region matching. The method does elliptic region fitting to each MSER, and then selects the elliptic regions which meet some constraints. These selected elliptic regions are normalized to unity circular regions. The right matched elliptic regions are gotten by rotational invariant vectors calculation, histogram density estimation and weighted average distance ca

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14

Elías-Zúñiga, Alex. "On The Elliptic Balance Method." Mathematics and Mechanics of Solids 8, no. 3 (2003): 263–79. http://dx.doi.org/10.1177/1081286503008003002.

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15

Noguchi, Tetsuo, and Tsutomu Ezumi. "OS01W0062 A study about the elliptic inclusion by optical method and finite element method." Abstracts of ATEM : International Conference on Advanced Technology in Experimental Mechanics : Asian Conference on Experimental Mechanics 2003.2 (2003): _OS01W0062. http://dx.doi.org/10.1299/jsmeatem.2003.2._os01w0062.

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16

Roknujjaman, Md, Mohammad Asif Arefin, and Atish Kumar Joarder. "Numerical Solution of Elliptic Partial Differential Equation: Method of Lines and Crank-Nicholson Method." Pan-American Journal of Mathematics 3 (December 23, 2024): 24. https://doi.org/10.28919/cpr-pajm/3-24.

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The method of lines (MOL) is a solution procedure for solving partial differential equation (PDE) and the Crank-Nicholson method (CNM) is an implicit finite difference method, used to solve the elliptic equation and similar partial differential equations numerically. In this study, the numerical techniques were introduced to solve elliptic partial differential equation (PDE) together with initial and boundary conditions. The Poisson equation was considered as an elliptic PDE. Particularly, two methods were used to solve a two-dimensional Poisson equation numerically, such as the method of line

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17

Zhang, Li Hong, and Shu Qian Chen. "Implementation of Embedded Mobile Device Elliptic Curve Algorithm Fast Generating Algorithm." Advanced Materials Research 694-697 (May 2013): 2599–603. http://dx.doi.org/10.4028/www.scientific.net/amr.694-697.2599.

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Elliptic curve cryptosystem is used in the process of embedded systems, the selection and generation algorithm of the elliptic curve will directly affect the efficiency of systems. From Elliptic Curve's selection, Elliptic Curve's structure, Elliptic Curve's generation, this paper discussed the realization of a random elliptic curve method of Embedded Mobile Device, the SEA algorithm and its improved algorithm. The results show that this method can achieve a quick implementation of the elliptic curve method to improve the operating efficiency of embedded systems in the same security guarantees

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18

Antariksha, Verma, and K. Suhas H. "Efficient FEM-FBM for Simulation of Elliptic Particle Sedimentation with Thermal Convection." International Journal of Engineering and Advanced Technology (IJEAT) 9, no. 3 (2020): 1326–35. https://doi.org/10.35940/ijeat.C5375.029320.

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The dynamic sedimentation of large particles including thermal convection gained the significant attentions in various applications using the Direct Numeral Solution (DNS) methods. The current solutions are mainly focused on isothermal suspended particles without the thermal convection separating dissolved particles and enveloping fluids. The systems beside thermal convection having the lack of sufficient investigations like missing the hot and cold elliptic particle in infinity long channels. In this work, we work on two challenges efficient DSN method designing and simulation of elliptic par

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19

Wang, Jun, and Xuexing Li. "Calibration Method for Line-Structured Light Three-Dimensional Measurements Based on a Single Circular Target." Applied Sciences 12, no. 2 (2022): 588. http://dx.doi.org/10.3390/app12020588.

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Single circular targets are widely used as calibration objects during line-structured light three-dimensional (3D) measurements because they are versatile and easy to manufacture. This paper proposes a new calibration method for line-structured light 3D measurements based on a single circular target. First, the target is placed in several positions and illuminated by a light beam emitted from a laser projector. A camera captures the resulting images and extracts an elliptic fitting profile of the target and the laser stripe. Second, an elliptical cone equation defined by the elliptic fitting p

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20

Gepreel, Khaled A., and Amr M. S. Mahdy. "Algebraic computational methods for solving three nonlinear vital models fractional in mathematical physics." Open Physics 19, no. 1 (2021): 152–69. http://dx.doi.org/10.1515/phys-2021-0020.

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Abstract This research paper uses a direct algebraic computational scheme to construct the Jacobi elliptic solutions based on the conformal fractional derivatives for nonlinear partial fractional differential equations (NPFDEs). Three vital models in mathematical physics [the space-time fractional coupled Hirota Satsuma KdV equations, the space-time fractional symmetric regularized long wave (SRLW equation), and the space-time fractional coupled Sakharov–Kuznetsov (S–K) equations] are investigated through the direct algebraic method for more explanation of their novel characterizes. This appro

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21

Pandir, Yusuf, and Humaira Yasmin. "Optical soliton solutions of the generalized sine-Gordon equation." Electronic Journal of Applied Mathematics 1, no. 2 (2023): 71–86. http://dx.doi.org/10.61383/ejam.20231239.

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In this study, the extended trial equation method based on the general form of the nonlinear elliptic ordinary differential equation isemployed to solve the nonlinear generalized sine-Gordon equations. By using this method, we achieve, unlike new types of exact wave solutions such as Elliptic-F, Elliptic-E, and Elliptic-Π functions that are known as elliptic integrals.

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22

Zhang, Lihong, Shuqian Chen, and Yanglie Fu. "Fast Elliptic Curve Algorithm of Embedded Mobile Equipment." Open Electrical & Electronic Engineering Journal 7, no. 1 (2013): 138–42. http://dx.doi.org/10.2174/1874129001307010138.

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Selection Algorithm and Generation Algorithm of elliptic curves have been the focus of research and hotspot of the Elliptic Curve Cryptosystem. This paper discusses a random elliptic curve realization method of Embedded Mobile Equipment, the SEA algorithm and its improved algorithm from Elliptic Curve's selection, Elliptic Curve's structure and Elliptic Curve's generation. Ensuring that the embedded system in the security situation goes through invariable situation causes the embedded system to realize a fast elliptic curve realization method, which enhances the efficiency of embedded system.

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23

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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24

Liu, Chih-Yu, and Cheng-Yu Ku. "A Novel ANN-Based Radial Basis Function Collocation Method for Solving Elliptic Boundary Value Problems." Mathematics 11, no. 18 (2023): 3935. http://dx.doi.org/10.3390/math11183935.

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Elliptic boundary value problems (BVPs) are widely used in various scientific and engineering disciplines that involve finding solutions to elliptic partial differential equations subject to certain boundary conditions. This article introduces a novel approach for solving elliptic BVPs using an artificial neural network (ANN)-based radial basis function (RBF) collocation method. In this study, the backpropagation neural network is employed, enabling learning from training data and enhancing accuracy. The training data consist of given boundary data from exact solutions and the radial distances

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25

Hu, Jian Jun. "Constructing Elliptic Curves over Ramanujan's Class Invariants." Advanced Materials Research 915-916 (April 2014): 1336–40. http://dx.doi.org/10.4028/www.scientific.net/amr.915-916.1336.

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The Complex Multiplication (CM) method is a widely used technique for constructing elliptic curves over finite fields. The key point in this method is parameter generation of the elliptic curve and root compution of a special type of class polynomials. However, there are several class polynomials which can be used in the CM method, having much smaller coefficients, and fulfilling the prerequisite that their roots can be easily transformed to the roots of the corresponding Hilbert polynomials.In this paper, we provide a method which can construct elliptic curves by Ramanujan's class invariants.

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26

Jingzhi Li, Shanqiang Li, and Hongyu Liu. "RESTARTED NONLINEAR CONJUGATE GRADIENT METHOD FOR PARAMETER IDENTIFICATION IN ELLIPTIC SYSTEM." Eurasian Journal of Mathematical and Computer Applications 1, no. 1 (2013): 62–77. http://dx.doi.org/10.32523/2306-3172-2013-1-1-62-77.

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27

Neamah, Ammar Ali. "A NEW PROPOSED METHOD FOR SOLVING AN ELLIPTIC CURVE DISCRETE LOGARITHM PROBLEM." Journal of Kufa for Mathematics and Computer 1, no. 6 (2012): 15–20. http://dx.doi.org/10.31642/jokmc/2018/010603.

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In this work, we present a new approach for solving Elliptic Curve Discrete Logarithm Problem. This method provides a new access to the field of attacking methods the Elliptic Curve Cryptosystems. Beside this paper gives a program for executing the proposed method by using MATLAP.

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28

Xue, Jin Xue, and Bo Zhao. "Research on Grinding Temperature of Nano Z_rO₂ Ceramics Using Diamond Grinding Wheel Dressed by Elliptic Ultrasonic Vibration." Applied Mechanics and Materials 42 (November 2010): 313–16. http://dx.doi.org/10.4028/www.scientific.net/amm.42.313.

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In order to investigate the influence of dressing methods on grinding temperature, two kinds of diamond grinding wheels dressed by traditional dressing(TD) and elliptic ultrasonic vibration dressing(ED) respectively were used to grind the same nano-ceramic material. Through grinding experiments, the comparative analysis of the grinding temperature was conducted. The results show that diamond grinding wheel dressed by elliptical ultrasonic vibration method can decrease the grinding temperature.

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29

Amir, Supri Bin Hj, and Bagas Prasetyo. "Comparison of Elliptic Envelope Method and Isolation Forest Method on Imbalance Dataset." Jurnal Matematika, Statistika dan Komputasi 17, no. 1 (2020): 42–49. http://dx.doi.org/10.20956/jmsk.v17i1.10899.

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The problem of unbalanced data is important in the field of Data Mining. Dataset with unbalanced classes is a dataset whose frequency of occurrence of certain classes is very much different from other classes. This imbalance problem will bias the classifier's performance. Many researchers have examined both the development of algorithms and modifications to the preprocessing stage to overcome this problem. This study discusses the comparison of One Class Classification algorithms, namely Elliptic Envelope and Isolation Forest on unbalanced data. From this study, the Elliptic Envelope Method sh

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30

Liu, Xiang-Qing, Jia-Quan Liu, and Zhi-Qiang Wang. "Quasilinear elliptic equations via perturbation method." Proceedings of the American Mathematical Society 141, no. 1 (2012): 253–63. http://dx.doi.org/10.1090/s0002-9939-2012-11293-6.

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31

Kaplan, A., and R. Tichatschke. "Proximal point method and elliptic regularization." Nonlinear Analysis: Theory, Methods & Applications 71, no. 10 (2009): 4525–43. http://dx.doi.org/10.1016/j.na.2009.03.010.

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32

Gepreel, Khaled A. "Improved General Mapping Deformation Method for Nonlinear Partial Differential Equations in Mathematical Physics." Journal of Applied Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/258396.

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We use the improved general mapping deformation method based on the generalized Jacobi elliptic functions expansion method to construct some of the generalized Jacobi elliptic solutions for some nonlinear partial differential equations in mathematical physics via the generalized nonlinear Klein-Gordon equation and the classical Boussinesq equations. As a result, some new generalized Jacobi elliptic function-like solutions are obtained by using this method. This method is more powerful to find the exact solutions for nonlinear partial differential equations.

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33

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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34

Zhang, Weimin. "Extended Jacobi Elliptic Function Expansion Method to the ZK-MEW Equation." International Journal of Differential Equations 2011 (2011): 1–11. http://dx.doi.org/10.1155/2011/451420.

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The extended Jacobi elliptic function expansion method is applied for Zakharov-Kuznetsov-modified equal-width (ZK-MEW) equation. With the aid of symbolic computation, we construct some new Jacobi elliptic doubly periodic wave solutions and the corresponding solitary wave solutions and triangular functional (singly periodic) solutions.

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35

Ajgoun, S., J. Khalid Naciri, and R. Khatyr. "Semi analytical method for calculating Dean's vortex in Torus of elliptical cross section." MATEC Web of Conferences 286 (2019): 07004. http://dx.doi.org/10.1051/matecconf/201928607004.

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Based on the work of Dean (1927 and 1928) [1-2] and Cuming (1952) [3], the stationary flow of an incompressible Newtonian fluid through a curved pipe of uniform curvature and with elliptic cross section is studied. The Navier-Stokes equations are expressed in toroïdal coordinates system (s,r,θ). Following Dean’s approach, the governing equations for the fluid motion through a curved elliptical channel are solved by using an original semi analytical method for the resolution of a biharmonic equation. The main interest in this study is to test and validate in the case of an elliptical cross sect

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36

Wang, Qiuliang, and Jinru Chen. "An Unfitted Discontinuous Galerkin Method for Elliptic Interface Problems." Journal of Applied Mathematics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/241890.

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An unfitted discontinuous Galerkin method is proposed for the elliptic interface problems. Based on a variant of the local discontinuous Galerkin method, we obtain the optimal convergence for the exact solutionuin the energy norm and its fluxpin theL2norm. These results are the same as those in the case of elliptic problems without interface. Finally, some numerical experiments are presented to verify our theoretical results.

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Chen, Yong, Qi Wang, and Biao Lic. "Jacobi Elliptic Function Rational Expansion Method with Symbolic Computation to Construct New Doubly-periodic Solutions of Nonlinear Evolution Equations." Zeitschrift für Naturforschung A 59, no. 9 (2004): 529–36. http://dx.doi.org/10.1515/zna-2004-0901.

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A new Jacobi elliptic function rational expansion method is presented by means of a new general ansatz and is very powerful, with aid of symbolic computation, to uniformly construct more new exact doubly-periodic solutions in terms of rational form Jacobi elliptic function of nonlinear evolution equations (NLEEs). We choose a (2+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we obtain the solutions found by most existing Jacobi elliptic function expansion methods and find other new and more general solutions at the same time. When the modulus of the Jacobi

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38

Joye, Marc. "Protecting ECC Against Fault Attacks: The Ring Extension Method Revisited." Journal of Mathematical Cryptology 14, no. 1 (2020): 254–67. http://dx.doi.org/10.1515/jmc-2019-0030.

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AbstractDue to its shorter key size, elliptic curve cryptography (ECC) is gaining more and more popularity. However, if not properly implemented, the resulting cryptosystems may be susceptible to fault attacks. Over the past few years, several techniques for secure implementations have been published. This paper revisits the ring extension method and its adaptation to the elliptic curve setting.

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39

Juhari, Juhari, and Mohamad Febry Andrean. "On the Application of Noiseless Steganography and Elliptic Curves Cryptography Digital Signature Algorithm Methods in Securing Text Messages." CAUCHY: Jurnal Matematika Murni dan Aplikasi 7, no. 3 (2022): 483–92. http://dx.doi.org/10.18860/ca.v7i3.17358.

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Elliptic curve cryptography includes symmetric key cryptography systems that base their security on mathematical problems of elliptic curves. There are several ways that can be used to define the elliptic curve equation that depends on the infinite field used, one of which is the infinite field prima ( where ). Elliptic curve cryptography can be used for multiple protocol purposes, digital signatures, and encryption schemes.The purpose of this study is to determine the process of hiding encrypted messages using the Noiseless Steganography method as well as the generation of private keys and pu

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40

SMART, N. P., and N. M. STEPHENS. "Integral points on elliptic curves over number fields." Mathematical Proceedings of the Cambridge Philosophical Society 122, no. 1 (1997): 9–16. http://dx.doi.org/10.1017/s0305004196001211.

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In recent years there has been an interest in using elliptic logarithms to find integral points on elliptic curves defined over the rationals, see [23], [17], [6] and [12]. This has been partly due to work of David [5], who gave an explicit lower bound for linear forms in elliptic logarithms. Previously, integral points on elliptic curves had been found by Siegel's method; that is, a reduction to a set of Thue equations which could be solved, in principle, by the methods in [19]. For examples of this method see [3], [7], [16], [18], [21], [22] and [8]. Other techniques can be used to find all

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41

Pallikaris, Athanasios, and George Latsas. "New Algorithm for Great Elliptic Sailing (GES)." Journal of Navigation 62, no. 3 (2009): 493–507. http://dx.doi.org/10.1017/s0373463309005323.

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An analytical method and algorithm for great elliptic sailing (GES) calculations is presented. The method solves the complete GES problem calculating not only the great elliptic arc distance, but also other elements of the sailing such as the geodetic coordinates of intermediate points along the great elliptic arc. The proposed formulas provide extremely high accuracies and are straightforward to be exploited immediately in the development of navigational software, without the requirement to use advanced numerical methods. Their validity and effectiveness have been verified with numerical test

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Antony, S. N. F. M. A., C. H. K. Yion,, H. Kamarulhaili,, M. R. K. Ariffin, and F. Yunos,. "Fast Endomorphisms in Integer Sub-Decomposition Method on Secp192k1." Malaysian Journal of Mathematical Sciences 18, no. 3 (2024): 501–14. http://dx.doi.org/10.47836/mjms.18.3.03.

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Elliptic curve cryptography involves numerous scalar multiplications, incurring high operational costs. In view of this, fast endomorphism is used to represent scalar multiplications, kP on elliptic curves. In the past, techniques such as Gallant-Lambert-Vanstone (GLV) method and Integer Sub-Decomposition (ISD) method have been proposed to reduce the cost of scalar multiplication on elliptic curves by using fast endomorphism. The GLV method employs a single-layer decomposition, breaking k into k1 and k2, while the ISD method uses a bilayer decomposition. The existence of fast endomorphisms whi

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Antonietti, Paola F., Blanca Ayuso de Dios, Susanne C. Brenner, and Li-yeng Sung. "Schwarz Methods for a Preconditioned WOPSIP Method for Elliptic Problems." Computational Methods in Applied Mathematics 12, no. 3 (2012): 241–72. http://dx.doi.org/10.2478/cmam-2012-0021.

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Abstract We propose and analyze several two-level non-overlapping Schwarz methods for a preconditioned weakly over-penalized symmetric interior penalty (WOPSIP) discretization of a second order boundary value problem. We show that the preconditioners are scalable and that the condition number of the resulting preconditioned linear systems of equations is independent of the penalty parameter and is of order H/h, where H and h represent the mesh sizes of the coarse and fine partitions, respectively. Numerical experiments that illustrate the performance of the proposed two-level Schwarz methods a

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Mokin, Yu I. "The capacitance matrix method in numerical methods for elliptic equations." USSR Computational Mathematics and Mathematical Physics 26, no. 6 (1986): 199–200. http://dx.doi.org/10.1016/0041-5553(86)90171-0.

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Decker, Luke, and Qunshan Zhang. "Quantifying and correcting residual azimuthal anisotropic moveout in image gathers using dynamic time warping." GEOPHYSICS 85, no. 5 (2020): O71—O82. http://dx.doi.org/10.1190/geo2019-0324.1.

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We have developed a novel application of dynamic time warping (DTW) for correcting residual moveout in image gathers, enhancing seismic images, and determining azimuthal anisotropic orientation and relative intensity when moveout is caused by wave propagation through a medium possessing elliptical horizontally transverse isotropy (HTI). The method functions by first using DTW to determine the sequences of integer shifts that most closely match seismic traces within an image gather to its stack and then applying those shifts to flatten the gather. Flattening shifts are fitted to an ellipse to p

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Rattapasakorn, Sountaree, Jesda Panichakorn, and Mongkol Mongkolwongrojn. "Effects of Surface Roughness on Elastohydrodynamic Lubrication in Elliptical Contact with Non-Newtonian Fluids." Advanced Materials Research 482-484 (February 2012): 1057–61. http://dx.doi.org/10.4028/www.scientific.net/amr.482-484.1057.

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This paper presents the effect of surface roughness on the performance characteristics of elastohydrodynamic lubrication with non-Newtonian fluid base on Carreau viscosity model in elliptical contact. The time independent modified Reynolds equation and elastic equation were formulated for compressible fluid. Perturbation method, Newton Raphson method and full adaptive multigrid method were implemented to obtain the film pressure, film thickness profiles and friction coefficient in the contact region at various amplitude of combined surface roughness, applied loads, speeds and elliptic ratio. S

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Xiang, Chun Huan. "Travelling Wave Solutions of Nonlinear Evolution Equation by Using an Auxiliary Elliptic Equation Method." Applied Mechanics and Materials 166-169 (May 2012): 3228–32. http://dx.doi.org/10.4028/www.scientific.net/amm.166-169.3228.

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The Camassa-Holm and Degasperis-Procesi equation describing unidirectional nonlinear dispersive waves in shallow water is reconsidered by using an auxiliary elliptic equation method. Detailed analysis of evolution solutions of the equation is presented. Some entirely new periodic-soliton solutions, include Jacobi elliptic function solutions, hyperbolic solutions and trigonal solutions, are obtained. The employed auxiliary elliptic equation method is powerful and can be also applied to solve other nonlinear differential equations. This method adds a new route to explore evolution solutions of n

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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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Kirillova, I. V. "Elliptic Boundary Layer in Shells of Revolution under Surface Shock Loading of Normal Type." Mechanics of Solids 59, no. 5 (2024): 2686–93. https://doi.org/10.1134/s0025654424604397.

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Abstract In the present article, a method for solving a boundary value problem for an elliptical boundary layer occurring in thin-walled shells of revolution under normal-type impacts on the front surfaces is constructed. The elliptical boundary layer is constructed in the vicinity of a conditional front of Rayleigh surface waves and is described by elliptic equations with boundary conditions specified by hyperbolic equations. In the general case of shells of revolution, the methods for solving equations for an elliptical boundary layer developed for shells of revolution of zero Gaussian curva

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Blaheta, Radim. "A multilevel method with correction by aggregation for solving discrete elliptic problems." Applications of Mathematics 31, no. 5 (1986): 365–78. http://dx.doi.org/10.21136/am.1986.104214.

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