3,092 Results Found

We revisit Edwards normal form for elliptic curves, and show how elementary symmetry arguments lead to a more general expression for his addition formula on these curves. Using the free parameter in our formula, we describe Edwards addition via a con...

In this research paper, the negative order Korteweg–de Vries equation expressed as nonlinear partial differential equation, firstly introduced by Wazwaz, is solved for the exact Jacobi elliptic function solution. For this purpose, the Jacobi el...

In recent decades there has been an increasing interest in Elliptic curve cryptography (ECC) and, especially, the Elliptic Curve Digital Signature Algorithm (ECDSA) in practice. The rather recent developments of emergent technologies, such as blockch...

The Fibonacci sequence is a well-known sequence of numbers with numerous applications in mathematics, computer science, and other fields. In recent years, there has been growing interest in studying Fibonacci-like sequences on elliptic curves. These...

We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this sy...

It is a famous hypothesis that orbifold D-brane charges in string theory can be classified in twisted equivariant K-theory. Recently, it is believed that the hypothesis has a non-trivial lift to M-branes classified in twisted real equivariant 4-Cohom...

Elliptic curves with the special quality known as supersingularity have gained much popularity in the rapidly developing field of cryptography. The conventional method of employing random search is quite ineffective in finding these curves. This pape...

In this study, we obtained results for the computation of eigen-pairs, singular value decomposition, pseudoinverse, and the least squares problem for elliptic quaternion matrices. Moreover, we established algorithms based on these results and provide...

Elliptic Curve Cryptography (ECC) is a technology based on the arithmetic of elliptic curves used to build strong and efficient cryptosystems and infrastructures. Several ECC systems, such as the Diffie–Hellman key exchange and the Elliptic Cur...

In order to construct the border solutions for nonsupersingular elliptic curve equations, some common used models need to be adapted from linear treated cases for use in particular nonlinear cases. There are some approaches that conclude with these s...

The linear Weingarten condition with ellipticity for the mean curvature and the extrinsic Gaussian curvature on a surface in the three-sphere can define a Riemannian metric which is called the elliptic linear Weingarten metric. We established some lo...

We are concerned with positive solutions of two types of nonlinear elliptic boundary value problems (BVPs). We present conditions for existence, uniqueness and multiple positive solutions of a first type of elliptic BVPs. For a second type of ellipti...

The existence of two positive solutions for an elliptic differential inclusion is established, assuming that the nonlinear term is an upper semicontinuous set-valued mapping with compact convex values having subcritical growth. Our approach is based...

An analytical–numerical method for determining the two-dimensional (2D) thermal field in a layer-inhomogeneous elliptic cylinder (elliptical roller) was developed in the article. A mathematical model was formulated in the form of a boundary pro...

In this study, we developed a MATLAB 2024a toolbox that performs advanced algebraic calculations in the algebra of elliptic numbers and elliptic quaternions. Additionally, we introduce color image processing methods, such as principal component analy...

Circuit-based zero-knowledge proofs have arose as a solution to the implementation of privacy in blockchain applications, and to current scalability problems that blockchains suffer from. The most efficient circuit-based zero-knowledge proofs use a p...

We study the regularizing effect of the zero order term in some elliptic problems, which present in the principal part a nonlocal operator, i.e., the fractional Laplacian operator. We prove the existence of bounded energy solutions, even if the data...

The purpose of this article is to introduce the concept of elliptic-valued suprametric spaces and to establish some common fixed point theorems within this newly proposed framework. The development of elliptic-valued suprametric spaces, along with th...

Background/Objectives: In computer graphics, virtual worlds are constructed and visualized through algorithmic processes. These environments are typically populated with objects defined by mathematical models, traditionally based on Euclidean geometr...

Firstly, we present a more explicit formulation of the complete system $D(N)$ of representatives of Manin’s symbols over $\mathbb{Q}$, which was initially given by Shimura. Then, we establish a bijection between $D(M)\times D(N)$ and $D(MN)$ for $(M,N)=1$, which...

In this article, we propose an optimal control problem for generalized elliptic quasi-variational inequality with unilateral constraints. Then, we discuss the sufficient assumptions that ensure the convergence of the solutions to the optimal control...

We investigate the half-space Dirichlet problem with summable boundary-value functions for an elliptic equation with an arbitrary amount of potentials undergoing translations in arbitrary directions. In the classical case of partial differential equa...

This work presents a new concept to implement the elliptic curve point multiplication (PM). This computation is based on a new modular arithmetic over Gaussian integer fields. Gaussian integers are a subset of the complex numbers such that the real a...

In this paper, we report a multi-ring disk resonator with elliptic spokes for compensating the aniso-elasticity of (100) single crystal silicon. The structural coupling between each ring segments can be controlled by replacing the straight beam spoke...

We consider an elliptic variational–hemivariational inequality $\mathcal{P}$ in a real reflexive Banach space, governed by a set of constraints K. Under appropriate assumptions of the data, this inequality has a unique solution $u\in K$. We associate inequ...

In this work, we study a nonlocal boundary value problem for a quasilinear elliptic equation. Using the method of regularization and parameter continuation, we prove the existence and uniqueness of a regular solution to the nonlocal boundary value pr...

The averaging effect is a distinctive property possessed by fractional operators. In recent years, it has emerged as a powerful tool in the study of qualitative properties of solutions to fractional elliptic and parabolic equations. In this article,...

We construct examples of billiards where two chaotic flows are moving in opposite directions around a non-chaotic core or vice versa; the dynamics in the core are chaotic but flows that are moving in opposite directions around it are non-chaotic. The...

In this paper, we prove existence and regularity results for a nonlinear elliptic problem of p-Laplacian type with a singular potential like ${\displaystyle \frac{f}{u^{\gamma }}}$ and a lower order term $bu$, where u is the solution and b and f are only assumed to be summable func...

We implement elliptic curve cryptography on the MSP430 which is a commonly used microcontroller in wireless sensor network nodes. We use the number theoretic transform to perform finite field multiplication and squaring as required in elliptic curve...

Radio Frequency Identification (RFID) is an important technique for wireless sensor networks and the Internet of Things. Recently, considerable research has been performed in the combination of public key cryptography and RFID. In this paper, an effi...

In this paper, we propose a finite volume element method of primal-dual type to solve the ill-posed elliptic problem, that is, the elliptic problem with lacking or overlapping boundary value condition. We first establish the primal-dual finite volume...

In this paper, we consider a class of degenerate elliptic equations with arbitrary power degeneration. The issues about the existence, uniqueness, and smoothness of solutions of the semiperiodic Dirichlet problem for a class of degenerate elliptic eq...

We studied paraxial light beams, obtained by a continuous superposition of off-axis Gaussian beams with their phases chosen so that the whole superposition is invariant to free-space propagation, i.e., does not change its transverse intensity shape....

Cybersecurity is a critical issue for Real-Time IoT applications since high performance and low latencies are required, along with security requirements to protect the large number of attack surfaces to which IoT devices are exposed. Elliptic Curve C...

In this paper, we study a hyperbolic–elliptic system with $L^1$-initial data, which arises as a mathematical model for chemotaxis. In particular, after introducing the notion of entropy solutions in this setting, we prove results concerning the ex...

Let $\mathcal{K}\left(r\right)$ be the complete elliptic integral of the first kind. Then, the inequality $2\mathcal{K}\left(r\right)/\pi >{tanh}^{-1}\left(r\right)/{sin}^{-1}\left(r\right)$ holds for all $r\in (0,1)$. This conclusion does not match those in the existing literature.

This paper addresses the elliptic interface problem involving jump conditions across the interface. We propose a hybrid mixed finite element method on the triangulation where the interfaces are aligned with the mesh. The second-order elliptic equatio...

We propose an image encryption scheme based on quasi-resonant Rossby/drift wave triads (related to elliptic surfaces) and Mordell elliptic curves (MECs). By defining a total order on quasi-resonant triads, at a first stage we construct quasi-resonant...

The role played by explicit formulas for solving boundary value problems for elliptic equations and systems is well known. In this paper, explicit formulas for a general solution of the Dirichlet problem for second-order elliptic systems in the unit...

In this paper, we present a novel lightweight elliptic curve scalar multiplication architecture for random Weierstrass curves over prime field ${\mathbb{F}}_p$. The elliptic curve scalar multiplication is executed in Jacobian coordinates based on the Montgomery la...

This paper deals with the second-order semi-linear degenerate elliptic equation $y{u}_{yy}+b{u}_y+{\Delta }_{x}u+{|u|}^{\alpha -1}u=0,(x,y)\in {\mathbb{R}}^n\times (0,\infty )$, where $n\ge 1,\alpha >1$. We establish a Liouville theorem of stable solution of the degenerate...

We study the solvability in Sobolev spaces of boundary value problems for elliptic and parabolic equations with variable coefficients in the presence of an involution (involutive deviation) at higher derivatives, both in the nondegenerate and degener...

The velocity obstacles (VO) method is widely employed in real-time obstacle avoidance research for UAVs due to its succinct mathematical foundation and rapid, dynamic planning abilities. Traditionally, VO assumes a circle protection domain with a fix...

In this paper, we propose a new scheme based on ephemeral elliptic curves over a finite ring with an RSA modulus. The new scheme is a variant of both the RSA and the KMOV cryptosystems and can be used for both signature and encryption. We study the s...

This work presents an Elliptic-curve Point Multiplication (ECP) architecture with a focus on low latency and low area for radio-frequency-identification (RFID) applications over $GF\left(2^{163}\right)$. To achieve low latency, we have reduced the clock cycles by us...

The Sumudu transform of the Dixon elliptic function with non-zero modulus α ≠ 0 for arbitrary powers N is given by the product of quasi C fractions. Next, by assuming the denominators of quasi C fractions as one and applying the Heliermannco...

In our previous works, we developed the superconvergence of a nonconforming finite element method based on unfitted meshes for an elliptic interface problem and elliptic problem, respectively. In this paper, a nonconforming interface penalty finite e...

In this paper, we proposed an enhanced asymmetric cryptosystem scheme for image encryption using a combination of Elliptic Curve and Fourier transformations. Our proposed encryption and decryption process is highly secure with a smaller key size comp...

This paper presents unified counterexamples for which standard elliptic regularity results break down for linear elliptic equations with highly singular coefficients in dimensions $d\ge 3$. First, we establish well-posedness for the case where the drif...