Results 21 to 30 of about 651 (161)

Transcendental entire solutions of several complex product-type nonlinear partial differential equations in ℂ2

Open Mathematics, 2023
Our purpose in this article is to describe the solutions of several product-type nonlinear partial differential equations (PDEs) (a1u+b1uz1+c1uz2)(a2u+b2uz1+c2uz2)=1,\left({a}_{1}u+{b}_{1}{u}_{{z}_{1}}+{c}_{1}{u}_{{z}_{2}})\left({a}_{2}u+{b}_{2}{u}_{{z}_{
Xu Yi Hui, Li Yan Fang, Liu Xiao Lan, Xu Hong Yan   +3 more
doaj   +1 more source

The fermat equation over quadratic fields

, 1984
Kummer's method of proof is applied to the Fermat equation over quadratic fields. The concept of an m-regular prime, p, is introduced and it is shown that for certain values of m, the Fermat equation with exponent p has no nontrivial solutions over the ...
Parry, Charles J., Hao, Fred H.
core   +1 more source

SPECIAL COURSE FOR SCHOOLCHILDREN: PROOF OF FERMAT'S GREAT THEOREM BY EXAMPLE x^3+y^3+z^3=0 [PDF]

Vestnik Issyk-Kulʹskogo universiteta
It is difficult to find a person among mathematicians who is not familiar with and does not study the solution of the equation x^2+y^2+z^2=0, or x^3+y^3+z^3=0 in integers.
Srashidinov A.
doaj   +1 more source

Data supporting Extended Fermat Equation

, 2018
<p>Data supporting draft paper "Prabhakar, Giri. (2018, June 20). On Triangles as Real Analytic Varieties of an Extended Fermat Equation (Version Draft). Zenodo.
Prabhakar, Giri (5455286), Prabhakar, Giri   +1 more
core   +1 more source

The Fermat equation over Q(2)

, 2004
We study solutions of the Fermat equation defined over Q(2), and prove a version of `Fermat's Last Theorem' over Q(2), assuming an unpublished result of ...
Meekin, Paul, Jarvis, Frazer
core   +1 more source

Fermat Operational Matrix for Solving Nonlinear Fractional Differential Equations Using Spectral Galerkin Method

Wasit Journal for Pure Sciences
This paper presents a truncated series of Fermat polynomials as a quick and effective way to solve fractional differential equations numerically. The suggested method converts the fractional differential equation with its beginning conditions into a set ...
Abdullah Hussain, Ali Khalaf
doaj   +1 more source

The generalized fermat equation in function fields

, 1991
We show that if r > n!(n! − 2) the set of solutions xj ∈ C(t) of a Fermat equation Σ1najxjr = 0, aj ∈ C(t), is the union of at most n!n! families with an explicitly given simple structure.
Bombieri, E., Mueller, J.
core   +1 more source

Analytical solution of non-exponential decay in a simple resistor-capacitor circuit using the Lambert-Tsallis Wq function [PDF]

Revista Brasileira de Ensino de Física
In this work, using the Lambert-Tsallis Wq function, we present the analytical solution for the non-exponential decay in a simple electrical circuit composed by two resistors, two capacitors and a DC power supply.
L.A.B. Ramos, R.V. Ramos
doaj   +1 more source

On solutions of certain compatible systems of quadratic trinomial Partial differential-difference equations

Математичні Студії
This paper has involved the use of a variety of variations of the Fermat-type equation $f^n(z)+g^n(z)=1$, where $n(\geq 2)\in\mathbb{N}$. Many researchers have demonstrated a keen interest to investigate the Fermat-type equations for entire and ...
R. Mandal, R. Biswas
doaj   +1 more source

Guiding and Manipulating Light Fields in Microstructured Liquid Crystals

Advanced Physics Research, EarlyView.
This review summarizes recent advances in guided‐wave optics enabled by microstructured liquid crystal (LC) devices, covering their fundamental material properties, key degree of freedom for dynamic light field manipulations. The advances of linear guided‐wave optics, nonlinear‐optics with spatial optical solitons, and microlasers in LC‐based devices ...
Shan‐shan Chang, Yong‐shuai Li, Jin‐hui Chen   +2 more
wiley   +1 more source