Results 221 to 230 of about 37,919 (260)

On p Laplace polynomial solutions

The Journal of Analysis, 2016
This paper investigates the existence of real homogeneous polynomial solutions of the \(p\)-Laplace equation \(\mathrm{div}(\left| \nabla u\right| ^{p-2}\nabla u)=0\) on \(\mathbb{R}^{n}\) (\(n\geq 3\)), where \(p\in \mathbb{R}\backslash \{1,2\}\). Recently, Tkachev showed that there are no such solutions of degree \(3\).
Lewis, John L., Vogel, Andrew
openaire   +1 more source

Simultaneous solution of polynomial equations

Applied Mathematics and Computation, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Celik, E, Bayram, M
openaire   +3 more sources

Algebraic Traveling Wave Solutions, Darboux Polynomials and Polynomial Solutions

Qualitative Theory of Dynamical Systems, 2017
A traveling wave solution \(u= U(x-ct)\) of a partial differential equation \(u_{xx}= F(u,u_x,u_t)\) is called an algebraic traveling wave solution if there exists a polynomial \(p\) such that \(p(U,U')= 0\). The author completely characterizes the existence of algebraic traveling wave solutions of the partial differential equation \[ u_t= du_{xx}- a(u-
openaire   +2 more sources

RETRACTED ARTICLE: Trigonometric polynomial solutions of Bernouilli trigonometric polynomial differential equations

Analysis and Mathematical Physics, 2023
The paper investigates two types of real trigonometric polynomial equations: \[ A(\theta)y'=B_1(\theta)+B_n(\theta)y^n \] and \[ A(\theta)y^{n-1}y'=B_1(\theta)+B_n(\theta)y^n \] The authors focus on the first equation and demonstrate that when $n\geq 4$, it has a maximum of 3 real trigonometric polynomial solutions if $n$ is even and 5 real ...
openaire   +1 more source

Polynomial solutions to piezoelectric beams (I)—Several exact solutions

Applied Mathematics and Mechanics, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ding, Hao-Jiang, Jiang, Ai-Min
openaire   +2 more sources

Solutions to Problems: Factorization of Polynomials

2021
In this chapter, the problems of the ninth chapter are fully solved, in detail, step-by-step, and with different methods.
openaire   +1 more source

Orthonormal Polynomials in Wavefront Analysis: Analytical Solution

Frontiers in Optics, 2006
Zernike circle polynomials are in widespread use for wavefront analysis because of their orthogonality over a circular pupil and their representation of balanced classical aberrations. In recent papers, we derived closed-form polynomials that are orthonormal over a hexagonal pupil, such as the hexagonal segments of a large mirror. We extend our work to
Virendra N, Mahajan, Guang-ming, Dai
openaire   +2 more sources

FIXED DEGREE SOLUTIONS OF POLYNOMIAL EQUATIONS

IFAC Proceedings Volumes, 1992
Abstract Given the linear polynomial equation AX+ BY=C we study the existence of solutionpairs X, Y having prespecified degrees, and parametrize all such pairs. This result proves useful in the analysis and design of linear control systems.
openaire   +1 more source

Constant solutions of polynomial equations

International Journal of Control, 1991
Abstract A necessary and sufficient condition is given for the equation AX + BY = C in polynomial matrices to have a constant solution pair X, Y and also for X to be non-singular. A sufficient condition is then established under which the equation with A and B fixed has a constant solution for each C from a given class. Applications to the construction
VLADIMÍR KUČERA, PETR ZAGALAK
openaire   +1 more source

NUMERICAL SOLUTIONS OF POLYNOMIAL EQUATIONS

1968
Abstract : The report describes the FORTRAN Subroutine POLYR and a related complete program BRL-RSSR for finding all roots (real and complex) of a real polynomial equation P(x) = Summation from i = o to i = N of ((A sub i)(x to the power (N-i)))=0. The method which is used combines the root squaring and the subresultant (extracting quadratic factors ...
Henry Wisniewski, Tadeusz Leser
openaire   +1 more source