scholarly journals On some further properties of solutions to a certain semi-linear system of partial differential equations

1973 ◽  
Vol 9 (3) ◽  
pp. 577-595 ◽  
Author(s):  
Atsushi Yoshikawa ◽  
Masaya Yamaguti
Keyword(s):  
Partial Differential Equations ◽  
Linear System ◽  
Differential Equations ◽  
Partial Differential

A linear system of partial differential equations modeling the resting potential of a heart with regional ischemia

2007 ◽  
Vol 210 (1) ◽  
pp. 238-252 ◽  
Author(s):  
Mary C. MacLachlan ◽  
Joakim Sundnes ◽  
Ola Skavhaug ◽  
Marius Lysaker ◽  
Bjørn Fredrik Nielsen ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Linear System ◽  
Differential Equations ◽  
Resting Potential ◽  
Partial Differential ◽  
Regional Ischemia

Construction of metric and vector potential perturbations of a Reissner–Nordström black hole

1979 ◽  
Vol 369 (1736) ◽  
pp. 67-81 ◽  
Keyword(s):  
Black Hole ◽  
Partial Differential Equations ◽  
Linear System ◽  
Differential Equations ◽  
Vector Potential ◽  
Maxwell Equations ◽  
Coupled System ◽  
System Of Equations ◽  
Partial Differential ◽  
Explicit Formulae

When an appropriate decoupling of variables in a coupled linear system of partial differential equations is obtained, a recently described procedure enables one to construct solutions to the full coupled system of equations. We employ this procedure here to generate solutions of the linearized Einstein–Maxwell equations describing perturbations of a Reissner–Nordström black hole, using Chandrasekhar’s recent decoupling of these equations. Explicit formulae are given for the metric and vector potential perturbations for each parity type.

scholarly journals Topology and factorization of polynomials

2009 ◽  
Vol 104 (1) ◽  
pp. 51 ◽  
Author(s):  
Hani Shaker
Keyword(s):  
Partial Differential Equations ◽  
Linear System ◽  
Differential Equations ◽  
Vector Space ◽  
System Of Equations ◽  
Partial Differential ◽  
Linear System Of Equations ◽  
Complete Factorization ◽  
Factorization Of Polynomials

For any polynomial $P\in {\mathsf C} [X_1,X_2,\ldots,X_n]$, we describe a $\mathsf C$-vector space $F(P)$ of solutions of a linear system of equations coming from some algebraic partial differential equations such that the dimension of $F(P)$ is the number of irreducible factors of $P$. Moreover, the knowledge of $F(P)$ gives a complete factorization of the polynomial $P$ by taking gcd's. This generalizes previous results by Ruppert and Gao in the case $n=2$.

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