arXiv subjects

Ali Reza

Publications and source records attributed to Ali Reza.

2 recordsLinked to original sources

arXiv2023

Optimal System and Conservation Laws for the Generalized Fisher Equation in Cylindrical Coordinates

The reaction diffusion equation arises in physical situations in problems from population growth, genetics and physical sciences. We consider the generalised Fisher equation in cylindrical coordinates from Lie theory stand point. An invariance method is performed and the optimal set of nonequivalent symmetries is obtained. Finally, the conservation laws are constructed using 'multiplier method'. We determine multipliers as functions of the dependent and independent variables only. The conservation laws are computed and presented in terms of conserved vector corresponding to each multiplier.

math.AP↗

arXiv2017

Functors induced by Cauchy extension of C*-algebras

In this paper we give three functors $\mathfrak{P}$, $[\cdot]_K$ and $\mathfrak{F}$ on the category of C$^\ast$-algebras. The functor $\mathfrak{P}$ assigns to each C$^\ast$-algebra $\mathcal{A}$ a pre-C$^\ast$-algebra $\mathfrak{P}(\mathcal{A})$ with completion $[\mathcal{A}]_K$. The functor $[\cdot]_K$ assigns to each C$^\ast$-algebra $\mathcal{A}$ the Cauchy extension $[\mathcal{A}]_K$ of $\mathcal{A}$ by a non-unital C$^\ast$-algebra $\mathfrak{F}(\mathcal{A})$. Some properties of these functors are also given. In particular, we show that the functors $[\cdot]_K$ and $\mathfrak{F}$ are exact and the functor $\mathfrak{P}$ is normal exact.

math.OA↗