arXiv subjects
Publications and source records attributed to H. R. Rezazadeh.
In this short letter we show that the one dimensional non linear Schrödinger equation(NLS)can be solved by a Hopf-Cole transformation which converts it to the Burgers equation in turbulence.
This paper presents some mathematical aspects of Classical Liouville theorem and we have noted some mathematical theorems about its initial value problem. Furthermore, we have implied on the formal frame work of Stochastic Liouville equation (SLE).
In this letter we proved this theorem: \emph{if $F$ be a holomorphic mapping of $T_Ω$ to a mapping manifold $X$ such that for every compact subset $K\subset Ω$ the mapping $F$ is uniformly continues on $T_{K}$ and $F(T_{K})$ is a relatively compact subset of $X$. If the restriction of $F(z)$ to some hyperplane $\mathbb{R}^{m}+iy'$ is semi periodic, then $F(z)$ is an semi mapping of $T_Ω$ to $X$.}
In this short paper we review and extract some features of the Fredholm Alternative problem .
In this paper we found an Exact solution for massless scalar field with cosmological constant. This exact solution generalized the Levi-Civita vacuum solution\cite{8} to a massless scalar field,with a cosmological constant term. This solution in the absence of the Cosmological constant recovers the spacetime of a massless scalar field with cylindrical symmetry (\emph{Buchdahl metric}\cite{2}). Also if the scalar field disappears, the spacetime is a representation of de-Sitter space. We prove that the form of the metric's function which was purposed in \cite{1} is valid even if we assume a general form. Too we show that in which conditions this solution satisfies energy conditions. Finally the validity of focusing theorem is proved.