Tariq Ismaeel - Academia.edu (original) (raw)
Papers by Tariq Ismaeel
AIMS Mathematics, 2022
In this article, we discuss the positive measure reducibility for quasi-periodic linear systems c... more In this article, we discuss the positive measure reducibility for quasi-periodic linear systems close to a constant which is defined as: \begin{document}$ \begin{align*} \frac{dx}{dt} = (A(\lambda) + Q(\varphi,\lambda))x, \dot{\varphi} = \omega, \end{align*} enddocumentwhere\end{document} where enddocumentwhere \omega $ is a Brjuno vector and parameter $ \lambda\in (a, b) $. The result is proved by using the KAM method, Brjuno-Rüssmann condition, and non-degeneracy condition.
Boundary Value Problems, 2017
The Wiener criterion is a sufficient and necessary condition for the solvability of the Dirichlet... more The Wiener criterion is a sufficient and necessary condition for the solvability of the Dirichlet problem. However, its geometric interpretation is not clear. In the case that the domain satisfies an exterior spine condition, the requirement for the spine is clear in dimension 3. In this note, we intend to obtain the condition that the exterior spine should satisfy in higher dimensions.
Applied Mathematics, 2015
Applied Mathematics, 2015
Communications in Theoretical Physics, 2007
It has been pointed by Hall et al. [1] that matter collinations can be defined by using three dif... more It has been pointed by Hall et al. [1] that matter collinations can be defined by using three different methods. But there arises the question of whether one studies matter collineations by using the L ξ T ab = 0, or L ξ T ab = 0 or L ξ T b a = 0. These alternative conditions are, of course, not generally equivalent. This problem has been explored by applying these three definitions to general static spherically symmetric spacetimes. We compare the results with each definition.
Modern Physics Letters A, 2007
We investigate matter collineations of plane symmetric spacetimes when the energy–momentum tensor... more We investigate matter collineations of plane symmetric spacetimes when the energy–momentum tensor is degenerate. There exists three interesting cases where the group of matter collineations is finite-dimensional. The matter collineations in these cases are either four, six or ten in which four are isometries and the rest are proper.
Arxiv preprint arXiv:1106.1785, 2011
This paper is devoted to explore the energy-momentum of nonstatic plane symmetric spacetimes in t... more This paper is devoted to explore the energy-momentum of nonstatic plane symmetric spacetimes in the context of General Relativity and teleparallel theory of gravity. For this purpose, we use four prescriptions, namely, Einstein, Landau-Lifshitz, Bergmann-Thomson and Møller in both theories. It is shown that the results for the first three prescriptions turn out to be same in both the theories but different for last prescription. It is mentioning here that our results coincide with the results obtained by Sharif and kanwal [1] for Bell-Szekeres metric under certain choice of the metric functions.
The matter collineations of plane symmetric spacetimes are studied according to the degenerate en... more The matter collineations of plane symmetric spacetimes are studied according to the degenerate energy-momentum tensor. We have found many cases where the energy-momentum tensor is degenerate but the group of matter collineations is finite. Further we obtain different constraint equations on the energy-momentum tensor. Solving these constraints may provide some new exact solutions of Einstein field equations.
Journal of Inequalities and Applications
This paper studies the reducibility of almost-periodic Hamiltonian systems with small perturbatio... more This paper studies the reducibility of almost-periodic Hamiltonian systems with small perturbation near the equilibrium which is described by the following Hamiltonian system: dx dt = J A + εQ(t, ε) x + εg(t, ε) + h(x, t, ε). It is proved that, under some non-resonant conditions, non-degeneracy conditions, the suitable hypothesis of analyticity and for the sufficiently small ε, the system can be reduced to a constant coefficients system with an equilibrium by means of an almost-periodic symplectic transformation.
AIMS Mathematics, 2022
In this article, we discuss the positive measure reducibility for quasi-periodic linear systems c... more In this article, we discuss the positive measure reducibility for quasi-periodic linear systems close to a constant which is defined as: \begin{document}$ \begin{align*} \frac{dx}{dt} = (A(\lambda) + Q(\varphi,\lambda))x, \dot{\varphi} = \omega, \end{align*} enddocumentwhere\end{document} where enddocumentwhere \omega $ is a Brjuno vector and parameter $ \lambda\in (a, b) $. The result is proved by using the KAM method, Brjuno-Rüssmann condition, and non-degeneracy condition.
Boundary Value Problems, 2017
The Wiener criterion is a sufficient and necessary condition for the solvability of the Dirichlet... more The Wiener criterion is a sufficient and necessary condition for the solvability of the Dirichlet problem. However, its geometric interpretation is not clear. In the case that the domain satisfies an exterior spine condition, the requirement for the spine is clear in dimension 3. In this note, we intend to obtain the condition that the exterior spine should satisfy in higher dimensions.
Applied Mathematics, 2015
Applied Mathematics, 2015
Communications in Theoretical Physics, 2007
It has been pointed by Hall et al. [1] that matter collinations can be defined by using three dif... more It has been pointed by Hall et al. [1] that matter collinations can be defined by using three different methods. But there arises the question of whether one studies matter collineations by using the L ξ T ab = 0, or L ξ T ab = 0 or L ξ T b a = 0. These alternative conditions are, of course, not generally equivalent. This problem has been explored by applying these three definitions to general static spherically symmetric spacetimes. We compare the results with each definition.
Modern Physics Letters A, 2007
We investigate matter collineations of plane symmetric spacetimes when the energy–momentum tensor... more We investigate matter collineations of plane symmetric spacetimes when the energy–momentum tensor is degenerate. There exists three interesting cases where the group of matter collineations is finite-dimensional. The matter collineations in these cases are either four, six or ten in which four are isometries and the rest are proper.
Arxiv preprint arXiv:1106.1785, 2011
This paper is devoted to explore the energy-momentum of nonstatic plane symmetric spacetimes in t... more This paper is devoted to explore the energy-momentum of nonstatic plane symmetric spacetimes in the context of General Relativity and teleparallel theory of gravity. For this purpose, we use four prescriptions, namely, Einstein, Landau-Lifshitz, Bergmann-Thomson and Møller in both theories. It is shown that the results for the first three prescriptions turn out to be same in both the theories but different for last prescription. It is mentioning here that our results coincide with the results obtained by Sharif and kanwal [1] for Bell-Szekeres metric under certain choice of the metric functions.
The matter collineations of plane symmetric spacetimes are studied according to the degenerate en... more The matter collineations of plane symmetric spacetimes are studied according to the degenerate energy-momentum tensor. We have found many cases where the energy-momentum tensor is degenerate but the group of matter collineations is finite. Further we obtain different constraint equations on the energy-momentum tensor. Solving these constraints may provide some new exact solutions of Einstein field equations.
Journal of Inequalities and Applications
This paper studies the reducibility of almost-periodic Hamiltonian systems with small perturbatio... more This paper studies the reducibility of almost-periodic Hamiltonian systems with small perturbation near the equilibrium which is described by the following Hamiltonian system: dx dt = J A + εQ(t, ε) x + εg(t, ε) + h(x, t, ε). It is proved that, under some non-resonant conditions, non-degeneracy conditions, the suitable hypothesis of analyticity and for the sufficiently small ε, the system can be reduced to a constant coefficients system with an equilibrium by means of an almost-periodic symplectic transformation.