Fredholm pseudo-gradients for the action functional on a sub-manifold of dual Legendrian curves of a three dimensional contact manifold (M3, α)Arabian Journal of Mathematics - Tập 3 - Trang 189-198 - 2014
A. Bahri
We prove in this paper that the intersection numbers between periodic orbits have an intrinsic meaning for the variational problem (J,C
β
) {Bahri (Pseudo-Orbits of Contact Forms Pitman Research Notes in Mathematics Series No. 173, 1984), Bahri (C R Acad Sci Paris 299, Serie I 15:757–760, 1984), Bahri (Classical and Quantic periodic motions of multiply polarized spin-manifolds. Pitman Research Notes in Mathematics Series No. 378, 1998)}, corresponding to the periodic orbit problem on a sub-manifold of the loop space of a three dimensional compact contact manifold (M, α).
Existence, uniqueness and Ulam stability results for a mixed-type fractional differential equations with p-Laplacian operatorArabian Journal of Mathematics - Tập 12 Số 3 - Trang 633-645 - 2023
Esma Kenef, I. Merzoug, A. Guezane-Lakoud
AbstractIn this paper, we study a nonlinear fractional p-Laplacian boundary value problem containing both left Riemann–Liouville and right Caputo fractional derivatives with initial and integral conditions. Some new results on the existence and uniqueness of a solution for the model are obtained as well as the Ulam stability of the solutions. Two examples are provided to show the applicability of our results.
FR-type algorithm for finding approximate solutions to nonlinear monotone operator equationsArabian Journal of Mathematics - Tập 10 - Trang 261-270 - 2021
Auwal Bala Abubakar, Kanikar Muangchoo, Abdulkarim Hassan Ibrahim, Jamilu Abubakar, Sadiya Ali Rano
This paper focuses on the problem of convex constraint nonlinear equations involving monotone operators in Euclidean space. A Fletcher and Reeves type derivative-free conjugate gradient method is proposed. The proposed method is designed to ensure the descent property of the search direction at each iteration. Furthermore, the convergence of the proposed method is proved under the assumption that the underlying operator is monotone and Lipschitz continuous. The numerical results show that the method is efficient for the given test problems.
General stability for a Cohen–Grossberg neural network systemArabian Journal of Mathematics - - Trang 1-15 - 2023
Mohammed D. Kassim, Nasser-Eddine Tatar
Of concern is a Cohen–Grossberg neural network (CGNNs) system taking into account distributed and discrete delays. The class of delay kernels ensuring exponential stability existing in the previous papers is enlarged to an extended class of functions guaranteeing more general types of stability. The exponential and polynomial (or power type) type stabilities becomes particular cases of our result. This is achieved using appropriate Lyapunov-type functionals and the characteristics of the considered class.
Analysis of non-linear pulsatile blood flow in artery through a generalized multiple stenosisArabian Journal of Mathematics - Tập 5 Số 1 - Trang 51-61 - 2016
Changdar, Satyasaran, De, Soumen
The non-linear blood flow under the influence of periodic body acceleration through a generalized multiple stenosed artery is investigated with the help of numerical simulation. The arterial segment is simulated by a cylindrical tube filled with a viscous incompressible Newtonian fluid described by the Navier–Stokes equation. The non-linear equation is solved numerically using finite difference with the proper boundary conditions and pressure gradient that arise from the heart. The effect of Reynolds number is also discussed. Results are shown in comparison with the existing models.
On the representations of the braid group constructed by C. M. Egea and E. GalinaArabian Journal of Mathematics - Tập 11 Số 2 - Trang 303-311 - 2022
Rana S. Kahil, Mohammad N. Abdulrahim
AbstractIn this paper, we determine a sufficient condition for the irreducibility of the family of representations of the braid group constructed by C. M. Egea and E. Galina without requiring that the representations are self-adjoint. Then, we construct a new subfamily of multi-parameter representations $$(\psi _m,V_m), $$
(
ψ
m
,
V
m
)
,
$$1\le m< n$$
1
≤
m
<
n
, of dimension $$ V_m =\left( {\begin{array}{c}n\\ m\end{array}}\right) $$
V
m
=
n
m
. Finally, we study the irreducibility of $$(\psi _m,V_m) $$
(
ψ
m
,
V
m
)
.
Qualitative behavior of solutions of difference equations with several oscillating coefficientsArabian Journal of Mathematics - Tập 3 - Trang 1-13 - 2013
Martin Bohner, George E. Chatzarakis, Ioannis P. Stavroulakis
Sufficient conditions which guarantee the convergence of the nonoscillatory solutions or oscillation of all solutions of a difference equation with several deviating arguments and oscillating coefficients are presented. Corresponding difference equations of both retarded and advanced type are studied. Examples illustrating the results are also given.
