26 citations · 47 across the 17 of their papers we have counts for
17 papers
Linearization Problem for a System of Two Second-Order ODEs via Cartan's Method: Branch I
Batoul M. Raddad, Ahmad Y. Al-Dweik, Marwan Aloqeili +1
Cartan's method classifies the class of linearizable system of two second-order ODEs into many branches. This paper investigates Branch I of the classification, characterized by a…
Linearization Problem for Third-Order ODEs with Four- and Five-Dimensional Lie Symmetry Algebras under Contact Transformations
Omar A. Abuloha, Marwan Aloqeili, Ahmad Y. Al-Dweik +1
Using Cartan equivalence method, invariant coframes are constructed for two branches of rank one and zero, which characterize linearizable third-order ODEs under contact transforma…
Equivalence Problem for Non-Linearizable Fourth-Order ODEs with Five-Dimensional Lie Symmetry subalgebra via Inductive Cartan Equivalence Method
Sondos R. Khalil, Ahmad Y. Al-Dweik, Marwan Aloqeili +1
Four coframes of invariant 1-forms are explicitly constructed using the Inductive Cartan equivalence method with rank zero corresponding to four distinct branches. These coframes a…
Equivalence Problem for Non-Linearizable Third-Order ODEs with Four-Dimensional Lie Symmetry Subalgebras under Point Transformations
Omar A. Abuloha, Marwan Aloqeili, Ahmad Y. Al-Dweik +1
Cartan's equivalence method is applied to explicitly construct invariant coframes for four branches, which are used to characterize all non-linearizable third-order ODEs with a fou…
Efficient tensor-based approach to solving linear systems involving Kronecker sum of matrices
Ahmad Y. Al-Dweik, Abdallah Sayyed-Ahmad
A novel tensor-based formula for solving the linear systems involving Kronecker sum is proposed. Such systems are directly related to the matrix and tensor forms of Sylvester equat…
Algorithms for Simultaneous Block Triangularization and Block Diagonalization of Sets of Matrices
Ahmad Y. Al-Dweik, Ryad Ghanam, Gerard Thompson +1
In a recent paper, a new method was proposed to find the common invariant subspaces of a set of matrices. This paper invstigates the more general problem of putting a set of matric…
A novel procedure for constructing invariant subspaces of a set of matrices
Ahmad Y. Al-Dweik, Ryad Ghanam, Gerard Thompson +1
A problem that is frequently encountered in a variety of mathematical contexts, is to find the common invariant subspaces of a single, or set of matrices. A new method is proposed…
A Novel Method to Generate Key-Dependent S-Boxes with Identical Algebraic Properties
Ahmad Y. Al-Dweik, Iqtadar Hussain, Moutaz S. Saleh +1
The s-box plays the vital role of creating confusion between the ciphertext and secret key in any cryptosystem, and is the only nonlinear component in many block ciphers. Dynamic s…
Invariant characterization of scalar third-order ODEs that admit the maximal contact symmetry Lie algebra
Omar A. Abuloha, Marwan Aloqeili, Ahmad Y. Al-Dweik +2
The Cartan equivalence method is utilized to deduce an invariant characterization of the scalar third-order ordinary differential equation which admits the max…
Linearization of third-order ordinary differential equations u'''=f(x,u,u',u'') via point transformations
Ahmad Y. Al-Dweik, M. T. Mustafa, F. M. Mahomed +1
The linearization problem by use of the Cartan equivalence method for scalar third-order ODEs via point transformations was solved partially in [1,2]. In order to solve this proble…
Invariant characterization of third-order ODEs that admit a five-dimensional point symmetry Lie algebra
Ahmad Y. Al-Dweik, M. T. Mustafa, F. M. Mahomed
The Cartan equivalence method is applied to provide an invariant characterization of the third-order ordinary differential equation which admits a five-dimensi…
A point symmetry based method for transforming ODEs with three-dimensional symmetry algebras to their canonical forms
H. Azad, Ahmad Y. Al-Dweik, F. M. Mahomed +1
We provide an algorithmic approach to the construction of point transformations for scalar ordinary differential equations that admit three-dimensional symmetry algebras which lead…
On invariants of second-order ordinary differential equations via point transformations
Ahmad Y. Al-Dweik
Bagderina \cite{Bagderina2013} solved the equivalence problem for a family of scalar second-order ordinary differential equations (ODEs), with cubic nonlinearity in the first-order…
Invariants of third-order ordinary differential equations via fiber preserving transformations
Ahmad Y. Al-Dweik, M. T. Mustafa, H. Azad +1
Bagderina \cite{Bagderina2008} solved the equivalence problem for scalar third-order ordinary differential equations (ODEs), quadratic in the second-order derivative, via point tra…
-symmetry criteria for linearization of second order ODEs via point transformations
Ahmad Y. Al-Dweik, M. T. Mustafa, Raed A. Mara'beh +1
An alternative proof of Lie's approach for linearization of scalar second order ODEs is derived using the relationship between -symmetries and first integrals. This relation fur…
On the Linearization of Second-Order Ordinary Differential Equations to the Laguerre Form via Generalized Sundman Transformations
M. Tahir Mustafa, Ahmad Y. Al-Dweik, Raed A. Mara'beh
The linearization problem for nonlinear second-order ODEs to the Laguerre form by means of generalized Sundman transformations (S-transformations) is considered, which has been inv…
Generalization of the double reduction theory
Ashfaque H. Bokhari, Ahmad Y. Dweik, F. D. Zaman +2
In a recent work [1, 2] Sjoberg remarked that generalization of the double reduction theory to partial differential equations of higher dimensions is still an open problem. In this…