Ayman Alahmade
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Ayman Alahmade has a total of 34 co-authors. Here are the top co-authors by number of shared publications:
- Abdallah Al-Husban
Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, JORDAN
3 shared publications - Khaled Aldwoah
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia
3 shared publications - Malik Bataineh
Jordan University of Science and Technology
2 shared publications - Naglaa Mohammed
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
2 shared publications - Wael Mahmoud Mohammad Salameh
Faculty of Information Technology, Abu Dhabi University, Abu Dhabi 59911, United Arab Emirates
2 shared publications - Abdallah Shihadeh
Department of Mathematics Faculty of Science The Hashemite University PO box 330127 13133 Zarqa Jordan
1 shared publication
Latest Publications
- Open Access
- 14 August 2026
- Published by MDPI AG in Mathematics
- Vol. 14 (16) , 2953
Classical and Free Cumulants of the ω-Gaussian Central Limit Law
We study the classical and free cumulants of the -Gaussian central limit laws arising from braidable quantum coin tosses. Taking the known central limit theorem and oriented-pairing moment formula as input, we carry out a cumulant-level analysis of the resulting laws. At the imaginary parameter, we show that the first obstruction to semicircularity occurs at the eighth free cumulant, thereby identifying precisely where the limiting law first departs from semicircular behavior. Near the Gaussian endpoint, we prove that all higher even classical cumulants of order at least six vanish to at least second order. We further compute the classical cumulants through even order 16 and find a stronger order-dependent vanishing pattern, indicating increasing cancellation at the Gaussian endpoint as the cumulant order grows. These results reveal higher-order effects of the underlying quantum braiding that are not apparent from the first few moments alone and lead to an all-order divisibility conjecture together with several related open problems for the oriented-pairing expansion.- 14 August 2026
- Published by MDPI AG in Mathematics
- Vol. 14 (16) , 2953
Open AccessClassical and Free Cumulants of the ω-Gaussian Central Limit Law
We study the classical and free cumulants of the -Gaussian central limit laws arising from braidable quantum coin tosses. Taking the known central limit theorem and oriented-pairing moment formula as input, we carry out a cumulant-level analysis of the resulting laws. At the imaginary parameter, we show that the first obstruction to semicircularity occurs at the eighth free cumulant, thereby identifying precisely where the limiting law first departs from semicircular behavior. Near the Gaussian endpoint, we prove that all higher even classical cumulants of order at least six vanish to at least second order. We further compute the classical cumulants through even order 16 and find a stronger order-dependent vanishing pattern, indicating increasing cancellation at the Gaussian endpoint as the cumulant order grows. These results reveal higher-order effects of the underlying quantum braiding that are not apparent from the first few moments alone and lead to an all-order divisibility conjecture together with several related open problems for the oriented-pairing expansion. - Open Access
A Free Algebraic Model for Averaged Z-Weighted Wick Functionals
This paper constructs a universal algebraic realization model for Hermitian parameter matrices whose entries have modulus at most one and whose diagonal entries are normalized. The entries of the parameter matrix are used as weights of oriented crossings in averaged Wick-type moment formulas. The construction separates each crossing parameter into its unit complex factor and its modulus. We first construct a universal free algebraic unimodular factor model whose moments are defined by a balanced pair-oriented crossing formula. The modulus factors are then encoded by an auxiliary commutative algebra and recombined with the unimodular factors by tensorization. The resulting normalized sums converge in joint algebraic moments to the averaged weighted Wick moment functional, whose moments are given by a fully averaged pair-partition formula. In the general complex Hermitian case, the construction is purely algebraic, and no positivity, traciality, operator boundedness, or operator algebraic realization is claimed. In the real symmetric specialization, the averaged oriented formula reduces to the standard mixed Gaussian pair-partition formula with color-dependent crossing parameters, so the construction contains the known Fock-representable mixed Gaussian cases as positive Fock-space examples. Moreover, the averaged functional satisfies a uniform Gaussian-type moment growth bound.
Open AccessA Free Algebraic Model for Averaged Z-Weighted Wick Functionals
This paper constructs a universal algebraic realization model for Hermitian parameter matrices whose entries have modulus at most one and whose diagonal entries are normalized. The entries of the parameter matrix are used as weights of oriented crossings in averaged Wick-type moment formulas. The construction separates each crossing parameter into its unit complex factor and its modulus. We first construct a universal free algebraic unimodular factor model whose moments are defined by a balanced pair-oriented crossing formula. The modulus factors are then encoded by an auxiliary commutative algebra and recombined with the unimodular factors by tensorization. The resulting normalized sums converge in joint algebraic moments to the averaged weighted Wick moment functional, whose moments are given by a fully averaged pair-partition formula. In the general complex Hermitian case, the construction is purely algebraic, and no positivity, traciality, operator boundedness, or operator algebraic realization is claimed. In the real symmetric specialization, the averaged oriented formula reduces to the standard mixed Gaussian pair-partition formula with color-dependent crossing parameters, so the construction contains the known Fock-representable mixed Gaussian cases as positive Fock-space examples. Moreover, the averaged functional satisfies a uniform Gaussian-type moment growth bound.
- Open Access
- 8 March 2026
- Published by Springer Nature in Journal of Nonlinear Mathematical Physics
- Vol. 33 (1) , 33
Fixed Point Methods for Rational-Type Contractions: Applications to Nonlinear Integral and Boundary Value Problems
- 8 March 2026
- Published by Springer Nature in Journal of Nonlinear Mathematical Physics
- Vol. 33 (1) , 33
Open AccessFixed Point Methods for Rational-Type Contractions: Applications to Nonlinear Integral and Boundary Value Problems
- Open Access
- 1 January 2026
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 11 (9) , 29848-29874
Complexification of $ z $-semicircular systems and orientation-averaged $ z $-circular lawsIn this work, we study whether taking the complexification of a $ z $-semicircular system naturally gives rise to a $ z $-circular system. Starting from a semicircular family $ (s_r) $, we form complex variables $ c_r = \frac{1}{\sqrt{2}}\, (s_{2r-1} + i\, s_{2r}) $ and analyze their joint $ * $-moments using the combinatorics of pairings with oriented crossings. In the classical case where the deformation parameter is real $ q \in (-1, 1) $, this construction yields a $ q $-circular system, recovering the known correspondence between semicircular and circular variables. However, we show that this correspondence fails for general complex parameters $ z $ when $ |z| < 1 $. The obstruction is the additional averaging over balanced orientations, which agrees with the standard $ z $-circular law only when $ z $ is real. We show that the complexification of a $ z $-semicircular system introduces a new class of distributions, which we call orientation-averaged $ z $-circular systems, defined by averaging the contributions of oriented crossings over all admissible orientations. When $ z \in \mathbb{R} $, these systems coincide with the classical $ z $-circular systems. However, they are fundamentally different in the non-real case. As a result, we get a rigidity finding indicating that the only $ z $-circular systems formed by complexifying semicircular systems have a real deformation parameter.- 1 January 2026
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 11 (9) , 29848-29874
Open AccessComplexification of $ z $-semicircular systems and orientation-averaged $ z $-circular lawsIn this work, we study whether taking the complexification of a $ z $-semicircular system naturally gives rise to a $ z $-circular system. Starting from a semicircular family $ (s_r) $, we form complex variables $ c_r = \frac{1}{\sqrt{2}}\, (s_{2r-1} + i\, s_{2r}) $ and analyze their joint $ * $-moments using the combinatorics of pairings with oriented crossings. In the classical case where the deformation parameter is real $ q \in (-1, 1) $, this construction yields a $ q $-circular system, recovering the known correspondence between semicircular and circular variables. However, we show that this correspondence fails for general complex parameters $ z $ when $ |z| < 1 $. The obstruction is the additional averaging over balanced orientations, which agrees with the standard $ z $-circular law only when $ z $ is real. We show that the complexification of a $ z $-semicircular system introduces a new class of distributions, which we call orientation-averaged $ z $-circular systems, defined by averaging the contributions of oriented crossings over all admissible orientations. When $ z \in \mathbb{R} $, these systems coincide with the classical $ z $-circular systems. However, they are fundamentally different in the non-real case. As a result, we get a rigidity finding indicating that the only $ z $-circular systems formed by complexifying semicircular systems have a real deformation parameter. - Open Access
Unified Framework for Continuous and Discrete Relations of Gehring and Muckenhoupt Weights on Time Scales
This article contains some relations, which include some embedding and transition properties, between the Muckenhoupt classes and the Gehring classes of bi-Sobolev weights on a time scale . In addition, we establish the relations between Muckenhoupt and Gehring classes, where we define a new time scale , to indicate that if the derivative of the inverse of a bi-Sobolev weight belongs to the Gehring class, then the derivative of a bi-Sobolev weight on a time scale belongs to the Muckenhoupt class. Furthermore, our results, which will be established by a newly developed technique, show that the study of the properties in the continuous and discrete classes of weights can be unified. As special cases of our results, when , one can obtain classical continuous results, and when , one can obtain discrete results which are new and interesting for the reader.Open AccessUnified Framework for Continuous and Discrete Relations of Gehring and Muckenhoupt Weights on Time Scales
This article contains some relations, which include some embedding and transition properties, between the Muckenhoupt classes and the Gehring classes of bi-Sobolev weights on a time scale . In addition, we establish the relations between Muckenhoupt and Gehring classes, where we define a new time scale , to indicate that if the derivative of the inverse of a bi-Sobolev weight belongs to the Gehring class, then the derivative of a bi-Sobolev weight on a time scale belongs to the Muckenhoupt class. Furthermore, our results, which will be established by a newly developed technique, show that the study of the properties in the continuous and discrete classes of weights can be unified. As special cases of our results, when , one can obtain classical continuous results, and when , one can obtain discrete results which are new and interesting for the reader. - Open Access
- 11 October 2024
- Published by MDPI AG in Fractal and Fractional
- Vol. 8 (10) , 596
Modeling Ebola Dynamics with a Φ-Piecewise Hybrid Fractional Derivative Approach
Ebola virus disease (EVD) is a severe and often fatal illness posing significant public health challenges. This study investigates EVD transmission dynamics using a novel fractional mathematical model with five distinct compartments: individuals with low susceptibility (), individuals with high susceptibility (), infected individuals (), exposed individuals (), and recovered individuals (). To capture the complex dynamics of EVD, we employ a -piecewise hybrid fractional derivative approach. We investigate the crossover effect and its impact on disease dynamics by dividing the study interval into two subintervals and utilize the -Caputo derivative in the first interval and the -ABC derivative in the second interval. The study determines the basic reproduction number , analyzes the stability of the disease-free equilibrium and investigates the sensitivity of the parameters to understand how variations affect the system’s behavior and outcomes. Numerical simulations support the model and demonstrate consistent results with the theoretical analysis, highlighting the importance of fractional calculus in modeling infectious diseases. This research provides valuable information for developing effective control strategies to combat EVD.- 11 October 2024
- Published by MDPI AG in Fractal and Fractional
- Vol. 8 (10) , 596
Open AccessModeling Ebola Dynamics with a Φ-Piecewise Hybrid Fractional Derivative Approach
Ebola virus disease (EVD) is a severe and often fatal illness posing significant public health challenges. This study investigates EVD transmission dynamics using a novel fractional mathematical model with five distinct compartments: individuals with low susceptibility (), individuals with high susceptibility (), infected individuals (), exposed individuals (), and recovered individuals (). To capture the complex dynamics of EVD, we employ a -piecewise hybrid fractional derivative approach. We investigate the crossover effect and its impact on disease dynamics by dividing the study interval into two subintervals and utilize the -Caputo derivative in the first interval and the -ABC derivative in the second interval. The study determines the basic reproduction number , analyzes the stability of the disease-free equilibrium and investigates the sensitivity of the parameters to understand how variations affect the system’s behavior and outcomes. Numerical simulations support the model and demonstrate consistent results with the theoretical analysis, highlighting the importance of fractional calculus in modeling infectious diseases. This research provides valuable information for developing effective control strategies to combat EVD. - 6 October 2024
- Published by Springer Nature
- p. 325-333
A Certain Subclass of Analytic Functions Related to $\textsf{q}-$Calculus and Their Second Hankel Determinant- 6 October 2024
- Published by Springer Nature
- p. 325-333
A Certain Subclass of Analytic Functions Related to $\textsf{q}-$Calculus and Their Second Hankel Determinant- 12 March 2024
- Published by American Scientific Publishing Group (ASPG) LLC
On the Geometry of Weak Fuzzy Complex Numbers and Applications to the Classification of Some A-Curves
The concept of A-curves is considered as a novel application of real field extensions in solving some algebraic vectorial equations defined by Euclidean norms. In this paper, we present a novel insight through the classification of A-curves by illustrating many new semi-module isomorphisms between the direct product of weak fuzzy complex numbers with itself and the direct product of classical Euclidean vector spaces multiplied by itself. These isomorphisms will give us a full classification of A-curves that are related to weak fuzzy complex ring. Also, we provide many examples to explain the contribution of our work.
- 12 March 2024
- Published by American Scientific Publishing Group (ASPG) LLC
On the Geometry of Weak Fuzzy Complex Numbers and Applications to the Classification of Some A-Curves
The concept of A-curves is considered as a novel application of real field extensions in solving some algebraic vectorial equations defined by Euclidean norms. In this paper, we present a novel insight through the classification of A-curves by illustrating many new semi-module isomorphisms between the direct product of weak fuzzy complex numbers with itself and the direct product of classical Euclidean vector spaces multiplied by itself. These isomorphisms will give us a full classification of A-curves that are related to weak fuzzy complex ring. Also, we provide many examples to explain the contribution of our work.
- 1 January 2024
- Published by American Scientific Publishing Group (ASPG) LLC
- Vol. 23 (4) , 386-394
An Effective Algorithm for Solving Weak Fuzzy Complex Diophantine Equations in Two Variables
Weak fuzzy complex numbers are defined as , with as an extension of real numbers with . This paper is dedicated to studying weak fuzzy complex linear Diophantine equations in two weak fuzzy complex variables, by transforming the weak fuzzy complex Diophantine equation to a classical equivalent Diophantine system and going directly from the solutions of classical system into the desired equation. Algorithms for generating solutions of the previous equation will be presented in terms of theorems with many related examples that clarify the validity of our work.
- 1 January 2024
- Published by American Scientific Publishing Group (ASPG) LLC
- Vol. 23 (4) , 386-394
An Effective Algorithm for Solving Weak Fuzzy Complex Diophantine Equations in Two Variables
Weak fuzzy complex numbers are defined as , with as an extension of real numbers with . This paper is dedicated to studying weak fuzzy complex linear Diophantine equations in two weak fuzzy complex variables, by transforming the weak fuzzy complex Diophantine equation to a classical equivalent Diophantine system and going directly from the solutions of classical system into the desired equation. Algorithms for generating solutions of the previous equation will be presented in terms of theorems with many related examples that clarify the validity of our work.
- 1 January 2024
- Published by American Scientific Publishing Group (ASPG) LLC
- Vol. 24 (1) , 171-185
Computer purchasing using new type neutrosophic sets and its extension based on aggregation operators
American scientific publishing group
- 1 January 2024
- Published by American Scientific Publishing Group (ASPG) LLC
- Vol. 24 (1) , 171-185
Computer purchasing using new type neutrosophic sets and its extension based on aggregation operators
American scientific publishing group