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A. S. Hegazi

Publications and source records attributed to A. S. Hegazi.

16 recordsLinked to original sources
arXiv2016

Classification of five-dimensional nilpotent Jordan algebras

The paper is devoted to classify nilpotent Jordan algebras of dimension up to five over an algebraically closed field of characteristic not 2. We obtained a list of 35 isolated non-isomorphic 5-dimensional nilpotent non-associative Jordan algebras and 6 families of non-isomorphic 5-dimensional nilpotent non-associative Jordan algebras depending either on one or two parameters over an algebraically closed field of characteristic not 2 or 3. In addition to these algebras we obtained two non-isomorphic 5-dimensional nilpotent non-associative Jordan algebras over an algebraically closed field of characteristic 3.

math.RA↗
arXiv2015

Five-dimensional nilpotent evolution algebras

The paper is devoted to give a complete classification of five-dimension nilpotent evolution algebras over an algebraically closed field. We obtained a list of 27 isolated non-isomorphic nilpotent evolution algebras and 2 families of non-isomorphic algebras depending on one parameter.

math.AC↗
arXiv2015

Nilpotent evolution algebras over arbitrary fields

The paper is devoted to the study of annihilator extensions of evolution algebras and suggests an approach to classify finite-dimensional nilpotent evolution algebras. Subsequently nilpotent evolution algebras of dimension up to four are classfied.

math.AC↗
arXiv2013

Construction of Nilpotent Jordan Algebras Over any Arbitrary Fields

We give a computional method to construct and classify nilpotent Jordan algebras over any arbitrary fields by the second cohomolgy of nilpotent Jordan algebras of low dimension "analogue of Skjelbred-Sund method", we see that every nilpotent Jordan algebras can be constructed by the second cohomolgy of nilpotent Jordan algebras of low dimension. We use this method to classify nilpotent Jordan algebras up to dimension three over any field and nilpotent Jordan algebras of dimension four over an algebraic closed field of characteristic not 2 and over the real field R. Also commutative nilpotent associative algebras are classified, we show that there are up to isomorphism 13 nilpotent Jordan algebras of dimension 4 over an algebraic closed field of characteristic not 2, four of those are not associative, yielding 9 commutative nilpotent associative algebras. Also up to isomorphism there are 17 nilpotent Jordan algebras of dimension 4 over the real field R, five of those are not associative, yielding 12 commutative nilpotent associative algebras.

math.RA↗
arXiv2008

Survival May Not be for the Fittest (Lessons from some TV games)

In this paper we argue that biological fitness is a multi-objective concept hence the statement "fittest" is inappropriate. The following statement is proposed "Survival is mostly for those with non-dominated fitness". Also we use some TV games to show that under the following conditions: i) There are no dominant players. ii) At each time step successful players may eliminate some of their less successful competitors, Then the ultimate winner may not be the fittest (but close).

q-bio.PE↗
arXiv2006

Geometry and reducibility of induction of Hopf group co-algebras

In this work we study the induction (induced and coinduced)theory for Hopf group coalgebra. We define a substructure B of a Hopf group coalgebra $H$, called subHopf group coalgebra. Also, we have introduced the definition of Hopf group suboalgebra and group coisotropic quantum subgroup of $H$. The properties of the algebraic structure of the induced and coinduced are given. Moreover, a framework of the geometric interperation and simplicity theory of such representation strructure are stuided.

math.QA↗
arXiv2005

Induced and Coinduced Representations of Hopf Group Coalgebra

In this work we study the induction theory for Hopf group coalgebra. To reach this goal we define a substructure B of a Hopf group coalgebra $H$, called subHopf group coalgebra. Also, we introduced the definition of Hopf group suboalgebra and group coisotropic quantum subgroup of $H$.

math.QA↗
arXiv2005

Differential calculus on Hopf Group Coalgebra

In this paper we construct the Differential calculus on the Hopf Group Coalgebra introduced by Turaev [10]. We proved that the concepts introduced by S.L.Woronowicz in constructing Differential calculus on Hopf Compact Matrix Pseudogroups (Quantum Groups)[7] can be adapted to serve again in our construction.

math.QA↗
arXiv2005

An Overview of Complex Adaptive Systems

Almost every biological, economic and social system is a complex adaptive system (CAS). Mathematical and computer models are relevant to CAS. Some approaches to modeling CAS are given. Applications in vaccination and the immune system are studied. Mathematical topics motivated by CAS are discussed.

nlin.AO↗
arXiv2005

On complex adaptive systems and terrorism

Complex adaptive systems (CAS) are ubiquitous in nature. They are basic in social sciences. An overview of CAS is given with emphasize on the occurrence of bad side effects to seemingly wise decisions. Hence application to terrorism is given. Some conclusions on how to deal with this phenomena are proposed.

nlin.AO↗
arXiv2004

On Persistence and Stability of some Biological Systems with Cross Diffusion

The concept of cross diffusion is applied to some biological systems. The conditions for persistence and Turing instability in the presence of cross diffusion are derived. Many examples including: predator-prey, epidemics (with and without delay), hawk-dove-retaliate and prisoner's dilemma games are given.

nlin.AO↗
arXiv2003

Sato-Crutchfield formulation for some Evolutionary Games

The Sato-Crutchfield equations are studied analytically and numerically. The Sato-Crutchfield formulation is corresponding to losing memory. Then Sato-Crutchfield formulation is applied for some different types of games including hawk-dove, prisoner's dilemma and the battle of the sexes games. The Sato-Crutchfield formulation is found not to affect the evolutionarily stable strategy of the ordinary games. But choosing a strategy becomes purely random independent on the previous experiences, initial conditions, and the rules of the game itself. Sato-Crutchfield formulation for the prisoner's dilemma game can be considered as a theoretical explanation for the existence of cooperation in a population of defectors.

nlin.CG↗
arXiv2002

On Spatial Asymmetric Games

The stability of some spatial asymmeric games is discussed. Both linear and nonlinear asymptotic stability of asymmetric hawk-dove and prisoner's dilemma are studied. Telegraph reaction diffusion equations for the asymmetric spatial games are presented. Asymmetric game of parental investment is studied in the presence of both ordinary and cross diffusions.

cond-mat.stat-mech↗
arXiv2001

An Epidemic Model on Small-World Networks and Ring Vaccination

A modified version of susceptible-infected-recovered-susceptible (SIRS) model for the outbreaks of foot-and-mouth disease (FMD) is introduced. The model is defined on small-world networks, and a ring vaccination programme is included. This model can be a theoretical explanation for the nonlocal interactions in epidemic spreading. Ring vaccination is capable of eradicating FMD provided that the probability of infection is high enough. Also an analytical approximation for this model is studied.

nlin.CG↗
arXiv2001

On Synchronization, Persistence and Seasonality in some Spatially Inhomogeneous Models in Epidemics and Ecology

Recent studies in ecology and epidemiology indicate that it is important to include spatial heterogeneity, synchronization and seasonality in the theoretical models. In this work, spatial heterogeneity is introduced via coupled map lattices (CML) and partial differential equations. Stability and persistence of some realistic CML are discussed. Chaos control, synchronization and persistence are studied for some CML. Some applications in population biology and ecology are given. A simple method for finding the sufficient conditions for the existence of periodic solutions for differential equations with periodic coefficients is given. This will simplify the study of seasonality.

cond-mat.stat-mech↗