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El-Nabulsi R.A.,Neijiang Normal University
Nonlinear Dynamics | Year: 2013

Two mathematical physics' approaches have recently gained increasing importance both in mathematical and in physical theories: (i) the fractional action-like variational approach which founds its significance in dissipative and non-conservative systems and (ii) the theory of non-standard Lagrangians which exist in some group of dissipative dynamical systems and are entitled "non-natural" by Arnold. Both approaches are discussed independently in the literature; nevertheless, we believe that the combination of both theories will help identifying more hidden solutions in certain classes of dynamical systems. Accordingly, we generalize the fractional action-like variational approach for the case of non-standard power-law Lagrangians of the form L1+γ (γ∈ℝ}) recently introduced by the author (Qual. Theory Dyn. Syst. doi: 10.1007/s12346-012-0074-0, 2012). Many interesting features are discussed in some details. © 2013 Springer Science+Business Media Dordrecht.


El-Nabulsi A.R.,Neijiang Normal University
Indian Journal of Physics | Year: 2013

This work discusses some developments in classical gauge field theory which have grown out of the ideas of non-standard Lagrangians in the framework of the calculus of variations. A substantial part of this work is concerned with the modification of some basic equations of classical field theories starting from a power-law Lagrangian functional with time-dependent power and which belongs to the class of non-standard Lagrangians. Many equations principally the modified Proca equation and some modified dispersion relations for the consequent field equations are derived. © 2013 Indian Association for the Cultivation of Science.


El-Nabulsi R.A.,Neijiang Normal University
Canadian Journal of Physics | Year: 2013

Nonstandard Lagrangians are generating functions of different equations of motion. They have gained increasing importance in many different fields. In fact, nonstandard Lagrangians date back to 1978, when Arnold entitled them "non-natural" in his classic book, Mathematical Methods of Classical Mechanics (Springer, New York. 1978). In applied mathematics, most dynamical equations can be obtained by using generating Lagrangian functions (e.g., power-law and exponential Lagrangians), which has been shown by mathematicians, who have also demonstrated that there is an infinite number of such functions. Besides this interesting field, the topic of fractional calculus of variations has gained growing importance because of its wide application in different fields of science. In this paper, we generalize the fractional actionlike variational approach for the case of a nonstandard exponential Lagrangian. To appreciate this new approach, we explore some of its main consequences in Einstein's general relativity. Some results are revealed and discussed accordingly mainly the transition from general relativity to complex relativity and emergence of a discrete gravitational coupling constant. © 2013 Published by NRC Research Press.


El-Nabulsi A.R.,Neijiang Normal University
Indian Journal of Physics | Year: 2013

In this paper we set up a fractional generalization of Einstein's field equations based on fractional derivatives inside the geodesic action integral and obtained non-local fractional Einstein's field equations. More specifically, the total derivative of any generalized coordinate is considered to take the special form D = Dclassical + kDfractional,k is a real parameter, Dclassical is the classical derivative operator and D fractional is the modified left Riemann-Liouville fractional derivative operator so that the classical result of the calculus of variations is considered as a particular case. Many attractive astrophysical and cosmological solutions have been obtained and discussed in some details. © 2012 Indian Association for the Cultivation of Science.


El-Nabulsi A.R.,Neijiang Normal University
Indian Journal of Physics | Year: 2013

In this paper, we study cosmological models in scalar tensor theory of gravity a la Brans-Dicke with a dynamical equation of state parameter, a dynamical effective cosmological constant and a Hubble parameter varying like H = εts + H0 with ε and H0 are real positive parameters and s is some pending power index. It is observed that the universe is accelerating in time and it is dominated by a decreasing energy density and a vacuum energy density. However the vacuum energy density is increasing logarithmically at early epoch of time and then decaying toward its present positive value at late-time epoch. For specific choices of the free parameters in the theory, it is observed that the phantom divide line is crossed in the presence of a cosmological constant and the universe expands asymptotically a la de-Sitter at very large time. Additional features are discussed as well. © 2012 Indian Association for the Cultivation of Science.


El-Nabulsi A.R.,Neijiang Normal University
Indian Journal of Physics | Year: 2013

In recent years plentiful research papers have been advocated to the study of analytical techniques in calculus of variations. Many important applications are found in such fields as quantum field theories and many new properties have been raised, studied and explicit solutions have been achieved by many authors. In this work we derive a modification of the Klein-Gordon and Dirac equations of quantum field theories starting from an exponential action functional recently introduced by the author of the present work. Both standard and non-standard Lagrangians are considered. It was observed that some quantum field equations which appear in many field theories dealing with quantum gravitational corrections are raised. © 2012 Indian Association for the Cultivation of Science.


El-Nabulsi R.A.,Neijiang Normal University
Canadian Journal of Physics | Year: 2013

We introduce the notion of a "generalized time-dependent Hubble parameter" for the case of Friedmann-Robertson-Walker cosmology. We obtain a Riccati differential equation for the Hubble parameter, H, and it was observed that the effective equation of state in our framework can cross the phantom divide line as supported by recent astrophysical observations. In addition, the model is able to evolve without initial singularity. © 2013 Published by NRC Research Press.


El-Nabulsi R.A.,Neijiang Normal University
Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences | Year: 2015

In this article, we investigated a generalised scalar field cosmology characterised by a time-dependent coupling function, a time-dependent cosmological constant, a chameleonic field, and a time-dependent equation of state parameter. Based on a particular choice of the Hubble parameter as function of the scalar field and its time derivative, we have investigated the dynamics of the Friedmann-Robertson-Walker flat universe. We have observed that for a particular choice of the free parameters in the theory, the universe accelerates with time and asymptotically tends toward a static universe. For specific values of the free parameters, the asymptotically static universe may be dominated by phantom energy or a cosmological constant without the need to implement in the theory multiple scalar fields or additional interactions. It is also pointed out that an asymptotically static universe is as well one special class of solutions for Horndeski and generalised galileons cosmologies. Special properties and features are discussed accordingly.


Mou L.,Neijiang Normal University
CCIS2011 - Proceedings: 2011 IEEE International Conference on Cloud Computing and Intelligence Systems | Year: 2011

The Generalized Traveling Salesman Problem (GTSP) is an extension of the classical traveling salesman problem and has many interesting applications. In this paper we present a New Generalized Traveling Salesman Problem (NGTSP), and the current GTSP is only a special case of the NGTSP. To solve effectively the NGTSP, we extend the ant colony system method from TSP to NGTSP. Meanwhile, to improve the quality of solution, a local searching technique is introduced into this method to speed up the convergence, and a novel parameter adaptive technique is also introduced into this method to avoid locking into local minima. Experimental results on numerous TSPlib instances show that the proposed method can deal with the NGTSP problems fairly well, and the developed improvement techniques is significantly effective. © 2011 IEEE.


In this paper, we study modified homogeneous and isotropic cosmological models based on the Gauss-Bonnet invariant term as models of an accelerating universe. We discuss and criticize the late-time dynamics of six independent cosmological models: in the first model, we discuss the case of the modified gravity f(R) R1+δ for δ =-1/2 and 1 augmented by the Gauss-Bonnet invariant term; in the second model, we discuss the general case of f(R) R1+δ accompanied by a nonminimal coupling between the scalar field and the Ricci curvature as well as the Gauss-Bonnet invariant; in the third model, we discuss a generalized modified gravity model that includes the Einstein-Hilbert action, a dynamical cosmological constant, and an effective gravitational coupling constant; in the fourth model, we discuss a more generalized modified scalar-tensor cosmology that includes in addition to the Gauss-Bonnet invariant term, stringy corrections motivated from string and heterotic superstring arguments; in the fifth model, we discuss the cosmological dynamics of a nonminimal scalar Gauss-Bonnet gravity theory motivated from string theory; and finally in the sixth model, we discuss the possibility of having an extension of the generalized modified gravity theory, free from nonminimal coupling with δ = 0, with a Hubble expansion rate and an equation of state parameter that depend on the Gauss-Bonnet invariant term. In the first five models, we conjecture that the Hubble parameter is related to the scalar field by the relation Ḣ, which is applied merely to the late time epoch. This ansatz is in fact motivated by some recent advances in scalar-tensor theory and string theory. All of the six models reveal interesting consequences, which are discussed in some detail. Our main objective in this work is to analyze, criticize, and differentiate between viable realistic models and those that are not. Many critical points are discussed in some detail. © 2013 Published by NRC Research Press.

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