In this paper, we introduce the property of *-rigid and \alpha -*-rigid for rings with involution (*-rings). These concepts generalize that of rigid and \alpha-rigid properties, respectively. We show that *-rigid is equivalent to *-reduced and \alpha -*-rigid *-rings are semiprime. Also, we show that reduced *-rings are \alpha-*-reversible and \alpha-rigid *-rings are \alpha-*-Armendariz. Moreover, sufficient conditions are given for *-rigid and \alpha-*-rigid *-rings to be rigid and \alpha-rigid, respectively. We give also sufficient condition for \alpha-*-Armendariz *-rings to be \alpha-*-rigid. Furthermore, we investigate the transfer of the properties of *-rigid, \alpha-*-rigid, \alpha-*-reversible and \alpha-*-Armendariz from a *-ring R to some of its extensions; such as polynomial *-ring $R[x]$, localization S^{-1}R of R at S, Laurent polynomial *-ring R[x, x^{-1}], Dorroh extension $D(R,\mathbb{Z})$ and from Ore *-ring to its classical Quotient Q. Finally, we discuss when the skew polynomial *-ring of a *-Baer (*-reversible) *-ring is *-Baer (*-reversible). Also, we show that the polynomial *-ring o f \alpha-*-reversible *-ring R is \alpha-*-reversible if R is *-Armendariz.
ا.د اسامة عبدالله ابورواش, (1-2019)

It is perhaps noteworthy in the locomotion literature of recent years that different forms of locomotion can be found by genetic algorithms using patterns formed by uncoupled, unidirectional and bidirectional two Central Pattern Generators (CPGs). This paper outlines the kinematic model of one leg with two degrees of freedom (DOF), analyzes stability and bifurcation, and pinpoints CPGs and their implementations. Specifically, this paper presents an evolutionary method of gait generation for the one leg structure. It attempts to utilize genetic algorithms with hybrid function and adapt the CPGs to robotic systems that perform one-leg movement, with the objective of figuring out optimal walking gaits.
, , , (12-2017)

In this paper, with the aid of the Wolfram Mathematica or Matlab software the powerful, the Adomian decomposition method (ADM) is used to found the numerical solution of Lorenz chaotic system. It is shown that the method is straightforward and effective mathematical tool for solving this system. We make a comparison between our method and another method to illustrate the accuracy of this method. Finally, we submit comprehensive conclusions.
ا.د. محمود محمد مصطفى البرعى ----ا.د. وجدى جمعة السيد, (5-2018)