Let be a 2-torsion free prime ring and let be automorphisms of . For any , set . Suppose that is a -derivation defined on . In the present paper it is shown that if satisfies , then either or is commutative if is a nonzero ideal of such that , for all , and commutes with both and , then either or is commutative. if is a nonzero ideal of such that , for all , and commutes with , then is commutative. Finally a related result has been obtain for -derivation....
Let be a 2-torsion free prime ring and let be a Lie ideal of such that for all . In the present paper it is shown that if is an additive mappings of into itself satisfying for all , then for all .
Let be a prime ring with center and be a nonzero ideal of . In this manuscript, we investigate the action of skew derivation of which acts as a homomorphism or an anti-homomorphism on . Moreover, we provide an example for semiprime case.
In this paper a steering control algorithm for the Extended Nonholonomic Double Integrator is presented. An adaptive backstepping based controller is proposed which yields asymptotic stabilization and convergence of the closed loop system to the origin. This is achieved by transforming the original system into a new system which can be globally asymptotically stabilized. Once the new system is stabilized, the stability of the original system can be easily established. Stability of the closed loop...
In this article, a new solution to the steering control problem of nonholonomic systems, which are transformable into chained form is investigated. A smooth super twisting sliding mode control technique is used to steer nonholonomic systems. Firstly, the nonholonomic system is transformed into a chained form system, which is further decomposed into two subsystems. Secondly, the second subsystem is steered to the origin by using smooth super twisting sliding mode control. Finally, the first subsystem...
In this paper, we discuss some properties of beta function of several variables which are the extension of beta function of two variables. We define k-beta function of several variables and derive some properties of this function which are the extension of k-beta function of two variables, recently defined by Diaz and Pariguan [4]. Also, we extend the formula Γk(2z) proved by Kokologiannaki [5] via properties of k-beta function.
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