Central Automorphisms and Inner Automorphisms in Finitely Generated Groups

Let G be a group and Aut_c(G) be the group of all central automorphisms of G. We know that in a finite p-group G, Aut_c(G) = Inn(G) if and only if Z(G) = G′ and Z(G) is cyclic. But we shown that we cannot extend this result for infinite groups. In fact, there exist finitely generated nilpotent groups of class 2 in which G′ =Z(G) is infinite cyclic and Inn(G) < C* = Aut_c(G). In this article, we characterize all finitely generated groups G for which the equality Aut_c(G) = Inn(G) holds.     

2, 4, 6-Trichloro-1, 3, 5-triazine/dimethylformamide as an efficient reagent for one-pot conversion of alcohols into N-alkylphthalimides

<正>An efficient and mild method for the direct conversion of alcohols into N-alkylphthalimides using 2,4,6-trichloro-1,3,5-triazine and dimethylformamide was described.The reaction was preceded via(alcoxymethylene) dimethylammonium chloride intermediate and produced corresponding N-alkylphthalimides in good-to-excellent yields.     

On inner automorphisms and certain central automorphisms of groups

Let G be a group, let M and N be two normal subgroups of G. We denote by Aut _N ^M (G), the set of all automorphisms of G which centralize G/M and N. In this paper we investigate the structure of a group G in which one of the Inn(G) = Aut _N ^M (G), Aut _N ^M (G) ≤ Inn(G) or Inn(G) ≤ Aut _N ^M (G) holds. We also discuss the problem: “what conditions on G is sufficient to ensure that G has a non-inner automorphism which centralizes G/M and N”.     

Dynamic modeling of a revolute-prismatic flexible robot arm fabricated from advanced composite materials

A dynamic model for a two degree-of-freedom planar robot arm is derived in this study. The links of the arm, connected to prismatic and revolute joints, are considered to be flexible. They are assumed to be fabricated from either aluminum or laminated composite materials. The model is derived based on the Timoshenko beam theory in order to account for the rotary inertia and shear deformation. These effects are significant in modeling flexible links connected to prismatic joints. The deflections of the links are approximated by using a shear-deformable beam finite element. Hamilton's principle is implemented to derive the equations describing the combined rigid and flexible motions of the arm. The resulting equations are coupled and highly nonlinear. In view of the large number of equations involved and their geometric nonlinearity (topological and quadratic), the solution of the equations of motion is obtained numerically by using a stiff integrator.The digital simulation studies examine the interaction between the flexible and the rigid body motions of the robot arm, investigate the improvement in the accuracy of the model by considering the flexibility of all rather than some of the links of the arm, assess the significance of the rotary inertia and shear deformation, and illustrate the advantages of using advanced composites in the structural design of robotic manipulators.