Necessary and/or sufficient conditions are studied for the existence, uniqueness and holonomicity of bases in which on sufficiently general subsets of a differentiable manifold the components of derivations of the tensor algebra over it vanish. The linear connections and the equivalence principle are considered form that point of view.

The purpose of this paper is to present explicitly the solution curve for commutative affine control systems on Lie groups under assumption that automorphisms associated with linear vector fields commutes. If we assume derivations system are inner, obtain a simpler and show some results controllability. To finish, work conjugation by homomorphism between systems.

Robust H output feedback control problem for a class of switched linear discrete-time systems possessing normbounded uncertainty and time-varying delay is investigated. A switched dynamic output feedback controller is sought that can robust exponentially stabilize and reduce to a prescribed level the effect of disturbance input on the controlled output in the closed loop. A delay depen dent lin...

Abstract Complete hom-Lie superalgebras are considered and some equivalent conditions for a superalgebra to be complete established. In particular, the relation between decomposition completeness is described. Moreover, that linear space of $$\alpha ^{s}$$ α s -derivati...

the notion of $f$-derivations of up-algebras is introduced, some useful examples are discussed, and related properties are investigated. moreover, we show that the fixed set and the kernel of $f$-derivations are up-subalgebras of up-algebras,and also give examples to show that the two sets are not up-ideals of up-algebras in general.