The problem of deadbeat control is now to find a feedback law F that will drive an arbitrary initial state Xo to Xk = 0 after a minimum number of steps k. All subsequent xi (for i > k) are then also zero, which explains the term 'deadbeat'. For standard state-space systems (i.e. E In) this is known to be equivalent to finding a feedback F such that all eigenvalues of A + BF lie at h = O, and A ...

Let $mathcal{H}$ and $mathcal{K}$ be infinite dimensional Hilbert spaces, while $mathcal{B(H)}$ and $mathcal{B(K)}$ denote the algebras of all linear bounded operators on $mathcal{H}$ and $mathcal{K}$, respectively. We characterize the forms of additive mappings from $mathcal{B(H)}$ into $mathcal{B(K)}$ that preserve the nonzero idempotency of either Jordan products of operators or usual produc...

In this talk we introduce the notion of a generalized representation of a Jordan algebra with unit which has the following properties: 1) Usual representations and Jacobson representations correspond to special cases of generalized representations. 2) Every simple Jordan algebra has infinitely many nonequivalent generalized representations. 3) There is a one-to-one correspondence between irredu...

In the study of pre-Lie algebras, concept pre-morphism arises naturally as a generalization standard notion morphism. Pre-morphisms can be defined for arbitrary (not-necessarily associative) algebras over any commutative ring k with identity, and dualized in various ways to generalized morphisms (related pre-Jordan algebras) anti-pre-morphisms anti-pre-Lie algebras). We consider idempotent pre-...

abstract in this paper, we study the generalized order- jacobsthal sequences modulo for and the generalized order-k jacobsthal-padovan sequence modulo for . also, we define the generalized order-k jacobsthal orbit of a k-generator group for and the generalized order-k jacobsthal-padovan orbit a k-generator group for . furthermore, we obtain the lengths of the periods of the generalized order-3 ...

Abstract In this paper, we study the generalized order- Jacobsthal sequences modulo for and the generalized order-k Jacobsthal-Padovan sequence modulo for . Also, we define the generalized order-k Jacobsthal orbit of a k-generator group for and the generalized order-k Jacobsthal-Padovan orbit a k-generator group for . Furthermore, we obtain the lengths of the periods of the generalized order-3 ...

In this paper, we examine some questions concerned with certain “skew” properties of the range of a Jordan *-derivation. In the first part we deal with the question, for example, when the range of a Jordan *-derivation is a complex subspace. The second part of this note treats a problem in relation to the range of a generalized Jordan *-derivation.

We introduced a new nonassociative algebra, namely, left almost algebra, and discussed some of its genetic properties. We discussed the relation of this algebra with flexible algebra, Jordan algebra, and generalized Jordan algebra.