Let Mn be the set of n × n complex matrices, and for every A ∈ Mn, let Sp(A) denote the spectrum of A. For various types of products A1 ∗ · · · ∗ Ak on Mn, it is shown that a mapping φ : Mn → Mn satisfying Sp(A1 ∗ · · · ∗ Ak) = Sp(φ(A1) ∗ · · · ∗ φ(Ak)) for all A1, . . . , Ak ∈ Mn has the form X → ξS−1XS or A → ξS−1XtS for some invertible S ∈ Mn and scalar ξ. The result covers the special cases...

We present a method of control of chaos in area-preserving maps. This method gives an explicit expression of a control term which is added to a given area-preserving map. The resulting controlled map which is a small and suitable modification of the original map, is again area-preserving and has an invariant curve whose equation is explicitly known.

‎Let $R$ be a ring‎ ‎with the Jacobson radical $J(R)$ and let $picolon Rto R/J(R)$ be‎ the canonical map‎. ‎Then $pi$ induces an order preserving group homomorphism‎ ‎$K_0picolon K_0(R)to K_0(R/J(R))$ and an‎ ‎affine continuous map $S(K_0pi)$ between the state space $St(R/J(R))$ and the‎ ‎state space $St(R).$‎ ‎In this paper‎, ‎we consider the natural affine map $S(K_0pi).$ We give a condition ...

In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...

‎let $mathcal{a}$ be a unital banach algebra‎, ‎$mathcal{m}$ be a left $mathcal{a}$-module‎, ‎and $w$ in $mathcal{z}(mathcal{a})$ be a left separating point of $mathcal{m}$‎. ‎we show that if $mathcal{m}$ is a unital left $mathcal{a}$-module and $delta$ is a linear mapping from $mathcal{a}$ into $mathcal{m}$‎, ‎then the following four conditions are equivalent‎: ‎(i) $delta$ is a jordan left de...