We discuss the harmonicity of horizontally conformal maps and their relations with the spectrum of the Laplacian. We prove that if φ : M → N is a horizontally conformal map such that the tension field is divergence free, then φ is harmonic. Furthermore, if N is noncompact, then φ must be constant. Also we show that the projection of a warped product manifold onto the first component is harmonic...

We study a general Kishimoto’s problem for automorphisms on simple C∗-algebras with tracial rank zero. Let A be a unital separable simple C∗-algebra with tracial rank zero and let α be an automorphism. Under the assumption that α has certain Rokhlin property, we present a proof that A ⋊α Z has tracial rank zero. We also show that if the induced map α∗0 on K0(A) fixes a “dense” subgroup of K0(A)...

Let A and B be n × m matrices. The matrix B is said to be g-row majorized (respectively g-column majorized) by A, if every row (respectively column) of B, is g-majorized by the corresponding row (respectively column) of A. In this paper all kinds of g-majorization are studied on Mn,m, and the possible structure of their linear preservers will be found. Also all linear operators T : Mn,m ---> Mn...

The zero-error capacity of a discrete classical channel was first defined by Shannon as the least upper bound of rates for which one transmits information with zero probability of error [C. Shannon, IRE Trans. Inform. Theory, IT-2(3):8–19, 1956]. Here, we define the quantum zero-error capacity, a new kind of classical capacity of a noisy quantum channel C represented by a trace-preserving map (...

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 ...