‎Let $A$ be a $C^{*}$ algebra‎, ‎$T‎: ‎Arightarrow A$ be a linear map which satisfies the functional equation $T(x)T(y)=T^{2}(xy),;;T(x^{*})=T(x)^{*} $‎. ‎We prove that under each of the following conditions‎, ‎$T$ must be the trivial map $T(x)=lambda x$ for some $lambda in mathbb{R}$: ‎‎ ‎i) $A$ is a simple $C^{*}$-algebra‎. ‎ii) $A$ is unital with trivial center and has a faithful trace such ...

We show that every trivial 3-strand braid diagram contains a disk, defined as a ribbon ending in opposed crossings. Under a convenient algebraic form, the result extends to every Artin–Tits group of dihedral type, but it fails to extend to braids with 4 strands and more. The proof uses a partition of the Cayley graph and a continuity argument.

We characterize left Noetherian rings which have only trivial derivations.

Trivium is a stream cipher designed in 2005 by C. De Cannière and B. Preneel for the European project eSTREAM. It has successfully passed the first phase of the project and has been selected for a special focus in the second phase for the hardware portfolio of the project. Trivium has an internal state of size 288 bits and the key of length 80 bits. Although the design has a simple and elegant ...

A knot diagram is called everywhere n-trivial, if it turns into an unknot diagram by switching any set of n of its crossings. We show several partial cases of the conjecture that the knots with everywhere 1-trivial knot diagrams are exactly the trivial, trefoil and figure eight knots. We discuss a relation to 2-trivadjacent knots and prove some properties of such knots mainly concerning their H...