Abstract:
The narrow temperature-window for obtaining a crystalline MgO film on Fe(001) has been found using in-situ STM. When Mg was deposited on Fe(001) at RT, post-oxidized at 300 °C, and additionally annealed at 400 °C, an ultrathin and crystalline MgO film was formed. It has been concluded that, in order to grow a high-quality and crystalline MgO film on Fe(001), it requires two steps, i.e., Mg film formation on the substrate at RT and subsequent annealing at the proper substrate temperature under O2 exposure for Mg atoms to be oxidized and crystallized at their deposited sites without being agglomerated.

Abstract:
Category of fibrant objects is a convenient framework to do homotopy theory, introduced and developed by Ken Brown. In this paper, we apply it to the category of C^{*}-algebras. In particular, we get a unified treatment of (ordinary) homotopy theory for C^{*}-algebras, KK-theory and E-theory, as all of these can be expressed as the homotopy category of a category of fibrant objects.

Abstract:
In this expository note, we present a simple proof of the Fredholm Alternative for compact operators that are norm limits of finite rank operators. We also prove a Fredholm Alternative for pseudodifferential operators of order < 0.

Abstract:
We extend McClure's results on the restriction maps in equivariant $K$-theory to bivariant $K$-theory: Let $G$ be a compact Lie group and $A$ and $B$ be $G$-$C^*$-algebras. Suppose that $KK^{H}_{n}(A, B)$ is a finitely generated $R(G)$-module for every $H \le G$ closed and $n \in \Z$. Then, if $KK^{F}_{*}(A, B) = 0$ for all $F \le G$ {\em finite cyclic}, then $KK^{G}_{*}(A, B) = 0$.

Abstract:
It is well known that the functor of taking the minimal tensor product with a fixed $C^*$-algebra preserves inductive limits if and only if it preserves extensions. In other words, tensor continuity is equivalent to tensor exactness. We consider a $K$-theoretic analogue of this result and show that $K$-continuity is equivalent to $K$-exactness, using a result of M. Dadarlat.

Abstract:
We introduce a notion of an algebra of generalized pseudo-differential operators and prove that a spectral triple is regular if and only if it admits an algebra of generalized pseudo-differential operators. We also provide a self-contained proof of the fact that the product of regular spectral triples is regular.

Abstract:
In this mostly expository note, we revisit the K\"unneth theorem in $K$-theory of nonnuclear C*-algebras. We show that, using examples considered by Skandalis, there are algebras satisfying the K\"unneth theorem for the minimal tensor product but not for the maximal tensor product and vice versa.

Abstract:
We prove connective versions of results by Shulman [Shu10] and Dadarlat-Loring [DL94]. As a corollary, we see that two separable $C^*$-algebras of the form $C_0(X) \otimes A$, where $X$ is a based, connected, finite CW-complex and $A$ is a unital properly infinite algebra, are $\bu$-equivalent if and only if they are asymptotic matrix homotopy equivalent.

Abstract:
We define and compare two bivariant generalizations of the topological $K$-group $K^\top(G)$ for a topological group $G$. We consider the Baum-Connes conjecture in this context and study its relation to the usual Baum-Connes conjecture.