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Search Results: 1 - 10 of 14 matches for " Otgonbayar Dugerjav "
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Growth of a crystalline and ultrathin MgO film on Fe(001)
Otgonbayar Dugerjav,Hidong Kim,Jae M. Seo
AIP Advances , 2011, DOI: 10.1063/1.3642601
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.
Homotopy Theory for C^{*}-algebras
Otgonbayar Uuye
Mathematics , 2010,
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.
A simple proof of the Fredholm Alternative
Otgonbayar Uuye
Mathematics , 2010,
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.
Restriction maps in equivariant $KK$-theory
Otgonbayar Uuye
Mathematics , 2011, DOI: 10.1017/is011010005jkt168
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 $KK^{G}_{*}(A, B) = 0$.
$K$-continuity is equivalent to $K$-exactness
Otgonbayar Uuye
Mathematics , 2012,
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.
Pseudo-differential Operators and Regularity of Spectral Triples
Otgonbayar Uuye
Mathematics , 2009,
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.
Multiplicativity of the JLO-character
Otgonbayar Uuye
Mathematics , 2009, DOI: 10.4171/JNCG/80
Abstract: We prove that the Jaffe-Lesniewski-Osterwalder character is compatible with the $A_{\infty}$-structure of Getzler and Jones.
A note on the Künneth theorem for nonnuclear C*-algebras
Otgonbayar Uuye
Mathematics , 2011,
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.
Unsuspended Connective $E$-Theory
Otgonbayar Uuye
Mathematics , 2011,
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.
The Baum-Connes Conjecture for KK-theory
Otgonbayar Uuye
Mathematics , 2004, DOI: 10.1017/is010003012jkt114
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.
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