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Search: All articles in the CMB digital archive with keyword classification

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1. CMB Online first

Zhang, Tao; Zhou, Chunqin
Classification of solutions for harmonic functions with Neumann boundary value
In this paper, we classify all solutions of \[ \left\{ \begin{array}{rcll} -\Delta u &=& 0 \quad &\text{ in }\mathbb{R}^{2}_{+}, \\ \dfrac{\partial u}{\partial t}&=&-c|x|^{\beta}e^{u} \quad &\text{ on }\partial \mathbb{R}^{2}_{+} \backslash \{0\}, \\ \end{array} \right. \] with the finite conditions \[ \int_{\partial \mathbb{R}^{2}_{+}}|x|^{\beta}e^{u}ds \lt C, \qquad \sup\limits_{\overline{\mathbb{R}^{2}_{+}}}{u(x)}\lt C. \] Here, $c$ is a positive number and $\beta \gt -1$.

Keywords:Neumann problem, singular coefficient, classification of solutions
Categories:35A05, 35J65

2. CMB 2011 (vol 55 pp. 73)

Dean, Andrew J.
Classification of Inductive Limits of Outer Actions of ${\mathbb R}$ on Approximate Circle Algebras
In this paper we present a classification, up to equivariant isomorphism, of $C^*$-dynamical systems $(A,{\mathbb R},\alpha )$ arising as inductive limits of directed systems $\{ (A_n,{\mathbb R},\alpha_n),\varphi_{nm}\}$, where each $A_n$ is a finite direct sum of matrix algebras over the continuous functions on the unit circle, and the $\alpha_n$s are outer actions generated by rotation of the spectrum.

Keywords:classification, $C^*$-dynamical system
Categories:46L57, 46L35

3. CMB 2006 (vol 49 pp. 213)

Dean, Andrew J.
On Inductive Limit Type Actions of the Euclidean Motion Group on Stable UHF Algebras
An invariant is presented which classifies, up to equivariant isomorphism, $C^*$-dynamical systems arising as limits from inductive systems of elementary $C^*$-algebras on which the Euclidean motion group acts by way of unitary representations that decompose into finite direct sums of irreducibles.

Keywords:classification, $C^*$-dynamical system
Categories:46L57, 46L35

4. CMB 1999 (vol 42 pp. 274)

Dădărlat, Marius; Eilers, Søren
The Bockstein Map is Necessary
We construct two non-isomorphic nuclear, stably finite, real rank zero $C^\ast$-algebras $E$ and $E'$ for which there is an isomorphism of ordered groups $\Theta\colon \bigoplus_{n \ge 0} K_\bullet(E;\ZZ/n) \to \bigoplus_{n \ge 0} K_\bullet(E';\ZZ/n)$ which is compatible with all the coefficient transformations. The $C^\ast$-algebras $E$ and $E'$ are not isomorphic since there is no $\Theta$ as above which is also compatible with the Bockstein operations. By tensoring with Cuntz's algebra $\OO_\infty$ one obtains a pair of non-isomorphic, real rank zero, purely infinite $C^\ast$-algebras with similar properties.

Keywords:$K$-theory, torsion coefficients, natural transformations, Bockstein maps, $C^\ast$-algebras, real rank zero, purely infinite, classification
Categories:46L35, 46L80, 19K14

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