1. CMB 2016 (vol 60 pp. 197)
 Tang, Zikai; Deng, Hanyuan

Degree Kirchhoff Index of Bicyclic Graphs
Let $G$ be a connected graph with vertex set $V(G)$. The degree
Kirchhoff index of $G$ is defined as $S'(G) =\sum_{\{u,v\}\subseteq
V(G)}d(u)d(v)R(u,v)$, where $d(u)$ is the degree of vertex $u$,
and
$R(u, v)$ denotes the resistance distance between vertices $u$
and
$v$. In this paper, we characterize the graphs having maximum
and
minimum degree Kirchhoff index among all $n$vertex bicyclic
graphs
with exactly two cycles.
Keywords:degree Kirchhoff index, resistance distance, bicyclic graph, extremal graph Categories:05C12, 05C35 

2. CMB 2015 (vol 59 pp. 435)
 Yao, Hongliang

On Extensions of Stably Finite C*algebras (II)
For any $C^*$algebra $A$ with an approximate
unit of projections, there is a smallest ideal $I$ of $A$ such
that the quotient $A/I$ is stably finite.
In this paper, a sufficient and necessary condition is obtained
for an ideal of a $C^*$algebra with real rank zero is this smallest
ideal by $K$theory.
Keywords:extension, stably finite C*algebra, index map Categories:46L05, 46L80 

3. CMB 2014 (vol 57 pp. 520)
4. CMB 2011 (vol 55 pp. 368)
 Nie, Zhaohu

The Secondary ChernEuler Class for a General Submanifold
We define and study the secondary ChernEuler class for a general submanifold of a Riemannian manifold. Using this class, we define and study the index for a vector field with nonisolated singularities on a submanifold. As an application, we give conceptual proofs of a result of Chern.
Keywords:secondary ChernEuler class, normal sphere bundle, Euler characteristic, index, nonisolated singularities, blowup Category:57R20 

5. CMB 2008 (vol 51 pp. 217)
 Filippakis, Michael E.; Papageorgiou, Nikolaos S.

A Multivalued Nonlinear System with the Vector $p$Laplacian on the SemiInfinity Interval
We study a second order nonlinear system driven by the vector
$p$Laplacian, with a multivalued nonlinearity and defined on
the positive time semiaxis $\mathbb{R}_+.$ Using degree
theoretic techniques we solve an auxiliary mixed boundary value
problem defined on the finite interval $[0,n]$ and then via a
diagonalization method we produce a solution for the original
infinite timehorizon system.
Keywords:semiinfinity interval, vector $p$Laplacian, multivalued nonlinear, fixed point index, Hartman condition, completely continuous map Category:34A60 

6. CMB 2006 (vol 49 pp. 472)
7. CMB 2005 (vol 48 pp. 607)
 Park, Efton

Toeplitz Algebras and Extensions of\\Irrational Rotation Algebras
For a given irrational number $\theta$, we define Toeplitz operators with
symbols in the irrational rotation algebra ${\mathcal A}_\theta$,
and we show that the $C^*$algebra $\mathcal T({\mathcal
A}_\theta)$ generated by these Toeplitz operators is an extension
of ${\mathcal A}_\theta$ by the algebra of compact operators. We
then use these extensions to explicitly exhibit generators of the
group $KK^1({\mathcal A}_\theta,\mathbb C)$. We also prove an
index theorem for $\mathcal T({\mathcal A}_\theta)$ that
generalizes the standard index theorem for Toeplitz operators on
the circle.
Keywords:Toeplitz operators, irrational rotation algebras, index theory Categories:47B35, 46L80 
