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1. CMB 2014 (vol 57 pp. 520)
Maximizing the Index of Trees with Given Domination Number The index of a graph $G$ is the maximum
eigenvalue of its adjacency matrix $A(G)$. In this paper we
characterize the extremal tree with given
domination number that attains the maximum index.
Keywords:trees, spectral radius, index, domination number Category:05C50 |
2. CMB 2011 (vol 55 pp. 368)
The Secondary Chern-Euler Class for a General Submanifold We define and study the secondary Chern-Euler class for a general submanifold of a Riemannian manifold. Using this class, we define and study the index for a vector field with non-isolated singularities on a submanifold. As an application, we give conceptual proofs of a result of Chern.
Keywords:secondary Chern-Euler class, normal sphere bundle, Euler characteristic, index, non-isolated singularities, blow-up Category:57R20 |
3. CMB 2008 (vol 51 pp. 217)
A Multivalued Nonlinear System with the Vector $p$-Laplacian on the Semi-Infinity Interval We study a second order nonlinear system driven by the vector
$p$-Laplacian, with a multivalued nonlinearity and defined on
the positive time semi-axis $\mathbb{R}_+.$ 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 time-horizon system.
Keywords:semi-infinity interval, vector $p$-Laplacian, multivalued nonlinear, fixed point index, Hartman condition, completely continuous map Category:34A60 |
4. CMB 2006 (vol 49 pp. 472)
Cyclic Cubic Fields of Given Conductor and Given Index The number of cyclic cubic fields with a given conductor and a given index is determined.
Keywords:Discriminant, conductor, index, cyclic cubic field Categories:11R16, 11R29 |
5. CMB 2005 (vol 48 pp. 607)
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 |