## Search

Now showing items 1-10 of 16

#### Rota's basis conjecture for paving matroids

(University of Canterbury, 2006)

Rota conjectured that, given n disjoint bases of a
rank-n matroid M, there are n disjoint transversals of these bases
that are all bases of M. We prove a stronger statement for the
class of paving matroids.

#### Experimental and theoretical analysis of hybridization

(University of Canterbury, 2006)

We develop new heuristics and
an exact algorithm for calculating the
amount of hybridization between two
rooted binary phylogenetic trees. Calculating
the minimum number of hybridization
events is NP-hard, but essential ...

#### A nonlinear model of size-structured populations with applications to cell cycles

(University of Canterbury, 2006)

The Sharpe-Lotka-McKendrick (or von Foerster) equations for an age-structured population,
with a nonlinear term to represent overcrowding or competition for resources, are considered. The
model is extended to include a ...

#### Wild triangles in 3-connected matroids

(University of Canterbury, 2006)

Tutte's Triangle Lemma proves that if {a, b, c} is a triangle in a 3-connected matroid and neither M\a nor M\b is 3-connected, then M has a triad that contains a and exactly one of b and c. Hence {a, b, c} is contained in ...

#### Nesting polynormals [i.e. polynomials] in infinite radicals

(University of Canterbury, 2006)

We consider infinite nested radicals in which the arguments
are positive polynomial sequences. It is shown that the
evaluation of such a nesting is always finite, and we prove necessary
and sufficient conditions for the ...

#### On a conjecture of J.C. Butcher and H. Podhaisky

(University of Canterbury. Department of Mathematics and Statistics, 2006)

#### Sobolev spaces and approximation by affine spanning systems.

(University of Canterbury. Dept. of Mathematics and Statistics, 2006)

We develop conditions on a Sobolev function 𝜓∈Wm,p(ℝd) such that if 𝜓̂ (0) = 1 and 𝜓 satisfies the Strang-Fix conditions to order m - 1, then a scale averaged approximation formula holds for all 𝑓 ∈ Wm,p(ℝd):
[FORMULA]
The ...

#### A chain theorem for matroids

(University of Canterbury, 2006)

Tutte's Wheels-and-Whirls Theorem proves that if M is a 3-connected matroid other than a wheel or a whirl, then M has a 3-connected minor N such that |E(M)| - |E(N)| = 1. Geelen and Whittle extended this theorem by showing ...

#### Encoding phylogenetic trees in terms of weighted quartets

(University of Canterbury, 2006)

For a finite set X, an edge-weighted phylogenetic X -tree, or phylogenetic tree for short, is a tree T having leaf set X and no degree 2 vertices, together with a map from the edge set of T to ℝ≥₀. Within the field of ...

#### Optimizing phylogenetic diversity under constraints

(University of Canterbury, 2006)

Phylogenetic diversity (PD) is a measure of the extent to which different subsets of taxa span an evolutionary tree, and provides a quantitative tool for studying biodiversity conservation. Recently, it was shown that the ...