


Contributed Papers
Org: Bill Weiss (Toronto) [PDF]
 BHAGWAN AGGARWALA, University of Calgary, Calgary, Canada
HIV: From Infection to AIDS
[PDF] 
We present a model consisting of four first order ODE's to model the
progression of HIV from infection to AIDS. The model clarifies the
role of protease inhibitors and reverse transcriptase inhibitors in
this progression. We also show that, depending upon the viral
activity, the solution may exhibit progression to an endemic state, or
what appears to be a limit cycle around this state. In this model, the
disease may be eradicated by sufficiently strong doses of protease
inhibitors or reverse transcriptase inhibitors or a combination
thereof. An attempt is made to understand the phenomenon of HIV
blips.
 A. BASS BAGAYOGO, University College of Saint Boniface, 200 avenue de la
Cathédrale, Winnipeg, MB, Canada
Hybrid Grid Generation: A Symbolic Programming Approach
[PDF] 
Over the past 25 years, grid generation has been identified as one of
the most challenging and key components in a variety of areas in
Science and Engineering. We present a novel grid generation based on
the octree technique suitable for the decomposition of the 3D
geometries in order to generate the hybrid grids. This kind of grids
are useful when we want to resolve viscous problems characterized by a
high Reynolds number. In this study we will introduce new algorithms
to:
(1) perform a triangular faces recognition and triangular
faces ordering, with a complexity of O(N);
(2) perform the projection of the nodes of the triangular
faces on the object with a complexity of O(N^{2}).
The emphasis is on the rapid production of the geometry with a minimum
of the user input. We will also show the feasibility of combining
Maple and C++ programming languages as a suitable tool for generating
hybrid grids by using specially designed data structures.
 ADAM COFFMAN, IUPurdue Fort Wayne, Fort Wayne, IN 46805, USA
Unfolding CR singularities of real 4manifolds in
C^{5}
[PDF] 
A real 4submanifold in C^{5} is "CR singular" at a
point where the tangent space contains a complex line. The local
extrinsic geometry of a real analytic embedding near a CR singularity
is studied by finding a normal form for the defining equations under
biholomorphic transformations. We also consider oneparameter
families of embeddings, and find a normal form for a family exhibiting
a cancellation of a pair of CR singularities.
 MUHAMMAD DUREAHMAD, Arizona State University
A model of activitydependent changes in dendritic spine
density and spine structure
[PDF] 
Recent evidence indicates that the geometry of a dendritic spine
influences the dynamics of calcium in the spine and is regulated
during synaptic plasticity. For instance, a moderate rise in calcium
can cause elongation, while a very large increase in calcium causes
fast shrinkage and the eventual collapse of a spine. This expansion
and shrinkage depends on the frequency of the synaptic input to a
spine. Here, we extend previous modeling studies due to Verzi
et al. (J. Neurophys., 2005) by combining models for
activitydependent spine density and spine stem resistence with one
for calciummediated spinestem restructuring. The spine density
model is based on the standard dimensionless cable equation, which is
used to model the changes in transmembrane potential in a passive
dendrite. Additional equations represent the activity dependent
changes in spine density along the dendrite, the current balance
equation for the spine head, the calcium concentration in the spine
head, and the spine stem resistance. For this continuum model,
HodgkinHuxley type kinetics represent the changes in transmembrane
potential in the spine head. We are using computational studies to
investigate the changes in spine density and structure for a variety
of synaptic inputs of different frequencies. In particular, we are
using the model to investigate the mechanisms underlying changes in
spine density and morphology and the role of spine plasticity in
longterm depression (LTD) and longterm potentiation (LTP), which are
thought to contribute to learning and memory.
 HADI JORATI, UBC
Mikhlin multiplier theorem for nonhomogeneous dilations
[PDF] 
We seek an analogue of Mikhlin multiplier theorem for nonhomogeneous
dilations by analyzing a specific family of curved flag kernels
adapted to a parabola in the euclidean plane R^{2}.
 ANH VINH LE, Harvard University, Mathematics Department, 1 Oxford St., MA
02138, US
Some colouring problems of unitquadrance graphs
[PDF] 
The quadrance between two points A_{1} = (x_{1}, y_{1}) and A_{2} = (x_{2},y_{2}) is the number Q(A_{1}, A_{2}) = (x_{1}  x_{2})^{2} + (y_{1}  y_{2})^{2}.
Let q be an odd prime power and F_{q} be the finite field with q
elements. The unitquadrance graph D_{q} has the vertex set F_{q}^{2},
and X, Y in F_{q}^{2} are adjacent if and only if Q(A_{1}, A_{2}) = 1.
In this talk, we will discuss various colouring problems for the
unitquadrance graph D_{q}.
 JING LI, The University of Western Ontario, Middlesex College,
1151 Richmond St. N., London, ON, N6A 5B7
Modeling the Latency and Spatial NonLocality in
SusceptibleInfectious Epidemic Models
[PDF] 
With the assumptions that the infectious disease has a fixed latent
period, and the exposed individuals are capable of moving around, we
reformulate the SI models under the discrete spatial space called
patches. Some ordinary differential system models over patches with
delay representing the latency of the diseases and the dispersion
accounting for the mobility of the population between the patches are
obtained. We will show how the disease latency and population
mobility jointly affect the dynamical behaviour of the diseases by
using mathematical analysis and computer simulations.
 FRANKLIN MENDIVIL, Acadia Univesity
Fractal setvalued measures
[PDF] 
In this talk we discuss setvalued measures and give two frameworks
for constructing selfsimilar setvalued measures. We also discuss
the general idea of selfsimilar measures and give several examples.
 JIE XIAO, Memorial University
The sharp Sobolev and isoperimetric inequalities split twice
[PDF] 
In this talk, we will show that each of the sharp (endpoint) Sobolev
inequality and the isoperimetric inequality can be split into two
sharp and stronger inequalities through either the 1variational
capacity or the 1integral affine surface area. Furthermore, some
related sharp analytic and geometric inequalities will be explored as
well.
 KATE (FANG) ZHANG, University of New Brunswick
Asymptotic Behavior of A ReactionDiffusion Model With A
Quiescent
[PDF] 
This research is devoted to the investigation of the asymptotic
behavior for a reactiondiffusion model with a quiescent stage. We
first establish the existence of asymptotic speed of spread and show
that it coincides with the minimal wave speed for monotone traveling
waves. Then we obtain a threshold result on the global attractivity
of either zero or positive steady state in the case where the spatial
domain is bounded. The numerical simulations are also provided to
illustrate these analytic results.

