SCHEDULE
JANUARY 2008
Wednesday, January 17 - Organizational
Meeting: 12:00 Noon in Minard 304A
Monday,
January 21 - Martin Luther
King, Jr. Day - No seminar
Monday, January 28 - Nikita
Barabanov (NDSU Mathematics Department) -
Introduction to Financial Mathematics I
Abstract:
Key objects and structures. Financial markets. Market
derivatives. Financial
instruments. Financial markets under uncertainty. Aims and problems of
financial theory.
FEBRUARY 2008
Monday, February 4 - Nikita
Barabanov (NDSU Mathematics Department) -
Introduction to Financial Mathematics II
Abstract:
Key objects and structures. Financial markets. Market
derivatives. Financial
instruments. Financial markets under uncertainty. Aims and problems of
financial theory.
Monday, February 11 - Cody Nitschke
(NDSU Mathematics Department) -
An Introduction to
Discrete Financial Market Models I
Abstract:
A general financial market model is discussed in discrete
time. The important properties of these models will also be discussed.
In end,
I will arrive at the famous Cox-Ross-Rubinstein model which is a
special
case of these discrete models. Finally, some properties of this model
will be proved.
Monday, February 18 - Presidents
Day - No seminar
Monday, February 25 - Alexander
Wagner (NDSU
Physics Department) - The
lattice Boltzmann method applied to multi-component phase-separation
problems
Abstract:
I will briefly introduce the theory of the lattice Boltzmann method and
show how we apply it to multi-phase multi-component fluid simulations.
I will show some results for inhomogeneous phase separation and phase
separation in conserved order parameter vector models.
MARCH 2008
Monday, March 10 - Cody Nitschke
(NDSU Mathematics Department) -
An Introduction to
Discrete Financial Market Models II
Abstract:
A general financial market model is discussed in discrete
time. The important properties of these models will also be discussed.
In end,
I will arrive at the famous Cox-Ross-Rubinstein model which is a
special
case of these discrete models. Finally, some properties of this model
will be proved.
Wednesday, March 12 - Cody Nitschke
(NDSU Mathematics Department) -
An Introduction to
Discrete Financial Market Models III
Abstract:
A general financial market model is discussed in discrete
time. The important properties of these models will also be discussed.
In end,
I will arrive at the famous Cox-Ross-Rubinstein model which is a
special
case of these discrete models. Finally, some properties of this model
will be proved.
Monday, March 17 - Farkhad Abdullaev
(NDSU Mathematics Department) - Calculus of Variations for L-infinity
Functionals I
Abstract:We introduce the necessary and
sufficient condition for lower semicontinuity of L-infinity
functionals, and we prove the existence of minimizers for such
functionals using the Direct Method of the Calculus of Variations.
Monday, March 24 - Easter
Monday - No seminar
Monday, March 31 - Farkhad Abdullaev
(NDSU Mathematics Department) - Calculus of Variations for L-infinity
Functionals II
Abstract:We introduce the necessary and
sufficient condition for lower semicontinuity of L-infinity
functionals, and we prove the existence of minimizers for such
functionals using the Direct Method of the Calculus of Variations.
APRIL 2008
Monday, April 7 -
Stéphane
Rainville
(NDSU Psychology Department) - The Hodgkin-Huxley model of action
potentials
Abstract: Hodgkin & Huxely (H
& H) earned the
1963 Nobel Prize in Physiology or Medicine for their elegant electrophysiological
studies on the axon of giant-squid neurons.
In particular, H & H used a voltage-clamp technique that allowed
them to study the dynamics
of ion-specific
voltage-dependent
currents that govern the generation of action potentials – short
all-or-none depolarizations that travel along the cells' membrane and
allow communication between neurons. In this seminar, I will describe
the H & H model (a system of
coupled
nonlinear differential
equations) and will illustrate its key behaviors using Matlab
simulations. The H & H model not only exhibits known properties of
neurons but highlights how mathematical modeling, especially of the
nonlinear kind, can predict unexpected and
empirically-verifiable
biophysiological phenomena.
Wednesday,
April 9 - Farkhad Abdullaev
(NDSU Mathematics Department) - Calculus of Variations for L-infinity
Functionals III
Abstract:We introduce the necessary and
sufficient condition for lower semicontinuity of L-infinity
functionals, and we prove the existence of minimizers for such
functionals using the Direct Method of the Calculus of Variations.
Monday, April 14 - Tayo Omotoyinbo
(NDSU Mathematics Department) - Absolute stability of 2nd order feedback
systems in class of sector time-varying nonlinearities I
Abstract:
We consider the absolute stability problem of 2nd order
systems in the class of sector time-varying non-linearities. The
problem under investigation is to find the largest sector such that
system is absolutely stable if all eigenvalues of linear systems belong
to this sector. Known results proved using Lyapunov functions of
different types show that this sector is not less than
$\pm\frac{\pi}{4}$. It is also known that this approach provides only
sufficient conditions for absolute stability. We use a different
technique, which provides necessary and sufficient conditions for
absolute stability. The problem setting, the approach, and methods to
solve the problem will be described.
Monday,
April 21 - Tayo
Omotoyinbo
(NDSU Mathematics Department) - Absolute stability of 2nd order feedback
systems in class of sector time-varying nonlinearities II
Abstract:
We consider the absolute stability problem of 2nd order systems in the
class of sector time-varying non-linearities. The problem under
investigation is to find the largest sector such that system is
absolutely stable if all eigenvalues of linear systems belong to this
sector. Known results proved using Lyapunov functions of different
types show that this sector is not less than $\pm\frac{\pi}{4}$. It is
also known that this approach provides only sufficient conditions for
absolute stability. We use a different technique, which provides
necessary and sufficient conditions for absolute stability. The problem
setting, the approach, and methods to solve the problem will be
described.
Monday,
April 28 -
Tayo
Omotoyinbo
(NDSU Mathematics Department) - Absolute stability of 2nd order feedback
systems in class of sector time-varying nonlinearities III
Abstract:
We consider the absolute stability problem of 2nd order systems in the
class of sector time-varying non-linearities. The problem under
investigation is to find the largest sector such that system is
absolutely stable if all eigenvalues of linear systems belong to this
sector. Known results proved using Lyapunov functions of different
types show that this sector is not less than $\pm\frac{\pi}{4}$. It is
also known that this approach provides only sufficient conditions for
absolute stability. We use a different technique, which provides
necessary and sufficient conditions for absolute stability. The problem
setting, the approach, and methods to solve the problem will be
described.