Applied Mathematics Seminar - Spring 2008

   Room: Minard 135, Time: 9:00AM-10:00AM

Organizer: Marian Bocea

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.