MONDAY, MARCH 27, 2006

COLLOQUIUM
TIME: 3:35 p.m. – 4:30 p.m.
ROOM: Ayres Hall 214
SPEAKER: Maeve McCarthy, Murray State University
TITLE: Constrained optimization of eigenvalues for a particular class of singular Sturm-Liouville operators
ABSTRACT: We investigate the spectral properties of a certain Sturm-Liouville operator that encompasses many mechanical problems, including the buckling of elastic columns. We consider design problems related to the least eigenvalue of these Sturm-Liouville operators. Specifically, we will maximize height for a class of elastic columns, including annular columns. We will discuss the impact of tapering and singular coefficients from both a spectral and design perspective. Singularities leading to limit-circle and limit-point classifications are possible. We will present criteria for the existence of a purely discrete spectrum and hence a least eigenvalue. Integral constraints will be used to specify our objective class. Classical rearrangement techniques will be used to establish the existence of an optimal design in the presence of two design coefficients.

ANALYSIS SEMINAR

TIME: 3:35 p.m. – 4:25 p.m.
ROOM: Ayres Hall 102
SPEAKER: Professor Ignacio Uriarte-Tuero, University of Missouri
TITLE: “On Marcinkiewicz integrals and harmonic measure”

TUESDAY, MARCH 28, 2006

SIAM STUDENT CHAPTER AND APPLIED MATH SEMINAR
TIME: 3:30 p.m.
ROOM: Ayres Hall 214
SPEAKER: Professor Beverly L. Brechner, University of Florida
TITLE: Mathematics and Parkinson’s Disease
ABSTRACT: This talk will center on recent joint work with a medical physics/nuclear engineering UF graduate student, Atchar Sudhyadhom. In this work, we apply mathematics to partially automate a portion of DBS (Deep Brain Stimulation) surgery for Parkinson’s disease.

WEDNESDAY, MARCH 29, 2006

ANALYSIS SEMINAR

TIME: 3:35 p.m. – 4:25 p.m.
ROOM: Ayres Hall 309A
SPEAKER: Professor Ignacio Uriarte-Tuero, University of Missouri
TITLE: “Improved Painleve removability for planar quasiregular mappings”

THURSDAY, MARCH 30, 2006

PROBABILITY SEMINAR

TIME: 10:10 a.m. – 11:00 a.m.
ROOM: Ayres Hall 209A
SPEAKER: Professor Józef Zajac, and Dr. Beata Falda, State College in Chelm, Poland
TITLE: Nonclassical statistics

COLLOQUIUM
TIME: 3:35 p.m. – 4:25 p.m.
ROOM: Ayres Hall 214
SPEAKER: Professor Józef Zajac, Rector of the State College in Chelm, Poland
TITLE: Harmonic representation of the universal Teichmüller space the Paprocki space[1]
ABSTRACT: One of the most powerful tools, when studying Riemann surfaces, is the notion of Teichmüller space i.e. a metrizable and complete quotient space of closed Riemann surfaces with genus [] While the conception was introduced by ingenious German mathematician O. Teichmüller before WW II, the name appears because of L. Bers and L. Ahlfors in the late fifties. The function-theoretic models of this, not easy understandable original Teichmüller space, was built up by the use of equivalence classes of quasiconformal automorphismus of the unit disc or its boundary representation called quasihomographies, know as quasisymmetric functions in the case of the real line.

The main purpose of this lecture is to present a new, very simple and readable, even for nonprofessionalists, model of the universal Teichmüller space built up by certain harmonic, self-mappings of the unit disc. The idea is as follows:

To each element of the universal Teichmüller space represented by certain automorphisms []of the unit circle [] one associates uniquely a harmonic automorphism of the unit disk [], defined as Poisson integral [] of a given []in question. Hence, the universal Teichmüller space can be represented by the family of harmonic automorphisms of the unit disk, denoted by [] and called the Paprocki space. Among []and real analytic representations of the universal Teichmüller space this one particularly leads directly to two classes of analytic functions defined in the unit disk []denoted by [] and [] called the conjugate Paprocki spaces of analytic functions. Formally, [] [1] The name Paprocki space has been introduced by the author in memory of E. Paprocki – a very promising young mathematician killed in a road accident on June 25, 1998. Paprocki initiated the study of this topic within his doctoral thesis and received a special KBN Grant in order to complete his research.

FRIDAY, MARCH 31, 2006

COLLOQUIUM
TIME: 3:35 p.m. – 4:25 p.m.
ROOM: Ayres Hall 214
SPEAKER: Professor Konstantina Trivisa, Mathematics, University of Maryland
TITLE: On phase transition dynamics
ABSTRACT: A multidimensional model is introduced for the phase transition dynamics of a binary mixture of compressible fluids. The model presented here can accommodate various physical contexts, namely “liquid-liquid”, “gas-liquid” phase equilibria, as well as the phase transition of a mixture of two distinct gases, to produce species due to combustion, the evolution of gaseous stars in astrophysics, the phase transition dynamics associated with semiconductors, and others.

The model is formulated by the Navier-Stokes equations in Euler coordinates, which is now expressed by the conservation of mass, the balance of momentum and entropy and the species conservation equation. These equations take a new form due to the choice of rather complex constitutive relations which are able to accommodate the multicomponent character of the mixture.