Weekly Calendar
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Items for inclusion in the Weekly Calendar should be submitted via e-mail to Hilda Britt. Deadline for inclusion in the Weekly Calendar is 5 p.m. Thursdays. Speakers are encouraged to provide abstracts.
In the case of ellipse, the illuminated region is either the whole
table, or an annulus between the table's boundary and a confocal
ellipse, or a region between two confocal hyperbolas.
The proof is based on the consideration of the reduced phase space for
circular and elliptical billiards. All definitions and notions
required will be given at the talk.
H. Enomoto and the author proved that the family of all k-subsets
of X can be paired (omitting one if their number is odd) in such a way
that the distance for each pair is at least k. The proof used a Hamiltonian
theorem. It does not answer however the coding question ``what is the maximum
number of pairs with pairwise distance at least k'' since here every
k-element set can be used only once. Now we give some lower and
upper bounds on the maximum size of such ``codes'' with distance d.
Other coding type questions are also posed.
U.S. v. Alabama
The U.S. women's basketball team won the Olympics.
Women now enjoy the same pension rights as their male colleagues.
Over a third of medical school graduates today are women and yearly
half of law school graduates are women.
Women faculty-at some institutions-have achieved salary equity
with their male colleagues.
All of these victories for sex equality are due, at least in part, to
statistical evidence brought before the courts. But what are
statistics-or rather statisticians-telling the courts and what are
the courts really hearing? This talk addresses some of the statistical
techniques employed in notable cases. The focus is more on the
implications than on the statistical theory.
To exploit the capabilities of these novel actuators, control designers may
take advantage of a rich dynamic structure. Energy-based methods can lead to
physically intuitive control laws which are valid over large regions of
phase space. For example, three internal rotors may be used to stabilize
steady, long-axis translation of a cigar-shaped underwater vehicle by
shaping the system's kinetic energy through feedback. For a conservative
system model, this approach provides stability within a large, easily
estimated region of attraction. Physical dissipation (that is, viscous drag)
enhances stability, making the equilibrium globally asymptotically stable.
The notion of stabilizing a mechanical system by shaping its kinetic energy
is a topic of current research. For example, the method of controlled
Lagrangians provides a kinetic shaping algorithm for a class of mechanical
systems. Since kinetic shaping can obscure the effect of physical
dissipation, an important question is "How does damping affect closed-loop
stability?" The encouraging results concerning drag on underwater vehicles
have led to a more general study of the effect of physical dissipation on
controlled Lagrangian systems. After discussing the specific application of
an underwater vehicle with internal rotors, I will briefly describe the
method of controlled Lagrangians and present some recent results concerning
the influence of physical dissipation.
Abstract: The long polyelectrolyte of the DNA double helix is
partially neutralized by its association with histones and is thus
converted into a flexible, segmented string of nucleosomes. In this
way it can be compacted and stored within the eukaryotic nucleus.
Naked DNA molecules can be driven to this compaction state by
appropriate manipulation of their micro-environment. The core histone
octamer "catalyzes" an analogous transformation under physiological
conditions and also adds specificity to the ensemble and the potential
for regulation of the genetic activity in chromatin. It thus becomes
a gene endoskeleton. We will discuss the architecture of the system,
the symmetries that have been conserved through evolution in the
histone fold and their thermodynamic implications in DNA-histone
interactions. Finally, we will examine the dynamics of the
nucleosome and its potential modulations during the on and off cycling
of genetic activity.
Abstract: Uni High students will present projects that they will be
submitting to the American Statistical Association.
Abstract: In previous work we settled several conjectures on multiple
zeta values. The method used involved certain generating
functions. Since then research on these generating functions has led
to the discovery of a class of representations of fundamental
groups. This talk will survey some of this research.
Abstract: We continue to discuss the Thesis of Kachurivskii, where a
new proof of ergodic theorem based on Rokhlin-Halmos Lemma and
nonstandard analysis was introduced.
Abstract: I will present the Cartan-Hadamard Theorem for complete connected metric spaces. This theorem strongly resembles the Cartan-Hadamard Theorem of Riemannian geometry because it uses local curvature conditions to draw powerful conclusions about the global geometry and topology of a space.
Abstract: We investigate vortex pinning in solutions to the
Ginzburg-Landau system corresponding to an energy in which a
coefficient, a(x), vanishes at a finite number of points in the
domain. This model has been used to describe a non-uniform
superconducting material. For all sufficiently large applied magnetic
fields and for all sufficiently large values of the Ginzburg-Landau
paramater, we show that minimizers of the Ginzburg-Landau energy have
nontrivial vortex structures. We also show the existence of local
minimizers exhibiting vortex patterns pinned near the zeros of a(x).
Abstract: We investigate the behavior of the set of all rays emanating
from the vertex of an arbitrary small angle-a search light-inside or
on the boundary of a circular or elliptical billiard table. The
position of the search light on the table is fixed; and each ray
emanating from the vertex is reflected from the table's boundary
according to the billiard law. It turns out that, unlike the
illumination of a square table, the circular table will be illuminated
entirely if and only if one of the rays emanating from the search
light passes through the center. If there is no ray through the
table's center, a special circular annulus will be illuminated
entirely and the rest of the table will be dark.
Abstract: Let X be an n-set, and let k be a positive integer
less than n/2. Suppose that (A1,B1) and (A2,B2) are
pairs of disjoint k-element subsets of X. Define the distance
between them by d((A1,B1),(A2,B2)) = min {|A1-A2|+|B1-B2|, |A1-B2|+|B1-A2|} . This is a metric
on the space of such pairs.
Abstract: ``Statistics tell us much and the Courts are willing to
listen.''
Abstract: Autonomous underwater vehicles are performing expanding
roles as ocean surveyors. As the operational demands on these vehicles
increase, designers are becoming more concerned with reliability and
efficiency. In light of these concerns, internal actuators, such as
moving masses or spinning rotors, provide an appealing alternative to
conventional underwater vehicle actuators. Furthermore, internal
actuators can improve an underwater vehicle's maneuverability and can
reduce its environmental footprint.
Abstract: For curves with automorphisms of large order, we show how to
speed up the discrete logarithm computation in the Jacobian
of the curve through parallel collision search. We give the
results of some simulations and compare these with statistics
for random walks in a graph.
Abstract: This will be the second lecture in a series of talks on the
positive solution (joint with Olga Kharlampovich) to the celebrated
Tarski conjecture for free groups. Namely, we will outline the proof
that the elementary theory of a finitely generated nonabelian free
group is decidable and that any two such groups are elementarily
equivalent.
Abstract: A dihedral group of maps is a group of homeomorphisms of
some topological space that is generated by two involutions (-an
involution is a map t such that tƒt = identity). The
talk will not be about the 'general theory' of such animals. I will
describe a number of quite different and interesting contexts, in
dynamics, approximation theory, complex analysis and geometry, in each
of which there is a naturally-occurring pair of non-commuting
involutions. In such situations, one finds that techniques of ergodic
theory or dynamical systems can be put to work, and it is usually
possible to make progress.