Open Access. Powered by Scholars. Published by Universities.®

Physical Sciences and Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

Mathematics

2007

Loyola Marymount University and Loyola Law School

Articles 1 - 10 of 10

Full-Text Articles in Physical Sciences and Mathematics

Macroscopic Consequences Of Calcium Signaling In Microdomains: A First-Passage-Time Approach, Robert Rovetti Nov 2007

Macroscopic Consequences Of Calcium Signaling In Microdomains: A First-Passage-Time Approach, Robert Rovetti

Mathematics Faculty Works

Calcium (Ca) plays an important role in regulating various cellular processes. In a variety of cell types, Ca signaling occurs within microdomains where channels deliver localized pulses of Ca activating a nearby collection of Ca-sensitive receptors. The small number of channels involved ensures that the signaling process is stochastic. The aggregate response of several thousand of these microdomains yields a whole-cell response which dictates the cell behavior. Here, we study the statistical properties of a population of these microdomains in response to a trigger signal. We use a first-passage-time approach to show analytically how Ca release in the whole cell …

Go to article

The Probability Of Relatively Prime Polynomials, Arthur T. Benjamin, Curtis D. Bennett Jun 2007

The Probability Of Relatively Prime Polynomials, Arthur T. Benjamin, Curtis D. Bennett

Mathematics Faculty Works

No abstract provided.

Go to article

Exotic Statistics For Strings In 4d Bf Theory, John C. Baez, Derek K. Wise, Alissa S. Crans Jan 2007

Exotic Statistics For Strings In 4d Bf Theory, John C. Baez, Derek K. Wise, Alissa S. Crans

Mathematics Faculty Works

After a review of exotic statistics for point particles in 3d BF theory, and especially 3d quantum gravity, we show that string-like defects in 4d BF theory obey exotic statistics governed by the 'loop braid group'. This group has a set of generators that switch two strings just as one would normally switch point particles, but also a set of generators that switch two strings by passing one through the other. The first set generates a copy of the symmetric group, while the second generates a copy of the braid group. Thanks to recent work of Xiao-Song Lin, we can …

Go to article

Derived Categories And The Analytic Approach To General Reciprocity Laws. Part Ii, Michael Berg Jan 2007

Derived Categories And The Analytic Approach To General Reciprocity Laws. Part Ii, Michael Berg

Mathematics Faculty Works

Building on the topological foundations constructed in Part I, we now go on to address the homological algebra preparatory to the projected final arithmetical phase of our attack on the analytic proof of general reciprocity for a number field. In the present work, we develop two algebraic frameworks corresponding to two interpretations of Kubota's n-Hilbert reciprocity formalism, presented in a quasi-dualized topological form in Part I, delineating two sheaf-theoretic routes toward resolving the aforementioned (open) problem. The first approach centers on factoring sheaf morphisms eventually to yield a splitting homomorphism for Kubota's n-fold cover of the adelized special linear group …

Go to article

Computing Boundary Slopes Of 2-Bridge Links, Jim Hoste, Patrick Shanahan Jan 2007

Computing Boundary Slopes Of 2-Bridge Links, Jim Hoste, Patrick Shanahan

Mathematics Faculty Works

We describe an algorithm for computing boundary slopes of 2-bridge links. As an example, we work out the slopes of the links obtained by 1/k surgery on one component of the Borromean rings. A table of all boundary slopes of all 2-bridge links with 10 or less crossings is also included.

Go to article

Intrinsic Linking And Knotting In Virtual Spatial Graphs, Thomas Fleming, Blake Mellor Jan 2007

Intrinsic Linking And Knotting In Virtual Spatial Graphs, Thomas Fleming, Blake Mellor

Mathematics Faculty Works

We introduce a notion of intrinsic linking and knotting for virtual spatial graphs. Our theory gives two filtrations of the set of all graphs, allowing us to measure, in a sense, how intrinsically linked or knotted a graph is; we show that these filtrations are descending and nonterminating. We also provide several examples of intrinsically virtually linked and knotted graphs. As a byproduct, we introduce the virtual unknotting number of a knot, and show that any knot with nontrivial Jones polynomial has virtual unknotting number at least 2.

Go to article

Virtual Spatial Graphs, Thomas Fleming, Blake Mellor Jan 2007

Virtual Spatial Graphs, Thomas Fleming, Blake Mellor

Mathematics Faculty Works

Two natural generalizations of knot theory are t he study of spatially embedded graphs, and Kauffman's theory of virtual knots. In this paper we combine these approaches to begin the study of virtual spat ial graphs.

Go to article

Cohomology Of The Adjoint Of Hopf Algebras, J. Scott Carter, Alissa S. Crans, Mohamed Elhamdadi, Masahico Saito Jan 2007

Cohomology Of The Adjoint Of Hopf Algebras, J. Scott Carter, Alissa S. Crans, Mohamed Elhamdadi, Masahico Saito

Mathematics Faculty Works

A cohomology theory of the adjoint of Hopf algebras, via deformations, is presented by means of diagrammatic techniques. Explicit calculations are provided in the cases of group algebras, function algebras on groups, and the bosonization of the super line. As applications, solutions to the YBE are given and quandle cocycles are constructed from groupoid cocycles.

Go to article

Boundary Slopes Of 2-Bridge Links Determine The Crossing Number, Jim Hoste, Patrick D. Shanahan Jan 2007

Boundary Slopes Of 2-Bridge Links Determine The Crossing Number, Jim Hoste, Patrick D. Shanahan

Mathematics Faculty Works

A diagonal surface in a link exterior M is a properly embedded, incompressible, boundary incompressible surface which furthermore has the same number of boundary components and the same slope on each component of the boundary of M. We derive a formula for the boundary slope of a diagonal surface in the exterior of a 2-bridge link which is analogous to the formula for the boundary slope of a 2-bridge knot found by Hatcher and Thurston. Using this formula we show that the diameter of a 2-bridge link, that is, the difference between the smallest and largest finite slopes of …

Go to article

An Introduction To Virtual Spatial Graph Theory, Thomas Fleming, Blake Mellor Jan 2007

An Introduction To Virtual Spatial Graph Theory, Thomas Fleming, Blake Mellor

Mathematics Faculty Works

Two natural generalizations of knot theory are the study of spatial graphs and virtual knots. Our goal is to unify these two approaches into the study of virtual spatial graphs. We state the definitions, provide some examples, and survey the known results. We hope that this paper will help lead to rapid development of the area.

Go to article