A Sharp Diameter Bound For Unipotent Groups Of Classical Type Overℤ /Pℤ,
2010
University of Wisconsin
A Sharp Diameter Bound For Unipotent Groups Of Classical Type Overℤ /Pℤ, Jordan S. Ellenberg, Julianna Tymoczko
Mathematics Sciences: Faculty Publications
The unipotent subgroup of a finite group of Lie type over a prime field Fp comes equipped with a natural set of generators; the properties of the Cayley graph associated to this set of generators have been much studied. In the present paper, we show that the diameter of this Cayley graph is bounded above and below by constant multiples of np + n2 log p, where n is the rank of the associated Lie group. This generalizes the result of Ellenberg, A sharp diameter bound for an upper triangular matrix group, Harvard University, 1993, which treated the case of …
When Is The Numerical Range Of A Nilpotent Matrix Circular?,
2010
University of Nebraska at Omaha
When Is The Numerical Range Of A Nilpotent Matrix Circular?, Valentin Matache, Mihaela Teodora Matache
Mathematics Faculty Publications
The problem formulated in the title is investigated. The case of nilpotent matrices of size at most 4 allows a unitary treatment. The numerical range of a nilpotent matrix M of size at most 4 is circular if and only if the traces tr M∗M2 and tr M∗M3 are null. The situation becomes more complicated as soon as the size is 5. The conditions under which a 5×5nilpotent matrix has circular numerical range are thoroughly discussed.
Subclinical Myocardial Necrosis And Cardiovascular Risk In Stable Patients Undergoing Elective Cardiac Evaluation,
2010
Lerner Research Institute
Subclinical Myocardial Necrosis And Cardiovascular Risk In Stable Patients Undergoing Elective Cardiac Evaluation, W.H. Wilson Tang, Yuping Wu, Stephen J. Nicholls, Danielle M. Brennan, Michael Pepoy, Shirley Mann, Alan Pratt, Frederick Van Lente, Stanley L. Hazen
Mathematics and Statistics Faculty Publications
Objective— The presence of subclinical myocardial necrosis as a prodrome to longer-term adverse cardiac event risk has been debated. The debate has focused predominantly within patients with acute coronary syndrome, and on issues of troponin assay variability and accuracy of detection, rather than on the clinical significance of the presence of subclinical myocardial necrosis (ie, “troponin leak”) within stable cardiac patients. Herein, we examine the relationship between different degrees of subclinical myocardial necrosis and long-term adverse clinical outcomes within a stable cardiac patient population with essentially normal renal function. Methods and Results— Sequential consenting patients (N=3828; median creatinine clearance, 100 …
Lie Algebroid Structures On Double Vector Bundles And Representation Theory Of Lie Algebroids,
2010
University of Toronto
Lie Algebroid Structures On Double Vector Bundles And Representation Theory Of Lie Algebroids, Alfonso Gracia-Saz, Rajan Amit Mehta
Mathematics Sciences: Faculty Publications
A VB-algebroid is essentially defined as a Lie algebroid object in the category of vector bundles. There is a one-to-one correspondence between VB-algebroids and certain flat Lie algebroid superconnections, up to a natural notion of equivalence. In this setting, we are able to construct characteristic classes, which in special cases reproduce characteristic classes constructed by Crainic and Fernandes. We give a complete classification of regular VB-algebroids, and in the process we obtain another characteristic class of Lie algebroids that does not appear in the ordinary representation theory of Lie algebroids.
Incompressibility And Global Inversion,
2010
Trinity University
Incompressibility And Global Inversion, Eduardo C. Balreira
Mathematics Faculty Research
Given a local diffeomorphism ƒ : ℝn → ℝn, we consider certain in- compressibility conditions on the parallelepiped Dƒ(x) ([0, 1]n) which imply that the pre-image of an affine subspace is non-empty and has trivial homotopy groups. These conditions are then used to establish criteria for ƒ to be globally invertible, generalizing in all dimensions the previous results of M. Sabatini.
Application Of Combinatorial Structures To Key Predistribution In Sensor Networks And Traitor Tracing.,
2010
Indian Statistical Institute
Application Of Combinatorial Structures To Key Predistribution In Sensor Networks And Traitor Tracing., Sushmita Ruj Dr.
Doctoral Theses
From time immemorial people have used cryptography for secure communication. Cryptography has decided the fate of many kings and queens as well as the outcome of various wars. It has become all the more important nowadays, with the growing need of electronic communication. We now live in a society where electronic networks pervade all aspects of our professional and private lives. We all use cryptography when we do bank transfers by ATM, or SWIFT, while using the mobile phones and i-phones, SSL protocols or using password protected machines. Though electronic communication is fast and easy, it is vulnerable to security …
Sequences Of Positive Integers Containing No K-Term Arithmetic Progressions And Smooth Numbers In Short Intervals.,
2010
Indian Statistical Institute
Sequences Of Positive Integers Containing No K-Term Arithmetic Progressions And Smooth Numbers In Short Intervals., Goutam Pal Dr.
Doctoral Theses
In my thesis I have worked on two problems:1. On sequences of positive integers containing no k terms in arithmetic progressions.2. On smooth numbers in short intervals.The first two chapters of my thesis deal with the first problem and in the rest of the thesis I have focused on the 2nd problem.In the first chapter of my thesis I have considered the function rk(N) for a fixed k ≥ 3, where, by definition, rk(N) is the cardinality of a maximal subset of N consecutive natural numbers with the property that nork terms of it are in an Arithmetic Progression (A. …
Doubly Connected Minimal Surfaces And Extremal Harmonic Mappings,
2010
Syracuse University and University of Helsinki
Doubly Connected Minimal Surfaces And Extremal Harmonic Mappings, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen
Mathematics - All Scholarship
The concept of a conformal deformation has two natural extensions: quasiconformal and harmonic mappings. Both classes do not preserve the conformal type of the domain, however they cannot change it in an arbitrary way. Doubly connected domains are where one first observes nontrivial conformal invariants. Herbert Groetzsch and Johannes C. C. Nitsche addressed this issue for quasiconformal and harmonic mappings, respectively. Combining these concepts we obtain sharp estimates for quasiconformal harmonic mappings between doubly connected domains. We then apply our results to the Cauchy problem for minimal surfaces, also known as the Bjorling problem. Specifically, we obtain a sharp estimate …
Oxygen Regulates The Effective Diffusion Distance Of Nitric Oxide In The Aortic Wall,
2010
Ohio State University
Oxygen Regulates The Effective Diffusion Distance Of Nitric Oxide In The Aortic Wall, Xiaoping Liu, Parthasarathy Srinivasan, Eric Collard, Paula Grajdeanu, Kevin Lok, Sarah E. Boyle, Avner Friedman, Jay L. Zweier
Mathematics and Statistics Faculty Publications
Endothelium-derived nitric oxide (NO) is critical in maintaining vascular tone. Accumulating evidence shows that NO bioavailability is regulated by oxygen concentration. However, it is unclear to what extent the oxygen concentration regulates NO bioavailability in the vascular wall. In this study, a recently developed experimental setup was used to measure the NO diffusion flux across the aortic wall at various oxygen concentrations. It was observed that for a constant NO concentration at the endothelial surface, the measured NO diffusion flux out of the adventitial surface at [O2] = 0 μM is around fivefold greater than at [O2] = 150 μM, …
A Unified Theory Of Function Spaces And Hyperspaces: Local Properties,
2010
Burgundy University
A Unified Theory Of Function Spaces And Hyperspaces: Local Properties, Szymon Dolecki, Frédéric D. Mynard
Mathematical Sciences: Faculty Publications
Many classically used function space structures (including the topology of pointwise convergence, the compact-open topology, the Isbell topology and the continuous convergence) are induced by a hyperspace structure counterpart. This scheme is used to study local properties of function space structures on C(X,R), such as character, tighntess, fan-tightness, strong fan-tightness, the Fr{\'e}chet property and some of its variants. Under mild conditions, local properties of C(X,R) at the zero function correspond to the same property of the associated hyperspace structure at X. The latter is often easy to characterize in terms of covering properties …
On Type Of Periodicity And Ergodicity To A Class Of Fractional Order Differential Equations,
2010
Florida Institute of Technology
On Type Of Periodicity And Ergodicity To A Class Of Fractional Order Differential Equations, Ravi P. Agarwal, Bruno D. Andrade, Claudio Cuevas
Mathematics and System Engineering Faculty Publications
We study several types of periodicity to a class of fractional order differential equations.
Asian Spread Option Pricing Models And Computation,
2010
Brigham Young University - Provo
Asian Spread Option Pricing Models And Computation, Sijin Chen
Theses and Dissertations
In the commodity and energy markets, there are two kinds of risk that traders and analysts are concerned a lot about: multiple underlying risk and average price risk. Spread options, swaps and swaptions are widely used to hedge multiple underlying risks and Asian (average price) options can deal with average price risk. But when those two risks are combined together, then we need to consider Asian spread options and Asian-European spread options for hedging purposes. For an Asian or Asian-European spread call option, its payoff depends on the difference of two underlyings' average price or of one average price and …
Enhanced Metric Regularity And Lipschitzian Properties Of Variational Systems,
2010
University of Alicante, Spain
Enhanced Metric Regularity And Lipschitzian Properties Of Variational Systems, Francisco J. Aragón Artacho, Boris S. Mordukhovich
Mathematics Research Reports
This paper mainly concerns the study of a large class of variational systems governed by parametric generalized equations, which encompass variational and hemivariational inequalities, complementarity problems, first-order necessary optimality conditions, and other optimization-related models important for optimization theory and applications. An efficient approach to these issues has been developed in our preceding work [1] establishing qualitative and quantitative relationships between conventional metric regularity jsubregularity and Lipschitzian/calmness properties in the framework of parametric generalized equations in arbitrary Banach spaces. This paper provides, on one hand, significant extensions of the major results in [1] to new partial metric regularity and hemiregularity properties. …
A Stochastic Model Of Cell Cycle Desynchronization,
2010
Trinity University
A Stochastic Model Of Cell Cycle Desynchronization, Peter Olofsson, Thomas O. Mcdonald
Mathematics Faculty Research
A general branching process model is suggested to describe cell cycle desynchronization. Cell cycle phase times are modeled as random variables and a formula for the expected fraction of cells in S phase as a function of time is established. The model is compared to data from the literature and is also compared to previously suggested deterministic and stochastic models.
Improved Automated Monitoring And New Analysis Algorithm For Circadean Phototaxis Rhythms In Chlamydomonas,
2010
Western Kentucky University
Improved Automated Monitoring And New Analysis Algorithm For Circadean Phototaxis Rhythms In Chlamydomonas, Christa Gaskill, Jennifer Forbes-Stovall, Bruce Kessler, Mike Young, Claire A. Rinehart, Sigrid Jacobshagen
Mathematics Faculty Publications
Automated monitoring of circadian rhythms is an efficient way of gaining insight into oscillation parameters like period and phase for the underlying pacemaker of the circadian clock. Measurement of the circadian rhythm of phototaxis (swimming towards light) exhibited by the green alga Chlamydomonas reinhardtii has been automated by directing a narrow and dim light beam through a culture at regular intervals and determining the decrease in light transmittance due to the accumulation of cells in the beam. In this study, the monitoring process was optimized by constructing a new computercontrolled measuring machine that limits the test beam to wavelengths reported …
Integer Functions On The Cycle Space And Edges Of A Graph,
2010
Wright State University - Main Campus
Integer Functions On The Cycle Space And Edges Of A Graph, Dan Slilaty
Mathematics and Statistics Faculty Publications
A directed graph has a natural Z-module homomorphism from the underlying graph’s cycle space to Z where the image of an oriented cycle is the number of forward edges minus the number of backward edges. Such a homomorphism preserves the parity of the length of a cycle and the image of a cycle is bounded by the length of that cycle. Pretzel and Youngs (SIAM J. Discrete Math. 3(4):544–553, 1990) showed that any Z-module homomorphism of a graph’s cycle space to Z that satisfies these two properties for all cycles must be such a map induced from an edge direction …
Highway Hull Revisited,
2010
Universite Libre de Bruxelles
Highway Hull Revisited, Greg Aloupis, Jean Cardinal, Sébastien Collette, Ferran Hurtado, Stefan Langerman, Joseph O'Rourke, Belén Palop
Computer Science: Faculty Publications
A highway H is a line in the plane on which one can travel at a greater speed than in the remaining plane. One can choose to enter and exit H at any point. The highway time distance between a pair of points is the minimum time required to move from one point to the other, with optional use of H. The highway hull H(S,H) of a point set S is the minimal set containing S as well as the shortest paths between all pairs of points in H(S,H), using the highway time distance. We provide a Θ(nlogn) worst-case …
Perturbed Spherical Objects In Acoustic And Fluid Flow Fields,
2010
New Jersey Institute of Technology
Perturbed Spherical Objects In Acoustic And Fluid Flow Fields, Manmeet Kaur
Dissertations
In this study, the time averaged acoustic radiation force and drag on a small, nearly spherical object suspended freely in a stationary sound wave field in a compressible, low viscosity fluid is to be calculated. This problem has been solved for a spherical object, and it has many important engineering applications related to segregation and separation processes for particles in fluids such as water. Small but significant errors have occurred in the predicted behavior of the particles using the existing approximate solutions based on perfect spheres. The classical approach has been extended in this research to objects that deviate slightly …
Nonlinear Evolution Of Annular Layers And Liquid Threads In Electric Fields,
2010
New Jersey Institute of Technology
Nonlinear Evolution Of Annular Layers And Liquid Threads In Electric Fields, Qiming Wang
Dissertations
The nonlinear dynamics of viscous perfectly conducting liquid jets or threads under the action of a radial electric field are studied theoretically and numerically here. The field is generated by a potential difference between the jet surface and a concentrically placed electrode of given radius. A long-wave nonlinear model that is used to predict the dynamics of the system and in particular to address the effect of the radial electric field on jet breakup is developed, Two canonical regimes are identified that depend on the size of the gap between the outer electrode and the unperturbed jet surface. For relatively …
Modeling And Quasi-Monte Carlo Simulation Of Risk In Credit Portfolios,
2010
New Jersey Institute of Technology
Modeling And Quasi-Monte Carlo Simulation Of Risk In Credit Portfolios, Bo Ren
Dissertations
Credit risk is the risk of losing contractually obligated cash flows promised by a counterparty such as a corporation, financial institution, or government due to default on its debt obligations. The need for accurate pricing and hedging of complex credit derivatives and for active management of large credit portfolios calls for an accurate assessment of the risk inherent in the underlying credit portfolios. An important challenge for modeling a credit portfolio is to capture the correlations within the credit portfolio. For very large and homogeneous portfolios, analytic and semi-analytic approaches can be used to derive limiting distributions. However, for portfolios …
