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, …
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 …
Existence, Stability, And Dynamics Of Solitary Waves In Nonlinear Schroedinger Models With Periodic Potentials,
2010
University of Massachusetts Amherst
Existence, Stability, And Dynamics Of Solitary Waves In Nonlinear Schroedinger Models With Periodic Potentials, Kody John Hoffman Law
Open Access Dissertations
The focus of this dissertation is the existence, stability, and resulting dynamical evolution of localized stationary solutions to Nonlinear Schr¨odinger (NLS) equations with periodic confining potentials in 2(+1) dimensions. I will make predictions about these properties based on a discrete lattice model of coupled ordinary differential equations with the appropriate symmetry. The latter has been justified by Wannier function expansions in a so-called tight-binding approximation in the appropriate parametric regime. Numerical results for the full 2(+1)-D continuum model will be qualitatively compared with discrete model predictions as well as with nonlinear optics experiments in optically induced photonic lattices in photorefractive …
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 …
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 …
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. …
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
Bruce Kessler
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 …
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.
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 …
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 …
The Bernstein Problem For Embedded Surfaces In The Heisenberg Group H,
2010
Purdue University
The Bernstein Problem For Embedded Surfaces In The Heisenberg Group H, Donatella Danielli, Nicola Garofalo, Duy-Minh Nhieu, Scott D. Pauls
Dartmouth Scholarship
In the paper [13] we proved that the only stable C 2 minimal surfaces in the first Heisenberg group H 1 which are graphs over some plane and have empty characteristic locus must be vertical planes. This result represents a sub-Riemannian version of the celebrated theorem of Bernstein. In this paper we extend the result in [13] to C 2 complete em-bedded minimal surfaces in H 1 with empty characteristic locus. We prove that every such a surface without boundary must be a vertical plane. This result represents a sub-Riemannian coun-terpart of the classical theorems of Fischer-Colbrie and Schoen, [16], …
On The Convergence Of An Implicit Iterative Process For Generalized Asymptotically Quasi-Nonexpansive Mappings,
2010
Florida Institute of Technology
On The Convergence Of An Implicit Iterative Process For Generalized Asymptotically Quasi-Nonexpansive Mappings, Ravi P. Agarwal, Xiaolong Qin, Shinmin Kang
Mathematics and System Engineering Faculty Publications
The purpose of this paper is to introduce and consider a general implicit iterative process which includes Schu's explicit iterative processes and Sun's implicit iterative processes as special cases for a finite family of generalized asymptotically quasi-nonexpansive mappings. Strong convergence of the purposed iterative process is obtained in the framework of real Banach spaces.
Quantification Of Artistic Style Through Sparse Coding Analysis In The Drawings Of Pieter Bruegel The Elder,
2010
Dartmouth College
Quantification Of Artistic Style Through Sparse Coding Analysis In The Drawings Of Pieter Bruegel The Elder, James M. Hughes, Daniel J. Graham, Daniel N. Rockmore
Dartmouth Scholarship
Recently, statistical techniques have been used to assist art historians in the analysis of works of art. We present a novel technique for the quantification of artistic style that utilizes a sparse coding model. Originally developed in vision research, sparse coding models can be trained to represent any image space by maximizing the kurtosis of a representation of an arbitrarily selected image from that space. We apply such an analysis to successfully distinguish a set of authentic drawings by Pieter Bruegel the Elder from another set of well-known Bruegel imitations. We show that our approach, which involves a direct comparison …
Domains Of Water Molecules Provide Mechanisms Of Potentization In Homeopathy,
2010
Western Washington University
Domains Of Water Molecules Provide Mechanisms Of Potentization In Homeopathy, George Czerlinski, Tjalling Ypma
Mathematics Faculty Publications
In homeopathy, high potentization means such high dilution that there is no longer even one molecule of the original active agent per gram of the mixture. Nevertheless such high dilutions apparently remain effective. We develop a possible mechanism for homeopathic potentization to explain this phenomenon. This mechanism consists of three consecutive processes: initiation, multiplication, and amplification. Initiation is the mechano-chemical generation, by strong shaking following each dilution step, of radicals which remain in existence by mutual stabilization in simultaneously formed electronic domains. Multiplication transfers electronic excitation level structures from the original homeopathic agent to these radical-containing domains, stabilizing them further. …
Pattern-Avoiding Colored Partitions,
2010
Valparaiso University
Pattern-Avoiding Colored Partitions, Lara Pudwell
Lara K. Pudwell
No abstract provided.
Harmonic Mapping Problem And Affine Capacity,
2010
Syracuse University and University of Helsinki
Harmonic Mapping Problem And Affine Capacity, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen
Mathematics - All Scholarship
The Harmonic Mapping Problem asks when there exists a harmonic homeomorphism between two given domains. It arises in the theory of minimal surfaces and in calculus of variations, specifically in hyperelasticity theory. We investigate this problem for doubly connected domains in the plane, where it already presents considerable challenge and leads to several interesting open questions.
