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 …
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], …
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 …
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 …
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 …
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.
Cryptography: A History In Mathematics, An Application In The Classroom,
2010
Bemidji State University
Cryptography: A History In Mathematics, An Application In The Classroom, Brian Olmanson
Honors Capstones
Capstone submitted as a graduation requirement for the BSU Honors Program.
On The Interlace Polynomials Of Forests,
2010
University of Nebraska
On The Interlace Polynomials Of Forests, C. Anderson, Jonathan Cutler, A. J. Radcliffe, L. Traldi
Department of Mathematics Faculty Scholarship and Creative Works
The interlace polynomials were introduced by Arratia, Bollobás and Sorkin (2004) [3-5]. These invariants generalize to arbitrary graphs some special properties of the Euler circuits of 2-in, 2-out digraphs. Among many other results, Arratia, Bollobás and Sorkin (2004) [3-5] give explicit formulas for the interlace polynomials of certain types of graphs, including paths; it is natural to wonder whether or not it is possible to extend these formulas to larger classes of graphs. We give a combinatorial description of the interlace polynomials of trees and forests.
Singular Points Of Real Sextic Curves I,
2010
George Fox University
Singular Points Of Real Sextic Curves I, David A. Weinberg, Nicholas J. Willis
Faculty Publications - Department of Mathematics
A complete classification of the individual types of singular points is given for irreducible real sextic curves. This classification is derived by using the computer algebra system Maple. There are 191 types of singular points for real irreducible sextic curves. We clarify that the classification is based on computing just enough of the Puiseux expansion to separate the branches. A significant portion of the proof consists of a sequence of large symbolic computations that can be done nicely using Maple.
Covariant Quantum Fields On Noncommutative Spacetimes,
2010
Syracuse University
Covariant Quantum Fields On Noncommutative Spacetimes, A. P. Balachandran, A. Ibort, G. Marmo, M. Martone
Physics - All Scholarship
A spinless covariant field $\phi$ on Minkowski spacetime $\M^{d+1}$ obeys the relation $U(a,\Lambda)\phi(x)U(a,\Lambda)^{-1}=\phi(\Lambda x+a)$ where $(a,\Lambda)$ is an element of the Poincar\'e group $\Pg$ and $U:(a,\Lambda)\to U(a,\Lambda)$ is its unitary representation on quantum vector states. It expresses the fact that Poincar\'e transformations are being unitary implemented. It has a classical analogy where field covariance shows that Poincar\'e transformations are canonically implemented. Covariance is self-reproducing: products of covariant fields are covariant. We recall these properties and use them to formulate the notion of covariant quantum fields on noncommutative spacetimes. In this way all our earlier results on dressing, statistics, etc. for …
Numerical Investigation Of Aeroelastic Mode Distribution For Aircraft Wing Model In Subsonic Air Flow,
2010
University of New Hampshire
Numerical Investigation Of Aeroelastic Mode Distribution For Aircraft Wing Model In Subsonic Air Flow, Marianna A. Shubov, Stephen B. Wineberg, Robert Holt
Mathematics & Statistics
In this paper, the numerical results on two problems originated in aircraft wing modeling have been presented. The first problem is concerned with the approximation to the set of the aeroelastic modes, which are the eigenvalues of a certain boundary-value problem. The affirmative answer is given to the following question: can the leading asymptotical terms in the analytical formulas be used as reasonably accurate description of the aeroelastic modes? The positive answer means that these leading terms can be used by engineers for practical calculations. The second problem is concerned with the flutter phenomena in aircraft wings in a subsonic, …
An F4-Style Involutive Basis Algorithm,
2010
University of Southern Mississippi
An F4-Style Involutive Basis Algorithm, Miao Yu
Mathematics Student Presentations
This paper introduces a new algorithm for computing Gröbner bases. To avoid as much ambiguity as possible, this algorithm combines the F4 algorithm and basic algorithm of involutive bases and it replaces the symbolic precomputation of S-polynomials and ordinary division in F4 by a new symbolic precomputation of non-multiplicative prolongations and involutive division. This innovation makes the sparse matrix of F4 in a deterministic way. As an example the Cyclic-4 problem is presented.
