Upper And Lower Solutions For Regime-Switching Diffusions With Applications In Financial Mathematics,
2011
University of Dayton
Upper And Lower Solutions For Regime-Switching Diffusions With Applications In Financial Mathematics, Paul W. Eloe, R. H. Liu
Mathematics Faculty Publications
This paper develops a method of upper and lower solutions for a general system of second-order ordinary differential equations with two-point boundary conditions. Our motivation of study stems from a class of financial mathematics problems under regime-switching diffusion models. Two examples are double barrier option valuation and optimal selling rules in asset trading. We establish the existence of a unique C2 solution of the two-point boundary value problem. We construct monotone sequences of upper and lower solutions that are shown to converge to the unique solution of the boundary value problem. This construction provides a feasible numerical method to compute …
Optimal Intervals For Uniqueness Of Solutions For Nonlocal Boundary Value Problems,
2011
University of Dayton
Optimal Intervals For Uniqueness Of Solutions For Nonlocal Boundary Value Problems, Paul W. Eloe, Johnny Henderson
Mathematics Faculty Publications
For the nth order differential equation (see PDF for equation) we obtain optimal bounds on the length of intervals on which solutions are unique for certain nonlocal three point boundary value problems. These bounds are obtained through an application of the Pontryagin Maximum Principle from the theory of optimal control.
2011 Program And Abstracts,
2011
University of Dayton
2011 Program And Abstracts, University Of Dayton. Department Of Mathematics
Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials
Program and abstracts of papers presented at the 2011 Undergraduate Mathematics Day held at the University of Dayton.
Perfect And Abundant Numbers - A Perfect And Abundant Source For Undergraduate Research Projects (Abstract),
2011
University of Dayton
Perfect And Abundant Numbers - A Perfect And Abundant Source For Undergraduate Research Projects (Abstract), Judy Holdener
Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials
In June of 2009, the 47th perfect number was discovered by the Great Internet Mersenne Prime Search (GIMPS), a collaborative computing project involving volunteers from all over the world. Like all known perfect numbers before it, this number is even. Does an odd perfect number exist? Are there infinitely many perfect numbers?
Solitary Waves, Periodic And Elliptic Solutions To The Benjamin, Bona & Mahony (Bbm) Equation Modified By Viscosity,
2011
Embry-Riddle Aeronautical University
Solitary Waves, Periodic And Elliptic Solutions To The Benjamin, Bona & Mahony (Bbm) Equation Modified By Viscosity, S.C. Mancas, Harihar Khanal, Shahrdad G. Sajjadi
Publications
We introduce spatiotemporal solitons of the two-dimensional complex Ginzburg-Landau equation (2D CCQGLE) with cubic and quintic nonlinearities in which asymmetry between space-time variables is included. The 2D CCQGLE is solved by a powerful Fourier spectral method, i.e., a Fourier spatial discretization and an explicit scheme for time differencing. Varying the system’s parameters, and using different initial conditions, numerical simulations reveal 2D solitons in the form of stationary, pulsating and exploding solitons which possess very distinctive properties. For certain region of parameters, we have also found stable coherent structures in the form of spinning (vortex) solitons which exist as a result …
Determining A Patient Recovery From A Total Knee Replacement Using Fuzzy Logic And Active Databases,
2011
Minnesota State University, Mankato
Determining A Patient Recovery From A Total Knee Replacement Using Fuzzy Logic And Active Databases, Robert Azarbod
All Graduate Theses, Dissertations, and Other Capstone Projects
The purpose of the knowledge-based system is to predict the rehabilitation timeline of a patient in physical therapy for a total knee replacement. All patients have various attributes that contribute to their rehabilitation rate such as: weight, gender, smoking habit, medications, physical ability, or other medical problems. A combination of any one or several of these attributes will affect the recovery process. The proposed FRTP (Fuzzy Rehabilitation Timeline Predictor) is a fuzzy data mining model that can predict the recovery length of a patient in physical therapy for a total knee replacement and provide feedback to experts for revision of …
Multi-Dimensional Weiss Operators,
2011
TÜBİTAK
Multi-Dimensional Weiss Operators, Sergey Bori̇senok, Mehmet Hakan Erkut, Yaşar Polatoğlu, Rüştü Murat Demi̇rer
Turkish Journal of Mathematics
We present a solution of the Weiss operator family generalized for the case of R^d and formulate a d-dimensional analogue of the Weiss Theorem. Most importantly, the generalization of the Weiss Theorem allows us to find a subset of null class functions for a partial differential equation with the generalized Weiss operators. We illustrate the significance of our approach through several examples of both linear and non-linear partial differential equations.
A Class Of Generalized Shannon-Mcmillan Theorems For Arbitrary Discrete Information Source,
2011
TÜBİTAK
A Class Of Generalized Shannon-Mcmillan Theorems For Arbitrary Discrete Information Source, Kangkang Wang
Turkish Journal of Mathematics
In this study, a class of strong limit theorems for the relative entropy densities of random sum of arbitrary information source are discussed by constructing the joint distribution and nonnegative super martingales. As corollaries, some Shannon-McMillan theorems for arbitrary information source, mth-order Markov information source and non-memory information source are obtained and some results for the discrete information source which have been obtained by authors are extended.
The Unimodality Of Pure O-Sequences Of Type Three In Three Variables,
2011
Sacred Heart University
The Unimodality Of Pure O-Sequences Of Type Three In Three Variables, Bernadette Boyle
Mathematics Faculty Publications
We will give a positive answer for the unimodality of the Hilbert functions in the smallest open case, that of Artinian level monomial algebras of type three in three variables.
An Investigation Of The Conceptual Understanding Of Continuity And Derivatives In Calculus Of Emerging Scholars Versus Non-Emerging Scholars Program Students,
2011
University of Texas at Arlington
An Investigation Of The Conceptual Understanding Of Continuity And Derivatives In Calculus Of Emerging Scholars Versus Non-Emerging Scholars Program Students, Susan Lai Chan
Mathematics Theses - Archive
The Emerging Scholars Program (ESP) has been adapted at colleges and universities across the nation in efforts to increase student access to Science, Technology, Engineering and Mathematics (STEM) disciplines. This study uses a written assessment to gain insight regarding conceptual knowledge on continuity and derivatives for ESP students versus non-ESP students in the same lecture course in first semester calculus at large urban university in the southwest. We analyze the assessment results of 22 ESP and 48 non-ESP students and discuss findings, particularly, those that indicate statistically significant differences regarding continuity over an interval.
A Snapshot Of Advanced High School Students' Understanding Of Continuity,
2011
University of Texas at Arlington
A Snapshot Of Advanced High School Students' Understanding Of Continuity, Melissa Jo Vela
Mathematics Theses - Archive
We report on a study of sixteen high school calculus and seven precalculus students' concept image and concept definition of continuity after one-trimester of instruction at a large suburban high school in the southwestern United States. The researchers developed a questionnaire based upon the work of Tall and Vinner (1981) to determine if calculus students had developed a more sophisticated concept image and concept definition of continuity than students in pre-calculus after a typical treatment in both courses. Using data from the written assessment it was not evident that calculus students demonstrated a more sophisticated concept image and concept definition …
Predictive Model For Bigheaded Carps In Mississippi River,
2011
University of Texas at Arlington
Predictive Model For Bigheaded Carps In Mississippi River, Jitendra K. Shrestha
Mathematics Theses - Archive
Bigheaded carps refer to two species of fish called Silver carp and Bigheaded carp which have invaded the Upper Mississippi River System and are causing nuisance to the native fish like catfish, paddlefish and gizzard Shad by encroaching their habitat. The exponential growth of their population due to their overwhelming reproduction capability and adaptation features calls for a careful study of their population dynamics. In this study, we offer a mathematical model with artificial excessive fishing effort to reduce the population of Bigheaded carps. We numerically observe the correlation among growth rate, fishing rate and the future population of the …
Plasma Myeloperoxidase Predicts Incident Cardiovascular Risks In Stable Patients Undergoing Medical Management For Coronary Artery Disease,
2011
Lerner Research Institute
Plasma Myeloperoxidase Predicts Incident Cardiovascular Risks In Stable Patients Undergoing Medical Management For Coronary Artery Disease, W.H. Wilson Tang, Yuping Wu, Stephen J. Nicholls, Stanley L. Hazen
Mathematics and Statistics Faculty Publications
BACKGROUND: Myeloperoxidase (MPO) concentrations predict adverse clinical outcomes in the setting of acute coronary syndromes and heart failure, but the prognostic role of MPO in stable patients with known atherosclerotic burden is unclear. METHODS: We examined plasma MPO concentrations and their relationship with prevalent significant coronary artery disease (defined as >50% stenosis in any coronary vessel) and incident major adverse cardiovascular events (MACEs), including death, myocardial infarction, and stroke, in a 3-year prospective follow-up study of 1895 patients undergoing elective coronary angiography. RESULTS: The median plasma MPO concentration was 101 pmol/L (interquartile range 68–187 pmol/L). Patients with plasma MPO concentrations …
Diminished Antioxidant Activity Of High-Density Lipoprotein–Associated Proteins In Systolic Heart Failure,
2011
Lerner Research Institute
Diminished Antioxidant Activity Of High-Density Lipoprotein–Associated Proteins In Systolic Heart Failure, W.H. Wilson Tang, Yuping Wu, Shirley Mann, Michael Pepoy, Kevin Shrestha, Allen G. Borowski, Stanley L. Hazen
Mathematics and Statistics Faculty Publications
Background— Diminished serum arylesterase activity, catalyzed by the high-density lipoprotein–associated paraoxonase-1, is associated with heightened systemic oxidative stress and atherosclerosis risk. In the present study, we sought to determine the prognostic role of serum arylesterase activity in subjects with systolic heart failure, particularly in relation to established cardiac biomarkers. Methods and Results— We measured serum arylesterase activity in 760 subjects with impaired left ventricular systolic function (left ventricular ejection fraction <50%), and prospectively followed major adverse cardiac events (including death, nonfatal myocardial infarction, and stroke) for 3 years. In our study cohort (mean age, 64±11 years; 74% men; median left ventricular ejection fraction, 35%; median creatinine clearance, 96 mg/dL), mean serum arylesterase activity (98±25 μmol/L/min/mL) was lower compared with that in healthy control subjects (mean, 115±26 μmol/L/min/mL, P<0.01) but higher compared with advanced decompensated heart failure subjects (mean, 69±22 μmol/L/min/mL, P<0.01). Within our cohort, there was modest correlation between serum arylesterase activity and high-density lipoprotein cholesterol (r=0.33, P<0.01) as well as B-type natriuretic peptide (r=−0.23, P<0.01). Lower serum arylesterase activity was a strong predictor of poorer outcomes (hazard ratio, 2.94; 95% confidence interval, 1.54, 5.62; P<0.001). After adjusting for traditional risk factors, medication use, B-type natriuretic peptide, and creatinine clearance, lower serum arylesterase still conferred an increased risk of major adverse cardiac events at 3 years (hazard ratio, 2.69; 95% confidence interval, 1.37 to 5.28; P=0.004). Conclusions— In patients with systolic heart failure, decreased serum arylesterase activity, a measure of diminished antioxidant properties of high-density lipoprotein, predicts higher risk of incident long-term adverse cardiac event independent of established clinical and biochemical risk factors.
Discrete-Time Recurrent Neural Network And Its Application To Compression Of Infra-Red Spectrum,
2011
Hong Kong Polytechnic University
Discrete-Time Recurrent Neural Network And Its Application To Compression Of Infra-Red Spectrum, Leong-Kwan Li, Sally S. L. Shao
Mathematics and Statistics Faculty Publications
We study the discrete-time recurrent neural network that derived from the Leaky-integrator model and its application to compression of infra-red spec- trum. Our results show that the discrete-time Leaky-integrator recurrent neural network (RNN) model can be used to approximate the continuous-time model and inherit its dynamical characters if a proper step size is chosen. Moreover, the discrete-time Leaky-integrator RNN model is absolutely stable. By developing the double discrete integral method and employing the state space search algorithm for the discrete-time recurrent neural network model, we demonstrate with quality spectra regenerated from the compressed data how to compress the infra-red spectrum …
Analysis Of The Dpg Method For The Poisson Equation,
2011
University of Texas at Austin
Analysis Of The Dpg Method For The Poisson Equation, Leszek Demkowicz, Jay Gopalakrishnan
Mathematics and Statistics Faculty Publications and Presentations
We give an error analysis of the recently developed DPG method applied to solve the Poisson equation and a convection-dffusion problem. We prove that the method is quasioptimal. Error estimates in terms of both the mesh size h and the polynomial degree p (for various element shapes) can be derived from our results. Results of extensive numerical experiments are also presented.
On Socle-Regularity And Some Notions Of Transitivity For Abelian P-Groups,
2011
Technological University Dublin
On Socle-Regularity And Some Notions Of Transitivity For Abelian P-Groups, Brendan Goldsmith, Peter Danchev
Articles
In the present work the interconnections between various notions of transitivity for Abelian p-groups and the recently introduced concepts of socle-regular and strongly socle-regular groups are studied.
Bayesian Inference For Exponential Random Graph Models,
2011
Technological University Dublin
Bayesian Inference For Exponential Random Graph Models, Alberto Caimo, Nial Friel
Articles
Exponential random graph models are extremely difficult models to handle from a statistical viewpoint, since their normalising constant, which depends on model parameters, is available only in very trivial cases. We show how inference can be carried out in a Bayesian framework using a MCMC algorithm, which circumvents the need to calculate the normalising constants. We use a population MCMC approach which accelerates convergence and improves mixing of the Markov chain. This approach improves performance with respect to the Monte Carlo maximum likelihood method of Geyer and Thompson (1992).
On The Stability Of Basisness In L_P(1 < P < +\Infty) Of Cosines And Sines,
2011
TÜBİTAK
On The Stability Of Basisness In L_P(1 < P < +\Infty) Of Cosines And Sines, Ali Huseynli
Turkish Journal of Mathematics
We study the basis properties in L_p(0, \pi) (1 < p < \infty) of the solution system of Sturm--Liouville equations with different types of initial conditions. We first establish some results on the stability of the basis property of cosines and sines in L_p(0, \pi) (1 < p < \infty) and then show that the solution system above forms a basis in L_p(0, \pi) if and only if certain cosine system (or sine system, depending on type of initial conditions) forms a basis in L_p(0, \pi).
Existence Of Three Solutions To A Non-Homogeneous Multi-Point Bvp Of Second Order Differential Equations,
2011
TÜBİTAK
Existence Of Three Solutions To A Non-Homogeneous Multi-Point Bvp Of Second Order Differential Equations, Yuji Liu
Turkish Journal of Mathematics
This paper is concerned with a non-homogeneous multi-point boundary value problem of second order differential equation with one-dimensional p-Laplacian. Using multiple fixed point theorems, sufficient conditions to guarantee the existence of at least three solutions of this kind of BVP are established. Two examples are presented to illustrate the main results.
