Physical Sciences and Mathematics Commons^™

A Survey Of Ekeland's Variational Principle And Related Theorems And Applications, Jessica Robinson

UNLV Theses, Dissertations, Professional Papers, and Capstones

Ekeland's Variational Principle has been a key result used in various areas of analysis such as fixed point analysis, optimization, and optimal control theory. In this paper, the application of Ekeland's Variational Principle to Caristi's Fixed Point Theorem, Clarke's Fixed Point Theorem, and Takahashi's Minimization theorem is the focus. In addition, Ekeland produced a version of the classical Pontryagin Mini- mum Principle where his variational principle can be applied. A further look at this proof and discussion of his approach will be contrasted with the classical method of Pontryagin. With an understanding of how Ekeland's Variational Princple is used in …

Modeling And Analysis Of Pedestrian Flows, Romesh Khaddar

UNLV Theses, Dissertations, Professional Papers, and Capstones

According to the Traveler Opinion and Perception Survey of 2005, about 107.4 million Americans regularly use walking as a mode of transport during their commute, which amounts for 51% of the total American population. In 2009, 4092 pedestrian fatalities were reported nationwide, out of 59,000 pedestrian crashes. This amounts for 12% of the fatalities in the total traffic accidents recorded, and shows an over-representation of pedestrians incidents. Thus, it is imperative to understand the causes behind such statistics, and conduct a comprehensive research on pedestrian walking behavior and their interaction with surroundings.

A lot of researches on pedestrian flows have …

Empirical Studies On Interest Rate Derivatives, Xudong Sun

UNLV Theses, Dissertations, Professional Papers, and Capstones

Interest rate models are the building blocks of financial market and the interest rate derivatives market is the largest derivatives market in the world. In this dissertation, we shall focus on numerical pricing of interest rate derivatives, estimating model parameters by Kalman filter, and studying various models empirically. We shall propose a front-fixing finite element method to price the American put option under the quadratic term structure framework and compare it with a trinomial tree method and common finite element method. Numerical test results show the superiority of our front-fixing finite element method in the aspects of computing the option …

A Study Of Graphical Permutations, Jessica Thune

UNLV Theses, Dissertations, Professional Papers, and Capstones

A permutation π on a set of positive integers {a_1,a_2,...,a_n} is said to be graphical if there exists a graph containing exactly a_i vertices of degree (a_i) for each i. It has been shown that for positive integers with a_1

Exact Controllability Of The Lazer-Mckenna Suspension Bridge Equation, Lanxuan Yu

UNLV Theses, Dissertations, Professional Papers, and Capstones

It is well known that suspension bridges may display certain oscillations under external aerodynamic forces. Since the collapse of the Tacoma Narrows suspension bridge in 1940, suspension bridge models have been studied by many researchers. Based upon the fundamental nonlinearity in suspension bridges that the stays connecting the supporting cables and the roadbed resist expansion, but do not resist compression, new models describing oscillations in suspension bridges have been developed by Lazer and McKenna [Lazer and McKenna (1990)]. Except for a paper by Leiva [Leiva (2005)], there have been very few work on controls of the Lazer-McKenna suspension bridge models …

A Quasi-Classical Logic For Classical Mathematics, Henry Nikogosyan

Honors College Theses

Classical mathematics is a form of mathematics that has a large range of application; however, its application has boundaries. In this paper, I show that Sperber and Wilson’s concept of relevance can demarcate classical mathematics’ range of applicability by demarcating classical logic’s range of applicability. Furthermore, I introduce how to systematize Sperber and Wilson’s concept of relevance into a quasi-classical logic that can explain classical logic’s and classical mathematics’ range of applicability.

Approaches For Generating 2d Shapes, Pratik Shankar Hada

UNLV Theses, Dissertations, Professional Papers, and Capstones

Constructing a two dimensional shape from given a set of point sites is a well known problem in computation geometry. We present a critical review of the existing algorithms for constructing polygonal shapes. We present a new approach calledinward dentingfor constructing simple polygons. We then extend the proposed approach for modeling polygons with holes. This is the

first known algorithm for modeling holes in the interior of 2d shapes. We also present experimental investigations of the quality of the solutions generated by the proposed algorithms.

For this we implemented the proposed algorithms in Java programming language. The prototype program can …

Numerical Simulations Of Traffic Flow Models, Puneet Lakhanpal

UNLV Theses, Dissertations, Professional Papers, and Capstones

Traffic flow has been considered to be a continuum flow of a compressible liquid having a certain density profile and an associated velocity, depending upon density, position and time. Several one-equation and two-equation macroscopic continuum flow models have been developed which utilize the fluid dynamics continuity equation and help us find analytical solutions with simplified initial and boundary conditions. In this thesis, the one-equation Lighthill Witham and Richards (LWR) model combined with the Greenshield's model, is used for finding analytical and numerical solutions for four problems: Linear Advection, Red Traffic Light turning into Green, Stationary Shock and Shock Moving towards …

Observability In Traffic Modeling: Eulerian And Lagrangian Coordinates, Sergio Contreras

UNLV Theses, Dissertations, Professional Papers, and Capstones

Traditionally, one of the ways traffic flow has been studied is by using the kinematic wave model. This model is studied in the Eulerian framework. Recently, the kinematic wave model has been transformed into Lagrangian coordinates. This model of traffic flow together with the concept of observability for linear time invariant discrete time systems is applied to study the observability of four sections of a freeway in both Eulerian and Lagrangian coordinates. A system with densities in four sections of a freeway is designed, and the observability of the system is studied with different situations for sensors. When the system …

N-Dimensional Quasipolar Coordinates - Theory And Application, Tan Mai Nguyen

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this thesis, various generalizations to the n-dimension of the polar coordinates and spherical coordinates are introduced and compared with each other and the existent ones in the literature. The proof of the Jacobian of these coordinates is very often wrongfully claimed. Currently, prior to our proof, there are only two complete proofs of the Jacobian of these coordinates known to us. A friendlier definition of these coordinates is introduced and an original, direct, short, and elementary proof of the Jacobian of these coordinates is given. A method, which we call a perturbative (not perturbation) method, is introduced so that …

Lattice Methods For The Valuation Of Options With Regime Switching, Atul Sancheti

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this thesis, we have developed two numerical methods for evaluating option prices under the regime switching model of stock price processes: the Finite Difference lattice method and the Monte Carlo lattice method.

The Finite Difference lattice method is based on the explicit finite difference scheme for parabolic problems. The Monte Carlo lattice method is based on the simulation of the Markov chain. The advantage of these methods is their flexibility to compute the option prices for any given stock price at any given time. Numerical examples are presented to examine these methods. It has been shown that the proposed …