Physical Sciences and Mathematics Commons^™

Solving Differential Equations With Least Square And Collocation Methods, Katayoun Bodouhi Kazemi

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this work, we first discuss solving differential equations by Least Square Methods (LSM). Polynomials are used as basis functions for first-order ODEs and then B-spline basis are introduced and applied for higher-order Boundary Value Problems (BVP) and PDEs. Finally, Kansa's collocation methods by using radial basis functions are presented to solve PDEs numerically. Various numerical examples are given to show the efficiency of the methods.

Generalized Catalan Numbers And Some Divisibility Properties, Jacob Bobrowski

UNLV Theses, Dissertations, Professional Papers, and Capstones

I investigate the divisibility properties of generalized Catalan numbers by ex-

tending known results for ordinary Catalan numbers to their general case. First, I define the general Catalan numbers and provide a new derivation of a known formula. Second, I show several combinatorial representations of generalized Catalan numbers and survey bijections across these representation. Third, I extend several divisibility results proved by Koshy. Finally, I prove conditions under which sufficiently large primes form blocks of divisibility and indivisibility of the generalized Catalan numbers, extending a known result by Alter and Kubota.

Inverse Problem For Non-Viscous Mean Field Control: Example From Traffic, Shaurya Agarwal

UNLV Theses, Dissertations, Professional Papers, and Capstones

This thesis presents an inverse problem for mean field games where we find the

mean field problem statement for which the given dynamics is the solution. We use

distributed traffic as an example and derive the classic Lighthill Whitham Richards

(LWR) model as a solution of the non-viscous mean field game. We also derive

the same model by choosing a different problem where we use travel time, which

is a distributed parameter, as the cost for the optimal control. We then study the

stationary versions of these two problems and provide numerical solutions for the

same.

Efficient Estimation Of Cluster Population, Sanjeev K C

UNLV Theses, Dissertations, Professional Papers, and Capstones

Partitioning a given set of points into clusters is a well known problem in pattern recognition, data mining, and knowledge discovery. One of the well known methods for identifying clusters in Euclidean space is the K-mean algorithm. In using the K-mean clustering algorithm it is necessary to know the value of k (the number of clusters) in advance. We propose to develop algorithms for good estimation of k for points distributed in two dimensions. The techniques we pursue include a bucketing method, g-hop neighbors, and Voronoi diagrams. We also present experimental results for examining the performances of the bucketing method …

A Comparison Of Recent Results On The Unicity Conjecture Of The Markoff Equation, Brandon John Metz

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this thesis we discuss the positive integer solutions to the equation known as the Markoff equation

x² + y² + z² = 3xyz.

Each solution to the equation is a permutation of a triple (x,y,z) with [mathematical equation refer to PDF] which is called a Markoff triple and each integer of the triple is referred to as a Markoff number.

In 1913, Frobenius conjectured that given an ordered Markoff triple (x,y,z), then both x and y are uniquely determined by z. In other words, if both (x₁,y₁,z) and (x₂,y_{2 …}

Situational Assessment Using Graph Comparison, Pavan Kumar Pallapunidi

UNLV Theses, Dissertations, Professional Papers, and Capstones

In strategic operations, the assessment of any given situation is very important and may trigger the development of a mission plan. The mission plan consists of various actions that should be executed in order to successfully mitigate the situation. For a new mission plan to be designed or implemented, the effect of the previous mission plan should be accessed. These mission plans use various sensors to collect the data which can be very large and aggregate them to obtain detailed information of the situation. In order to implement an effective mission plan the current situation has to be assessed effectively. …

Generalized Markoff Equations, Euclid Trees, And Chebyshev Polynomials, Donald Joseph Mcginn

UNLV Theses, Dissertations, Professional Papers, and Capstones

The Markoff equation is x^2+y^2+z^2 = 3xyz, and all of the positive integer solutions

of this equation occur on one tree generated from (1, 1, 1), which is called the

Markoff tree. In this paper, we consider trees of solutions to equations of the form

x^2 + y^2 + z^2 = xyz + A. We say a tree of solutions satisfies the unicity condition

if the maximum element of an ordered triple in the tree uniquely determines the

other two. The unicity conjecture says that the Markoff tree satisifies the unicity

condition. In this paper, we show that there exists …

Modeling Studies And Numerical Analyses Of Coupled Pdes System In Electrohydrodynamics, Yuzhou Sun

UNLV Theses, Dissertations, Professional Papers, and Capstones

Electrohydrodynamics (EHD) is the term used for the hydrodynamics coupled with electrostatics, whose governing equations consist of the electrostatic potential (Poisson) equation, the ionic concentration (Nernst-Planck) equations, and Navier-Stokes equations for an incompressible, viscous dielectric liquid. In this dissertation, we focus on a specic application of EHD - fuel cell dynamics - in the eld of renewable and clean energy, study its traditional model and attempt to develop a new fuel cell model based on the traditional EHD model. Meanwhile, we develop a series of ecient and robust numerical methods for these models, and carry out their numerical analyses on …