Physical Sciences and Mathematics Commons^™

Numerical Studies Of Regularized Navier-Stokes Equations And An Application Of A Run-To-Run Control Model For Membrane Filtration At A Large Urban Water Treatment Facility, Jeffrey Belding

UNLV Theses, Dissertations, Professional Papers, and Capstones

This dissertation consists of two parts. The first part consists of research on accurate and efficient turbulent fluid flow modeling via a family of regularizations of the Navier-Stokes equation which are known as Time Relaxation models. In the second part, we look into the modeling application for the filtration/backwash process at the River Mountains Water Treatment Facility in Henderson, NV.

In the first two chapters, we introduce the Time Relaxation models and their associated differential filter equations. In addition, we develop the regularization method which employs the Nth van Cittert deconvolution operator, which gives rise to the family of models. …

Novel Theorems And Algorithms Relating To The Collatz Conjecture, Michael R. Schwob, Peter Shiue, Rama Venkat

Mathematical Sciences Faculty Research

Proposed in 1937, the Collatz conjecture has remained in the spotlight for mathematicians and computer scientists alike due to its simple proposal, yet intractable proof. In this paper, we propose several novel theorems, corollaries, and algorithms that explore relationships and properties between the natural numbers, their peak values, and the conjecture. These contributions primarily analyze the number of Collatz iterations it takes for a given integer to reach 1 or a number less than itself, or the relationship between a starting number and its peak value.

On The Solutions Of Three-Variable Frobenius-Related Problems Using Order Reduction Approach, Tian-Xiao He, Peter J.-S. Shiue, Rama Venkat

Mathematical Sciences Faculty Research

This paper presents a new approach to determine the number of solutions of three-variable Frobenius-related problems and to find their solutions by using order reducing methods. Here, the order of a Frobenius-related problem means the number of variables appearing in the problem. We present two types of order reduction methods that can be applied to the problem of finding all nonnegative solutions of three-variable Frobenius-related problems. The first method is used to reduce the equation of order three from a three-variable Frobenius-related problem to be a system of equations with two fixed variables. The second method reduces the equation of …

Tail-Measurable Functions And Their Corresponding Induced Classes, And Some Determinacy Conditions Involving 3-Player Games, Joshua K. Reagan

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this dissertation, we have two main categories of results. The first is regarding certain point-classes, and the second is regarding 3-player games.

The point-classes of Baire Space, \mathcal{N}, in the Borel and Projective Hierarchies, as well as Hausdorff's Difference Hierarchy have been well studied, and there has been much research into further stratifying these hierarchies. One area of particular interest falls in between the point-classes \mathbf{\Pi}_\mathbf{1}^\mathbf{1} and \Delta\left(\omega^2-\mathbf{\Pi}_\mathbf{1}^\mathbf{1}\right). It is well known that the point-classes \beta-\mathbf{\Pi}_\mathbf{1}^\mathbf{1}, for \beta\in\omega^2, stratify this region of the projective hierarchy, with the point-class \bigcup_{\beta\in\omega^2}\beta-\mathbf{\Pi}_\mathbf{1}^\mathbf{1} still falling strictly below \Delta\left(\omega^2-\mathbf{\Pi}_\mathbf{1}^\mathbf{1}\right). Dr. Derrick DuBose developed multiple …

Exploring The Choiceless Cardinal Hierarchy, David Linkletter

UNLV Theses, Dissertations, Professional Papers, and Capstones

In 1971, Kunen proved that the Axiom of Choice imposes a ceiling on the large cardinal hierarchy [7]. Much like the assumption V ≠ L unlocks measurable cardinals and beyond, dropping the Axiom of Choice enables Reinhardt cardinals and stronger cardinals to be explored. Some major notions of large cardinals beyond choice have recently been standardized by Woodin et. al. [2], with questions raised regarding their interconnectedness. Part 1 of this dissertation partially answers two of those questions, while conjecturing, with a partial solution, a much stronger answer which would simplify the existing cardinal charts - that Regular Berkeley Cardinals …