Mathematics Commons^™

Experiments On Surfactants And Thin Fluid Films, Peter Megson

HMC Senior Theses

We investigate the spatiotemporal dynamics of a surfactant monolayer on a thin fluid film spreading inward into a region devoid of surfactant, a system motivated by the alveolus of the human lung. We perform experiments that simultaneously measure the fluid height profile and the fluorescence intensity due to our fluorescent surfactant, NBD-PC. We perform experiments on both a Newtonian layer of glycerol and a shear-thinning fluid layer consisting of xanthan gum mixed with glycerol. We can very successfully extract height profiles on the xanthan gum fluid, although the simultaneous measurement of fluorescent intensity profiles proved problematic, as the laser tended …

Numerical Algorithms For Solving A Generalized Cancer Chemotherapy Problem, Frank Nani, Mingxian Jin

Math and Computer Science Faculty Working Papers

In this paper, two elaborate numerical algorithms are presented for solving the Nani- Oguztoreli functional differential equations associated with cell-cycle specific cancer chemotherapy. The generalized cell-cycle specific cancer chemotherapy model of Nani- Oguztoreli contains discrete time delays which represent the times that the cancer cells spend in each cell-cycle phase. The model also takes into account that inter-cell cycle phase transition rate constants, recruitment of resting cells from the GO phase, and effect of chemotherapy drug on cells in each phase. The algorithms utilize a modified version of the Method of Steps algorithms. The constructed numerical schemes can be implemented …

On Direct Products Of S-Posets Satisfying Flatness Properties, Roghaieh Khosravi

Turkish Journal of Mathematics

In this paper we characterize pomonoids over which various flatness properties of S-posets are preserved under direct products.

Gonality Of Curves With A Singular Model On An Elliptic Quadric Surface, Edoardo Ballico

Turkish Journal of Mathematics

Let W \subset P^3 be a smooth quadric surface defined over a perfect field K and with no line defined over K (e.g., an elliptic quadric surface over a finite field). In this note we study the gonality over K of smooth curves with a singular model contained in W and with mild singularities.

Colored Independence Of Cycle Graphs And Finite Grids, Michael Terhaar

Honors Theses, 1963-2015

Colored independence is a way in which we can understand scheduling/storage problems where events that cannot occur together are modeled by vertices connected by edges, and events that must occur together are modeled by vertices that have the same color. This research will be looking specifically at colored independence on cycles and grids. The number we strive to describe on said graphs is the independence partition number. The independence partition number can be defined as the minimum of the maximum independent set that exists on each partition of a graph G. This research will be able to contribute to the …

Modeling Tolerance In Dynamic Social Networks, Amanda Luby

Honors Theses, 1963-2015

The study of social networks has become increasingly important in recent years. Multi-agent systems research has proven to be an effective way of representing both static and dynamic social networks in order to model and analyze many different situations. Previous implementations of multi-agent systems have observed a phenomenon called tolerance between agents through simulation studies, which is defined as an agent maintaining an unrewarding connection. This concept has also arisen in the social sciences through the study of networks. We aim to bridge this gap between simulation studies in multi-agent systems and real-world observations. This project explores how local interactions …

Bifurcation And Non-Convergence In The Hansen-Patrick Root-Finding Method, Preston Hardy

Honors Theses, 1963-2015

The Hansen-Patrick Root-Finding Method is a one-parameter family of cubically convergent root-finding methods. The parameter is called alpha and can be any complex number. With a few different values of alpha, Hansen-Patrick becomes equivalent to other, more well-known root-finding methods. For example, when alpha equals -1, Hansen-Patrick becomes equivalent to Halley’s Method. There has been previous research into the dynamical systems that arise when varying the initial starting point or varying a family of functions. This paper deals with what happens when the initial point and function are fixed but the root-finding method varies. We are interested in spurious cycles …

A Standard Test Case Suite For Two-Dimensional Linear Transport On The Sphere: Results From A Collection Of State-Of-The-Art Schemes, D. Calhoun

Mathematics Faculty Publications and Presentations

Recently, a standard test case suite for 2-D linear transport on the sphere was proposed to assess important aspects of accuracy in geophysical fluid dynamics with a "minimal" set of idealized model configurations/runs/diagnostics. Here we present results from 19 state-of-the-art transport scheme formulations based on finite-difference/finite-volume methods as well as emerging (in the context of atmospheric/oceanographic sciences) Galerkin methods. Discretization grids range from traditional regular latitude–longitude grids to more isotropic domain discretizations such as icosahedral and cubed-sphere tessellations of the sphere. The schemes are evaluated using a wide range of diagnostics in idealized flow environments. Accuracy is assessed in single- …

Adaptive Stochastic Systems: Estimation, Filtering, And Noise Attenuation, Araz Ryan Hashemi

Wayne State University Dissertations

This dissertation investigates problems arising in identification and control of stochastic systems. When the parameters determining the underlying systems are unknown and/or time varying, estimation and adaptive filter- ing are invoked to to identify parameters or to track time-varying systems. We begin by considering linear systems whose coefficients evolve as a slowly- varying Markov Chain. We propose three families of constant step-size (or gain size) algorithms for estimating and tracking the coefficient parameter: Least-Mean Squares (LMS), Sign-Regressor (SR), and Sign-Error (SE) algorithms.

The analysis is carried out in a multi-scale framework considering the relative size of the gain (rate of …

(Visible) Tilings Of Squares And Hypercubes, John Randall Burt

Electronic Theses and Dissertations

More than eighty years ago, Erdos considered sums of the side lengths of squares packed into a unit square.Here we consider various classes of tilings , this is, packings where there is no empty space inside the unit square. Several types of questions will be explored here. Various construction techniques are introduced, especially methods of generating tilings from tilings with fewer tiles. For some small values of n, I determine all tilings of the unit square with n tiles. I have found a best possible upper bound for a visible tiling, that is a tiling which every tile shares a …

The Most-Perfect 4*4 Puzzle Game, Jeremiah Farrell, Karen Farrell

Scholarship and Professional Work - LAS

Draft of the 'Solution Page' for Jeremiah's puzzle "The Most Perfect 4*4 Puzzle Game", which was exchanged at the 2014 London International Puzzle Party. 100 puzzle designers create 100 copies of their puzzle and pass it out at the party and exhange them. Includes e-mail correspondence with editor of the book.

Moment Equalities For Sums Of Random Variables Via Integer Partitions And Faà Di Bruno's Formula, Dietmar Ferger

Turkish Journal of Mathematics

We give moment equalities for sums of independent and identically distributed random variables including, in particular, centered and specifically symmetric summands. Two different types of proofs, combinatorial and analytical, lead to 2 different types of formulas. Furthermore, the combinatorial method allows us to find the optimal lower and upper constants in the Marcinkiewicz--Zygmund inequalities in the case of even moment-orders. Our results are applied to give elementary proofs of the classical central limit theorem (CLT) and of the CLT for the empirical bootstrap. Moreover, we derive moment and exponential inequalities for self-normalized sums.

A Generalized Approach To Darboux Transformations For Differential Equations, Mehmet Unlu

Mathematics Dissertations - Archive

A Darboux transformation is a mathematical procedure to produce a solution to a differential equation when the solution to a related differential equation is known. The basic idea behind a Darboux transformation is to change the discrete spectrum of a linear differential operator in a controlled way without changing its continuous spectrum. For example, by using a Darboux transformation one can describe the change in a quantum mechanical system when some of its quantum levels are removed or some extra quantum levels are added. Darboux transformation formulas for various differential equations have been developed, but such formulas seem to be …

Properties Of The Pinched Tensor Product, Yousuf Alkhezi

Mathematics Dissertations - Archive

For complexes of modules we study a new construction, called the pinched tensor product, which was introduced by Lars Winther Christensen and David A. Jorgensen to study Tate homology. We explore properties of the pinched tensor product and their comparison to properties of the ordinary tensor product. For example; we show some isomorphisms no longer holds for the pinched tensor product. Although if we change isomorphism to quasi-isomorphism the pinched version holds. Plus if f is a map from C to D and g is a map from A to B are morphisms of complexes of R-modules with f homotopic …

Horizontally Submersions Of Contact Cr-Submanifolds, Fortune Massamba, Tshikunguila Tshikuna-Matamba

Turkish Journal of Mathematics

In this paper, we discuss some geometric properties of almost contact metric submersions involving symplectic manifolds. We show that the structures of quasi-K-cosymplectic and quasi-Kenmotsu manifolds are related to (1, 2)-symplectic structures. For horizontally submersions of contact CR-submanifolds of quasi-K-cosymplectic and quasi-Kenmotsu manifolds, we study the principal characteristics and prove that their total spaces are CR-product. Curvature properties between curvatures of quasi-K-cosymplectic and quasi-Kenmotsu manifolds and the base spaces of such submersions are also established. We finally prove that, under a certain condition, the contact CR-submanifold of a quasi Kenmotsu manifold is locally a product of a totally geodesic leaf …

Tiling The Integers, Shasha Li

Electronic Theses and Dissertations

A set tiles the integers if and only if the integers can be written as a disjoint union of translates of that set. Counterexamples based on finite Abelian groups show that Fuglede conjecture is false in high dimensions. A solution for the Fuglede conjecture in Z or all the groups ZN would provide a solution for the Fuglede conjecture in R. Focusing on tiles in dimension one, we will concentrate on the analysis of tiles in the finite groups ZN. Based on the Coven- Meyerowitz conjecture, it has been proved that if any spectral set in Z satisfies the the …

Stability And Controls For Stochastic Dynamic Systems, Zhixin (Harriet) Yang

Wayne State University Dissertations

This dissertation focuses on stability analysis and optimal controls for stochastic dynamic systems. It encompasses two parts. One part of our work gives an in-depth study of stability of linear jump diffusion, linear Markovian jump diffusion, multi-dimensional jump diffusion and

regime-switching jump diffusion together with the associated numerical solutions. The other part of our work is controls for stochastic dynamic systems, to be specific, we concentrated on mean variance types of control under different formulations. We obtained the nearly optimal

mean-variance controls under both two-time-scale and hidden Markov chain formulations and convergence for each case is achieved.

In Chapter 2, …

Properties Of Nonlinear Randomly Switching Dynamic Systems: Mean-Field Models And Feedback Controls For Stabilization, Guangliang Zhao

Wayne State University Dissertations

This dissertation concerns the properties of nonlinear dynamic systems hybrid with Markov switching. It contains two parts. The first part focus on the mean-field models with state-dependent regime switching, and the second part focus on the system regularization and stabilization using feedback control. Throughout this dissertation, Markov switching processes are used to describe the randomness caused by discrete events, like sudden environment change or other uncertainty.

In Chapter 2, the mean-field models we studied are formulated by nonlinear stochastic differential equations hybrid with state-dependent regime switching. It originates from the phase transition problem in statistical physics. The mean-field term is …

Counting Pseudo-Anosov Mapping Classes On The 3-Punctured Projective Plane, Blazej Szepietowski

Turkish Journal of Mathematics

We prove that in the pure mapping class group of the 3-punctured projective plane equipped with the word metric induced by certain generating set, the ratio of the number of pseudo-Anosov elements to the number of all elements in a ball centered at the identity tends to one, as the radius of the ball tends to infinity. We also compute growth functions of the sets of reducible and pseudo-Anosov elements.

Algorithms For Solving The Discrete Logarithm Problem, Ryan Edward Whaley

Online Theses and Dissertations

In mathematics, there are often many procedures to solve or prove the same problem. The discrete logarithm is one of these problems. The baby step, giant step algorithm and Pollard's kangaroo algorithm are two algorithms that attempt to solve discrete logarithm problems. Explanations on what these two algorithms are will be discussed as well as examples of each algorithm. In addition to these two algorithms, a modified form of Pollard's kangaroo algorithm will be provided with results. Throughout the text, Mathematica programs will be presented that simulate each of the three algorithms above.