Mathematics Commons^™

The Semigroups B2 And B0 Are Inherently Nonfinitely Based, As Restriction Semigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

The five-element Brandt semigroup B₂ and its four-element subsemigroup B₀, obtained by omitting one nonidempotent, have played key roles in the study of varieties of semigroups. Regarded in that fashion, they have long been known to be finitely based. The semigroup B₂ carries the natural structure of an inverse semigroup. Regarded as such, in the signature {⋅, ^-1}, it is also finitely based. It is perhaps surprising, then, that in the intermediate signature of restriction semigroups — essentially, "forgetting" the inverse operation x ↦ x^-1 and retaining the induced operations x ↦ x^{+ …}

Sub-Independence: An Expository Perspective, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Limit theorems as well as other well-known results in probability and statistics are often based on the distribution of the sums of independent random variables. The concept of sub-independence, which is much weaker than that of independence, is shown to be sufficient to yield the conclusions of these theorems and results. It also provides a measure of dissociation between two random variables which is much stronger than uncorrelatedness.

Examples Where The Conjunctive And Dempster’S Rules Are Insensitive, Florentin Smarandache, Jean Dezert, Valeri Kroumov

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we present several counter-examples to the Conjunctive rule and to Dempster rule of combinations in information fusion.

Four-Sided Boundary Problem For Two-Dimensional Random Walks, Miky Wright

Mahurin Honors College Capstone Experience/Thesis Projects

Within the four-sided boundaries of x = 0, y = 0, x = m and, y = n, a two-dimensional random walk begins at integer-valued coordinates (h,k) and moves one unit on each step either up, down, left, or right with non-zero probabilities that sum to 1. The process stops when hitting a boundary. Let P(U), P(D), P(L) and P(R) be the probabilities of hitting the upper, the lower, the left, and the right boundary first, respectively, when starting from a specific initial point within the boundaries. We use a Markov-Chain method to compute these probabilities. Let …

Constructing Wavelets With Good Frequency Response And Two Vanishing Moments, Chad Lillian, Dr. Andrew D. Pollington

Journal of Undergraduate Research

Recruitment of loudness is a hearing impairment in which certain frequency ranges are not as audible as others. If a common hearing aid is used to remedy this problem all frequencies will be amplified and there will be no advantage. The solution to this problem is a hearing aid that only selectively amplifies those frequencies that are less audible.

Metacalibration Proof Of The Triple Bubble Conjecture In R3, Donald Sampson, Dr. Gary Lawlor

Journal of Undergraduate Research

My project was to further develop the technique of metacalibration, a new method of minimization proof, in order to prove the triple bubble conjecture: that the standard triple bubble is the least surface area way to separately enclose three given volumes.

Option Pricing For Inventory Management And Control, Bryant Angelos, Dr. Jeffrey Humpherys

Journal of Undergraduate Research

In recent years, capital markets have experience remarkable growth in both the total volume of trades and in the complexity of the financial instruments being traded. Investors are becoming increasingly sophisticated as they search for newer and more effective ways of managing and protecting themselves from risk. Retail markets have undergone a similar transformation as retailers seek to maximize profit while minimizing risk. Supply chains are becoming more interconnected, and the contracts governing them have become more complex in recent years.

Geometry Of Optimal Control For Control-Affine Systems, Jeanne N. Clelland, Christopher G. Moseley, George R. Wilkens

University Faculty Publications and Creative Works

Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three. We compute local isometric invariants for point-affine distributions of constant type with metric structures for systems with 2 states and 1 control and systems with 3 states and 1 control, and use Pontryagin's maximum principle to find geodesic trajectories for homogeneous examples. Even in these low dimensions, the behavior of these systems is surprisingly rich and varied.

Geometry Of Optimal Control For Control-Affine Systems, Jeanne N. Clelland, Christopher G. Moseley, George R. Wilkens

University Faculty Publications and Creative Works

Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three. We compute local isometric invariants for point-affine distributions of constant type with metric structures for systems with 2 states and 1 control and systems with 3 states and 1 control, and use Pontryagin's maximum principle to find geodesic trajectories for homogeneous examples. Even in these low dimensions, the behavior of these systems is surprisingly rich and varied.

Flavonol-Rich Dark Cocoa Significantly Decreases Plasma Endothelin-1 And Improves Cognition In Urban Children, Partha S. Mukherjee

Mathematics Faculty Publications and Presentations

Air pollution exposures are linked to systemic inflammation, cardiovascular and respiratory morbidity and mortality, neuroinflammation and neuropathology in young urbanites. In particular, most Mexico City Metropolitan Area (MCMA) children exhibit subtle cognitive deficits, and neuropathology studies show 40% of them exhibiting frontal tau hyperphosphorylation and 51% amyloid-β diffuse plaques (compared to 0% in low pollution control children). We assessed whether a short cocoa intervention can be effective in decreasing plasma endothelin 1 (ET-1) and/or inflammatory mediators in MCMA children. Thirty gram of dark cocoa with 680 mg of total flavonols were given daily for 10.11 ± 3.4 days (range 9–24 …

Discrete Fourier Restriction Associated With Kdv Equations, Yi Hu, Xiaochun Li

Mathematical Sciences: Faculty Publications

In this paper, we consider a discrete restriction associated with KdV equations. Some new Strichartz estimates are obtained. We also establish the local well-posedness for the periodic generalized Korteweg-de Vries equation with nonlinear term $F(u)\p_x u$ provided F∈C5 and the initial data ϕ∈Hs with s>1/2.

A Journey Into Quantization In Astrophysics, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

The present book consists of 17 select scientific papers from ten years of work around 2003-2013. The topic covered here is quantization in Astrophysics. We also discuss other topics for instance Pioneer spacecraft anomaly. We discuss a number of sub-topics, for instance the use of Schrödinger equation to describe celestial quantization. Our basic proposition here is that the quantization of planetary systems corresponds to quantization of circulation as observed in superfluidity. And then we extend it further to the use of (complex) Ginzburg-Landau equation to describe possible nonlinearity of planetary quantization. Some of these papers have been published in journal …

A Study On Several Applications For Impulse Force Supporting Technique And The Controlling Problem, Dalong An

Math Theses

Motivated by the Space Elevator concept, several alternate space transportation systems are studied. Details, such as the structure, transporting capacity, and stability of the systems are explored. Further study shows that despite the difference in their structure, these transportation systems are all applications for the impulse force supporting technique. Moreover, we can show that the centrifugal force and the impulse force are merely two aspects of one kind of supporting force, each 1 of which can be used for different purposes.

A 2-Chain Can Interlock With An Open 10-Chain, Bin Lu, Joseph O'Rourke, Jianyuan K. Zhong

Computer Science: Faculty Publications

Abstract. It is an open problem, posed in [3], to determine the minimal k such that an open flexible k-chain can interlock with a flexible 2-chain. It was first established in [5] that there is an open 16-chain in a trapezoid frame that achieves interlocking. This was subsequently improved in [6] to establish interlocking between a 2-chain and an open 11-chain. Here we improve that result once more, establishing interlocking between a 2-chain and a 10-chain. We present arguments that indicate that 10 is likely the minimum.

Comparing The Effects Of Interactive And Noninteractive Complementary Nutrients On Growth In A Chemostat, James P. Braselton, Martha L. Abell, Lorraine Braselton

Mathematical Sciences: Faculty Publications

We compare the effects of interactive and noninteractive complementary nutrients on the growth of an organism in the chemostat. We also compare these two situations to the case when the nutrients are substitutable. In previous studies, complementary nutrients have been assumed to be noninteractive. However, more recent research indicates that some complementary nutrient relationships are interactive. We show that interactive complementary and substitutable nutrients can lead to higher population densities than do noninteractive complementary nutrients. We numerically illustrate that if the washout rate is high, an organism can persist at higher densities when the complementary nutrients are interactive than when …

On The Performance Of A Hybrid Genetic Algorithm In Dynamic Environments, Quan Yuan, Zhixin Yang

Mathematics Faculty Research Publications

The ability to track the optimum of dynamic environments is important in many practical applications. In this paper, the capability of a hybrid genetic algorithm (HGA) to track the optimum in some dynamic environments is investigated for different functional dimensions, update frequencies, and displacement strengths in different types of dynamic environments. Experimental results are reported by using the HGA and some other existing evolutionary algorithms in the literature. The results show that the HGA has better capability to track the dynamic optimum than some other existing algorithms.

Nonnegative Matrix Factorization, Gretchen Schillemat, Dr. Jeffrey Humpherys

Journal of Undergraduate Research

The purpose of this project was to study the nonnegative matrix factorization (NNMF) problem: Given a nonnegative matrix V, find the” best” nonnegative matrices W and H, such that V WH. The main focus in our project was when the data was sparse.

Long-Wave Model For Strongly Anisotropic Growth Of A Crystal Step, Mikhail Khenner

Mathematics Faculty Publications

A continuum model for the dynamics of a single step with the strongly anisotropic line energy is formulated and analyzed. The step grows by attachment of adatoms from the lower terrace, onto which atoms adsorb from a vapor phase or from a molecular beam, and the desorption is nonnegligible (the “one-sided” model). Via a multiscale expansion, we derived a long-wave, strongly nonlinear, and strongly anisotropic evolution PDE for the step profile. Written in terms of the step slope, the PDE can be represented in a form similar to a convective Cahn-Hilliard equation. We performed the linear stability analysis and computed …

Elementary Teacher Candidates' Images Of Mathematics, Diverse Students, And Teaching: An Exploratory Study With Implications For Culturally Responsive Mathematics Education, Bernd Richard Ferner

Dissertations and Theses

Children from many culturally diverse backgrounds do not achieve in mathematics at the same rates as their counterparts from the dominant White, European-American culture (Gay, 2010). This so-called achievement gap is an artifact of an educational system that continues to fail to provide equal learning opportunities to culturally diverse children (Ladson-Billings, 2006; Nieto & Bode, 2011). Teachers who employ culturally responsive teaching (Gay, 2010) may help to close this opportunity gap and hence, the achievement gap. This study investigated, "How do elementary teacher candidates perceive teaching mathematics in a multicultural environment"; Using a critical constructivism research paradigm, this qualitative instrumental …

Characterization Of The Drilling Via The Vibration Augmenter Of Rotary-Drills And Sound Signal Processing Of Impacted Pipe As A Potential Water Height Assessment Tool, Nicholas Morris

STAR Program Research Presentations

The focus of the internship has been on two topics: a) Characterize the drilling performance of a novel percussive augmenter – this drill was developed by the JPL’s Advanced Technologies Group and its performance was characterized; and b) Examine the feasibility of striking a pipe as a means of assessing the water height inside the pipe. The purpose of this investigation is to examine the possibility of using a simple method of applying impacts to a pipe wall and determining the water height from the sonic characteristic differences including damping, resonance frequencies, etc. Due to multiple variables that are relevant …

Geometry Of The Universe And Its Relation To Entropy And Information, Ioannis Haranas, Ioannis Gkigkitzis

Physics and Computer Science Faculty Publications

In an effort to investigate a possible relation between geometry and information, we establish a relation of the Ricci scalar in the Robertson-Walker metric of the cosmological Friedmann model to the number of information 𝑁 and entropy 𝑆.This is with the help of a previously derived result that relates the Hubble parameter to the number of information 𝑁.We find that the Ricci scalar has a dependence which is inversely proportional to the number of information 𝑁 and entropy 𝑆. Similarly, a nonzero number of information would imply a finite Ricci scalar, and therefore space time will unfold. Finally, using the …

Methods Of Nonparametric Multivariate Ranking And Selection, Jeremy Entner

Mathematics - Dissertations

In a Ranking and Selection problem, a collection of k populations is given which follow some (partially) unknown probability distributions. The problem is to select the "best" of the k populations where "best" is well defined in terms of some unknown population parameter. In many univariate parametric and nonparamentric settings, solutions to these ranking and selection problems exist. In the multivariate case, only parametric solutions have been developed. We have developed several methods for solving nonparametric multivariate ranking and selection problems. The problems considered allow an experimenter to select the "best" populations based on nonparametric notions of dispersion, location, and …

Every Scattered Space Is Subcompact, William Fleissner, Vladimir Tkachuk, Lynne Yengulalp

Mathematics Faculty Publications

We prove that every scattered space is hereditarily subcompact and any finite union of subcompact spaces is subcompact. It is a long-standing open problem whether every Čech-complete space is subcompact. Moreover, it is not even known whether the complement of every countable subset of a compact space is subcompact. We prove that this is the case for linearly ordered compact spaces as well as for ω -monolithic compact spaces. We also establish a general result for Tychonoff products of discrete spaces which implies that dense G_δ-subsets of Cantor cubes are subcompact.

Investigating Graph Clustering For The Power Grid, Gabriela Radu, Emilie Hogan

STAR Program Research Presentations

Given time series data from multiple power generators containing measurements of phase angle taken at many points in time. The goal is to cluster together generators which have similar phase angle behavior.

In order to achieve this goal, Fast Fourier Transforms and Euclidean distances were used to quantify similarities between generators. A graph was created in which two generators were connected if they were sufficiently similar (known as a nearest neighbor graph). Using different nearest neighbor values, matrices were generated based on similarities between generators. Specific time intervals were taken from the large data set to assess the time dependency …

Complete Description Of Idempotent Hedges In Fuzzy Logic, Jaime Nava

Departmental Technical Reports (CS)

In describing expert knowledge, it is often important to properly take into account hedges} like "very", "somewhat", etc. In particular, fuzzy logic provides a consistent way of describing hedges. For some of the hedges, a repetition changes the meaning: e.g., "very very small" is smaller than "very small". However, other hedges -- like "somewhat" -- are idempotent, in the sense that repeating this hedge twice does not change the meaning. In this paper, we provide a complete description of such idempotent hedges.

On Early Stages Of Idea Propagation, The Number Of Adopters Grows As N(T) ~ C * Ta: Theoretical Explanation Of The Empirical Observation, L. Octavio Lerma, Deana Pennington, Vladik Kreinovich

Departmental Technical Reports (CS)

New good ideas sometimes propagate too slowly. To speed up their propagation, we need to have a quantitative understanding of how ideas propagate. An intuitive understanding of ideas propagation has led to several reasonable first-approximation mathematical models. These models provide a good description of idea propagation on the later stages, when the ideas have already been adopted by a reasonably large number of people. However, at the critically important early stages, these models are not perfect: these models predict a linear growth with time, while empirical growth data is often better described by a power law. In this paper, we …

Vine Copulas As A Way To Describe And Analyze Multi-Variate Dependence In Econometrics: Computational Motivation And Comparison With Bayesian Networks And Fuzzy Approaches, Songsak Sriboonchitta, Jianxu Liu, Vladik Kreinovich, Hung T. Nguyen

Departmental Technical Reports (CS)

In the last decade, vine copulas emerged as a new efficient techniques for describing and analyzing multi-variate dependence in econometrics. Our experience has shown, however, that while these techniques have been successfully applied to many practical problems of econometrics, there is still a lot of confusion and misunderstanding related to vine copulas. In this paper, we provide a motivation for this new technique from the computational viewpoint. We show that other techniques used to described dependence -- Bayesian networks and fuzzy techniques -- can be viewed as a particular case of vine copulas.

Borel Complexity Of The Isomorphism Relation For O-Minimal Theories, Davender Singh Sahota '99

Doctoral Dissertations

In 1988, Mayer published a strong form of Vaught's Conjecture for o-minimal theories (1). She showed Vaught's Conjecture holds, and characterized the number of countable models of an o-minimal theory T if T has fewer than 2K ° countable models. Friedman and Stanley have shown in (2) that several elementary classes are Borel complete. This work addresses the class of countable models of an o-minimal theory T when T has 2N ° countable models, including conditions for when this class is Borel complete. The main result is as follows.

Theorem 1. Let T be an o-minimal theory in a countable …

Gr 20 Workshop, Warsaw, July 2013, Ian M. Anderson, Charles G. Torre

Presentations

These are the Maple worksheets used at the Differential Geometry in Maple Workshop, which was held at the 20th International Conference on General Relativity and Gravitation, in Warsaw, July 2013.

There are 6 worksheets which can be downloaded from the list of files below.

Conservation Of Energy Implies Conservation Of Momentum: How We Can Explain Conservation Of Momentum To Before-Calculus Students, Eric Freudenthal, Eric Hagedorn, Olga Kosheleva

Departmental Technical Reports (CS)

In solving physics problems, it is often important to use the laws of conservation of energy and momentum. While most people have intuitive understanding of energy and of its conservation, there is usually no intuition behind momentum, and known textbook derivations of conservation of momentum use calculus -- which is usually taught after momentum. In this paper, we show how the law of conservation of momentum can be explained to before-calculus student: by using the fact that this law can be derived from the more intuitive conservation of energy if we consider energy in different coordinate systems.