Mathematics Commons^™

Why Trapezoidal And Triangular Membership Functions Work So Well: Towards A Theoretical Explanation, Aditi Barua, Lalitha Snigdha Mudunuri, Olga Kosheleva

Departmental Technical Reports (CS)

In fuzzy logic, an imprecise ("fuzzy") property is described by its membership function μ(x), i.e., by a function which describes, for each real number x, to what degree this real number satisfies the desired property. In principle, membership functions can be of different shape, but in practice, trapezoidal and triangular membership functions are most frequently used. In this paper, we provide an interval-based theoretical explanation for this empirical fact.

Scitech Book News Reviews, Susan Fingerman

Sci-Tech News

No abstract provided.

Field Control Of The Surface Electroclinic Effect In Liquid Crystal Displays, Dana Hipolite

Physics

Liquid crystals (LCs) are a fascinating class of materials exhibiting a range of phases intermediate between liquid and crystalline. Smectic LCs consist of elongated molecules arranged in a periodic stack (along z) of liquid like layers. In the smectic-A (Sm-A) phase, the average molecular long axis (director) points along z. In the smectic-C (Sm-C) phase, it is tilted relative to z, thus picking out a special direction within the layers. Typically, the Sm-A* to Sm- C* transition will occur as temperature is decreased. In chiral smectics (Sm-*A or Sm-C*) it is possible to induce director titling (i.e. the Sm-C* phase) …

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 …

Characterizations Of Distributions Of Ratio Of Certain Independent Random Variables, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Various characterizations of the distributions of the ratio of two independent gamma and exponential random variables as well as that of two independent Weibull random variables are presented. These characterizations are based, on a simple relationship between two truncated moments ; on hazard function ; and on functions of order statistics.

On Generalized Gamma Convolution Distributions, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We present here characterizations of certain families of generalized gamma convolution distributions of L. Bondesson based on a simple relationship between two truncated moments. We also present a list of well-known random variables whose distributions or the distributions of certain functions of them belong to the class of generalized gamma convolutions.

The Pitman Inequality For Exchangeable Random Vectors, J. Behboodian, Naveen K. Bansal, Gholamhossein Hamedani, Hans Volkmer

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this short article the following inequality called the “Pitman inequality” is proved for the exchangeable random vector (X₁,X₂,…,X_n) without the assumption of continuity and symmetry for each component X_i:

P(|1n∑i=1nXi|≤|∑i=1nαiXi|)≥12 ,

where all αi≥0 are special weights with ∑i=1nαi=1.

On Fuzzy Soft Matrix Based On Reference Function, Florentin Smarandache, Said Broumi, Mamoni Dhar

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we study fuzzy soft matrix based on reference function. Firstly, we define some new operations such as fuzzy soft complement matrix and trace of fuzzy soft matrix based on reference function. Then, we introduced some related properties, and some examples are given. Lastly, we define a new fuzzy soft matrix decision method based on reference function.

Closure And Homological Properties Of (Auto)Stackable Groups, Ashley Johnson

Department of Mathematics: Dissertations, Theses, and Student Research

Let G be a finitely presented group with Cayley graph Γ. Roughly, G is a stackable group if there is a maximal tree T in Γ and a function φ, defined on the edges in Γ, for which there is a natural ‘flow’ on the edges in Γ\T towards the identity. Additionally, if graph (φ), which consists of pairs (e; φ(e)) for e an edge in Γ, forms a regular language, then G is autostackable. In 2011, Brittenham and Hermiller introduced stackable groups in [4], in part, as a means …

Decompositions Of Betti Diagrams, Courtney Gibbons

Department of Mathematics: Dissertations, Theses, and Student Research

In this dissertation, we are concerned with decompositions of Betti diagrams over standard graded rings and the information about that ring and its modules that can be recovered from these decompositions. In Chapter 2, we study the structure of modules over short Gorenstein graded rings and determine a necessary condition for a matrix of nonnegative integers to be the Betti diagram of such a module. We also describe the cone of Betti diagrams over the ring k[x,y]/(x²,y²), and we provide an algorithm for decomposing Betti diagrams, even for modules of infinite projective dimension. Chapter 3 …

Development And Application Of Difference And Fractional Calculus On Discrete Time Scales, Tanner J. Auch

Department of Mathematics: Dissertations, Theses, and Student Research

The purpose of this dissertation is to develop and apply results of both discrete calculus and discrete fractional calculus to further develop results on various discrete time scales. Two main goals of discrete and fractional discrete calculus are to extend results from traditional calculus and to unify results on the real line with those on a variety of subsets of the real line. Of particular interest is introducing and analyzing results related to a generalized fractional boundary value problem with Lidstone boundary conditions on a standard discrete domain N_a. We also introduce new results regarding exponential order for functions on …

A Pattern In The Lusternik-Schnirelmann Category Of Rational Spaces, Julie Dare Houck

Dissertations

The Lusternik-Schnirelmann (or LS) category of a space is one less than the number of contractible open sets with which we can cover the space. If we look at the LS categories of the skeleta of a CW complex, we find a sequence of dimensions where the LS category changes. I discuss whether certain of these "category sequences" (defined in the paper, "Categorical Sequences", by Nendorf, Scoville, and Strom) could be realized as the categorical sequences of rational spaces. I first reduce from looking at all rational spaces to only Postnikov sections of finite wedges of spheres. Using the Leray-Serre …

Results On Containments And Resurgences, With A Focus On Ideals Of Points In The Plane, Annika Denkert

Department of Mathematics: Dissertations, Theses, and Student Research

Let K be an algebraically closed field and I ⊆ R=K[P^N] a nontrivial homogeneous ideal. We can describe ordinary powers I^r and symbolic powers I^(m) of I. One question that has been of interest over the past couple of years is that of when we have containment of I^(m) in I^r. Bocci and Harbourne defined the resurgence of I as rho(I)=sup_m,r{m/r | I^(m) is not contained in I^r}. Hence in particular I^(m) ⊆ I^r whenever m/r is at least …

Invited Expert On Qr – Responder For Qr Focus, Robert L. Mayes

Teaching & Learning: Faculty Presentations (2012-2017)

No abstract provided.

Iterative Solvers For Large, Dense Matrices, Eowyn Wilhelmina Cenek

Dissertations

Stochastic Interpolation (SI) uses a continuous, centrally symmetric probability distribution function to interpolate a given set of data points, and splits the interpolation operator into a discrete deconvolution followed by a discrete convolution of the data. The method is particularly effective for large data sets, as it does not suffer from the problem of oversampling, where too many data points cause the interpolating function to oscillate wildly. Rather, the interpolation improves every time more data points are added. The method relies on the inversion of relatively large, dense matrices to solve Annx = b for x. Based on the probability …

Distributed Sparse Matrix Solver And Pivoting Algorithms For Large Linear Equations, Esteban Torres

Theses and Dissertations - UTB/UTPA

This thesis presents a distributed sparse direct solver and pivoting strategies for distributed sparse LU factorization. In Chapter I, we introduce some background concepts in linear algebra. In Chapter II, we discuss parallel hardware architectures and introduce our problem for discussion. In Chapter III, we describe the implementation of our sparse direct solver and our pivoting algorithms. Next, we present our simulation methodology and results in Chapter IV and we show that our pivoting algorithm yields up to 50% more accurate results than a current state-of-the-art solver, SuperLU_DIST. Finally, in Chapter V, we present some ideas to further improve the …

Synthetic Aperture Radar With Compressed Sensing, Yufeng Cao

Theses and Dissertations - UTB/UTPA

A general synthetic aperture radar (SAR) signal model is derived from the Maxwell’s equations, and compressed sensing are introduced to the signal model for SAR image reconstruction. Random Partial Fourier Matrices were applied to prove that compressed sensing can be used to this signal model from the viewpoint of mathematics. In the numerical simulation part, we show that the procedure of basis pursuit can reconstruct SAR image, based on our main results, which is shown efficient in comparison with the matched filter algorithm.

Examine Participant Dropout, Undiagnosed Diabetes And Undiagnosed Prediabetes In A Chronic Disease Prevention Education Program, Yiwen Cao

Theses and Dissertations - UTB/UTPA

There were 2768 participants enrolled in a chronic disease prevention education program. Survey and health measurements were obtained at three time points. We examine potential factors that might contribute to participant dropout, undiagnosed diabetes and undiagnosed prediabetes respectively. Logistic regression was used to examine the association between participant dropout and predictors, and to compare the odds of being undiagnosed with diabetes and prediabetes. We found that the potential predictors for participant dropout included age, employment, insurance, diabetes, self-reported health status, session type, program duration and curriculum. Factors affecting undiagnosed diabetes and prediabetes were age, self-reported health status birth country, limited …

Packings And Coverings Of Complete Graphs With A Hole With The 4-Cycle With A Pendant Edge, Yan Xia

Electronic Theses and Dissertations

In this thesis, we consider packings and coverings of various complete graphs with the 4-cycle with a pendant edge. We consider both restricted and unrestricted coverings. Necessary and sufficient conditions are given for such structures for (1) complete graphs K_v, (2) complete bipartite graphs K_m,n, and (3) complete graphs with a hole K(v,w).

Traveling Wave Solution To Two-Dimensional Burgers-Korteweg-De Vries Equation, Xiaoqian Gong

Theses and Dissertations - UTB/UTPA

In this thesis, we study the Two-Dimensional Burgers-Korteweg-de Vries (2D-BKdV) equation by analyzing the equivalent Abel equation, which indicates that under some particular conditions, the 2D-BKdV equation has a unique bounded traveling wave solution. By using the theorem of contractive mapping, a traveling wave solution to the 2D-BKdV equation is expressed explicitly. In the end, the behavior of the proper solution of the 2D-BKdV equation is established by applying the comparison theorem of differential equations.

On Cubic Multisections, Andrew Alaniz

Theses and Dissertations - UTB/UTPA

In this thesis, a systematic procedure is given for generating cubic multi-sections of Eisenstein series. The relevant series are determined from Fourier expansions for Eisenstein series by restricting the congruence class of the summation index modulo three. The resulting series are shown to be rational functions of the Dedekind eta function. A more general treatment of cubic dissection formulas is given by describing the dissection operators in terms of linear transformations.

3d Modeling And Design Optimization Of Rod Shaped Ionic Polymer Metal Composite Actuator, Siul A. Ruiz

UNLV Theses, Dissertations, Professional Papers, and Capstones

Ionic polymer-metal composites (IPMCs) are some of the most well-known electro-active polymers. This is due to their large deformation provided a relatively low voltage source. IPMCs have been acknowledged as a potential candidate for biomedical applications such as cardiac catheters and surgical probes; however, there is still no existing mass manufacturing of IPMCs. This study intends to provide a theoretical framework which could be used to design practical purpose IPMCs depending on the end users interest.

This study begins by investigating methodologies used to develop quantify the physical actuation of an IPMC in 3-dimensional space. This approach is taken in …

Estimation Of The Tax Rates Based On Vehicle Miles Traveled Using Stochastic Models, Pratik Verma

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this thesis, we shall study the alternative revenue collection system which is based on the vehicle miles traveled (VMT). In various studies, it has been found that the existing revenue collection system based on gas/fuel tax is not an appropriate option in the longer run. The main reasons include no effective tax process for vehicles based on alternative fuel vehicle, no effective changes in tax due to economical inflation, and more highway expenditure than generated revenue. Our main objective is to estimate the VMT tax rates that should be charged in order to generate same amount of revenue generated …

Lax Pairs For Some Nonlinear Equations, Ana Castillo

Theses and Dissertations - UTB/UTPA

Several methods have been proposed to approach the topic of integrable systems of nonlinear partial differential equations. One of these methods is called the Lax pair. The Lax pair is a pair of matrices or operators, that depend on time and satisfy the Lax equation. Based on the inverse scattering method introduced by Gardner, Greene, Kruskal and Miura (1967), Peter Lax introduced the Lax pair to derive soliton equations from the Lax equation. This thesis provides with a brief background on soliton theory, inverse scattering theory, and Lax pairs. The details missing in the work published by Ablowitz, Kaup, Newell, …

Geometric Study Of The Category Of Matrix Factorizations, Xuan Yu

Department of Mathematics: Dissertations, Theses, and Student Research

We study the geometry of matrix factorizations in this dissertation.
It contains two parts. The first one is a Chern-Weil style
construction for the Chern character of matrix factorizations; this
allows us to reproduce the Chern character in an explicit,
understandable way. Some basic properties of the Chern character are
also proved (via this construction) such as functoriality and that
it determines a ring homomorphism from the Grothendieck group of
matrix factorizations to its Hochschild homology. The second part is
a reconstruction theorem of hypersurface singularities. This is
given by applying a slightly modified version of Balmer's tensor
triangular geometry …

Mixture Of Poisson Distributions To Model Discrete Stock Price Changes., Rasitha Rangani Jayasekare Kodippuli Thanthillage Dona

Electronic Theses and Dissertations

An application of a mixture of Poisson distributions is proposed to model the discrete changes in stock price based on the minimum price movement known as `tick-size'. The parameters are estimated using the Expectation-Maximization (EM) algorithm with a constant mixing probability as well as mixing probabilities which depend on order size. The model is evaluated using simulations and real data. Both the simulated and real data show reasonable estimates. Several adjustments are made to the model implementation to improve the efficiency with user written codes for the Newton Raphson algorithm and also implementing one of the most recent versions of …

Harmonics In The Library, Charles Coppin

Journal of Humanistic Mathematics

Students of traditional calculus courses can discover significant mathematics original to themselves, especially if these courses are taught in a way that allows shafts of mathematical light to shine through. We tell a story of such an incident in the form of a dialogue between two fictional students. Our students, on their own, discover (or rediscover) a well-known problem based on the harmonic series. We believe opportunities for such discoveries are greater if students have had some experience with inquiry-based learning prior to entering a traditional course. More broadly, we aim to demonstrate what can occur when students feel no …

A Math Therapy Exercise, Gary Stogsdill

Journal of Humanistic Mathematics

Math anxiety prevents many liberal arts undergraduates from appreciating mathematics and realizing their potential in math courses and math-related endeavors. The author describes his development and use of a "math therapy exercise" that enables students to move beyond the paralyzing grip of math anxiety and cultivate a more positive relationship with mathematics.

Rock Art Tallies: Mathematics On Stone In Western North America, James V. Rauff

Journal of Humanistic Mathematics

Western North America abounds with rock art sites. From Alberta to New Mexico and from Minnesota to California one can find the enigmatic rock paintings and rock carvings left by the pre-Columbian inhabitants. The images left behind on the rocks of the American plains and deserts are those of humanoids and animals, arrows and spears, and a variety of geometric shapes and abstract designs. Also included, in great numbers, are sequences of repeated shapes and marks that scholars have termed "tallies." The tallies are presumed to be an ancient accounting of something or some things. This article examines rock art …

An Erp Study Of The Processing Of Common And Decimal Fractions: How Different They Are, Li Zhang, Qi Wang, Chongde Lin, Cody Ding, Xinlin Zhou

Education Sciences and Professional Programs Faculty Works

This study explored event-related potential (ERP) correlates of common fractions (1/5) and decimal fractions (0.2). Thirteen subjects performed a numerical magnitude matching task under two conditions. In the common fraction condition, a nonsymbolic fraction was asked to be judged whether its magnitude matched the magnitude of a common fraction; in the decimal fraction condition, a nonsymbolic fraction was asked to be matched with a decimal fraction. Behavioral results showed significant main effects of condition and numerical distance, but no significant interaction of condition and numerical distance. Electrophysiological data showed that when nonsymbolic fractions were compared to common fractions, they displayed …