Mathematics Commons^™

The Lattice Of Intuitionistic Fuzzy Topologies Generated By Intuitionistic Fuzzy Relations, Soheyb Milles

Applications and Applied Mathematics: An International Journal (AAM)

We generalize the notion of fuzzy topology generated by fuzzy relation given by Mishra and Srivastava to the setting of intuitionistic fuzzy sets. Some fundamental properties and necessary examples are given. More specifically, we provide the lattice structure to a family of intuitionistic fuzzy topologies generated by intuitionistic fuzzy relations. To that end, we study necessary structural characteristics such as distributivity, modularity and complementary of this lattice.

Fuzzy Solutions To Second Order Three Point Boundary Value Problem, Dimplekumar N. Chalishajar, R. Ramesh

Applications and Applied Mathematics: An International Journal (AAM)

In this manuscript, the proposed work is to study the existence of second-order differential equations with three point boundary conditions. Existence is proved using fuzzy set valued mappings of a real variable whose values are normal, convex, upper semi continuous and compactly supported fuzzy sets. The sufficient conditions are also provided to establish the existence results of fuzzy solutions of second order differential equations for three point boundary value problem. By using Banach fixed point principle, a new existence theorem of solutions for these equations in the metric space of normal fuzzy convex sets with distance given by the maximum …

Optimization Framework For Reconstructing Biomedical Images By Efficient Sample-Based Parameterization, Paul Richard Arbic Ii

Theses and Dissertations

An efficient computational approach for optimal reconstruction of binary-type images suitable for models in various biomedical applications is developed and validated. The methodology includes derivative-free optimization supported by a set of sample solutions with customized geometry generated synthetically. The entire framework has an easy to follow design due to a nominal number of tuning parameters which makes the approach simple for practical implementation in various settings, adjusting it to new models, and enhancing the performance. High efficiency in computational time is achieved through applying the coordinate descent method to work with individual controls in the predefined custom order. This technique …

Onboard Autonomous Controllability Assessment For Fixed Wing Suavs, Brian Edward Duvall

Mechanical & Aerospace Engineering Theses & Dissertations

Traditionally fixed-wing small Unmanned Arial Vehicles (sUAV) are flown while in direct line of sight with commands from a remote operator. However, this is changing with the increased popularity and ready availability of low-cost flight controllers. Flight controllers provide fixed-wing sUAVs with functions that either minimize or eliminate the need for a remote operator. Since the remote operator is no longer controlling the sUAV, it is impossible to determine if the fixed-wing sUAV has proper control authority. In this work, a controllability detection system was designed, built, and flight-tested using COTS hardware. The method features in-situ measurement and analysis of …

A Nevanlinna-Type Counting Function And Pullback Measure, John Nguyen

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this dissertation, we introduce a Nevanlinna-type counting function, $M_{\varphi, \alpha}$. We show that $M_{\varphi, \alpha}$ is subharmonic and continuous on $\theset$ by exhibiting certain properties of the logarithmic potential of the associated pullback measure of two-dimensional Lebesgue measure on $\mathbb{D}$. Different identities of $M_{\varphi, \alpha}$ are presented. A change-of-variable formula calculates precisely the weighted Bergman norms of composition functions in terms of $M_{\varphi, \alpha}$. Certain estimates involving $M_{\varphi, \alpha}$ and the associated pullback measure on Carleson windows and semi-disks are demonstrated. For weighted Bergman space $A^2_\alpha$, we characterize orthogonal self-maps and give the Hilbert Schmidt norm of $C_\varphi$.

Bayesian Variable Selection Methods For Genome-Wide Association Studies With Categorical Phenotypes, Benazir Rowe

UNLV Theses, Dissertations, Professional Papers, and Capstones

Genome-wide association studies (GWAS) attempt to find the associations between genetic markers and studied traits (phenotypes). The problem of GWAS is complex and various methods have been developed to approach it. One of such methods is Bayesian variable selection (BVS). We describe the BVS methods in detail and demonstrate the ability of BVS method Posterior Inference via Model Averaging and Subset Selection (piMASS) to improve the power of detecting phenotype-associated genetic loci, potentially leading to new discoveries from existing data without increasing the sample size.

We present several ways to improve and extend the applicability of piMASS for GWAS. The …

Equivalences Of Determinacy Between Levels Of The Borel Hierarchy And Long Games, And Some Generalizations, Katherine Aimee Yost

UNLV Theses, Dissertations, Professional Papers, and Capstones

This thesis will be primarily focused on directly proving that the determinacy of Borel games in X^ω is equivalent to the determinacy of certain long open games, from a fragment of ZFC that’s well-known to be insufficient to prove Borel determinacy. The main theorem is a level by level result which shows the equivalence between determinacy of open games in a long tree, [Υ^α], and determinacy of Σ_0^α games in X^ω. In Chapter 9, we mimic the proof used in our main theorem to show that the determinacy of clopen games in the product space X^ω × ω^ω is equivalent …

Sigma Coloring And Edge Deletions, Agnes Garciano, Reginaldo M. Marcelo, Mari-Jo P. Ruiz, Mark Anthony C. Tolentino

Mathematics Faculty Publications

A vertex coloring c : V(G) → N of a non-trivial graph G is called a sigma coloring if σ(u) is not equal to σ(v) for any pair of adjacent vertices u and v. Here, σ(x) denotes the sum of the colors assigned to vertices adjacent to x. The sigma chromatic number of G, denoted by σ(G), is defined as the fewest number of colors needed to construct a sigma coloring of G. In this paper, we consider the sigma chromatic number of graphs obtained by deleting one or more of its edges. In particular, we study the difference σ(G)−σ(G−e) …

On Coupled Reaction Diffusion Equations And Their Applications, Juan J. Huerta

Theses and Dissertations

Reaction-diffusion equations are nonlinear partial differential equations that have been used extensively in mathematical modeling. An interesting case in this type of equation is the Fisher-Kolmogorov system, which has been used to study a low-grade glioma, a group of primary brain tumors. In the first part of this thesis, a stochastic version of the Fisher-Kolmogorov system will be studied, and exact and numerical solutions will be presented.

The second part of this thesis will show how the speed of information propagation affects disease spread and vaccination uptake through networks in epidemics. In this model, the information reaches different people at …

Bivariate Markov Chain Model Of Irritable Bowel Syndrome (Ibs) Subtypes And Abdominal Pain, Ricardo Reyna Jr.

Theses and Dissertations

Researchers use stochastic models like continuous-time Markov chains (CTMC) to model progression of morbidities of public health impact, like HIV and Hepatitis C. Most of the research in that area is done for a single disease. In this research, we use a bivariate continuous-time Markov chain (CTMC) to model progression of co-morbidities. In particular, we use a bivariate CTMC to model the joint progression of Irritable Bowel Syndrome (IBS) and abdominal pain. Symptoms of IBS are known to change throughout the duration of the disorder. Hence, patients are normally asked to make a journal of the stool type, symptoms, and …

An Update On The Computational Theory Of Hamiltonian Period Functions, Bradley Joseph Klee

Graduate Theses and Dissertations

Lately, state-of-the-art calculation in both physics and mathematics has expanded to include the field of symbolic computing. The technical content of this dissertation centers on a few Creative Telescoping algorithms of our own design (Mathematica implementations are given as a supplement). These algorithms automate analysis of integral period functions at a level of difficulty and detail far beyond what is possible using only pencil and paper (unless, perhaps, you happen to have savant-level mental acuity). We can then optimize analysis in classical physics by using the algorithms to calculate Hamiltonian period functions as solutions to ordinary differential equations. The simple …

Sum Of Cubes Of The First N Integers, Obiamaka L. Agu

Electronic Theses, Projects, and Dissertations

In Calculus we learned that 􏰅Sum^{n}_{k=1} k = [n(n+1)]/2 , that Sum^{􏰅n}_{k=1} k^2 = [n(n+1)(2n+1)]/6 , and that Sum^{n}_{k=1} k^{3} = (n(n+1)/2)^{2}. These formulas are useful when solving for the area below quadratic or cubic function over an interval [a, b]. This tedious process, solving for areas under a quadratic or a cubic, served as motivation for the introduction of Riemman integrals. For the overzealous math student, these steps were replaced by a simpler method of evaluating antiderivatives at the endpoints a and b. From my recollection, a former instructor informed us to do the value of memorizing these formulas. …

Classification Of Jacobian Elliptic Fibrations On A Special Family Of K3 Surfaces Of Picard Rank Sixteen, Thomas Hill

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

K3 surfaces are an important tool used to understand the symmetries in physics that link different string theories, called string dualities. For example, heterotic string theory compactified on an elliptic curve describes a theory physically equivalent to (dual to) F-theory compactified on a K3 surface. In fact, M-theory, the type IIA string, the type IIB string, the Spin(32)/Z₂ heterotic string, and the E₈ x E₈ heterotic string are all related by compactification on Calabi-Yau manifolds.

We study a special family of K3 surfaces, namely a family of rank sixteen K3 surfaces polarized by the lattice H⊕E …

Delta Hedging Of Financial Options Using Reinforcement Learning And An Impossibility Hypothesis, Ronak Tali

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In this thesis we take a fresh perspective on delta hedging of financial options as undertaken by market makers. The current industry standard of delta hedging relies on the famous Black Scholes formulation that prescribes continuous time hedging in a way that allows the market maker to remain risk neutral at all times. But the Black Scholes formulation is a deterministic model that comes with several strict assumptions such as zero transaction costs, log normal distribution of the underlying stock prices, etc. In this paper we employ Reinforcement Learning to redesign the delta hedging problem in way that allows us …

An Exploration Of The Numeracy Skills Required For Safe, Quality Nursing Practice, Anna Wendel

UNLV Theses, Dissertations, Professional Papers, and Capstones

The purpose of this study was to explore the numeracy skills required for safe, quality nursing practice. Using a descriptive mixed methods design, this study answered two research questions: 1) What numeracy skills do nurses perceive as important for providing safe, quality nursing care in the first three years of practice? 2) How do nurses incorporate numeracy skills into daily patient care during the first three years of practice? Early career nurses from a not-for-profit health care organization in the mid-Atlantic region of the United States (n=109) responded to an online survey tool developed by the student investigator that ranked …

On The Local Theory Of Profinite Groups, Mohammad Shatnawi

Dissertations

Let G be a finite group, and H be a subgroup of G. The transfer homomorphism emerges from the natural action of G on the cosets of H. The transfer was first introduced by Schur in 1902 [22] as a construction in group theory, which produce a homomorphism from a finite group G into H/H^' an abelian group where H is a subgroup of G and H' is the derived group of H. One important first application is Burnside’s normal p-complement theorem [5] in 1911, although he did not use the transfer homomorphism explicitly to prove it. …

Existence And Stability Of The Doubly Nonlinear Anisotropic Parabolic Equation, Huashui Zhan, Zhaosheng Feng

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we are concerned with a doubly nonlinear anisotropic parabolic equation, in which the diffusion coefficient and the variable exponent depend on the time variable t. Under certain conditions, the existence of weak solution is proved by applying the parabolically regularized method. Based on a partial boundary value condition, the stability of weak solution is also investigated.

Nato And The Ifrc: A Comparative Case Study, Abigail Kosiak

Undergraduate Honors Capstone Projects

This research analyzes the North Atlantic Treaty Organization's (NATO) Multinational Telemedicine System (MnTS) Project and works to answer five main questions:

1) What challenges did the NATO MnTS Project face that are directly related to the fact that the project included members from different countries and worked to create a system that operates across national borders?

2) How do these challenges compare to those faced by a non-governmental organization (NGO) like the International Federation of the Red Cross and Red Crescent Societies (IFRC)?

3) What successes has the IFRC had with its current operational model?

4) In what ways could …

Extending Power Series Methods For The Hodgkin-Huxley Equations, Including Sensitive Dependence, James S. Sochacki

CODEE Journal

A neural cell or neuron is the basic building block of the brain and transmits information to other neurons. This paper demonstrates the complicated dynamics of the neuron through a numerical study of the Hodgkin-Huxley differential equations that model the ionic mechanisms of the neuron: slight changes in parameter values and inputted electrical impulses can lead to very different (unexpected) results. The methods and ideas developed for the ordinary differential equations are extended to partial differential equations for Hodgkin-Huxley networks of neurons in one, two and three dimensions.

Functional Kernel Density Estimation: Point And Fourier Approaches To Time Series Anomaly Detection, Michael R. Lindstrom, Hyuntae Jung, Denis Larocque

School of Mathematical & Statistical Sciences Faculty Publications

We present an unsupervised method to detect anomalous time series among a collection of time series. To do so, we extend traditional Kernel Density Estimation for estimating probability distributions in Euclidean space to Hilbert spaces. The estimated probability densities we derive can be obtained formally through treating each series as a point in a Hilbert space, placing a kernel at those points, and summing the kernels (a “point approach”), or through using Kernel Density Estimation to approximate the distributions of Fourier mode coefficients to infer a probability density (a “Fourier approach”). We refer to these approaches as Functional Kernel Density …

Essays In Monetary Policy For Emergingmarket Economies., Sargam Gupta Dr.

Doctoral Theses

The eectiveness of monetary policy in emerging market economies (EMEs) depends on both internal and external factors. Central banks in EMEs have been grappling with volatile capital ows and instability in exchange rates, as a result of unconventional monetary policies adopted by advanced economies (AEs) in the post Global Financial Crisis (GFC) period of 2008-2009 (see Dedola et al. (2017) and Korinek (2018)).1 Concerns related to the inadequacy of monetary policy in EMEs in stabilizing exchange rates have also been raised in a recent speech delivered by Agustin Carstens at the London School of Economics.2 Domestically, what makes monetary policy …

Subnormality Of Powers Of Multivariable Weighted Shifts, Sang Hoon Lee, Woo Young Lee, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

Given a pair of commuting subnormal Hilbert space operators, the Lifting Problem for Commuting Subnormals (LPCS) asks for necessary and sufficient conditions for the existence of a commuting pair of normal extensions of and ; in other words, is a subnormal pair. The LPCS is a longstanding open problem in the operator theory. In this paper, we consider the LPCS of a class of powers of -variable weighted shifts. Our main theorem states that if a “corner” of a 2-variable weighted shift is subnormal, then is subnormal if and only if a power is subnormal for some . As a …

Covariant Quantum White Noise From Light-Like Quantum Fields, Radhakrishnan Balu

Journal of Stochastic Analysis

No abstract provided.

Year 7 Students’ Interpretation Of Letters And Symbols In Solving Routine Algebraic Problems, Madihah Khalid Dr., Faeizah Yakop Dr., Hasniza Ibrahim

The Qualitative Report

In this study wefocused on one of the recurring issues in the learning of mathematics, which is students’ errors and misconceptions in learning algebra. We investigated Year 7 students on how they manipulate and interpret letters in solving routine algebraic problems to understand their thinking process. This is a case study of qualitative nature, focusing on one pencil and paper test, observation, and in-depth interviews of students in one particular school in Brunei Darussalam. The themes that emerged from interviews based on the test showed students’ interpretation of letters categorized as “combining” - which involved the combining of numbers during …

Development Of A Mobile Ten Frames App For Philippine K-12 Schools, Debbie Marie Versoza, Ma. Louise Antonette N. De Las Peñas, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Mark L. Loyola

Mathematics Faculty Publications

This paper reports on the Quick Images app, whose design framework is informed by research on ten-structured thinking and gamification principles. Inclusivity was also a major consideration, especially in the context of a developing country. Thus, the app was made freely available and required only moderate system requirements. Pilot studies revealed that the app has the potential to promote children’s ability to see two-digit numbers in relation to tens and ones, which is a major goal of elementary school mathematics. Collaborations with the Philippine Department of Education to ensure the app’s sustained use are also discussed.

Grim Under A Compensation Variant, Aaron Davis, Aaron Davis

Honors College Theses

Games on graphs are a well studied subset of combinatorial games. Balance and strategies for winning are often looked at in these games. One such combinatorial graph game is Grim. Many of the winning strategies of Grim are already known. We note that many of these winning strategies are only available to the first player. Hoping to develop a fairer Grim, we look at Grim played under a slighlty different rule set. We develop winning strategies and known outcomes for this altered Grim. Throughout, we discuss whether our altered Grim is a fairer game then the original.

An Analysis Of Growth Of The Community Integration Psychological Score In An Ethnically Diverse Population Experiencing Homelessness In A Permanent Supportive Housing Program Using Hierarchical Mixed Modeling, Leah Hollis Puglisi

Mathematics & Statistics ETDs

Hierarchical models are becoming increasingly common in epidemiological and psychological research. When analyzing data from such studies, the nested structure of the data must be taken into account. Mixed modeling in conjunction with hierarchical mixed modeling allows researchers to ask broad questions about the population of interest. Modeling under restricted maximum likelihood estimation (REML), as opposed to full maximum likelihood estimation (ML), increases the accuracy of estimates for the random effects in the model. We use hierarchical mixed modeling under REML estimation to analyze which factors increase “community integration”, a concept and a construct developed and used in the mental …

Super Sudoku Squares, Dean Hoffman

Communications on Number Theory and Combinatorial Theory

We refer to a completed Sudoku puzzle as a Sudoku Square of order 3. We define a more restricted, but natural, extension --- a Super Sudoku Square of order n, and determine for which orders n one exists.

Crash Risk-Based Prioritization Of Basic Safety Message In Dsrc, Seungmo Kim, Byung Jun Kim

Michigan Tech Publications, Part 1

Dedicated short-range communications (DSRC) is one of the key technologies enabling safety-critical applications for intelligent transportation system (ITS). Considering the significance of such safety-of-life applications, it is of utmost importance to guarantee reliable delivery of basic safety messages (BSMs). However, in accordance with a V2X network being inherently dynamic in key aspects such as vehicle density and velocity, the networking behavior of a DSRC system is usually highly complicated to analyze. In addition, the United States Federal Communications Commission (US FCC) recently proposed the so-called “5.9 GHz band innovation”, which includes a plan to reduce bandwidth for DSRC to 10 …

On The Global Operator And Fueter Mapping Theorem For Slice Polyanalytic Functions, Daniel Alpay, Kamal Diki, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper, we prove that slice polyanalytic functions on quaternions can be considered as solutions of a power of some special global operator with nonconstant coefficients as it happens in the case of slice hyperholomorphic functions. We investigate also an extension version of the Fueter mapping theorem in this polyanalytic setting. In particular, we show that under axially symmetric conditions it is always possible to construct Fueter regular and poly-Fueter regular functions through slice polyanalytic ones using what we call the poly-Fueter mappings. We study also some integral representations of these results on the quaternionic unit ball.