Mathematics Commons^™

Explicit Synchronized Solitary Waves For Some Models For The Interaction Of Long And Short Waves In Dispersive Media., Bruce Brewer

Fall Student Research Symposium 2021

Four systems have recently been proposed for the study of the interaction of long and short waves in dispersive media. This poster establishes the synchronized solitary wave solutions for one of these systems.

Measuring Irregularity Via Approximate Entropy: How Does Perceived Human Instability Affect One's Own Stability?, Madi Braunersrither

Fall Student Research Symposium 2021

In a study performed at Utah State University, participants were prompted to evaluate the stability of pictured human postures while standing on a force plate. The force plate was used to collect the center of pressure of the subjects by recording measurements in the vertical and horizontal directions. The way these factors fluctuate over time and the irregularity in this fluctuation, specifically, can give insight into the subject’s postural stability. Rather than working with summary statistics such as means and variances of fitting parameters of a distribution as commonly done in statistics, we want to measure irregularity through analyzing the …

Computer Program Simulation Of A Quantum Turing Machine With Circuit Model, Shixin Wu

Mathematical Sciences Technical Reports (MSTR)

Molina and Watrous present a variation of the method to simulate a quantum Turing machine employed in Yao’s 1995 publication “Quantum Circuit Complexity”. We use a computer program to implement their method with linear algebra and an additional unitary operator defined to complete the details. Their method is verified to be correct on a quantum Turing machine.

Oscillation Of Nonlinear Third-Order Difference Equations With Mixed Neutral Terms, Jehad Alzabut, Martin Bohner, Said R. Grace

Mathematics and Statistics Faculty Research & Creative Works

In this paper, new oscillation results for nonlinear third-order difference equations with mixed neutral terms are established. Unlike previously used techniques, which often were based on Riccati transformation and involve limsup or liminf conditions for the oscillation, the main results are obtained by means of a new approach, which is based on a comparison technique. Our new results extend, simplify, and improve existing results in the literature. Two examples with specific values of parameters are offered.

Fourth Derivative Singularly P-Stable Method For The Numerical Solution Of The Schrödinger Equation, Ali Shokri, Higinio Ramos, Mohammad Mehdizadeh Khalsaraei, Fikret A. Aliev, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we construct a method with eight steps that belongs to the family of Obrechkoff methods. Due to the explicit nature of the new method, not only does it not require another method as predictor, but it can also be considered as a suitable predictive technique to be used with implicit methods. Periodicity and error terms are studied when applied to solve the radial Schrödinger equation, considering different energy levels. We show its advantages in terms of accuracy, consistency, and convergence in comparison with other methods of the same order appearing in the literature.

(R1519) On Some Geometric Properties Of Non-Null Curves Via Its Position Vectors In \Mathbb{R}_1^3, Emad Solouma, Ibrahim Al-Dayel

Applications and Applied Mathematics: An International Journal (AAM)

In this work, the geometric properties of non-null curves lying completely on spacelike surface via its position vectors in the dimensional Minkowski 3-space \mathbb{R}_1^3 are studied. Also, we give a few portrayals for the spacelike curves which lie on certain subspaces of \mathbb{R}_1^3. Finally, we present an application to demonstrate our insights.

(R1466) Ideals And Filters On A Lattice In Neutrosophic Setting, Lemnaouar Zedam, Soheyb Milles, Abdelhamid Bennoui

Applications and Applied Mathematics: An International Journal (AAM)

The notions of ideals and filters have studied in many algebraic (crisp) fuzzy structures and used to study their various properties, representations and characterizations. In addition to their theoretical roles, they have used in some areas of applied mathematics. In a recent paper, Arockiarani and Antony Crispin Sweety have generalized and studied these notions with respect to the concept of neutrosophic sets introduced by Smarandache to represent imprecise, incomplete and inconsistent information. In this article, we aim to deepen the study of these important notions on a given lattice in the neutrosophic setting. We show their various properties and characterizations, …

(R1488) Transformation Of Glucokinase Under Variable Rate Constants And Thermal Conditions: A Mathematical Model, Mukhtar Ahmad Khanday, Roohi Bhat

Applications and Applied Mathematics: An International Journal (AAM)

The glucokinase (GK) in cells plays a pivotal role in the regulation of carbohydrate metabolism and acts as a sensor of glucose. It helps us to control glucose levels during fast and food intake conditions through triggering shifts in metabolism or cell functions. Various forms of hypoglycaemia and hyperglycaemia occur due to the transformations of the gene of the Glucokinase. The mathematical modelling of enzyme dynamics is an emerging research area to serve its role in biological investigations. Thus, it is imperative to establish a mathematical model to understand the kinetics of native and denatured forms of enzyme-GK under thermal …

Biofilm Viscoelasticity And Nutrient Source Location Control Biofilm Growth Rate, Migration Rate, And Morphology In Shear Flow, Hoa Nguyen, Abraham Ybarra, H. Başağaoğlu, Orrin Shindell

Mathematics Faculty Research

We present a numerical model to simulate the growth and deformation of a viscoelastic biofilm in shear flow under different nutrient conditions. The mechanical interaction between the biofilm and the fluid is computed using the Immersed Boundary Method with viscoelastic parameters determined a priori from measurements reported in the literature. Biofilm growth occurs at the biofilm-fluid interface by a stochastic rule that depends on the local nutrient concentration. We compare the growth, migration, and morphology of viscoelastic biofilms with a common relaxation time of 18 min over the range of elastic moduli 10–1000 Pa in different nearby nutrient source configurations. …

Negations Of Probability Distributions: A Survey, Ildar Z. Baryrshin, Nailya I. Kubysheva, Venera R. Bayrasheva, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In recent years many papers have been devoted to the analysis and applications of negations of finite probability distributions (PD), first considered by Ronald Yager. This paper gives a brief overview of some formal results on the definition and properties of negations of PD. Negations of PD are generated by negators of probability values transforming element-by-element PD into a negation of PD. Negators are non-increasing functions of probability values. There are two types of negators: PD-independent and PD-dependent negators. Yager's negator is fundamental in the characterization of linear PD-independent negators as a convex combination of Yager's negator and uniform negator. …

(R1514) Nano Continuous Mappings Via Nano M Open Sets, A. Vadivel, A. Padma, M. Saraswathi, G. Saravanakumar

Applications and Applied Mathematics: An International Journal (AAM)

Nano M open sets are a union of nano θ semi open sets and nano δ pre open sets. The properties of nano M open sets with their interior and closure operators are discussed in a previous paper. In this paper, we discuss about nano M-continuous and nano M-irresolute functions are introduced in a nano topological spaces along with their continuous and irresolute mappings. Also, nano M-open and nano M-closed functions are introduced and compare with their near open and closed mappings in a nano topological spaces. Further, nano M homeomorphism is also discussed in nano …

Predicting Lifespan Of Drosophila Melanogaster: A Novel Application Of Convolutional Neural Networks And Zero-Inflated Autoregressive Conditional Poisson Model, Yi Zhang, V. A. Samaranayake, Gayla R. Olbricht, Matthew S. Thimgan

Mathematics and Statistics Faculty Research & Creative Works

A model to classify the lifespan of Drosophila, the fruit fly, into short- and long-lived categories based on a sleep characteristic, extracted from activity data, is developed using a two-stage process. Stage 1 models the per-minute activity counts of each fly using a zero-inflated autoregressive conditional Poisson model. These probabilities are allowed to vary hourly, reflecting the circadian and other cycles present in a fly's sleep architecture. A 5-day moving window is used to model data allowing the model parameters to vary over the course of the fly's life. The resulting probabilities capture information about changes in sleep patterns with …

Generalization Of Mitrinović–Pečarić Inequalities On Time Scales, Ahmed A. El-Deeb, Elvan Akin, Billur Kaymakçalan

Mathematics and Statistics Faculty Research & Creative Works

We prove some new inequalities of Mitrinović–Pečarić inequalities for convex functions on an arbitrary time scale using delta integrals. These inequalities extend and improve some known dynamic inequalities in the literature. The main results will be proved by using Hölder and Jensen inequalities and a simple consequence of Keller's and Poetzsche's chain rules on time scales.

Discrete Fractional Boundary Value Problems And Inequalities, Martin Bohner, Nick Fewster-Young

Mathematics and Statistics Faculty Research & Creative Works

In this paper, a general nonlinear discrete fractional boundary value problem is considered, of order between one and two. The main result is an existence theorem, proving the existence of at least one solution to the boundary value problem, subject to validity of a certain key inequality that allows unrestricted growth in the problem. The proof of this existence theorem is accomplished by using Brouwer's fixed point theorem as well as two other main results of this paper, namely, first, a result showing that the solutions of the boundary value problem are exactly the solutions to a certain equivalent integral …

Oscillation And Nonoscillation Criteria For Four-Dimensional Advanced And Delay Time-Scale Systems, Elvan Akin, Gülşah Yenpi

Mathematics and Statistics Faculty Research & Creative Works

We obtain oscillation and Non oscillation criteria for solutions to four-dimensional advanced and delay systems of first-order dynamic equations on time scales. To establish oscillation criteria, we eliminate Non oscillatory solutions of the systems based on the sign of components of the solutions. Furthermore, some of our results are new in the discrete case.

An Extension Of Asgeirsson's Mean Value Theorem For Solutions Of The Ultra-Hyperbolic Equation In Dimension Four, Guillem Cobos, Brendan Guilfoyle

Publications

In 1937 Asgeirsson established a mean value property for solutions of the general ultra-hyperbolic equation in 2n variables. In the case of four variables, it states that the integrals of a solution over certain pairs of conjugate circles are the same. In this paper we extend this result to non-degenerate conjugate conics, which include the original case of conjugate circles and adds the new case of conjugate hyperbolae. The broader context of this result is the geometrization of Fritz John’s 1938 analysis of the ultra-hyperbolic equation. Solutions of the equation arise as the compatibility for functions on line space to …

How To Select Typical Objects, Mariana Benitez, Jeffrey Weidner, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we have a large number of objects, too many to be able to thoroughly analyze each of them. To get a general understanding, we need to select a representative sample. For us, this problem was motivated to analyze the possible effect of an earthquake on buildings in El Paso, Texas. In this paper, we provide a reasonable formalization of this problem, and provide a feasible algorithm for solving thus formalized problem.

How To Simulate If We Only Have Partial Information But We Want Reliable Results?, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

The main objective of a smart energy system is to make control decisions that would make energy systems more efficient and more reliable. To select such decisions, the system must know the consequences of different possible decisions. Energy systems are very complex, they cannot be described by a simple formula, the only way to reasonably accurately find such consequences is to test each decision on a simulated system. The problem is that the parameters describing the system and its environment are usually known with uncertainty, and we need to produce reliable results -- i.e., results that will be true for …

Tractor Connections For Killing Tensors And Their Generalizations, Benjamin D. Shaw

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We create new symbolic software tools for the analysis of Killing tensors. Central to our work is the construction of the tractor connection defined on the tractor bundle, which allows one to obtain information about the space of Killing tensors without solving the Killing equations–an approach termed the tractor approach. We give a new application of the tractor approach which allows one to more easily check explicitly for linear independence of a given set of Killing tensors. We develop software to implement such methods in the case of rank 2 Killing tensors; similarly, we develop software to implement analogous methods …

Liutex Analysis By Pod And Dmd In Turbulent Flow After/ In Micro Vortex Generator, Xuan My Trieu

Mathematics Dissertations - Archive

Although vortex has been studied more than one hundred year, we still have not had universally accepted definition. A few well-known vortex identification methods are introduced ��,∆, ��2,������ criteria to identify coherent vortex structures the last three decades. A new Omega vortex identification method, which is defined as a ratio of the vorticity tensor norm squared over the sum of the vorticity tensor norm squared and deformation norm squared, was proposed in 2016. Two year later, the new vortex vector named Liutex (previously called Rotex) was proposed by Liu et al. with direction of local rotation axis (an eigenvector of …

An Alternative Class Of Ratio-Regression-Type Estimator Under Two-Phase Sampling Scheme, Muhammad Isah, Zakari Yahaya, Audu Ahmed

CBN Journal of Applied Statistics (JAS)

In this study, a new exponential ratio-regression estimator is developed using an auxiliary variable for estimating the finite population mean under a two-phase sampling system. The Bias and Mean Square Error (MSE) of the proposed estimator are derived and compared with some of the estimators in extant literature. Thus, the conditions under which the proposed estimator is better than some existing estimators are provided. Empirically, using four real datasets and simulation study, the proposed estimator performs better than the classical ratio, classical regression, exponential ratio, and exponential regression cum ratio estimator when compared using the criteria of bias, mean square …

A Practical Extension To The Ab/Ba Design, My T.A Nguyen

Electronic Theses and Dissertations

In this work, we take a close look at a general extension to the traditional AB/BA
crossover design that is commonly used in clinical trials to determine the effectiveness
of new candidate drugs. While the traditional crossover design requires each patient
in the study to be measured on both treatment A and treatment B, we consider the
possibility of additional measurements being available on each patient. This produces
designs such as the AABB/BBAA design which has been used in previous studies.
A general test statistic will be derived to test for treatment effects as well as its
corresponding power function …

An Algorithm For Biobjective Mixed Integer Quadratic Programs, Pubudu Jayasekara Merenchige

All Dissertations

Multiobjective quadratic programs (MOQPs) are appealing since convex quadratic programs have elegant mathematical properties and model important applications. Adding mixed-integer variables extends their applicability while the resulting programs become global optimization problems. Thus, in this work, we develop a branch and bound (BB) algorithm for solving biobjective mixed-integer quadratic programs (BOMIQPs). An algorithm of this type does not exist in the literature.

The algorithm relies on five fundamental components of the BB scheme: calculating an initial set of efficient solutions with associated Pareto points, solving node problems, fathoming, branching, and set dominance. Considering the properties of the Pareto set of …

Polynomial Embeddings Of Unilateral Weighted Shifts In 2-Variable Weighted Shifts, Raul E. Curto, Sang H. Lee, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

Given a bounded sequence omega of positive numbers, and its associated unilateral weighted shift W-omega, acting on the Hilbert space l(2) (Z+), we consider natural representations of W-omega as a 2-variable weighted shift, acting on the Hilbert space l(2)(Z(+)(2)). Alternatively, we seek to examine the various ways in which the sequence omega can give rise to a 2-variable weight diagram, corresponding to a 2-variable weighted shift. Our best (and more general) embedding arises from looking at two polynomials p and q nonnegative on a closed interval I subset of R+ and the double-indexed moment sequence {integral p(r)(k) q(r)(l) d sigma(r)}(k,l …

Dihedral Linking Invariants, Patricia Cahn, Elise Catania, Sarangoo Chimgee, Olivia Del Guercio, Jack Kendrick

Mathematics Sciences: Faculty Publications

A Fox p-colored knot K in S³ gives rise to a p-fold branched cover M of S³ along K. The pre-image of the knot K under the covering map is a p+1/2-component link L in M, and the set of pairwise linking numbers of the components of L is an invariant of K. This powerful invariant played a key role in the development of early knot tables, and appears in formulas for many other important knot and manifold invariants. We give an algorithm for computing this invariant for all odd p, generalizing an …

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. …

(R1524) The Existence And Uniqueness Of Solution For Fractional Newel-Whitehead-Segel Equation Within Caputo-Fabrizio Fractional Operator, Ali Khalouta

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we introduce and study the existence and uniqueness theorem of the solution for the fractional Newell-Whitehead-Segel equation within Caputo-Fabrizio fractional operator. Also, we propose a new numerical method known as natural reduced differential transform method (NRDTM) for solving this equation. We confirm our theoretical discussion with two numerical examples in order to achieve the validity and accuracy of the proposed method. The computations, associated with these examples, are performed by MATLAB software package.

(R1499) Family Of Surfaces With A Common Bertrand D-Curve As Isogeodesic, Isoasymptotic And Line Of Curvature, Süleyman Şenyurt, Kebire Hilal Ayvacı, Davut Canlı

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we establish the necessary and sufficient conditions to parameterize a surface family on which the Bertrand D-partner of any given curve lies as isogeodesic, isoasymptotic or curvature line in \mathbb{E}^3. Then, we calculate the fundamental forms of these surfaces and determine the developability and minimality conditions with the Gaussian and mean curvatures. We also extend this idea on ruled surfaces and provide the required conditions for those to be developable. Finally, we present some examples and graph the corresponding surfaces.

Finite Groups In Which The Number Of Cyclic Subgroups Is 3/4 The Order Of The Group, James Alexander Cayley

Graduate Theses/Dissertations

Let $G$ be a finite group, c(G) denotes the number of cyclic subgroups of G and α(G) = c(G)/|G|. In this thesis we go over some basic properties of alpha, calculate alpha for some families of groups, with an emphasis on groups with α(G) = 3/4, as all groups with α(G) > 3/4 have been classified by Garonzi and Lima (2018). We find all Dihedral group with this property, show all groups with α(G) = 3/4 have at least |G|/2-1 involutions, and discuss existing work by Wall (1970) and Miller (1919) classifying all such groups.

A Statistical Comparison Of Covid-19 In The United States Across Political Affiliations And Census Regions, Margarito Torres

Theses and Dissertations

In mid-January 2020, the United States reported their first cases of the coronavirus disease (COVID-19) from a passenger returning from Wuhan, China. Initially, the situation wasn’t very alarming as in China and European countries, but the situation began to worsen in March 2020 when the number of cases began to multiply. Then, in a matter of a few months, the United States became the number one country in terms of total cases and total deaths from COVID-19. We have been closely observing the United States and the world since July 2020. Our study aims to compare the political affiliations and …