University of Missouri-St. Louis
University of Nebraska-Lincoln
University of New Mexico
Shawnee State University
University of South Florida
Trinity University
Minnesota State University Moorhead
Math 115: College Algebra For Pre-Calculus,
2023
CUNY Queens College
Math 115: College Algebra For Pre-Calculus, Seth Lehman
Open Educational Resources
OER course syllabus for Math 115, College Algebra, at Queens College
On The Second Case Of Fermat's Last Theorem Over Cyclotomic Fields,
2023
The Graduate Center, City University of New York
On The Second Case Of Fermat's Last Theorem Over Cyclotomic Fields, Owen Sweeney
Dissertations, Theses, and Capstone Projects
We obtain a new simpler sufficient condition for Kolyvagin's criteria, regarding the second case of Fermat's last theorem with prime exponent p over the p-th cyclotomic field, to hold. It covers cases when the existing simpler sufficient conditions do not hold and is important for the theoretical study of the criteria.
An Interval-Valued Random Forests,
2023
Utah State University
An Interval-Valued Random Forests, Paul Gaona Partida
All Graduate Theses and Dissertations
There is a growing demand for the development of new statistical models and the refinement of established methods to accommodate different data structures. This need arises from the recognition that traditional statistics often assume the value of each observation to be precise, which may not hold true in many real-world scenarios. Factors such as the collection process and technological advancements can introduce imprecision and uncertainty into the data.
For example, consider data collected over a long period of time, where newer measurement tools may offer greater accuracy and provide more information than previous methods. In such cases, it becomes crucial …
Stressor: An R Package For Benchmarking Machine Learning Models,
2023
Utah State University
Stressor: An R Package For Benchmarking Machine Learning Models, Samuel A. Haycock
All Graduate Theses and Dissertations
Many discipline specific researchers need a way to quickly compare the accuracy of their predictive models to other alternatives. However, many of these researchers are not experienced with multiple programming languages. Python has recently been the leader in machine learning functionality, which includes the PyCaret library that allows users to develop high-performing machine learning models with only a few lines of code. The goal of the stressor package is to help users of the R programming language access the advantages of PyCaret without having to learn Python. This allows the user to leverage R’s powerful data analysis workflows, while simultaneously …
Topological Comparison Of Some Dimension Reduction Methods Using Persistent Homology On Eeg Data,
2023
Trinity University
Topological Comparison Of Some Dimension Reduction Methods Using Persistent Homology On Eeg Data, Eddy Kwessi
Mathematics Faculty Research
In this paper, we explore how to use topological tools to compare dimension reduction methods. We first make a brief overview of some of the methods often used in dimension reduction such as isometric feature mapping, Laplacian Eigenmaps, fast independent component analysis, kernel ridge regression, and t-distributed stochastic neighbor embedding. We then give a brief overview of some of the topological notions used in topological data analysis, such as barcodes, persistent homology, and Wasserstein distance. Theoretically, when these methods are applied on a data set, they can be interpreted differently. From EEG data embedded into a manifold of high dimension, …
On Solutions Of First Order Pde With Two-Dimensional Dirac Delta Forcing Terms,
2023
Murray State University
On Solutions Of First Order Pde With Two-Dimensional Dirac Delta Forcing Terms, Ian Robinson
Rose-Hulman Undergraduate Mathematics Journal
We provide solutions of a first order, linear partial differential equation of two variables where the nonhomogeneous term is a two-dimensional Dirac delta function. Our results are achieved by applying the unilateral Laplace Transform, solving the subsequently transformed PDE, and reverting back to the original space-time domain. A discussion of existence and uniqueness of solutions, a derivation of solutions of the PDE coupled with a boundary and initial condition, as well as a few worked examples are provided.
Effect Of Total Population, Population Density And Weighted Population Density On The Spread Of Covid-19 In Malaysia,
2023
The University of Texas Rio Grande Valley
Effect Of Total Population, Population Density And Weighted Population Density On The Spread Of Covid-19 In Malaysia, Hui Shan Wong, Md Zobaer Hasan, Omar Sharif, Azizur Rahman
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Since November 2019, most countries across the globe have suffered from the disastrous consequences of the Covid-19 pandemic which redefined every aspect of human life. Given the inevitable spread and transmission of the virus, it is critical to acknowledge the factors that catalyse transmission of the disease. This research investigates the relation of the external demographic parameters such as total population, population density and weighted population density on the spread of Covid-19 in Malaysia. Pearson correlation and simple linear regression were utilized to identify the relation between the population-related variables and the spread of Covid-19 in Malaysia using data from …
Some New Techniques And Their Applications In The Theory Of Distributions,
2023
Louisiana State University
Some New Techniques And Their Applications In The Theory Of Distributions, Kevin Kellinsky-Gonzalez
LSU Doctoral Dissertations
This dissertation is a compilation of three articles in the theory of distributions. Each essay focuses on a different technique or concept related to distributions.
The focus of the first essay is the concept of distributional point values. Distribu- tions are sometimes called generalized functions, as they share many similarities with ordi- nary functions, with some key differences. Distributional point values, among other things, demonstrate that distributions are even more akin to ordinary functions than one might think.
The second essay concentrates on two major topics in analysis, namely asymptotic expansions and the concept of moments. There are many variations …
The Existence Of Solutions To A System Of Nonhomogeneous Difference Equations,
2023
University of Central Oklahoma
The Existence Of Solutions To A System Of Nonhomogeneous Difference Equations, Stephanie Walker
Rose-Hulman Undergraduate Mathematics Journal
This article will demonstrate a process using Fixed Point Theory to determine the existence of multiple positive solutions for a type of system of nonhomogeneous even ordered boundary value problems on a discrete domain. We first reconstruct the problem by transforming the system so that it satisfies homogeneous boundary conditions. We then create a cone and an operator sufficient to apply the Guo-KrasnoselâA˘Zskii Fixed Point Theorem. The majority of the work involves developing the constraints ´ needed to utilized this fixed point theorem. The theorem is then applied three times, guaranteeing the existence of at least three distinct solutions. Thus, …
Interpolation Problems And The Characterization Of The Hilbert Function,
2023
University of Arkansas, Fayetteville
Interpolation Problems And The Characterization Of The Hilbert Function, Bryant Xie
Mathematical Sciences Undergraduate Honors Theses
In mathematics, it is often useful to approximate the values of functions that are either too awkward and difficult to evaluate or not readily differentiable or integrable. To approximate its values, we attempt to replace such functions with more well-behaving examples such as polynomials or trigonometric functions. Over the algebraically closed field C, a polynomial passing through r distinct points with multiplicities m1, ..., mr on the affine complex line in one variable is determined by its zeros and the vanishing conditions up to its mi − 1 derivative for each point. A natural question would then be to consider …
Lagrange’S Study Of Wilson’S Theorem,
2023
Ursinus College
Lagrange’S Study Of Wilson’S Theorem, Carl Lienert
Number Theory
No abstract provided.
Lagrange’S Proof Of Wilson’S Theorem—And More!,
2023
Ursinus College
Lagrange’S Proof Of Wilson’S Theorem—And More!, Carl Lienert
Number Theory
No abstract provided.
Lagrange’S Proof Of The Converse Of Wilson’S Theorem,
2023
Ursinus College
Lagrange’S Proof Of The Converse Of Wilson’S Theorem, Carl Lienert
Number Theory
No abstract provided.
Lagrange’S Alternate Proof Of Wilson’S Theorem,
2023
Ursinus College
Lagrange’S Alternate Proof Of Wilson’S Theorem, Carl Lienert
Number Theory
No abstract provided.
Fuzzy Techniques Explain The Effectiveness Of Relu Activation Function In Deep Learning,
2023
The University of Texas at El Paso
Fuzzy Techniques Explain The Effectiveness Of Relu Activation Function In Deep Learning, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In the last decades, deep learning has led to spectacular successes. One of the reasons for these successes was the fact that deep neural networks use a special Rectified Linear Unit (ReLU) activation function s(x) = max(0,x). Why this activation function is so successful is largely a mystery. In this paper, we show that common sense ideas -- as formalized by fuzzy logic -- can explain this mysterious effectiveness.
How To Make Decision Under Interval Uncertainty: Description Of All Reasonable Partial Orders On The Set Of All Intervals,
2023
Universidad de Tarapacá
How To Make Decision Under Interval Uncertainty: Description Of All Reasonable Partial Orders On The Set Of All Intervals, Tiago M. Costa, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, we need to make a decision while for each alternative, we only know the corresponding value of the objective function with interval uncertainty. To help a decision maker in this situation, we need to know the (in general, partial) order on the set of all intervals that corresponds to the preferences of the decision maker. For this purpose, in this paper, we provide a description of all such partial orders -- under some reasonable conditions. It turns out that each such order is characterized by two linear inequalities relating the endpoints of the corresponding intervals, and …
Why 6-Labels Uncertainty Scale In Geosciences: Probability-Based Explanation,
2023
The University of Texas at El Paso
Why 6-Labels Uncertainty Scale In Geosciences: Probability-Based Explanation, Aaron Velasco, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
To describe uncertainty in geosciences, several researchers have recently proposed a 6-labels uncertainty scale, in which one the labels corresponds to full certainty, one label to the absence of any knowledge, and the remaining four labels correspond to the degrees of confidence from the intervals [0,0.25], [0.25,0.5], [0.5,0.75], and [0.75,1]. Tests of this 6-labels scale indicate that it indeed conveys uncertainty information to geoscientists much more effectively than previously proposed uncertainty schemes. In this paper, we use probability-related techniques to explain this effectiveness.
How To Propagate Interval (And Fuzzy) Uncertainty: Optimism-Pessimism Approach,
2023
São Paulo State University
How To Propagate Interval (And Fuzzy) Uncertainty: Optimism-Pessimism Approach, Vinícius F. Wasques, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, inputs to a data processing algorithm are known with interval uncertainty, and we need to propagate this uncertainty through the algorithm, i.e., estimate the uncertainty of the result of data processing. Traditional interval computation techniques provide guaranteed estimates, but from the practical viewpoint, these bounds are too pessimistic: they take into account highly improbable worst-case situations when all the measurement and estimation errors happen to be strongly correlated. In this paper, we show that a natural idea of having more realistic estimates leads to the use of so-called interactive addition of intervals, techniques that has already …
Which Fuzzy Implications Operations Are Polynomial? A Theorem Proves That This Can Be Determined By A Finite Set Of Inequalities,
2023
University of Balearic Islands
Which Fuzzy Implications Operations Are Polynomial? A Theorem Proves That This Can Be Determined By A Finite Set Of Inequalities, Sebastia Massanet, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
To adequately represent human reasoning in a computer-based systems, it is desirable to select fuzzy operations that are as close to human reasoning as possible. In general, every real-valued function can be approximated, with any desired accuracy, by polynomials; it is therefore reasonable to use polynomial fuzzy operations as the appropriate approximations. We thus need to select, among all polynomial operations that satisfy corresponding properties -- like associativity -- the ones that best fit the empirical data. The challenge here is that properties like associativity mean satisfying infinitely many constraints (corresponding to infinitely many possible triples of values), while most …
How To Combine Probabilistic And Fuzzy Uncertainty: Theoretical Explanation Of Clustering-Related Empirical Result,
2023
Sapientia University
How To Combine Probabilistic And Fuzzy Uncertainty: Theoretical Explanation Of Clustering-Related Empirical Result, Lázló Szilágyi, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In contrast to crisp clustering techniques that assign each object to a class, fuzzy clustering algorithms assign, to each object and to each class, a degree to which this object belongs to this class. In the most widely used fuzzy clustering algorithm -- fuzzy c-means -- for each object, degrees corresponding to different classes add up to 1. From this viewpoint, these degrees act as probabilities. There exist alternative fuzzy-based clustering techniques in which, in line with the general idea of the fuzzy set, the largest of the degrees is equal to 1. In some practical situations, the probability-type fuzzy …
