University of New Mexico
Washington University in St. Louis
Boise State University
University of North Dakota
Linfield College
University of Nebraska at Omaha
Governors State University
University of Richmond
Unomaha Problem Of The Week (2021-2022 Edition),
2022
University of Nebraska at Omaha
Unomaha Problem Of The Week (2021-2022 Edition), Brad Horner, Jordan M. Sahs
Student Research and Creative Activity Fair
The University of Omaha math department's Problem of the Week was taken over in Fall 2019 from faculty by the authors. The structure: each semester (Fall and Spring), three problems are given per week for twelve weeks, with each problem worth ten points - mimicking the structure of arguably the most well-regarded university math competition around, the Putnam Competition, with prizes awarded to top-scorers at semester's end. The weekly competition was halted midway through Spring 2020 due to COVID-19, but relaunched again in Fall 2021, with massive changes.
Now there are three difficulty tiers to POW problems, roughly corresponding ...
Unknowable Truths: The Incompleteness Theorems And The Rise Of Modernism,
2022
Belmont University
Unknowable Truths: The Incompleteness Theorems And The Rise Of Modernism, Caroline Tvardy
Honors Theses
This thesis evaluates the function of the current history of mathematics methodologies and explores ways in which historiographical methodologies could be successfully implemented in the field. Traditional approaches to the history of mathematics often lack either an accurate portrayal of the social and cultural influences of the time, or they lack an effective usage of mathematics discussed. This paper applies a holistic methodology in a case study of Kurt Gödel’s influential work in logic during the Interwar period and the parallel rise of intellectual modernism. In doing so, the proofs for Gödel’s Completeness and Incompleteness theorems will be ...
Introduction To Discrete Mathematics: An Oer For Ma-471,
2021
CUNY Queensborough Community College
Introduction To Discrete Mathematics: An Oer For Ma-471, Mathieu Sassolas
Open Educational Resources
The first objective of this book is to define and discuss the meaning of truth in mathematics. We explore logics, both propositional and first-order , and the construction of proofs, both formally and human-targeted. Using the proof tools, this book then explores some very fundamental definitions of mathematics through set theory. This theory is then put in practice in several applications. The particular (but quite widespread) case of equivalence and order relations is studied with detail. Then we introduces sequences and proofs by induction, followed by number theory. Finally, a small introduction to combinatorics is given.
Algebraic Structures And Variations: From Latin Squares To Lie Quasigroups,
2021
Northern Michigan University
Algebraic Structures And Variations: From Latin Squares To Lie Quasigroups, Erik Flinn
All NMU Master's Theses
In this Master's Thesis we give an overview of the algebraic structure of sets with a single binary operation. Specifically, we are interested in quasigroups and loops and their historical connection with Latin squares; considering them in both finite and continuous variations. We also consider various mappings between such algebraic objects and utilize matrix representations to give a negative conclusion to a question concerning isotopies in the case of quasigroups.
Optimizing Networking Topologies With Shortest Path Algorithms,
2021
University of Nebraska at Omaha
Optimizing Networking Topologies With Shortest Path Algorithms, Jordan Sahs
Student Research and Creative Activity Fair
Communication networks tend to contain redundant devices and mediums of transmission, thus the need to locate, document, and optimize networks is increasingly becoming necessary. However, many people do not know where to start the optimization progress. What is network topology? What is this “Shortest Path Problem”, and how can it be used to better my network? These questions are presented, taught, and answered within this paper. To supplement the reader’s understanding there are thirty-eight figures in the paper that are used to help convey and compartmentalize the learning process needed to grasp the materials presented in the ending sections ...
The Encyclopedia Of Neutrosophic Researchers - 4th Volume (2021),
2021
University of New Mexico
The Encyclopedia Of Neutrosophic Researchers - 4th Volume (2021), Florentin Smarandache, Maykel Leyva-Vazquez
Mathematics and Statistics Faculty and Staff Publications
Este es el cuarto volumen de la Enciclopedia de Investigadores Neutróficos, editados a partir de materiales ofrecidos por los autores que respondieron a la invitación del editor. Los autores se enumeran alfabéticamente. La introducción contiene una breve historia de la neutrosófica, y en especial se su impacto en Latinoamérica junto con enlaces a los principales artículos y libros. Los conjuntos neutrosóficos, la lógica neutrosófica, la probabilidad neutrosófica, la estadística neutrosófica, el precálculo neutrosófico, el cálculo neutrosófico, la psicología neutrosófica, la sociología neutrosófica etc., están ganando una atención significativa en resolver muchos problemas de la vida real que implican incertidumbre, imprecisión ...
Introduction To Neutrosophic Genetics,
2020
University of New Mexico
Introduction To Neutrosophic Genetics, Florentin Smarandache
Mathematics and Statistics Faculty and Staff Publications
Neutrosophic Genetics is the study of genetics using neutrosophic logic, set, probability, statistics, measure and other neutrosophic tools and procedures. In this paper, based on the Neutrosophic Theory of Evolution (that includes degrees of Evolution, Neutrality (or Indeterminacy), and Involution) – as extension of Darwin’s Theory of Evolution, we show the applicability of neutrosophy in genetics, and we present within the frame of neutrosophic genetics the following concepts: neutrosophic mutation, neutrosophic speciation, and neutrosophic coevolution.
Structure, Neutrostructure, And Antistructure In Science,
2020
University of New Mexico
Structure, Neutrostructure, And Antistructure In Science, Florentin Smarandache
Mathematics and Statistics Faculty and Staff Publications
In any science, a classical Theorem, defined on a given space, is a statement that is 100% true (i.e. true for all elements of the space). To prove that a classical theorem is false, it is sufficient to get a single counter-example where the statement is false. Therefore, the classical sciences do not leave room for partial truth of a theorem (or a statement). But, in our world and in our everyday life, we have many more examples of statements that are only partially true, than statements that are totally true. The NeutroTheorem and AntiTheorem are generalizations and alternatives ...
True-False Set Is A Particular Case Of The Refined Neutrosophic Set,
2020
University of New Mexico
True-False Set Is A Particular Case Of The Refined Neutrosophic Set, Florentin Smarandache, Said Broumi
Mathematics and Statistics Faculty and Staff Publications
Borzooei, Mohseni Takallo, and Jun recently proposed a new type of set, called True-False Set [1], and they claimed it is a generalization of Neutrosophic Set [2]. We prove that this assertion is untrue. Actually it’s the opposite, the True-False Set is a particular case of the Refined Neutrosophic Set.
A Novel Framework Using Neutrosophy For Integrated Speech And Text Sentiment Analysis,
2020
University of New Mexico
A Novel Framework Using Neutrosophy For Integrated Speech And Text Sentiment Analysis, Florentin Smarandache, Kritika Mishra, Ilanthenral Kandasamy, Vasantha Kandasamy W.B.
Mathematics and Statistics Faculty and Staff Publications
With increasing data on the Internet, it is becoming difficult to analyze every bit and make sure it can be used efficiently for all the businesses. One useful technique using Natural Language Processing (NLP) is sentiment analysis. Various algorithms can be used to classify textual data based on various scales ranging from just positive-negative, positive-neutral-negative to a wide spectrum of emotions. While a lot of work has been done on text, only a lesser amount of research has been done on audio datasets. An audio file contains more features that can be extracted from its amplitude and frequency than a ...
Numerical Computations Of Vortex Formation Length In Flow Past An Elliptical Cylinder,
2020
University of Pittsburgh
Numerical Computations Of Vortex Formation Length In Flow Past An Elliptical Cylinder, Matthew Karlson, Bogdan Nita, Ashwin Vaidya
Department of Mathematics Facuty Scholarship and Creative Works
We examine two dimensional properties of vortex shedding past elliptical cylinders through numerical simulations. Specifically, we investigate the vortex formation length in the Reynolds number regime 10 to 100 for elliptical bodies of aspect ratio in the range 0.4 to 1.4. Our computations reveal that in the steady flow regime, the change in the vortex length follows a linear profile with respect to the Reynolds number, while in the unsteady regime, the time averaged vortex length decreases in an exponential manner with increasing Reynolds number. The transition in profile is used to identify the critical Reynolds number which ...
Length Neutrosophic Subalgebras Of Bck/Bci-Algebras,
2020
University of New Mexico
Length Neutrosophic Subalgebras Of Bck/Bci-Algebras, Florentin Smarandache, Young Bae Jun, Madad Khan, Seok-Zun Song
Mathematics and Statistics Faculty and Staff Publications
the notion of (i, j, k)-length neutrosophic subalgebras in BCK/BCI-algebras is introduced, and their properties are investigated. Characterizations of length neutrosophic subalgebras are discussed by using level sets of interval neutrosophic sets. Conditions for level sets of interval neutrosophic sets to be subalgebras are provided.
Plithogenic Cubic Sets,
2020
University of New Mexico
Plithogenic Cubic Sets, Florentin Smarandache, S.P. Priyadharshini, F. Nirmala Irudayam
Mathematics and Statistics Faculty and Staff Publications
In this article, using the concepts of cubic set and plithogenic set, the ideas of plithogenic fuzzy cubic set, plithogenic intuitionistic fuzzy cubic set, plithogenic neutrosophic cubic set are introduced and its corresponding internal and external cubic sets are discussed with examples.
A Novel Approach For Assessing The Reliability Of Data Contained In A Single Valued Neutrosophic Number And Its Application In Multiple Criteria Decision Making,
2020
University of New Mexico
A Novel Approach For Assessing The Reliability Of Data Contained In A Single Valued Neutrosophic Number And Its Application In Multiple Criteria Decision Making, Florentin Smarandache, Dragisa Stanujkic, Darjan Karabasevic, Gabrijela Popovic
Mathematics and Statistics Faculty and Staff Publications
Multiple criteria decision making is one of the many areas where neutrosophic sets have been applied to solve various problems so far.
On Product Of Smooth Neutrosophic Topological Spaces,
2020
University of New Mexico
On Product Of Smooth Neutrosophic Topological Spaces, Florentin Smarandache, Kalaivani Chandran, Swathi Sundari Sundaramoorthy, Saeid Jafari
Mathematics and Statistics Faculty and Staff Publications
In this paper, we develop the notion of the basis for a smooth neutrosophic topology in a more natural way. As a sequel, we define the notion of symmetric neutrosophic quasi-coincident neighborhood systems and prove some interesting results that fit with the classical ones, to establish the consistency of theory developed. Finally, we define and discuss the concept of product topology, in this context, using the definition of basis.
The Polar Form Of A Neutrosophic Complex Number,
2020
University of New Mexico
The Polar Form Of A Neutrosophic Complex Number, Florentin Smarandache, Riad K. Al-Hamido, Mayas Ismail
Mathematics and Statistics Faculty and Staff Publications
In this paper, we will define the exponential form of a neutrosophic complex number. We have proven some characteristics and theories, including the conjugate of the exponential form of a neutrosophic complex number, division of the exponential form of a neutrosophic complex numbers, multiplication of the exponential form of a neutrosophic complex numbers. In addition, we have given the method of changing from the exponential to the algebraic form of a complex number.
A Review Of Fuzzy Soft Topological Spaces, Intuitionistic Fuzzy Soft Topological Spaces And Neutrosophic Soft Topological Spaces,
2020
University of New Mexico
A Review Of Fuzzy Soft Topological Spaces, Intuitionistic Fuzzy Soft Topological Spaces And Neutrosophic Soft Topological Spaces, Florentin Smarandache, M. Parimala, M. Karthika
Mathematics and Statistics Faculty and Staff Publications
The notion of fuzzy sets initiated to overcome the uncertainty of an object. Fuzzy topological space, intuitionistic fuzzy sets in topological structure space, vagueness in topological structure space, rough sets in topological space, theory of hesitancy and neutrosophic topological space, etc. are the extension of fuzzy sets. Soft set is a family of parameters which is also a set. Fuzzy soft topological space, intuitionistic fuzzy soft and neutrosophic soft topological space are obtained by incorporating soft sets with various topological structures. This motivates to write a review and study on various soft set concepts. This paper shows the detailed review ...
An Expanded Model Of Unmatter From Neutrosophic Logic Perspective: Towards Matter-Spirit Unity View,
2020
University of New Mexico
An Expanded Model Of Unmatter From Neutrosophic Logic Perspective: Towards Matter-Spirit Unity View, Florentin Smarandache, Victor Christianto, Robert Neil Boyd
Mathematics and Statistics Faculty and Staff Publications
In Neutrosophic Logic, a basic assertion is that there are variations of about everything that we can measure; the variations surround three parameters called T, I, F (truth, indeterminacy, falsehood) which can take a range of values. A previous paper in IJNS, 2020 shortly reviews the links among aether and matter creation from the perspective of Neutrosophic Logic. In any case, matter creation process in nature stays a major puzzle for physicists, scientists and other science analysts. To this issue neutrosophic logic offers an answer: "unmatter." This paper examines an extended model of unmatter, to incorporate issue soul solidarity. So ...
Combination Of The Single-Valued Neutrosophic Fuzzy Set And The Soft Set With Applications In Decision-Making,
2020
University of New Mexico
Combination Of The Single-Valued Neutrosophic Fuzzy Set And The Soft Set With Applications In Decision-Making, Florentin Smarandache, Ahmed Mostafa Khalil, Dunqian Chao, A. A. Azzam, W. Alharby
Mathematics and Statistics Faculty and Staff Publications
In this article, we propose a novel concept of the single-valued neutrosophic fuzzy soft set by combining the single-valued neutrosophic fuzzy set and the soft set. For possible applications, five kinds of operations (e.g., subset, equal, union, intersection, and complement) on single-valued neutrosophic fuzzy soft sets are presented. Then, several theoretical operations of single-valued neutrosophic fuzzy soft sets are given. In addition, the first type for the fuzzy decision-making based on single-valued neutrosophic fuzzy soft set matrix is constructed. Finally, we present the second type by using the AND operation of the single-valued neutrosophic fuzzy soft set for fuzzy ...
Intelligent Algorithm For Trapezoidal Interval Valued Neutrosophic Network Analysis,
2020
University of New Mexico
Intelligent Algorithm For Trapezoidal Interval Valued Neutrosophic Network Analysis, Florentin Smarandache, Said Broumi, Deivanayagampillai Nagarajan, Malayalan Lathamaheswari, Mohamed Talea, Assia Bakali
Mathematics and Statistics Faculty and Staff Publications
The shortest path problem has been one of the most fundamental practical problems in network analysis. One of the good algorithms is Bellman-Ford, which has been applied in network, for the last some years. Due to complexity in the decision-making process, the decision makers face complications to express their view and judgment with an exact number for single valued membership degrees under neutrosophic environment. Though the interval number is a special situation of the neutrosophic, it did not solve the shortest path problems in an absolute manner. Hence, in this work, the authors have introduced the score function and accuracy ...
