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Articles 1  30 of 528
FullText Articles in Logic and Foundations
Generations Of Reason: A Family’S Search For Meaning In PostNewtonian England (Book Review), Calvin Jongsma
Generations Of Reason: A Family’S Search For Meaning In PostNewtonian England (Book Review), Calvin Jongsma
Faculty Work Comprehensive List
Reviewed Title: Generations of Reason: A Family's Search for Meaning in PostNewtonian England by Joan L. Richards. New Haven, CT: Yale University Press, 2021. 456 pp. ISBN: 9780300255492.
Richard Whately's Revitalization Of Syllogistic Logic, Calvin Jongsma
Richard Whately's Revitalization Of Syllogistic Logic, Calvin Jongsma
Faculty Work Comprehensive List
This is an expanded version of the first chapter Richard Whately’s Revitalization of Syllogistic Logic in Aristotle’s Syllogism and the Creation of Modern Logic edited by Lukas M. Verburgt and Matteo Cosci (Bloomsbury, 2023). Drawing upon the author’s 1982 Ph. D. dissertation (https://digitalcollections.dordt.edu/faculty_work/230/ ) and more current scholarship, this essay traces the critical historical background to Whately’s work in more detail than could be done in the published version.
SelfReference And Diagonalisation, Joël A. Doat
SelfReference And Diagonalisation, Joël A. Doat
Journal of Humanistic Mathematics
This poem is an exercise on selfreference and diagonalisation in mathematics featuring Turing’s proof of the undecidability of the halting problem, Cantor’s cardinality argument, the BuraliForti paradox, and Epimenides' liar paradox.
Using Bloom's Taxonomy For Math Outreach Within And Outside The Classroom, Manmohan Kaur
Using Bloom's Taxonomy For Math Outreach Within And Outside The Classroom, Manmohan Kaur
Journal of Humanistic Mathematics
Not everyone is a great artist, but we don’t often hear, “I dislike art.” Most people are able to appreciate visual arts, music and sports, without necessarily excelling in it themselves. On the other hand, the phrase “I dislike math” is widely prevalent. This is especially ironic in our current society, where mathematics affects our daytoday activities in essential ways such as ecommerce and email. This paper describes the opportunity to popularize mathematics by focusing on its fun and creative aspects, and illustrates this opportunity through a brief discussion of interdisciplinary topics that expose the beauty, elegance and value of …
Completeness Of Nominal Props, Samuel Balco, Alexander Kurz
Completeness Of Nominal Props, Samuel Balco, Alexander Kurz
Engineering Faculty Articles and Research
We introduce nominal string diagrams as string diagrams internal in the category of nominal sets. This leads us to define nominal PROPs and nominal monoidal theories. We show that the categories of ordinary PROPs and nominal PROPs are equivalent. This equivalence is then extended to symmetric monoidal theories and nominal monoidal theories, which allows us to transfer completeness results between ordinary and nominal calculi for string diagrams.
(R1958) On Deferred Statistical Convergence Of Fuzzy Variables, Ömer Kişi, Mehmet Gürdal, Ekrem Savaş
(R1958) On Deferred Statistical Convergence Of Fuzzy Variables, Ömer Kişi, Mehmet Gürdal, Ekrem Savaş
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, within framework credibility theory, we examine several notions of convergence and statistical convergence of fuzzy variable sequences. The convergence of fuzzy variable sequences such as the notion of convergence in credibility, convergence in distribution, convergence in mean, and convergence uniformly virtually certainly via postponed Cesàro mean and a regular matrix are researched using fuzzy variables. We investigate the connections between these concepts. Significant results on deferred statistical convergence for fuzzy variable sequences are thoroughly investigated.
(R1509) Topsis And Vikor Methods For Spherical Fuzzy Soft Set Aggregating Operator Framework, M. Palanikumar, K. Arulmozhi, Lejo J. Manavalan
(R1509) Topsis And Vikor Methods For Spherical Fuzzy Soft Set Aggregating Operator Framework, M. Palanikumar, K. Arulmozhi, Lejo J. Manavalan
Applications and Applied Mathematics: An International Journal (AAM)
The Spherical Fuzzy Soft (SFS) set is a generalization of the Pythagorean fuzzy soft set and the intuitionistic fuzzy soft set. We introduce the concept of aggregating SFS decision matrices based on aggregated operations. The techniques for order of preference by similarity to ideal solution (TOPSIS) and viekriterijumsko kompromisno rangiranje (VIKOR) for the SFS approaches are the strong points of multi criteria group decision making (MCGDM), which is various extensions of fuzzy soft sets. We define a score function based on aggregating TOPSIS and VIKOR methods to the SFSpositive and SFSnegative ideal solutions. The TOPSIS and VIKOR methods provide decisionmaking …
(R1500) TypeI Generalized Spherical Interval Valued Fuzzy Soft Sets In Medical Diagnosis For Decision Making, M. Palanikumar, K. Arulmozhi
(R1500) TypeI Generalized Spherical Interval Valued Fuzzy Soft Sets In Medical Diagnosis For Decision Making, M. Palanikumar, K. Arulmozhi
Applications and Applied Mathematics: An International Journal (AAM)
In the present communication, we introduce the concept of TypeI generalized spherical interval valued fuzzy soft set and define some operations. It is a generalization of the interval valued fuzzy soft set and the spherical fuzzy soft set. The spherical interval valued fuzzy soft set theory satisfies the condition that the sum of its degrees of positive, neutral, and negative membership does not exceed unity and that these parameters are assigned independently. We also propose an algorithm to solve the decision making problem based on a TypeI generalized soft set model. We introduce a similarity measure based on the TypeI …
(Si10123) Comparison Between The Homotopy Perturbation Method And Variational Iteration Method For Fuzzy Differential Equations, P. Chandru, B. Radhakrishnan
(Si10123) Comparison Between The Homotopy Perturbation Method And Variational Iteration Method For Fuzzy Differential Equations, P. Chandru, B. Radhakrishnan
Applications and Applied Mathematics: An International Journal (AAM)
In this article, the authors discusses the numerical simulations of higherorder differential equations under a fuzzy environment by using Homotopy Perturbation Method and Variational Iteration Method. The fuzzy parameter and variables are represented by triangular fuzzy convex normalized sets. Comparison of the results are obtained by the homotopy perturbation method with those obtained by the variational iteration method. Examples are provided to demonstrate the theory.
Asymptotic Classes, Pseudofinite Cardinality And Dimension, Alexander Van Abel
Asymptotic Classes, Pseudofinite Cardinality And Dimension, Alexander Van Abel
Dissertations, Theses, and Capstone Projects
We explore the consequences of various modeltheoretic tameness conditions upon the behavior of pseudofinite cardinality and dimension. We show that for pseudofinite theories which are either Morley Rank 1 or uncountably categorical, pseudofinite cardinality in ultraproducts satisfying such theories is highly wellbehaved. On the other hand, it has been shown that pseudofinite dimension is not necessarily wellbehaved in all ultraproducts of theories which are simple or supersimple; we extend such an observation by constructing simple and supersimple theories in which pseudofinite dimension is necessarily illbehaved in all such ultraproducts. Additionally, we have novel results connecting various forms of asymptotic classes …
Unomaha Problem Of The Week (20212022 Edition), Brad Horner, Jordan M. Sahs
Unomaha Problem Of The Week (20212022 Edition), Brad Horner, Jordan M. Sahs
UNO 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 wellregarded university math competition around, the Putnam Competition, with prizes awarded to topscorers at semester's end. The weekly competition was halted midway through Spring 2020 due to COVID19, but relaunched again in Fall 2021, with massive changes.
Now there are three difficulty tiers to POW problems, roughly corresponding to …
(R1956) Neutrosophic Soft ECompact Spaces And Application Using Entropy Measure, P. Revathi, K. Chitirakala, A. Vadivel
(R1956) Neutrosophic Soft ECompact Spaces And Application Using Entropy Measure, P. Revathi, K. Chitirakala, A. Vadivel
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the concept of neutrosophic soft ecompactness is presented on neutrosophic soft topological spaces using the definition of eopen cover and its types. In addition, neutrosophic soft ecompactness and neutrosophic soft eseparation axioms are associated. Also, the concept of neutrosophic soft locally ecompactness is introduced in neutrosophic soft topological spaces and some of its properties are discussed. Added to that, an application in decision making problem is given using entropy.
Developing Critical Thinking Military Officers, Thor Martinsen
Developing Critical Thinking Military Officers, Thor Martinsen
Mathematica Militaris
Critical thinking is frequently identified as an important trait for military officers. This paper examines critical thinking from a historical, pedagogical, and warfighting perspective. The author uses his experience teaching mathematical reasoning at the Naval Postgraduate School to provide helpful advice for educators charged with teaching deductive and inductive reasoning. The paper argues that critical thinking should be taught early in an officer's career. It emphasizes a systematic and Socratic instructional approach along with the importance of equipping students with the necessary tools to evaluate problemsolving techniques and critique their associated solutions. Finally, the paper discusses Augmented Intelligence and the …
How To Guard An Art Gallery: A Simple Mathematical Problem, Natalie Petruzelli
How To Guard An Art Gallery: A Simple Mathematical Problem, Natalie Petruzelli
The Review: A Journal of Undergraduate Student Research
The art gallery problem is a geometry question that seeks to find the minimum number of guards necessary to guard an art gallery based on the qualities of the museum’s shape, specifically the number of walls. Solved by Václav Chvátal in 1975, the resulting Art Gallery Theorem dictates that ⌊n/3⌋ guards are always sufficient and sometimes necessary to guard an art gallery with n walls. This theorem, along with the argument that proves it, are accessible and interesting results even to one with little to no mathematical knowledge, introducing readers to common concepts in both geometry and graph …
Unknowable Truths: The Incompleteness Theorems And The Rise Of Modernism, Caroline Tvardy
Unknowable Truths: The Incompleteness Theorems And The Rise Of Modernism, Caroline Tvardy
Honors Scholars Collaborative Projects
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 discussed as …
Gödel's Incompleteness Theorems, Derick Swarey
Gödel's Incompleteness Theorems, Derick Swarey
Senior Honors Theses
The Incompleteness Theorems of Kurt Godel are very famous both within and outside of mathematics. They focus on independence and consistency within mathematics and hence a more thorough understanding of these is beneficial to their study. The proofs of the theorems involve many ideas which may be unfamiliar to many, including those of formal systems, Godel numbering, and recursive functions and relations. The arguments themselves mirror the Liar’s Paradox in that Godel constructs a statement asserting its own unprovability and then shows that such a statement and its negation must both be independent of the system, otherwise the system is …
The Algebra Of Type Unification, Verity James Scheel
The Algebra Of Type Unification, Verity James Scheel
Senior Projects Spring 2022
Type unification takes type inference a step further by allowing nonlocal flow of information. By exposing the algebraic structure of type unification, we obtain even more flexibility as well as clarity in the implementation. In particular, the main contribution is an explicit description of the arithmetic of universe levels and consistency of constraints of universe levels, with hints at how row types and general unification/subsumption can fit into the same framework of constraints. The compositional nature of the algebras involved ensure correctness and reduce arbitrariness: properties such as associativity mean that implementation details of type inference do not leak in …
(R1466) Ideals And Filters On A Lattice In Neutrosophic Setting, Lemnaouar Zedam, Soheyb Milles, Abdelhamid Bennoui
(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, …
Introduction To Discrete Mathematics: An Oer For Ma471, Mathieu Sassolas
Introduction To Discrete Mathematics: An Oer For Ma471, 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 firstorder , and the construction of proofs, both formally and humantargeted. 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 …
Contributions To The Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya
Contributions To The Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya
Department of Mathematics Facuty Scholarship and Creative Works
This issue showcases a compilation of papers on fluid mechanics (FM) education, covering different sub topics of the subject. The success of the first volume [1] prompted us to consider another followup special issue on the topic, which has also been very successful in garnering an impressive variety of submissions. As a classical branch of science, the beauty and complexity of fluid dynamics cannot be overemphasized. This is an extremely wellstudied subject which has now become a significant component of several major scientific disciplines ranging from aerospace engineering, astrophysics, atmospheric science (including climate modeling), biological and biomedical science …
Negative Representability Degree Structures Of Linear Orders With Endomorphisms, Nadimulla Kasymov, Sarvar Javliyev
Negative Representability Degree Structures Of Linear Orders With Endomorphisms, Nadimulla Kasymov, Sarvar Javliyev
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
The structure of partially ordered sets of degrees of negative representability of linear orders with endomorphisms is studied. For these structures, the existence of incomparable, maximum and minimum degrees, infinite chains and antichains is established,and also considered connections with the concepts of reducibility of enumerations, splittable degrees and positive representetions.
On The Generalization Of Interval Valued Fuzzy Generalized BiIdeals In Ordered Semigroups, Muhammad S. Ali Khan, Saleem Abdullah, Kostaq Hila
On The Generalization Of Interval Valued Fuzzy Generalized BiIdeals In Ordered Semigroups, Muhammad S. Ali Khan, Saleem Abdullah, Kostaq Hila
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a new general form than interval valued fuzzy generalized biideals in ordered semigroups is introduced. The concept of interval valued fuzzy generalized biideals is initiated and several properties and characterizations are provided. A condition for an interval valued fuzzy generalized biideal to be an interval valued fuzzy generalized biideal is obtained. Using implication operators and the notion of implicationbased an interval valued fuzzy generalized biideal, characterizations of an interval valued fuzzy generalized biideal and an interval valued fuzzy generalized biideal are considered.
Hamacher Operations Of Fermatean Fuzzy Matrices, I. Silambarasan
Hamacher Operations Of Fermatean Fuzzy Matrices, I. Silambarasan
Applications and Applied Mathematics: An International Journal (AAM)
The purpose of this study is to extend the Fermatean fuzzy matrices to the theory of Hamacher operations. In this paper, the concept of Hamacher operations of Fermatean fuzzy matrices are introduced and some desirable properties of these operations, such as commutativity, idempotency, and monotonicity are discussed. Further, we prove DeMorgan’s laws over complement for these operations. Furthermore, the scalar multiplication and exponentiation operations of Fermatean fuzzy matrices are constructed and their algebraic properties are investigated. Finally, some properties of necessity and possibility operators of Fermatean fuzzy matrices are proved.
Simplified Intuitionistic Neutrosophic Soft Set And Its Application On Diagnosing Psychological Disorder By Using Similarity Measure, Veerappan Chinnadurai, Albert Bobin
Simplified Intuitionistic Neutrosophic Soft Set And Its Application On Diagnosing Psychological Disorder By Using Similarity Measure, Veerappan Chinnadurai, Albert Bobin
Applications and Applied Mathematics: An International Journal (AAM)
The primary focus of this manuscript comprises three sections. Initially, we introduce the concept of a simplified intuitionistic neutrosophic soft set. We impose an intuitionistic condition between the membership values of truth and falsity such that their sum does not exceed unity. Similarly, for indeterminacy, the membership value is a real number from the closed interval [0, 1]. Hence, the sum of membership values of truth, indeterminacy, and falsity does not exceed two. We present the notion of necessity, possibility, concentration, and dilation operators and establish some of its properties. Second, we define the similarity measure between two simplified intuitionistic …
Applications Of Nonstandard Analysis In Probability And Measure Theory, Irfan Alam
Applications Of Nonstandard Analysis In Probability And Measure Theory, Irfan Alam
LSU Doctoral Dissertations
This dissertation broadly deals with two areas of probability theory and investigates how methods from nonstandard analysis may provide new perspectives in these topics. In particular, we use nonstandard analysis to prove new results in the topics of limiting spherical integrals and of exchangeability.
In the former area, our methods allow us to represent finite dimensional Gaussian measures in terms of marginals of measures on hyperfinitedimensional spheres in a certain strong sense, thus generalizing some previously known results on Gaussian Radon transforms as limits of spherical integrals. This first area has roots in the kinetic theory of gases, which is …
Zariski Geometries And Quantum Mechanics, Milan Zanussi
Zariski Geometries And Quantum Mechanics, Milan Zanussi
Boise State University Theses and Dissertations
Model theory is the study of mathematical structures in terms of the logical relationships they define between their constituent objects. The logical relationships defined by these structures can be used to define topologies on the underlying sets. These topological structures will serve as a generalization of the notion of the Zariski topology from classical algebraic geometry. We will adapt properties and theorems from classical algebraic geometry to our topological structure setting. We will isolate a specific class of structures, called Zariski geometries, and demonstrate the main classification theorem of such structures. We will construct some Zariski structures where the classification …
Lecture 04: Spatial Statistics Applications Of Hrl, Trl, And Mixed Precision, David Keyes
Lecture 04: Spatial Statistics Applications Of Hrl, Trl, And Mixed Precision, David Keyes
Mathematical Sciences Spring Lecture Series
As simulation and analytics enter the exascale era, numerical algorithms, particularly implicit solvers that couple vast numbers of degrees of freedom, must span a widening gap between ambitious applications and austere architectures to support them. We present fifteen universals for researchers in scalable solvers: imperatives from computer architecture that scalable solvers must respect, strategies towards achieving them that are currently well established, and additional strategies currently being developed for an effective and efficient exascale software ecosystem. We consider recent generalizations of what it means to “solve” a computational problem, which suggest that we have often been “oversolving” them at the …
Lecture 00: Opening Remarks: 46th Spring Lecture Series, Tulin Kaman
Lecture 00: Opening Remarks: 46th Spring Lecture Series, Tulin Kaman
Mathematical Sciences Spring Lecture Series
Opening remarks for the 46th Annual Mathematical Sciences Spring Lecture Series at the University of Arkansas, Fayetteville.
The Encyclopedia Of Neutrosophic Researchers  4th Volume (2021), Florentin Smarandache, Maykel LeyvaVazquez
The Encyclopedia Of Neutrosophic Researchers  4th Volume (2021), Florentin Smarandache, Maykel LeyvaVazquez
Branch 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, …
Covid19 And Knowledge Based Computation, Rohit J. Parikh
Covid19 And Knowledge Based Computation, Rohit J. Parikh
Publications and Research
The problem of dealing with Covid19, until a vaccine is universally administered, is to decrease the rate of transmission while getting some social and economic activity going.
Infection passes from one person A to another person B when A is infected and B is susceptible. That is to say that B is not infected and not yet immune.
Social activity also takes place when one person interacts with another. Perhaps A is a taxpayer and B is a tax consultant. Then filing the tax return may take the form of the two of them meeting. Much can be done electronically …