Logic and Foundations Commons^™

(R1500) Type-I 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 Type-I 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 Type-I generalized soft set model. We introduce a similarity measure based on the Type-I …

(R2022) Mathematical Modelling Of Tuberculosis And Covid-19 Co-Infection In India: A Real Data Analysis On Concomitant Diseases, Vijai Shanker Verma, Harshita Kaushik, Archana Singh Bhadauria

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we have proposed an epidemiological model to study the dynamics of two concomitant diseases Tuberculosis (TB) and COVID-19. Here, we have formulated a deterministic compartmental model as an extended form of the classical SIS model. First, the basic reproduction number R₀ is derived and then stability analysis of the model is done. It is observed that the disease-free equilibrium is stable when R₀ is less than one and the endemic equilibrium is stable only when R₀ is greater than one. Numerical simulation is carried out to illustrate the theoretical findings and to study the …

(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 SFS-positive and SFS-negative ideal solutions. The TOPSIS and VIKOR methods provide decision-making …

(R1960) Connectedness And Compactness In Fuzzy Nano Topological Spaces Via Fuzzy Nano Z Open Sets, R. Thangammal, M. Saraswathi, A. Vadivel, C. John Sundar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study the notion of fuzzy nano Z connected spaces, fuzzy nano Z disconnected spaces, fuzzy nano Z compact spaces and fuzzy nano Z separated sets in fuzzy nano topological spaces. We also give some properties and theorems of such concepts with connectedness and compactness in fuzzy nano topological spaces.

(R1976) A Novel Approach To Solve Fuzzy Rough Matrix Game With Two Players, Vinod Jangid, Ganesh Kumar, Gaurav Sharama, Vishnu Narayan Mishra

Applications and Applied Mathematics: An International Journal (AAM)

This paper proposes a new method for solving a two-person zero-sum fuzzy matrix game with goals, payoffs, and decision variables represented as triangular fuzzy rough numbers. We created a pair of fully fuzzy rough linear programming problems for players. Triangular fuzzy rough numbers can be used to formulate two fuzzy linear programming problems for the first player in the form of upper approximation intervals and lower approximation intervals. Two problems for the second player can be created in the same way. These problems have been split into five sub-crisp problems for the player first and five sub-crisp problems for the …

(Si10-123) 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 higher-order 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

Dissertations, Theses, and Capstone Projects

We explore the consequences of various model-theoretic 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 well-behaved. On the other hand, it has been shown that pseudofinite dimension is not necessarily well-behaved 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 ill-behaved in all such ultraproducts. Additionally, we have novel results connecting various forms of asymptotic classes …

Algorithmic Criterion Of Locally Finite Separability Of Algebras Represented Over Equivalence Α2 ∪ Id Ω, Sarvar Zhavliev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

It has been established that for equivalences of the form α² ∪ id ω, the locally finite separability of any universal algebra represented over it is equivalent to the immune of the complement α. It is shown that for finitely separable algebras this criterion does not meet.

Unomaha Problem Of The Week (2021-2022 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 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 to …

(R1956) Neutrosophic Soft E-Compact 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 e-compactness is presented on neutrosophic soft topological spaces using the definition of e-open cover and its types. In addition, neutrosophic soft e-compactness and neutrosophic soft e-separation axioms are associated. Also, the concept of neutrosophic soft locally e-compactness 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.

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

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

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

Senior Projects Spring 2022

Type unification takes type inference a step further by allowing non-local 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

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 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 …

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 follow-up 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 well-studied 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 …

Interpolation And Sampling In Analytic Tent Spaces, Caleb Parks

Graduate Theses and Dissertations

Introduced by Coifman, Meyer, and Stein, the tent spaces have seen wide applications in harmonic analysis. Their analytic cousins have seen some applications involving the derivatives of Hardy space functions. Moreover, the tent spaces have been a recent focus of research. We introduce the concept of interpolating and sampling sequences for analytic tent spaces analogously to the same concepts for Bergman spaces. We then characterize such sequences in terms of Seip's upper and lower uniform density. We accomplish this by exploiting a kind of Mobius invariance for the tent spaces.

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.

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 …