Logic and Foundations Commons^™

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 Bi-Ideals 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 bi-ideals in ordered semigroups is introduced. The concept of interval valued fuzzy generalized bi-ideals is initiated and several properties and characterizations are provided. A condition for an interval valued fuzzy generalized bi-ideal to be an interval valued fuzzy generalized bi-ideal is obtained. Using implication operators and the notion of implication-based an interval valued fuzzy generalized bi-ideal, characterizations of an interval valued fuzzy generalized bi-ideal and an interval valued fuzzy generalized bi-ideal are considered.

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

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

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 hyperfinite-dimensional 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

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

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

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 Leyva-Vazquez

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, …

Covid-19 And Knowledge Based Computation, Rohit J. Parikh

Publications and Research

The problem of dealing with Covid-19, 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 …

Theory And Application Of Hypersoft Set, Florentin Smarandache, Muhammad Saeed, Muhammad Saqlain, Mohamed Abdel-Baset

Branch Mathematics and Statistics Faculty and Staff Publications

Aims and Scope Florentin Smarandache generalize the soft set to the hypersoft set by transforming the function �� into a multi-argument function. This extension reveals that the hypersoft set with neutrosophic, intuitionistic, and fuzzy set theory will be very helpful to construct a connection between alternatives and attributes. Also, the hypersoft set will reduce the complexity of the case study. The Book “Theory and Application of Hypersoft Set” focuses on theories, methods, algorithms for decision making and also applications involving neutrosophic, intuitionistic, and fuzzy information. Our goal is to develop a strong relationship with the MCDM solving techniques and to …

Some Model Theory Of Free Groups, Christopher James Natoli

Dissertations, Theses, and Capstone Projects

There are two main sets of results, both pertaining to the model theory of free groups. In the first set of results, we prove that non-abelian free groups of finite rank at least 3 or of countable rank are not A-homogeneous. We then build on the proof of this result to show that two classes of groups, namely finitely generated free groups and finitely generated elementary free groups, fail to form A-Fraisse classes and that the class of non-abelian limit groups fails to form a strong A-Fraisse class.

The second main result is that if a countable group is elementarily …

Mathematical Zendo: A Game Of Patterns And Logic, Philip Deorsey, Corey Pooler, Michael Ferrara

Journal of Math Circles

Mathematical Zendo is a logic game that actively engages participants in pattern recognition, problem solving, and critical thinking while providing a fun opportunity to explore all manner of mathematical objects. Based upon the popular game of Zendo, created by Looney Labs, Mathematical Zendo centers on a secret rule, chosen by the leader, that must be guessed by teams of players. In each round of the game, teams provide examples of the mathematical object of interest (e.g. functions, numbers, sets) and receive information about whether their guesses do or do not satisfy the secret rule. In this paper, we introduce Mathematical …

Occam Manual, Martin Zwick

Systems Science Faculty Publications and Presentations

Occam is a Discrete Multivariate Modeling (DMM) tool based on the methodology of Reconstructability Analysis (RA). Its typical usage is for analysis of problems involving large numbers of discrete variables. Models are developed which consist of one or more components, which are then evaluated for their fit and statistical significance. Occam can search the lattice of all possible models, or can do detailed analysis on a specific model.

In Variable-Based Modeling (VBM), model components are collections of variables. In State-Based Modeling (SBM), components identify one or more specific states or substates.

Occam provides a web-based interface, which …

Using Mobile Technology To Promote Higher-Order Thinking Skills In Elementary Mathematics, Debbie Marie Versoza, Ma. Louise Antonette N. De Las Peñas, Jumela F. Sarmiento, Maria Alva Q. Aberin, Mark Anthony C. Tolentino, Mark L. Loyola

Mathematics Faculty Publications

The problem of rote-based learning in mathematics is well documented. Mobile technology can provide a potential solution, especially when application (app) design is based on sound pedagogical principles and gamification elements. However, an inventory of available mobile apps for mathematics reveals that many of the available apps are guided by a behaviorist perspective that favors repetition over meaningful learning. This paper reports on the design of mobile mathematics apps that harness gamification techniques to promote higher-order thinking skills (HOTS) even in basic elementary school concepts such as number comparison, and addition and subtraction. The integration of these apps in the …

Fuzzy Solutions To Second Order Three Point Boundary Value Problem, Dimplekumar N. Chalishajar, R. Ramesh

Applications and Applied Mathematics: An International Journal (AAM)

In this manuscript, the proposed work is to study the existence of second-order differential equations with three point boundary conditions. Existence is proved using fuzzy set valued mappings of a real variable whose values are normal, convex, upper semi continuous and compactly supported fuzzy sets. The sufficient conditions are also provided to establish the existence results of fuzzy solutions of second order differential equations for three point boundary value problem. By using Banach fixed point principle, a new existence theorem of solutions for these equations in the metric space of normal fuzzy convex sets with distance given by the maximum …

On Double Fuzzy M-Open Mappings And Double Fuzzy M-Closed Mappings, J. Sathiyaraj, A. Vadivel, O. U. Maheshwari

Applications and Applied Mathematics: An International Journal (AAM)

We introduce and investigate some new class of mappings called double fuzzy M-open map and double fuzzy M-closed map in double fuzzy topological spaces. Also, some of their fundamental properties are studied. Moreover, we investigate the relationships between double fuzzy open, double fuzzy θ semiopen, double fuzzy δ preopen, double fuzzy M open and double fuzzy e open and their respective closed mappings.

The Lattice Of Intuitionistic Fuzzy Topologies Generated By Intuitionistic Fuzzy Relations, Soheyb Milles

Applications and Applied Mathematics: An International Journal (AAM)

We generalize the notion of fuzzy topology generated by fuzzy relation given by Mishra and Srivastava to the setting of intuitionistic fuzzy sets. Some fundamental properties and necessary examples are given. More specifically, we provide the lattice structure to a family of intuitionistic fuzzy topologies generated by intuitionistic fuzzy relations. To that end, we study necessary structural characteristics such as distributivity, modularity and complementary of this lattice.

Structure, Neutrostructure, And Antistructure In Science, Florentin Smarandache

Branch 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 of …

Introduction To Neutrosophic Genetics, Florentin Smarandache

Branch 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.