Generalizations And Alternatives Of Classical Algebraic Structures To Neutroalgebraic Structures And Antialgebraic Structures, 2020 University of New Mexico

#### Generalizations And Alternatives Of Classical Algebraic Structures To Neutroalgebraic Structures And Antialgebraic Structures, Florentin Smarandache

*Mathematics and Statistics Faculty and Staff Publications*

In this paper we present the development from paradoxism to neutrosophy, which gave birth to neutrosophic set and logic and especially to NeutroAlgebraic Structures (or NeutroAlgebras) and AntiAlgebraic Structures (or AntiAlgebras) that are generalizations and alternatives of the classical algebraic structures.

Interval Valued Neutrosophic Shortest Path Problem By A* Algorithm, 2020 University of New Mexico

#### Interval Valued Neutrosophic Shortest Path Problem By A* Algorithm, Florentin Smarandache, S. Khrisna Prabha, Said Broumi

*Mathematics and Statistics Faculty and Staff Publications*

Many researchers have been proposing various algorithms to unravel different types of fuzzy shortest path problems. There are many algorithms like Dijkstra’s, Bellman-Ford,Floyd-Warshall and kruskal’s etc are existing for solving the shortest path problems. In this work a shortest path problem with interval valued neutrosophic numbers is investigated using the proposed algorithm. A* algorithm is extensively applied in pathfinding and graph traversal.Unlike the other algorithms mentioned above, A* algorithm entails heuristic function to uncover the cost of path that traverses through the particular state. In the structured work A* algorithm is applied to unravel the length ...

Neutroalgebra Is A Generalization Of Partial Algebra, 2020 University of New Mexico

#### Neutroalgebra Is A Generalization Of Partial Algebra, Florentin Smarandache

*Mathematics and Statistics Faculty and Staff Publications*

In this paper we recall, improve, and extend several definitions, properties and applications of our previous 2019 research referred to NeutroAlgebras and AntiAlgebras (also called NeutroAlgebraic Structures and respectively AntiAlgebraic Structures). Let be an item (concept, attribute, idea, proposition, theory, etc.). Through the process of neutrosphication, we split the nonempty space we work on into three regions {two opposite ones corresponding to and , and one corresponding to neutral (indeterminate) (also denoted ) between the opposites}, which may or may not be disjoint – depending on the application, but they are exhaustive (their union equals the whole space). A NeutroAlgebra is an algebra ...

Fifteenth International Photovideoanthology On Paradoxism, 2020 University of New Mexico

#### Fifteenth International Photovideoanthology On Paradoxism, Florentin Smarandache

*Mathematics and Statistics Faculty and Staff Publications*

*Paradoxism is an international movement in science and culture, founded by Florentin Smarandache in 1980s, based on excessive use of antitheses, oxymoron, contradictions, and paradoxes. During three decades (1980-2020) hundreds of authors from tenth of countries around the globe **contributed papers to 15 international paradoxist anthologies.*

*In 1995, the author extended the paradoxism to a new branch of philosophy called neutrosophy, that gave birth to many scientific branches, such as: neutrosophic logic, neutrosophic set, neutrosophic probability and statistics, neutrosophic algebraic structures and so on with multiple applications in engineering, computer science, administrative work, medical research etc.*

“May your imagination blossom ...

Generalizations And Alternatives Of Classical Algebraic Structures To Neutroalgebraic Structures And Antialgebraic Structures, 2020 University of New Mexico

#### Generalizations And Alternatives Of Classical Algebraic Structures To Neutroalgebraic Structures And Antialgebraic Structures, Florentin Smarandache

*Mathematics and Statistics Faculty and Staff Publications*

In this paper we present the development from paradoxism to neutrosophy, which gave birth to neutrosophic set and logic and especially to NeutroAlgebraic Structures (or NeutroAlgebras) and AntiAlgebraic Structures (or AntiAlgebras) that are generalizations and alternatives of the classical algebraic structures.

Introduction To Game Theory: A Discovery Approach, 2020 Linfield College

#### Introduction To Game Theory: A Discovery Approach, Jennifer Firkins Nordstrom

*Linfield Authors Book Gallery*

Game theory is an excellent topic for a non-majors quantitative course as it develops mathematical models to understand human behavior in social, political, and economic settings. The variety of applications can appeal to a broad range of students. Additionally, students can learn mathematics through playing games, something many choose to do in their spare time! This text also includes an exploration of the ideas of game theory through the rich context of popular culture. It contains sections on applications of the concepts to popular culture. It suggests films, television shows, and novels with themes from game theory. The questions in ...

A Coherent Proof Of Mac Lane's Coherence Theorem, 2020 Claremont Colleges

#### A Coherent Proof Of Mac Lane's Coherence Theorem, Luke Trujillo

*HMC Senior Theses*

Mac Lane’s Coherence Theorem is a subtle, foundational characterization of monoidal categories, a categorical concept which is now an important and popular tool in areas of pure mathematics and theoretical physics. Mac Lane’s original proof, while extremely clever, is written somewhat confusingly. Many years later, there still does not exist a fully complete and clearly written version of Mac Lane’s proof anywhere, which is unfortunate as Mac Lane’s proof provides very deep insight into the nature of monoidal categories. In this thesis, we provide brief introductions to category theory and monoidal categories, and we offer a ...

Modest Automorphisms Of Presburger Arithmetic, 2019 The Graduate Center, City University of New York

#### Modest Automorphisms Of Presburger Arithmetic, Simon Heller

*Dissertations, Theses, and Capstone Projects*

It is interesting to consider whether a structure can be expanded by an automorphism so that one obtains a nice description of the expanded structure's first-order properties. In this dissertation, we study some such expansions of models of Presburger arithmetic. Building on some of the work of Harnik (1986) and Llewellyn-Jones (2001), in Chapter 2 we use a back-and-forth construction to obtain two automorphisms of sufficiently saturated models of Presburger arithmetic. These constructions are done first in the quotient of the Presburger structure by the integers (which is a divisible ordered abelian group with some added structure), and then ...

A Hybrid Plithogenic Decision-Making Approach With Quality Function Deployment For Selecting Supply Chain Sustainability Metrics, 2019 University of New Mexico

#### A Hybrid Plithogenic Decision-Making Approach With Quality Function Deployment For Selecting Supply Chain Sustainability Metrics, Florentin Smarandache, Mohamed Abdel-Basset, Rehab Mohamed, Abd El-Nasser H. Zaied

*Mathematics and Statistics Faculty and Staff Publications*

Supply chain sustainability has become one of the most attractive decision management topics. There are many articles that have focused on this ﬁeld presenting many diﬀerent points of view. This research is centred on the evaluation of supply chain sustainability based on two critical dimensions. The ﬁrst is the importance of evaluation metrics based on economic, environmental and social aspects, and the second is the degree of diﬃculty of information gathering. This paper aims to increase the accuracy of the evaluation. The proposed method is a combination of quality function deployment (QFD) with plithogenic aggregation operations. The aggregation operation is ...

Category Theory And Universal Property, 2019 Union College - Schenectady, NY

#### Category Theory And Universal Property, Niuniu Zhang

*Honors Theses*

Category theory unifies and formalizes the mathematical structure and concepts in a way that various areas of interest can be connected. For example, many have learned about the sets and its functions, the vector spaces and its linear transformation, and the group theories and its group homomorphism. Not to mention the similarity of structure in topological spaces, as the continuous function is its mapping. In sum, category theory represents the abstractions of other mathematical concepts. Hence, one could use category theory as a new language to define and simplify the existing mathematical concepts as the universal properties. The goal of ...

Computable Reducibility Of Equivalence Relations, 2019 Boise State University

#### Computable Reducibility Of Equivalence Relations, Marcello Gianni Krakoff

*Boise State University Theses and Dissertations*

Computable reducibility of equivalence relations is a tool to compare the complexity of equivalence relations on natural numbers. Its use is important to those doing Borel equivalence relation theory, computability theory, and computable structure theory. In this thesis, we compare many naturally occurring equivalence relations with respect to computable reducibility. We will then define a jump operator on equivalence relations and study proprieties of this operation and its iteration. We will then apply this new jump operation by studying its effect on the isomorphism relations of well-founded computable trees.

Formally Verifying Peano Arithmetic, 2019 Boise State University

#### Formally Verifying Peano Arithmetic, Morgan Sinclaire

*Boise State University Theses and Dissertations*

This work is concerned with implementing Gentzen’s consistency proof in the Coq theorem prover.

In Chapter 1, we summarize the basic philosophical, historical, and mathematical background behind this theorem. This includes the philosophical motivation for attempting to prove the consistency of Peano arithmetic, which traces itself from the first attempted axiomatizations of mathematics to the maturation of Hilbert’s program. We introduce many of the basic concepts in mathematical logic along the way: first-order logic (*FOL*), Peano arithmetic (*PA*), primitive recursive arithmetic (*PRA*), Gödel's 2nd Incompleteness theorem, and the ordinals below ε_{0}.

In Chapter 2, we give ...

Algorithmic Randomness And Fourier Analysis, 2019 Hofstra University

#### Algorithmic Randomness And Fourier Analysis, Johanna N. Y. Franklin, Timothy H. Mcnicholl, Jason Rute

*Mathematics Publications*

Suppose 1 < p < ∞. Carleson’s Theorem states that the Fourier series of any function in Lᵖ[−π, π] converges almost everywhere. We show that the Schnorr random points are precisely those that satisfy this theorem for every f ∈ Lᵖ[−π, π] given natural computability conditions on f and p.

Extension Of Soft Set To Hypersoft Set, And Then To Plithogenic Hypersoft Set, 2019 University of New Mexico

#### Extension Of Soft Set To Hypersoft Set, And Then To Plithogenic Hypersoft Set, Florentin Smarandache

*Mathematics and Statistics Faculty and Staff Publications*

In this paper, we generalize the soft set tothe hypersoft set by transforming the function F into a multi-attribute function. Then we introduce the hybrids of Crisp, Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Hypersoft Set.

Experience Of A Noyce-Student Learning Assistant In An Inquiry-Based Learning Class, 2019 University of Nebraska at Omaha

#### Experience Of A Noyce-Student Learning Assistant In An Inquiry-Based Learning Class, Melissa Riley

*Student Research and Creative Activity Fair*

This presentation refers to an undergraduate course called introduction to abstract mathematics at the University of Nebraska at Omaha. During the academic year 2017-2018, undergraduate, mathematics student Melissa Riley was a Noyce-student learning assistant for the Inquiry Based Learning (IBL) section of the course. She assisted the faculty-in-charge with all aspects of the course. These included: materials preparation, class organization, teamwork, class leading, presentations, and tutoring. This presentation shall address some examples of how the IBL approach can be used in this type of class including: the structure of the course, the activities and tasks performed by the students, learning ...

Extending Set Functors To Generalised Metric Spaces, 2019 University Politehnica of Bucharest

#### Extending Set Functors To Generalised Metric Spaces, Adriana Balan, Alexander Kurz, Jiří Velebil

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

For a commutative quantale V, the category V-cat can be perceived as a category of generalised metric spaces and non-expanding maps. We show that any type constructor T (formalised as an endofunctor on sets) can be extended in a canonical way to a type constructor T_{V} on V-cat. The proof yields methods of explicitly calculating the extension in concrete examples, which cover well-known notions such as the Pompeiu-Hausdorff metric as well as new ones.

Conceptually, this allows us to to solve the same recursive domain equation X ≅ TX in different categories (such as sets and metric spaces) and we ...

A Short Remark On Gödel Incompleteness Theorem And Its Self-Referential Paradox From Neutrosophic Logic Perspective, 2019 University of New Mexico

#### A Short Remark On Gödel Incompleteness Theorem And Its Self-Referential Paradox From Neutrosophic Logic Perspective, Florentin Smarandache, Victor Christianto

*Mathematics and Statistics Faculty and Staff Publications*

It is known from history of mathematics, that Gödel submitted his two incompleteness theorems, which can be considered as one of hallmarks of modern mathematics in 20th century. Here we argue that Gödel incompleteness theorem and its self-referential paradox have not only put Hilbert’s axiomatic program into question, but he also opened up the problem deep inside the then popular Aristotelian Logic. Although there were some attempts to go beyond Aristotelian binary logic, including by Lukasiewicz’s three-valued logic, here we argue that the problem of self-referential paradox can be seen as reconcilable and solvable from Neutrosophic Logic perspective ...

Special Issue: New Types Of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/Under-/ Off-Set, Neutrosophic Refined Set, And Their Extension To Plithogenic Set/Logic/ Probability, With Applications, 2019 University of New Mexico

#### Special Issue: New Types Of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/Under-/ Off-Set, Neutrosophic Refined Set, And Their Extension To Plithogenic Set/Logic/ Probability, With Applications, Florentin Smarandache

*Mathematics and Statistics Faculty and Staff Publications*

No abstract provided.

Special Subset Vertex Multisubgraphs For Multi Networks, 2019 University of New Mexico

#### Special Subset Vertex Multisubgraphs For Multi Networks, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilanthenral K

*Mathematics and Statistics Faculty and Staff Publications*

In this book authors study special type of subset vertex multi subgraphs; these multi subgraphs can be directed or otherwise. Another special feature of these subset vertex multigraphs is that we are aware of the elements in each vertex set and how it affects the structure of both subset vertex multisubgraphs and edge multisubgraphs. It is pertinent to record at this juncture that certain ego centric directed multistar graphs become empty on the removal of one edge, there by theorising the importance, and giving certain postulates how to safely form ego centric multi networks. Given any subset vertex multigraph we ...

Plithogenic Fuzzy Whole Hypersoft Set, Construction Of Operators And Their Application In Frequency Matrix Multi Attribute Decision Making Technique, 2019 University of New Mexico

#### Plithogenic Fuzzy Whole Hypersoft Set, Construction Of Operators And Their Application In Frequency Matrix Multi Attribute Decision Making Technique, Florentin Smarandache, Shazia Rana, Madiha Qayyum, Muhammad Saeed, Bakhtawar Ali Khan

*Mathematics and Statistics Faculty and Staff Publications*

In this paper, initially a matrix representation of Plithogenic Hypersoft Set (PHSS) is introduced and then with the help of this matrix some local operators for Plithogenic Fuzzy Hypersoft set (PFHSS) are developed. These local operators are used to generalize PFHSS to Plithogenic Fuzzy Whole Hypersoft set (PFWHSS). The generalized PFWHSS set is hybridization of Fuzzy Hypersoft set (which represent multiattributes and their subattributes as a combined whole membership i.e. case of having an exterior view of the event) and the Plithogenic Fuzzy Hypersoft set (in which multi attributes and their subattributes are represented with individual memberships case of ...