There Is No Constant In Physics: A Neutrosophic Explanation, 2020 University of New Mexico

#### There Is No Constant In Physics: A Neutrosophic Explanation, Victor Christianto, Robert Neil Boyd, Florentin Smarandache

*Branch 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. Similarly, in this paper we consider NL applications in physics constants. Those constants actually all have a window of plus and minus values, relative to the average value of the constant. For example, speed of light, c, can vary in a window up to +/- 3000 m/s. Therefore it should be written: 300000 km/s +/- 3 km/s. We also discuss some implications of this new …

N-Refined Neutrosophic Vector Spaces, 2020 University of New Mexico

#### N-Refined Neutrosophic Vector Spaces, Florentin Smarandache, Mohammad Abobala

*Branch Mathematics and Statistics Faculty and Staff Publications*

This paper introduces the concept of n-refined neutrosophic vector spaces as a generalization of neutrosophic vector spaces, and it studies elementary properties of them. Also, this work discusses some corresponding concepts such as weak/strong n-refined neutrosophic vector spaces, and n-refined neutrosophic homomorphisms.

Plithogenic N- Super Hypergraph In Novel Multi -Attribute Decision Making, 2020 University of New Mexico

#### Plithogenic N- Super Hypergraph In Novel Multi -Attribute Decision Making, Florentin Smarandache, Nivetha Martin

*Branch Mathematics and Statistics Faculty and Staff Publications*

An optimal decision-making environment demands feasible Multi-Attribute Decision-Making methods. Plithogenic n – Super Hypergraph introduced by Smarandache is a novel concept and it involves many attributes. This article aims to bridge the concept of Plithogenic n-Super Hypergraph in the vicinity of optimal decision making. This research work introduces the novel concepts of enveloping vertex, super enveloping vertex, dominant enveloping vertex, classification of the dominant enveloping vertex (input, intervene, output dominant enveloping vertices), plithogenic connectors. An application of Plithogenic n-super hypergraph in making optimum decisions is discussed under various decision-making scenarios. Several insights are drawn from this research work and will …

Three Possible Applications Of Neutrosophic Logic In Fundamental And Applied Sciences, 2020 University of New Mexico

#### Three Possible Applications Of Neutrosophic Logic In Fundamental And Applied Sciences, Victor Christianto, Robert Neil Boyd, Florentin Smarandache

*Branch 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. This paper shortly reviews the links among aether and matter creation from the perspective of Neutrosophic Logic. Once we accept the existence of aether as physical medium, then we can start to ask on what causes matter ejection, as observed in various findings related to quasars etc. One particular cosmology model known as VMH (variable mass hypothesis) has been suggested by notable astrophysicists like Halton …

N-Refined Neutrosophic Rings, 2020 University of New Mexico

#### N-Refined Neutrosophic Rings, Florentin Smarandache, Mohammad Abobala

*Branch Mathematics and Statistics Faculty and Staff Publications*

The aim of this paper is to introduce the concept of n-refined neutrosophic ring as a generalization of refined neutrosophic ring. Also, we present concept of n-refined polynomial ring. We study some basic concepts related to these rings such as AH-subrings, AH-ideals, AH-factors, and AH-homomorphisms.

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 precise, clear development of …

Fuzzy Semi-S-Irresolute Continuous Mappings In Šostak’S Fuzzy Topological Spaces, 2019 Government Arts College, Chidambaram

#### Fuzzy Semi-S-Irresolute Continuous Mappings In Šostak’S Fuzzy Topological Spaces, B. Vijayalakshmi, J. Praba, M. Saraswathi, A. Vadivel

*Applications and Applied Mathematics: An International Journal (AAM)*

In this paper, the concepts of fuzzy semi-S-irresolute open map, fuzzy semi-S-irresolute closed map and fuzzy semi-S-irresolute homeomorphism to the fuzzy topological spaces in Šostak’s sense are introduced and studied. Some of their characteristic properties are considered. Also a comparison between these new types of functions are established by giving examples.

New Notions From (R; S)-Generalized Fuzzy E-Open Sets, 2019 Government Arts College (Autonomous), Karur

#### New Notions From (R; S)-Generalized Fuzzy E-Open Sets, A. Vadivel, P. Periyasamy, V. Chandrasekar, G. Saravanakumar

*Applications and Applied Mathematics: An International Journal (AAM)*

The present article discuss (r; s)-generalized fuzzy e-border, (r; s)-generalized fuzzy e-exterior and (r; s)-generalized fuzzy e-frontier in double fuzzy topologies. Furthermore, some characterizations of generalized double fuzzy e-continuous, generalized double fuzzy e-open, generalized double fuzzy e-closed and generalized double fuzzy e-closure-irresolute functions are studied and investigated. Moreover, the interrelations among the new concepts are discussed with some necessary examples.

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 lifted …

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

*Branch 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 …

Cubic Interior Ideals In Semigroups, 2019 University of Tabuk

#### Cubic Interior Ideals In Semigroups, G. Muhiuddin

*Applications and Applied Mathematics: An International Journal (AAM)*

In this paper we apply the cubic set theory to interior ideals of a semigroup. The notion of cubic interior ideals is introduced, and related properties are investigated. Characterizations of (cubic) interior ideals are established, and conditions for a semigroup to be left (right) simple are provided.

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 …

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 …

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.

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

*Branch 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

*UNO 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 …

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

*Branch 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. Motivation of …

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

*Branch 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

*Branch 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 having …