Logic and Foundations Commons^™

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen

Theses and Dissertations (Comprehensive)

The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …

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 …

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.

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 …

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.

Numerical Computations Of Vortex Formation Length In Flow Past An Elliptical Cylinder, Matthew Karlson, Bogdan Nita, Ashwin Vaidya

Department of Mathematics Facuty Scholarship and Creative Works

We examine two dimensional properties of vortex shedding past elliptical cylinders through numerical simulations. Specifically, we investigate the vortex formation length in the Reynolds number regime 10 to 100 for elliptical bodies of aspect ratio in the range 0.4 to 1.4. Our computations reveal that in the steady flow regime, the change in the vortex length follows a linear profile with respect to the Reynolds number, while in the unsteady regime, the time averaged vortex length decreases in an exponential manner with increasing Reynolds number. The transition in profile is used to identify the critical Reynolds number which marks the …

On Product Of Smooth Neutrosophic Topological Spaces, Florentin Smarandache, Kalaivani Chandran, Swathi Sundari Sundaramoorthy, Saeid Jafari

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we develop the notion of the basis for a smooth neutrosophic topology in a more natural way. As a sequel, we define the notion of symmetric neutrosophic quasi-coincident neighborhood systems and prove some interesting results that fit with the classical ones, to establish the consistency of theory developed. Finally, we define and discuss the concept of product topology, in this context, using the definition of basis.

Derivable Single Valued Neutrosophic Graphs Based On Km-Fuzzy Metric, Florentin Smarandache, Mohammad Hamidi

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we consider the concept of KM-fuzzy metric spaces and we introduce a novel concept of KM-single valued neutrosophic metric graphs based on KM-fuzzy metric spaces. Then we investigate the finite KM-fuzzy metric spaces with respect to KM-fuzzy metrics and we construct the KMfuzzy metric spaces on any given non-empty sets. We try to extend the concept of KM-fuzzy metric spaces to a larger class of KM-fuzzy metric spaces such as union and product of KM-fuzzy metric spaces and in this regard we investigate the class of products of KM-single valued neutrosophic metric graphs. In the final, we …

Collaboration (Reacting To The Past/Math/History/Writing), James Hayashi

Q2S Enhancing Pedagogy

This is an assignment for a Freshman level course in the College of Natural Science. By the end students will have an understanding of valid research, collaboration and communication skills. Faculty that chooses to use this assignment will be preparing students for an active learning environment, and understanding a “Big Idea”, valid research, technology and communication skills.

Faculty should give an example of what is valid research. As students are completing this assignment mini deadlines (check-ins) shall be set. With the check-ins for this assignment focus on how the group will communicate the check point and the collaboration.

The focus …

New Challenges In Neutrosophic Theory And Applications, Florentin Smarandache, Stefan Vladutescu, Miihaela Colhon, Wadei Al-Omeri, Saeid Jafari, Muhammad Zahir Khan, Muhammad Farid Khan, Muhammad Aslam, Abdur Razzaque Mughal

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic theory has representatives on all continents and, therefore, it can be said to be a universal theory. On the other hand, according to the three volumes of “The Encyclopedia of Neutrosophic Researchers” (2016, 2018, 2019), plus numerous others not yet included in Encyclopedia book series, about 1200 researchers from 73 countries have applied both the neutrosophic theory and method. Neutrosophic theory was founded by Professor Florentin Smarandache in 1998; it constitutes further generalization of fuzzy and intuitionistic fuzzy theories. The key distinction between the neutrosophic set/logic and other types of sets/logics lies in the introduction of the degree of …

Extension Of Hypergraph To N-Superhypergraph And To Plithogenic N-Superhypergraph, And Extension Of Hyperalgebra To N-Ary (Classical-/Neutro-/Anti-)Hyperalgebra, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

We recall and improve our 2019 concepts of n-Power Set of a Set, n-SuperHyperGraph, Plithogenic n-SuperHyperGraph, and n-ary HyperAlgebra, n-ary NeutroHyperAlgebra, n-ary AntiHyperAlgebra respectively, and we present several properties and examples connected with the real world.

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.

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 …

Induced Hesitant 2-Tuple Linguistic Aggregation Operators With Application In Group Decision Making, Tabasam Rashid, Ismat Beg, Raja N. Jamil

Applications and Applied Mathematics: An International Journal (AAM)

In this article, hesitant 2-tuple linguistic arguments are used to evaluate the group decision making problems which have inter dependent or inter active attributes. Operational laws are developed for hesitant 2-tuple linguistic elements and based on these operational laws hesitant 2- tuple weighted averaging operator and generalized hesitant 2- tuple averaging operator are proposed. Combining Choquet integral with hesitant 2-tuple linguistic information, some new aggregation operators are defined, including the hesitant 2-tuple correlated averaging operator, the hesitant 2-tuple correlated geometric operator and the generalized hesitant 2-tuple correlated averaging operator. These proposed operators successfully manage the correlations among the elements. After …

Strong Degrees In Single Valued Neutrosophic Graphs, Florentin Smarandache, Said Broumi, Assia Bakali, Seema Mehra, Mohamed Talea, Manjeet Singh

Branch Mathematics and Statistics Faculty and Staff Publications

The concept of single valued neutrosophic graphs (SVNGs) generalizes the concept of fuzzy graphs and intuitionistic fuzzy graphs. The purpose of this research paper is to define different types of strong degrees in SVNGs and introduce novel concepts, such as the vertex truth-membership, vertex indeterminacy-membership and falsity-membership sequence in SVNG with proof and numerical illustrations.

Some Studies On Algebraic Integers In Q(I,√3) By Using Coset Diagram, Florentin Smarandache, Saima Anis, Seok-Zun Song, Young Bae Jun

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we studied the action of Picard modular group PSL(2,Z[i])

What Makes A Theory Of Infinitesimals Useful? A View By Klein And Fraenkel, Vladimir Kanovei, Karin Katz, Mikhail Katz, Thomas Mormann

Journal of Humanistic Mathematics

Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the role of Abraham Robinson's framework therein.

Neutrosophic Logic: The Revolutionary Logic In Science And Philosophy -- Proceedings Of The National Symposium, Florentin Smarandache, Huda E. Khalid, Ahmed K. Essa

Branch Mathematics and Statistics Faculty and Staff Publications

The first part of this book is an introduction to the activities of the National Symposium, as well as a presentation of Neutrosophic Scientific International Association (NSIA), based in New Mexico, USA, also explaining the role and scope of NSIA - Iraqi branch. The NSIA Iraqi branch presents a suggestion for the international instructions in attempting to organize NSIA's work. In the second chapter, the pivots of the Symposium are presented, including a history of neutrosophic theory and its applications, the most important books and papers in the advancement of neutrosophics, a biographical note of Prof. Florentin Smarandache in Arabic …

Mod Rectangular Natural Neutrosophic Numbers, Florentin Smarandache, K. Ilanthenral, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors introduce the new notion of MOD rectangular planes. The functions on them behave very differently when compared to MOD planes (square). These are different from the usual MOD planes. Algebraic structures on these MOD rectangular planes are defined and developed. However we have built only MOD interval natural neutrosophic products

Graph Structures In Bipolar Neutrosophic Environment, Florentin Smarandache, Muhammad Akram, Muzzamal Sitara

Branch Mathematics and Statistics Faculty and Staff Publications

A bipolar single-valued neutrosophic (BSVN) graph structure is a generalization of a bipolar fuzzy graph. In this research paper, we present certain concepts of BSVN graph structures. We describe some operations on BSVN graph structures and elaborate on these with examples. Moreover, we investigate some related properties of these operations.

Complex Neutrosophic Soft Set, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Mumtaz Ali, Ganeshsree Selvachandran

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we propose the complex neutrosophic soft set model, which is a hybrid of complex fuzzy sets, neutrosophic sets and soft sets. The basic set theoretic operations and some concepts related to the structure of this model are introduced, and illustrated. An example related to a decision making problem involving uncertain and subjective information is presented, to demonstrate the utility of this model.

From Pythagoreans And Weierstrassians To True Infinitesimal Calculus, Mikhail Katz, Luie Polev

Journal of Humanistic Mathematics

In teaching infinitesimal calculus we sought to present basic concepts like continuity and convergence by comparing and contrasting various definitions, rather than presenting “the definition” to the students as a monolithic absolute. We hope that our experiences could be useful to other instructors wishing to follow this method of instruction. A poll run at the conclusion of the course indicates that students tend to favor infinitesimal definitions over epsilon-delta ones.

Curiozităţi Ale Funcţiilor Supermatematice, Florentin Smarandache, Mircea Eugen Selariu

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Mathematics. Possible Subjects For The High School Entrance Examination And The Capacity Examination In Romania, Florentin Smarandache, Constantin Coanda, Ionuț Ivanescu

Branch Mathematics and Statistics Faculty and Staff Publications

The present book tries to offer students and teachers knowledge evaluation tools for all the chapters from the current Romanian mathematics syllabus. In the evolution of teenagers, the phase of admission in high schools mobilizes particular efforts and emotions. The present workbook aims to be a permanent advisor in the agitated period starting with the capacity examination and leading to the admittance to high school. The tests included in this workbook have a complementary character as opposed to the many materials written with the purpose to support all those who prepare for such examinations and they refer to the entire …

Nidus Idearum. Scilogs, I: De Neutrosophia, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Welcome into my scientific lab! My lab[oratory] is a virtual facility with noncontrolled conditions in which I mostly perform scientific meditation and chats: a nest of ideas (nidus idearum, in Latin). I called the jottings herein scilogs (truncations of the words scientific, and gr. Λόγος – appealing rather to its original meanings "ground", "opinion", "expectation"), combining the welly of both science and informal (via internet) talks (in English, French, and Romanian). In this first books of scilogs collected from my nest of ideas, one may find new and old questions and solutions, some of them already put at work, others …

Nidus Idearum. Scilogs, Ii: De Rerum Consectatione, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Welcome into my scientific lab! My lab[oratory] is a virtual facility with noncontrolled conditions in which I mostly perform scientific meditation and chats: a nest of ideas (nidus idearum, in Latin). I called the jottings herein scilogs (truncations of the words scientific, and gr. Λόγος – appealing rather to its original meanings "ground", "opinion", "expectation"), combining the welly of both science and informal (via internet) talks (in English, French, and Romanian). In this second book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, some of them already put at work, others …

Special Type Of Topological Spaces Using [0, N), Florentin Smarandache, W.B Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the notion of special type of topological spaces using the interval [0, n). They are very different from the usual topological spaces. Algebraic structure using the interval [0, n) have been systemically dealt by the authors. Now using those algebraic structures in this book authors introduce the notion of special type of topological spaces. Using the super subset interval semigroup special type of super interval topological spaces are built. Several interesting results in this direction are obtained. Next six types of topological spaces using subset interval pseudo ring semiring of type …

Probleme De Geometrie Și Trigonometrie, Compilate Și Rezolvate, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Techno-Art Of Selariu Supermathematics Functions, 2nd Volume, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

An ALBUM, according to the dictionary, is defined as "notebook for storing photos, postcards, stamps, lyrics, quotes etc.", which, in other words, means gatherings of "pieces" of the same "species". Or, in the new Techno-Art of Selariu SuperMathematics Functions ALBUM (the second book of Selariu SuperMathematics Functions), one contemplates a unique COMPOSITION, INTER-, INTRA- and TRANS-DISCIPLINARY. (Capitalizing here is not a futility, but a harmony with the TRUTH.) One caveat I am indebted to do, as a consequent "reader" – over time, I received the ALBUM, chapter by chapter, pace by pace, which gave me the time to analyze / …

Neutrosophic Axiomatic System, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we introduce for the first time the notions of Neutrosophic Axiom, Neutrosophic Axiomatic System, Neutrosophic Deducibility and Neutrosophic Inference, Neutrosophic Proof, Neutrosophic Tautologies, Neutrosophic Quantifiers, Neutrosophic Propositional Logic, Neutrosophic Axiomatic Space, Degree of Contradiction (Dissimilarity) of Two Neutrosophic Axioms, and Neutrosophic Model. A class of neutrosophic implications is also introduced. A comparison between these innovatory neutrosophic notions and their corresponding classical notions is made. Then, three concrete examples of neutrosophic axiomatic systems, describing the same neutrosophic geometrical model, are presented at the end of the paper.