Digital Commons Network^™

Act Chapter 29: Art And Science And Theology In Dialogue, V. Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Where does a sparkling idea come to us, so out of the blue? Divine inspiration? I want a scientific explanation... Maybe, at present, with our current level of science, we are not able to understand the paranormal, or what we think is fantastic, but in fact it is real. A reality that we cannot reach with understanding, because of our low level... Are we not perhaps relevant and do we understand the incomprehensible? Some are connected to the universe better than others, do they have extra senses? How can we “gather” ideas from “air”? How does the spark in the …

A Compact Exploration Of Turiyam Neutrosophic Competition Graphs, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Graph theory, a branch of mathematics, examines relationships between entities using vertices and edges. Within this field, Uncertain Graph Theory has emerged to model uncertainties in real-world networks. A notable concept in this area is the competition graph, which captures interactions by connecting vertices that “compete” for the same neighbor, represented by directed edges indicating common neighbors in a digraph. This brief paper introduces the concept of the Generalized Turiyam Neutrosophic Competition Graph and explores its relationships with other graph classes.

A Hybrid Time Series Forecasting Method Based On Neutrosophic Logic With Applications In Financial Issues, Seyyed Ahmad Edalatpanah, Farnaz Sheikh Hassani, Florentin Smarandache, Ali Sorourkhah, Dragan Pamucar, Bing Cui

Branch Mathematics and Statistics Faculty and Staff Publications

Rising market demands, economic pressures, and technological advancements have spurred researchers to seek ways to enhance business environments and scientific productivity. Predictive science, crucial in this context, has gained prominence due to the rapid progress in information technology and forecasting algorithms. Time series forecasting, widely used in fields like engineering, economics, tourism, and energy, has inherent limitations with classical statistical methods, leading researchers to explore artificial intelligence and fuzzy logic for more accurate predictions. However, despite extensive efforts to improve accuracy, challenges persist. The research introduces a model aimed at surpassing existing methods in time series forecasting accuracy. This approach …

A Reconsideration Of Advanced Concepts In Neutrosophic Graphs: Smart, Zero Divisor, Layered, Weak, Semi, And Chemical Graphs, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

One of the most powerful tools in graph theory is the classification of graphs into distinct classes based on shared properties or structural features. Over time, many graph classes have been introduced, each aimed at capturing specific behaviors or characteristics of a graph. Neutrosophic Set Theory, a method for handling uncertainty, extends fuzzy logic by incorporating degrees of truth, indeterminacy, and falsity. Building on this framework, Neutrosophic Graphs [9,84,135] have emerged as significant generalizations of fuzzy graphs. In this paper, we extend several classes of fuzzy graphs to Neutrosophic graphs and analyze their properties.

Three Novel Approaches To Deep Space: Interstellar Travel That Transcend The Limitations Imposed By The Rocket Equation, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

At the time of writing this abstract, we read about Betelgeuse star has exploded in the last few days. While there are various explanations and interpretations on how that event would have impacted this Earth’s inhabitants, our interpretation asserts that there are several chains of stars that act to lock this Earth to the 3D realm, and the exploded Betelgeuse star can be considered as a signal from heaven that we, all Earth inhabitants, are allowed to be elevated to 5D consciousness and to explore the Deep Space beyond this solar system. Therefore, in the present paper, it is considered …

Breve Introducción A Los Conjuntos Y A La Lógica Neutrosófica Estándar Y No Estándar, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Se recuerdan las definiciones de Conjunto Neutrosófico de Valor Único (SVNS), Conjunto Neutrosófico de Valor Intervalo (IVNS), Conjunto Neutrosófico de Valor Subconjunto (SVNS) y, respectivamente, Conjunto Neutrosófico No Estándar [Con Valor Único ( SVNS NoS ), Con Valor Intervalo ( IVNS NoS ) y Con Valor Subconjunto ( SVNS NoS )], junto con sus operadores. De manera similar, para Conjunto Neutrosófico Estándar y No Estándar.

A Right-Brain-Based Epistemology Grounded On Local Wisdom: Intuilytics As A Culturally-Meaningful Alternative In Science, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Epistemology, the study of knowledge, has long grappled with the challenge of determining truth. While the combination of deductive and inductive reasoning has been a cornerstone of scientific inquiry, several limitations emerge in its application to contemporary epistemology. One significant issue lies within the core of falsificationism, a prominent philosophy championed by Karl Popper. Falsificationism posits that a scientific theory can only be proven false, not true. While this approach aims to prevent dogmatic adherence to untested ideas, it can lead to an endless cycle of trial and error. As Popper himself acknowledged, no single experiment can definitively prove a …

Decision Making In The Case Of Confirmed Data Neutrosophic Linear Models To Choose The Advertising Medium, Maissam Ahmad Jdid, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In light of the great development witnessed by our contemporary world, it has become necessary to focus on scientific methods and use the quantitative method to reach more accurate decisions, appropriate to the surrounding circumstances and factors. The process of decision-making and choosing the optimal alternative depends on the type and quality of data that describes the issue for which the decision is to be made. Regarding it, in this chapter we present a study of the issue of determining the ideal advertising medium to display a company’s products. This issue is considered one of the issues of decision-making in …

Recreational Mathematics: Where Is The Error?, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This short note is a funny problem for the trigonometry students!.

Soft Sets Extensions Used In Bioinformatics, Florentin Smarandache, Daniela Gifu

Branch Mathematics and Statistics Faculty and Staff Publications

This comprehensive review delves into the intricate realm of Soft Sets and their extensions, including HyperSoft Set, IndetermSoft Set, IndetermHyperSoft Set, and TreeSoft Set, within the context of biomedical data analysis. Soft Sets serve as a foundational framework for managing the inherent uncertainty and imprecision inherent in biological data, thereby facilitating informed decision-making and knowledge discovery. The exploration of Soft Set Products, particularly in the context of multiple soft sets, underscores their pivotal role in advancing biomedical research. By extending these concepts to HyperSoft Sets, researchers can unlock deeper insights into complex biological phenomena, enabling more accurate predictions and classification.

Shadow Hands, John Adam

Mathematics & Statistics Faculty Publications

The article titled "Shadow hands" discusses a statement made by authors Dave Lynch and Bill Livingston in their book "Color and Light in Nature." The authors state that when you cast a shadow with your hand onto a piece of paper, the sharpness of the shadow's edge diminishes as you raise your hand above the surface. This fuzzy outer edge of the shadow is called the penumbra, and its width divided by its distance from your hand is always a constant fraction of about 1/112. The article poses two questions related to this statement and asks readers to explain it …

Numerical Investigation And Statistical Analysis Of The Flow Patterns Behind Square Cylinders Arranged In A Staggered Configuration Utilizing The Lattice Boltzmann Method, M. Abid, N. Yasin, M. Saqlain, S. Ul-Islam, S. Ahmad

Mathematics & Statistics Faculty Publications

Flow past bluff bodies like square cylinders is important in engineering applications, but flow patterns behind staggered cylinder arrangements remain poorly understood. Existing studies have focused on tandem or side-by-side configurations, while offset orientations have received less attention. The aim of this paper is to numerically investigate flow dynamics and force characteristics behind two offset square cylinders using the single relaxation time lattice Boltzmann method. The effects of changing both the Reynolds number (Re = 1-150) and gap spacing ratio (g* = 0.5-5) between the cylinders are analyzed. Instantaneous vorticity contours, time histories of drag and lift coefficients, power spectra …

Shadow Hands: Solutions For Fermi Questions, September 2024, John Adam

Mathematics & Statistics Faculty Publications

The article titled "Shadow hands: Solutions for Fermi Questions, September 2024" discusses the enigmatic statement made by authors Dave Lynch and Bill Livingston in their book "Color and Light in Nature." The statement explains that the fuzzy outer edge of a shadow, known as the penumbra, is always a constant fraction of about 1/112 of its width divided by its distance from the object casting the shadow. The article provides a solution to Question 1, which asks for an explanation of this statement using elementary geometry. It also offers a solution to Question 2, which asks why the shadow of …

Numerical Solution Of Hybrid Nanofluid And Its Stability Over Permeable Wedge Sheet With Heat Transfer Analysis, Aisha M. Alqahtani, Zeeshan, Waris Khan, Florentin Smarandache, Nidhal Becheikh, Roobaea Alroobaea, Taseer Muhammad

Branch Mathematics and Statistics Faculty and Staff Publications

The inclusion of nanoparticles has the potential to improve the thermal efficiency of the base fluid. The field of nanofluid (NF) dynamics has attracted important attention due to its extensive range of practical uses like fuel cells, solar energy, medication administration, heat transfer, microfabrication, coolant applications, and other related domains. The aim of this study is to scrutinize the impact of Lorentz force, thermal energy, joule heating, heat source and injection parameters, and Brownian and thermoporetic diffusions on the hybrid nanofluid over the moving wedge. The stability inquiry is reported for the existing work in order to confirm the stable …

A Review Of The Hierarchy Of Plithogenic, Neutrosophic, And Fuzzy Graphs: Survey And Applications, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

As many readers may know, graph theory is a fundamental branch of mathematics that examines networks consisting of nodes and edges, with a focus on their paths, structures, and properties [157]. A Fuzzy Graph extends this concept by assigning a membership degree between 0 and 1 to each edge and vertex, capturing the level of uncertainty. Expanding on this idea, the Turiyam Neutrosophic Graph was introduced as an extension of both Neutrosophic and Fuzzy Graphs. Plithogenic graphs, in turn, offer a powerful approach for managing uncertainty. In this paper, we explore the relationships among various graph classes, including Plithogenic graphs, …

Note On The Spectra Of Steiner Distance Hypermatrices, Joshua Cooper, Zhibin Du

Faculty Publications

The Steiner distance of a set of vertices in a graph is the fewest number of edges in any connected subgraph containing those vertices. The order-k Steiner distance hypermatrix of a graph is the n-dimensional array indexed by vertices, whose entries are the Steiner distances of their corresponding indices. In the case of k = 2, this reduces to the classical distance matrix of a graph. Graham and Pollak showed in 1971 that the determinant of the distance matrix of a tree only depends on its number n of vertices. Here, we show that the hyperdeterminant of the Steiner distance …

Boundaries Of Overlapping Isosceles Triangles, Kirati Sriamorn

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

The Direct And Inverse Scattering Problems For The Third-Order Operator, Ivan Toledo

Mathematics Dissertations - Archive

We consider the full-line direct and inverse scattering problems for the third-order ordinary differential equation containing two potentials decaying sufficiently fast at infinity. The direct scattering problem consists of the determination of the scattering data set when the two potentials are known. The scattering data set is made up of the corresponding scattering coefficients and the bound-state information. On the other hand, the inverse scattering problem involves the recovery of the two potentials when the scattering data set is available. We formulate the inverse scattering problem via a related Riemann--Hilbert problem on the complex plane. We describe the recovery of …

Bicategorical Character Theory, Travis Wheeler

Theses and Dissertations--Mathematics

In 2007, Nora Ganter and Mikhail Kapranov defined the categorical trace, which they used to define the categorical character of a 2-representation. In 2008, Kate Ponto defined a shadow functor for bicategories. With the shadow functor, Dr. Ponto defined the bicategorical trace, which is a generalization of the symmetric monoidal trace for bicategories. How are these two notions of trace related to one another? We’ve used bicategorical traces to define a character theory for 2-representations, and the categorical character is an example.

Properties Of Skew-Polynomial Rings And Skew-Cyclic Codes, Kathryn Hechtel

Theses and Dissertations--Mathematics

A skew-polynomial ring is a polynomial ring over a field, with one indeterminate x, where one must apply an automorphism to commute coefficients with x. It was first introduced by Ore in 1933 and since the 1980s has been used to study skew-cyclic codes. In this thesis, we present some properties of skew-polynomial rings and some new constructions of skew-cyclic codes. The dimension of a skew-cyclic code depends on the degree of its generating skew polynomial. However, due to the skew-multiplication rule, the degree of a skew polynomial can be smaller than its number of roots and hence tricky to …

Adams Operations On The Burnside Ring From Power Operations, Lewis Dominguez

Theses and Dissertations--Mathematics

Topology furnishes us with many commutative rings associated to finite groups. These include the complex representation ring, the Burnside ring, and the G-equivariant K-theory of a space. Often, these admit additional structure in the form of natural operations on the ring, such as power operations, symmetric powers, and Adams operations. We will discuss two ways of constructing Adams operations. The goal of this work is to understand these in the case of the Burnside ring.

Pairs Of Quadratic Forms Over P-Adic Fields, John Hall

Theses and Dissertations--Mathematics

Given two quadratic forms $Q_1, Q_2$ over a $p$-adic field $K$ in $n$ variables, we consider the pencil $\mathcal{P}_K(Q_1, Q_2)$, which contains all nontrivial $K$-linear combinations of $Q_1$ and $Q_2$. We define $D$ to be the maximal dimension of a subspace in $K^n$ on which $Q_1$ and $Q_2$ both vanish. We define $H$ to be the maximal number of hyperbolic planes that a form in $\mathcal{P}_K(Q_1, Q_2)$ splits off over $K$. We will determine which values for $(D, H)$ are possible for a nonsingular pair of quadratic forms over a $p$-adic field $K$.

Dirichlet Problems In Perforated Domains, Robert Righi

Theses and Dissertations--Mathematics

We establish W^1,p estimates for solutions u_ε to the Laplace equation with Dirichlet boundary conditions in a bounded C¹ domain Ω_{ε, η} perforated by small holes in ℝ^d. The bounding constants will depend explicitly on epsilon and eta, where epsilon is the order of the minimal distance between holes, and eta denotes the ratio between the size of the holes and epsilon. The proof relies on a large-scale L^p estimate for ∇u_ε, whose proof is divided into two main parts. First, we show that solutions of an intermediate problem for a …

Slₖ-Tilings And Paths In ℤᵏ, Zachery T. Peterson

Theses and Dissertations--Mathematics

An SLₖ-frieze is a bi-infinite array of integers where adjacent entries satisfy a certain diamond rule. SL₂-friezes were introduced and studied by Conway and Coxeter. Later, these were generalized to infinite matrix-like structures called tilings as well as higher values of k. A recent paper by Short showed a bijection between bi-infinite paths of reduced rationals in the Farey graph and SL₂-tilings. We extend this result to higher k by constructing a bijection between SLₖ-tilings and certain pairs of bi-infinite strips of vectors in ℤᵏ called paths. The key ingredient in the proof is the relation to Plucker friezes and …

A Multiple-Case Study On The Impact Of An Introductory Real Analysis Course On Undergraduate Students' Understanding Of Function Continuity, Ryan Joseph Rogers

Theses and Dissertations--Mathematics

Undergraduate students' understanding of function continuity has not been explored broadly in previous research. The relevant findings in the literature are predominantly concerned with calculus students' understanding and misconceptions of continuity. Many of these misunderstandings are tied to the relationships which continuity has with limits and differentiability. This multiple-case study explores how, if at all, an introductory real analysis course impacts undergraduate students' understanding of function continuity and its connections to the notions of limits and differentiability. We embed our findings within the theoretical framework of Tall's three worlds of mathematics, namely, the embodied, symbolic, and formal worlds.

The cases …

Advanced Mathematical Graph-Based Machine Learning And Deep Learning Models For Drug Design, Farjana Tasnim Mukta

Theses and Dissertations--Mathematics

Drug discovery is a highly complicated and time-consuming process. One of the main challenges in drug development is predicting whether a drug-like molecule will interact with a specific target protein. This prediction accelerates target validation and drug development. Recent research in biomolecular sciences has shown significant interest in algebraic graph-based models for representing molecular complexes and predicting drug-target binding affinity. In this thesis, we present algebraic graph-based molecular representations to create data-driven scoring functions (SF) using extended atom types to capture wide-range interactions between targets and drug candidates. Our model employs multiscale weighted colored subgraphs for the protein-ligand complex, colored …

A Little More On Ideals Associated With Sublocales, Oghenetega Ighedo, Grace Wakesho Kivunga, Dorca Nyamusi Stephen

Mathematics, Physics, and Computer Science Faculty Articles and Research

As usual, let RL denote the ring of real-valued continuous functions on a completely regular frame L. Let βL and λL denote the Stone- Čech compactification of L and the Lindelöf coreflection of L, respectively. There is a natural way of associating with each sublocale of βL two ideals of RL, motivated by a similar situation in C(X). In [12], the authors go one step further and associate with each sublocale of λL an ideal of RL in a manner similar to one of the ways one does it for sublocales of βL. The intent in this paper …

On Graph Decompositions And Designs: Exploring The Hamilton-Waterloo Problem With A Factor Of 6-Cycles And Projective Planes Of Order 16, Zazil Santizo Huerta

Dissertations, Master's Theses and Master's Reports

This dissertation tackles the challenging graph decomposition problem of finding solutions to the uniform case of the Hamilton-Waterloo Problem (HWP). The HWP seeks decompositions of complete graphs into cycles of specific lengths. Here, we focus on cases with a single factor of 6-cycles. The dissertation then delves into the construction of 1-rotational designs, a concept from finite geometry. It explores the connection between these designs and finite projective planes, which are specific geometric structures. Finally, the dissertation proposes a potential link between these seemingly separate areas. It suggests investigating whether 1-rotational designs might hold the key to solving unsolved instances …

Neural Correlates Of Audiovisual Narrative Speech Perception In Children And Adults On The Autism Spectrum: A Functional Magnetic Resonance Imaging Study, Lars A. Ross, Sophie Molholm, John S. Butler, Victor A. Del Bene, Tufikameni Brima, John J. Foxe

Articles

Autistic individuals show substantially reduced benefit from observing visual articulations during audiovisual speech perception, a multisensory integration deficit that is particularly relevant to social communication. This has mostly been studied using simple syllabic or word-level stimuli and it remains unclear how altered lower-level multisensory integration translates to the processing of more complex natural multisensory stimulus environments in autism. Here, functional neuroimaging was used to examine neural correlates of audiovisual gain (AV-gain) in 41 autistic individuals to those of 41 age-matched non-autistic controls when presented with a complex audiovisual narrative. Participants were presented with continuous narration of a story in auditory-alone, …

Centers Of N-Degree Poncelet Circles, Georgia Corbett

Honors Theses

Given a circle inscribed in a polygon inscribed in the unit circle, if one connects all the vertices with line segments we get a family of circles called a package of Poncelet circles, due to its connection to a theorem of Poncelet. We are interested in where the centers of the Poncelet circles can be. Specifically, we have shown that if one of the circles in the Poncelet package is centered at 0, then all of the circles must be centered at 0 as well. This was proven by Spitkovsky and Wegert in 2021 using elliptic integrals but we …