Physical Sciences and Mathematics Commons^™

Neutrosophic Quadruple Algebraic Hyperstructures, A. A. A. Agboola, B. Davvaz, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The objective of this paper is to develop neutrosophic quadruple algebraic hyperstructures. Specifically, we develop neutrosophic quadruple semihypergroups, neutrosophic quadruple canonical hypergroups and neutrosophic quadruple hyperrings and we present elementary properties which characterize them.

Complex Valued Graphs For Soft Computing, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilanthenral K

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce in a systematic way the notion of complex valued graphs, strong complex valued graphs and complex neutrosophic valued graphs. Several interesting properties are defined, described and developed. Most of the conjectures which are open in case of usual graphs continue to be open problems in case of both complex valued graphs and strong complex valued graphs. We also give some applications of them in soft computing and social networks. At this juncture it is pertinent to keep on record that Dr. Tohru Nitta was the pioneer to use complex valued graphs …

Cycle Bases Of Reduced Powers Of Graphs, Richard H. Hammack, Gregory Smith

Arts & Sciences Articles

We define what appears to be a new construction. Given a graph G and a positive integer k, the reduced kth power of G, denoted G^(k), is the configuration space in which k indistinguishable tokens are placed on the vertices of G, so that any vertex can hold up to k tokens. Two configurations are adjacent if one can be transformed to the other by moving a single token along an edge to an adjacent vertex. We present propositions related to the structural properties of reduced graph powers and, most significantly, provide …

Approximate Statistical Solutions To The Forensic Identification Of Source Problem, Danica M. Ommen

Electronic Theses and Dissertations

Currently in forensic science, the statistical methods for solving the identification of source problems are inherently subjective and generally ad-hoc. The formal Bayesian decision framework provides the most statistically rigorous foundation for these problems to date. However, computing a solution under this framework, which relies on a Bayes Factor, tends to be computationally intensive and highly sensitive to the subjective choice of prior distributions for the parameters. Therefore, this dissertation aims to develop statistical solutions to the forensic identification of source problems which are less subjective, but which retain the statistical rigor of the Bayesian solution. First, this dissertation focuses …

P-Union And P-Intersection Of Neutrosophic Cubic Sets, Florentin Smarandache, Young Bae Jun, Chang Su Kim

Branch Mathematics and Statistics Faculty and Staff Publications

Conditions for the P-intersection and P-intersection of falsity-external (resp. indeterminacy-external and truth-external) neutrosophic cubic sets to be an falsity-external (resp. indeterminacy-external and truthexternal) neutrosophic cubic set are provided. Conditions for the Punion and the P-intersection of two truth-external (resp. indeterminacyexternal and falsity-external) neutrosophic cubic sets to be a truthinternal (resp. indeterminacy-internal and falsity-internal) neutrosophic cubic set are discussed.

Special Types Of Bipolar Single Valued Neutrosophic Graphs, Ali Hassan, Muhammad Aslam Malik, Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic theory has many applications in graph theory, bipolar single valued neutrosophic graphs (BSVNGs) is the generalization of fuzzy graphs and intuitionistic fuzzy graphs, SVNGs. In this paper we introduce some types of BSVNGs, such as subdivision BSVNGs, middle BSVNGs, total BSVNGs and bipolar single valued neutrosophic line graphs (BSVNLGs), also investigate the isomorphism, co weak isomorphism and weak isomorphism properties of subdivision BSVNGs, middle BSVNGs, total BSVNGs and BSVNLGs.

An Early Semester Mastery Activity And Intervention In First-Year Calculus, Allan P. Donsig, Nathan Wakefield

Department of Mathematics: Faculty Publications

Success in first-year mathematics courses is essential for students to pursue STEM careers, including teaching careers. We investigate a mastery activity given during the first two weeks of a first-year calculus course at the research site. Previous work showed a model using this activity in College Algebra, together with ACT and high school rank, was predictive of student success in precalculus. Here we do a similar analysis for such an activity in calculus, including an intervention for students who do not complete the activity. We also investigate the intervention’s effectiveness. These results show that the early mastery activity, especially when …

Forcing Optimality And Brandt's Principle, Domenico Napoletani, Marco Panza, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Books and Book Chapters

We argue that many optimization methods can be viewed as representatives of “forcing”, a methodological approach that attempts to bridge the gap between data and mathematics on the basis of an a priori trust in the power of a mathematical technique, even when detailed, credible models of a phenomenon are lacking or do not justify the use of this technique. In particular, we show that forcing is implied in particle swarms optimization methods, and in modeling image processing problems through optimization. From these considerations, we extrapolate a principle for general data analysis methods, what we call ‘Brandt’s principle’, namely the …

Flexibility Of Projective-Planar Embeddings, John Maharry, Neil Robertson, Vaidy Sivaraman, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given two embeddings σ1 and σ2 of a labeled nonplanar graph in the projective plane, we give a collection of maneuvers on projective-planar embeddings that can be used to take σ1 to σ2

Bounding And Stabilizing Realizations Of Biased Graphs With A Fixed Group, Nancy Ann Neudauer, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a group Γ and a biased graph (G, B), we define a what is meant by a Γ-realization of (G, B) and a notion of equivalence of Γ-realizations. We prove that for a finite group Γ and t ≥ 3, that there are numbers n(Γ) and n(Γ, t) such that the number of Γ-realizations of a vertically 3-connected biased graph is at most n(Γ) and that the number of Γ-realizations of a nonseparable biased graph without a (2Ct , ∅)-minor is at most n(Γ, t). Other results pertaining to contrabalanced biased graphs are presented as well as an analogue …

Management Of Invasive Allee Species, David Chan, C. M. Kent, D. M. Johnson

Mathematics and Applied Mathematics Publications

In this study, we use a discrete, two-patch population model of an Allee species to examine different methods in managing invasions. We first analytically examine the model to show the presence of the strong Allee effect, and then we numerically explore the model to test the effectiveness of different management strategies. As expected invasion is facilitated by lower Allee thresholds, greater carrying capacities and greater proportions of dispersers. These effects are interacting, however, and moderated by population growth rate. Using the gypsy moth as an example species, we demonstrate that the effectiveness of different invasion management strategies is context-dependent, combining …

A Mathematical System For Human Implantable Wound Model Studies, Salomonsky Paul-Michael, Rebecca Segal

Mathematics and Applied Mathematics Publications

In this work, we present a mathematical model, which accounts for two fundamental processes involved in the repair of an acute dermal wound. These processes include the inflammatory response and fibroplasia. Our system describes each of these events through the time evolution of four primary species or variables. These include the density of initial damage, inflammatory cells, fibroblasts and deposition of new collagen matrix. Since it is difficult to populate the equations of our model with coefficients that have been empirically derived, we fit these constants by carrying out a large number of simulations until there is reasonable agreement between …

Quantifying The Effect Of The Shift In Major League Baseball, Christopher John Hawke Jr.

Senior Projects Spring 2017

Baseball is a very strategic and abstract game, but the baseball world is strangely obsessed with statistics. Modern mainstream statisticians often study offensive data, such as batting average or on-base percentage, in order to evaluate player performance. However, this project observes the game from the opposite perspective: the defensive side of the game. In hopes of analyzing the game from a more concrete perspective, countless mathemeticians - most famously, Bill James - have developed numerous statistical models based on real life data of Major League Baseball (MLB) players. Large numbers of metrics go into these models, but what this project …

The Expectation For The Center Of Mass Of Finite Integer Grids, Finnegan Maximilan Muller Hardy

Senior Projects Spring 2017

Senior Project submitted to The Division of Science, Mathematics and Computing of Bard College.

Modeling Purple Sea Urchin And California Sheephead Populations In Southern California Kelp Forests, Olivia Rachel Williams

Senior Projects Spring 2017

In this project I am modelling the predator-prey relationship between California sheephead and purple sea urchin populations, respectively, in kelp forests off the coast of southern California. The Lotka-Volterra equations explain predator-prey relationships in their most basic form. These equations incorporate a set of biological assumptions that can be unrepresentative of many ecological systems. I will consider alternate models that incorporate variations of the Lotka-Volterra model which may better represent the biology of the purple sea urchins and California sheephead. Using biological characteristics of both species in kelp forests, I will set possible and likely parameters and solve for unknown …

From Random To Organized: The Architecture Of Neural Networks During Development, Avery Isabella Morris

Senior Projects Fall 2017

The brain is constantly changing during development as a result of various stimuli: memories, language, visual patterns and other sensory information. As a result, networks need to have specific learning rules to function being both plastic and stable. In this project, I’ve constructed a mathematical model based on a biological neural network during development. I’ve written differential equations to describe these specific learning rules as well as methods of visual input to the network. I’ve changed my model, using Euler’s method, to create a discrete-time version of this biological phenomenon to implement on the computer. I’ve successfully coded this, using …

Flow Conditions In The Intracranial Aneurysm Lumen Are Associated With Inflammation And Degenerative Changes Of The Aneurysm Wall, J. Cebral, E. Ollikainen, Bong Jae Chung, F. Mut, V. Sippola, B. R. Jahromi, R. Tulamo, J. Hernesniemi, M. Niemelä, A. Robertson, J. Frösen

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

BACKGROUND AND PURPOSE: Saccular intracranial aneurysm is a common disease that may cause devastating intracranial hemorrhage. Hemodynamics, wall remodeling, and wall inflammation have been associated with saccular intracranial aneurysm rupture.Weinvestigated how saccular intracranial aneurysm hemodynamics is associated with wall remodeling and inflammation of the saccular intracranial aneurysm wall. MATERIALS AND METHODS: Tissue samples resected during a saccular intracranial aneurysm operation (11 unruptured, 9 ruptured) were studied with histology and immunohistochemistry. Patient-specific computational models of hemodynamics were created from preoperative CT angiographies. RESULTS: More stable and less complex flows were associated with thick, hyperplastic saccular intracranial aneurysm walls, while slower flows …

Product Development Resilience Through Set-Based Design, Stephen H. Rapp

Wayne State University Dissertations

Often during a system Product Development program external factors or requirements change, forcing system design change. This uncertainty adversely affects program outcome, adding to development time and cost, production cost, and compromise to system performance. We present a development approach that minimizes the impacts, by considering the possibility of changes in the external factors and the implications of mid-course design changes. The approach considers the set of alternative designs and the burdens of a mid-course change from one design to another in determining the relative value of a specific design. The approach considers and plans parallel development of alternative designs …

Compressive Vector Reconstruction: Hypothesis For Blind Image Deconvolution, Alonso Orea Amador

Open Access Theses & Dissertations

Alternative imaging devices propose to acquire and compress images simultaneously. These devices are based on the compressive sensing (CS) theory. A reduction in the measurement required for reconstruction without a post-compression sub-system allows imaging devices to become simpler, smaller, and cheaper. In this research, we propose a new algorithm to compress and reconstruct blurred images for CS imaging devices. Blur effect in images is common due to relative motion, lens, limited aperture dimensions, lack of focus, and/or atmospheric turbulence. Our intention is to compress a blurred image with CS techniques and then reconstruct a blur-free version using the proposed algorithm. …

Numerical Solutions Of The Radiosity Equation By The Galerkin Method For The Spherical Pyramid (Mars Project), Qiuyang Deng

Mathematics Theses

The Radiosity of a surface is the rate at which energy leaves that surface. It includes the energy emitted by a surface as well as the energy reflected. In this thesis, a spherical shaped interior space was designed on a spacecraft, which one day might land on Mars. The Radiosity model was used to determine the brightness inside the space. A global Galerkin method is used to solve the Radiosity Equation for several spherical shapes. This research is based on the study of the Radiosity Equation for occluded surfaces using the Collocation Method by Atkinson and Chein. The previous research …

Series Solutions Of Polarized Gowdy Universes, Doniray Brusaferro

Theses and Dissertations

Einstein's field equations are a system of ten partial differential equations. For a special class of spacetimes known as Gowdy spacetimes, the number of equations is reduced due to additional structure of two dimensional isometry groups with mutually orthogonal Killing vectors. In this thesis, we focus on a particular model of Gowdy spacetimes known as the polarized T³ model, and provide an explicit solution to Einstein's equations.

Paving The Randomized Gauss-Seidel, Wei Wu

Scripps Senior Theses

The Randomized Gauss-Seidel Method (RGS) is an iterative algorithm that solves overdetermined systems of linear equations Ax = b. This paper studies an update on the RGS method, the Randomized Block Gauss-Seidel Method. At each step, the algorithm greedily minimizes the objective function L(x) = kAx bk2 with respect to a subset of coordinates. This paper describes a Randomized Block Gauss-Seidel Method (RBGS) which uses a randomized control method to choose a subset at each step. This algorithm is the first block RGS method with an expected linear convergence rate which can be described by the properties of the matrix …

2017-2018 Graduate Handbook For The Master Of Arts In Educational Mathematics, Otterbein Office Of Graduate Programs

Graduate School

Graduate Handbook on the MAEM Program at Otterbein University.

Computational Fluid Dynamics In A Terminal Alveolated Bronchiole Duct With Expanding Walls: Proof-Of-Concept In Openfoam, Jeremy Myers

Theses and Dissertations

Mathematical Biology has found recent success applying Computational Fluid Dynamics (CFD) to model airflow in the human lung. Detailed modeling of flow patterns in the alveoli, where the oxygen-carbon dioxide gas exchange occurs, has provided data that is useful in treating illnesses and designing drug-delivery systems. Unfortunately, many CFD software packages have high licensing fees that are out of reach for independent researchers. This thesis uses three open-source software packages, Gmsh, OpenFOAM, and ParaView, to design a mesh, create a simulation, and visualize the results of an idealized terminal alveolar sac model. This model successfully demonstrates that OpenFOAM can be …

The Bessel Function, The Hankel Transform And An Application To Differential Equations, Isaac C. Voegtle

Electronic Theses and Dissertations

In this thesis we explore the properties of Bessel functions. Of interest is how they can be applied to partial differential equations using the Hankel transform. We use an example in two dimensions to demonstrate the properties at work as well as formulate thoughts on how to take the results further.

Mathematical Models Of The Inflammatory Response In The Lungs, Sarah B. Minucci

Theses and Dissertations

Inflammation in the lungs can occur for many reasons, from bacterial infections to stretch by mechanical ventilation. In this work we compare and contrast various mathematical models for lung injuries in the categories of acute infection, latent versus active infection, and particulate inhalation. We focus on systems of ordinary differential equations (ODEs), agent-based models (ABMs), and Boolean networks. Each type of model provides different insight into the immune response to damage in the lungs. This knowledge includes a better understanding of the complex dynamics of immune cells, proteins, and cytokines, recommendations for treatment with antibiotics, and a foundation for more …

Neutrosophic Perspectives: Triplets, Duplets, Multisets, Hybrid Operators, Modal Logic, Hedge Algebras. And Applications (Second Extended And Improved), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This book is part of the book-series dedicated to the advances of neutrosophic theories and their applications, started by the author in 1998. Its aim is to present the last developments in the field. For the first time, we now introduce:

— Neutrosophic Duplets and the Neutrosophic Duplet Structures;

— Neutrosophic Multisets (as an extension of the classical multisets);

— Neutrosophic Spherical Numbers;

— Neutrosophic Overnumbers / Undernumbers / Offnumbers;

— Neutrosophic Indeterminacy of Second Type;

— Neutrosophic Hybrid Operators (where the heterogeneous t-norms and t-conorms may be used in designing neutrosophic aggregations);

— Neutrosophic Triplet Loop;

— Neutrosophic Triplet …

High Performance Techniques Applied In Partial Differential Equations Library, Shilei Lin

All College Thesis Program, 2016-2019

This thesis explores various Trilinos packages to determine a method for updating the deal.ii library, which specializes in solving partial differential equations by finite element methods. It begins with introducing related concepts and general goals, followed by exploring computational and mathematical methods which are analytical solutions of one-dimensional Boussinesq equations and developing newer prototypes for solvers in deal.ii based on Trilinos packages. After demonstrating the methods, it indicates the reducing solving time in newer prototypes. Based on results from the prototype, similar methods are applied to update the deal.ii library. In the end, a testing program is exploited to demonstrate …

Estimates Of Life Span Of Solutions Of A Cauchy Problem, Joon Hyuk Kang

Faculty Publications

In this paper we get estimates of life span of a Cauchy problem ut(x, t) = ∆ u(x, t) +u(x, t)p, x∈Rn, t >0,u(x,0) =λφ(x), x∈Rn in terms of the positive constant parameterλ whenφ(x)∈Lq is a nonnegative bounded continuous function in Rn but not identically zero, where q is large enough. The technique we used in this paper is the Comparison Principle.

Wronskian And Gram Solutions To Integrable Equations Using Bilinear Methods, Benjamin Wiggins

Graduate College Dissertations and Theses

This thesis presents Wronskian and Gram solutions to both the Korteweg-de Vries and Kadomtsev-Petviashvili equations, which are then scalable to arbitrarily large numbers of interacting solitons.

Through variable transformation and use of the Hirota derivative, these nonlinear partial differential equations can be expressed in bilinear form. We present both Wronskian and Gram determinants which satisfy the equations.

N=1,2,3 and higher order solutions are presented graphically; parameter tuning and the resultant behavioral differences are demonstrated and discussed. In addition, we compare these solutions to naturally occurring shallow water waves on beaches.