Applied Mathematics Commons^™

Neutrosophic Operational Research - Vol. 1, Florentin Smarandache, Mohamed Abdel Basset, Yongquan Zhou

Branch Mathematics and Statistics Faculty and Staff Publications

This book is an excellent exposition of the use of Data Envelopment Analysis (DEA) to generate data analytic insights to make evidence-based decisions, to improve productivity, and to manage cost-risk and benefitopportunity in public and private sectors. The design and the content of the book make it an up-to-date and timely reference for professionals, academics, students, and employees, in particular those involved in strategic and operational decisionmaking processes to evaluate and prioritize alternatives to boost productivity growth, to optimize the efficiency of resource utilization, and to maximize the effectiveness of outputs and impacts to stakeholders. It is concerned with the …

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 …

Neutrosophic Triplet Groups And Their Applications To Mathematical Modelling, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilanthenral K.

Branch Mathematics and Statistics Faculty and Staff Publications

The innovative notion of neutrosophic triplet groups, introduced by Smarandache and Ali in 2014-2016, happens to yield the anti-element and neutral element once the element is given. It is established that the neutrosophic triplet group collection forms the classical group under product for Zn, for some specific n. However the collection is not even closed under sum. These neutrosophic triplet groups are built using only modulo integers or Cayley tables. Several interesting properties related with them are defined. It is pertinent to record that in Zn, when n is a prime number, we cannot get a neutral element which can …

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.

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 …

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. …

On A Time Domain Boundary Integral Equation Formulation For Acoustic Scattering By Rigid Bodies In Uniform Mean Flow, Fang Q. Hu, Michelle E. Pizzo, Douglas M. Nark

Mathematics & Statistics Faculty Publications

It has been well-known that under the assumption of a uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation. However, the constant mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the assumed uniform flow. A customary boundary condition for rigid surfaces is that the normal acoustic velocity be zero. In this paper, a careful study of the acoustic energy conservation equation is presented that shows such a boundary condition would in fact lead to source …

Joint Hierarchical Models For Sparsely Sampled High-Dimensional Lidar And Forest Variables, Andrew O. Finley, Sudipto Banerjee, Yuzhen Zhou, Bruce D. Cook, Chad Babcock

United States National Aeronautics and Space Administration: Publications

Recent advancements in remote sensing technology, specifically Light Detection and Ranging (LiDAR) sensors, provide the data needed to quantify forest characteristics at a fine spatial resolution over large geographic domains. From an inferential standpoint, there is interest in prediction and interpolation of the often sparsely sampled and spatially misaligned LiDAR signals and forest variables. We propose a fully process-based Bayesian hierarchical model for above ground biomass (AGB) and LiDAR signals. The processbased framework offers richness in inferential capabilities, e.g., inference on the entire underlying processes instead of estimates only at pre-specified points. Key challenges we obviate include misalignment between the …

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 …

A Wasserstein Gradient Flow Approach To Poisson-Nernst-Planck Equations, David Kinderlehrer, Leinard Monsaingeon, Xiang Xu

Mathematics & Statistics Faculty Publications

The Poisson-Nernst-Planck system of equations used to model ionic transport is interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of probability measures with finite second moment. A variational scheme is then set up and is the starting point of the construction of global weak solutions in a unified framework for the cases of both linear and non-linear diffusion. The proof of the main results relies on the derivation of additional estimates based on the flow interchange technique developed by Matthes et al. in [D. Matthes, R.J. McCann and G. Savare, Commun. Partial …

Multiplicative Noise Removal With A Sparsity-Aware Optimization Model, Jian Lu, Lixin Shen, Chen Xu, Yuesheng Xu

Mathematics & Statistics Faculty Publications

Restoration of images contaminated by multiplicative noise (also known as speckle noise) is a key issue in coherent image processing. Notice that images under consideration are often highly compressible in certain suitably chosen transform domains. By exploring this intrinsic feature embedded in images, this paper introduces a variational restoration model for multiplicative noise reduction that consists of a term reflecting the observed image and multiplicative noise, a quadratic term measuring the closeness of the underlying image in a transform domain to a sparse vector, and a sparse regularizer for removing multiplicative noise. Being different from popular existing models which focus …

Direct Sampling Methods For Inverse Scattering Problems, Ala Mahmood Nahar Al Zaalig

Dissertations, Master's Theses and Master's Reports

Recently, direct sampling methods became popular for solving inverse scattering problems to estimate the shape of the scattering object. They provide a simple tool to directly reconstruct the shape of the unknown scatterer. These methods are based on choosing an appropriate indicator function f on R^d, d=2 or 3, such that f(z) decides whether z lies inside or outside the scatterer. Consequently, we can determine the location and the shape of the unknown scatterer.

In this thesis, we first present some sampling methods for shape reconstruction in inverse scattering problems. These methods, which are described in Chapter 1, …

Moduli Spaces Of Flat Gsp-Bundles, Neal David Livesay

LSU Doctoral Dissertations

A classical problem in the theory of differential equations is the classification of first-order singular differential operators up to gauge equivalence. A related algebro-geometric problem involves the construction of moduli spaces of meromorphic connections. In 2001, P. Boalch constructed well-behaved moduli spaces in the case that each of the singularities are diagonalizable. In a recent series of papers, C. Bremer and D. Sage developed a new approach to the study of the local behavior of meromorphic connections using a geometric variant of fundamental strata, a tool originally introduced by C. Bushnell for the study of p-adic representation theory. Not only …

Manifestations Of Symmetry In Polynomial Link Invariants, Kyle Istvan

LSU Doctoral Dissertations

The use and detection of symmetry is ubiquitous throughout modern mathematics. In the realm of low-dimensional topology, symmetry plays an increasingly significant role due to the fact that many of the modern invariants being developed are computationally expensive to calculate. If information is known about the symmetries of a link, this can be incorporated to greatly reduce the computation time. This manuscript will consider graphical techniques that are amenable to such methods. First, we discuss an obstruction to links being periodic, developed jointly with Dr. Khaled Qazaqzeh at Kuwait University, using a model developed by Caprau and Tipton. We will …

Reduced Order Models For Beam-Wave Interaction In High Power Microwave Sources, Lokendra Singh Thakur

LSU Doctoral Dissertations

We apply an asymptotic analysis to show that corrugated waveguides can be represented as cylindrical waveguides with smooth metamaterial coatings when the corrugtions are subwavelength. Here the metamaterial delivers an effective anisotropic surface impedance, effective dielectric constant, and imparts novel dispersive effects on signals traveling inside the waveguide. These properties arise from the subwavelength resonances of the metamaterial. For sufficiently deep corrugations, the waveguide exhibits backward wave propagation, which can be understood in the present context as a multi-scale phenomenon resulting from local resonances inside the subwavelength geometry. Our approach is well suited to numerical computation and we provide a …

On The Skein Theory Of 0-Framed Surgery Along The Trefoil Knot, Andrew Robert Holmes

LSU Doctoral Dissertations

In this dissertation, we will give a generating set of the Kauffman bracket skein module over the field Q(A) of 0-framed surgery along the trefoil knot. This generating set is described as a certain subset of a known basis for the skein module over Z[A^±1] of the trefoil exterior.

An Introduction To The Lebesgue Integral, Ikhlas Adi

All Student Theses and Dissertations

The Riemann integral is the simplest integral to define, and it allows one to integrate every continuous function. It is really important to have a definition of the integral that allows a wider class of functions to be integrated. However, there are many other types of integrals, the most important of which is the Lebesgue integral. The Lebesgue integral allows one to integrate unbounded or discontinuous functions whose Riemann integral does not exist, and it has mathematical properties that the Riemann integral does not. The definition of the Lebesgue integral requires the use of measure theory since picking out a …

Fitting A Linear Regression Model And Forecasting In R In The Presence Of Heteroskedascity With Particular Reference To Advanced Regression Technique Dataset On Kaggle.Com., Samuel Mbah Nde

All Student Theses and Dissertations

Since ancient times, men have built and sold houses. But just how much is a house worth? The challenge is to be able to use information about a house such as its location, and the area on which it is built to predict its price. Such predicted prices can be of great importance to any participant in the real estate business be it an agent, a buyer, seller or a bank to make intelligent decisions and the profit that come with such decisions. Since every company’s success depends on its ability to accurately predict financial outcomes, its profitability will depend …

The Effects Of Disturbance And Species Specific Interactions On Diversity In An Agent Based Forest Simulation, Matthew E. Mills

Theses and Dissertations

In ecology literature, there is much data which suggests that conspecific negative density dependence (CNDD) and abiotic disturbances increase biodiversity in forests. This thesis elucidates the notion that not only do these two forces increase diversity, but they may also interact with one another in order to achieve higher levels of biodiversity. Abiotic disturbances, like fires and hurricanes, can indirectly impact conspecific effects because when these forces remove individuals from the landscape, the role of the conspecific effects will change. The interaction of these two factors in biodiversity are explored in an agent based forest simulation through a resource surface. …

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 …

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.

Region Of Smooth Functions For Positive Solutions To An Elliptic Biological Model, Joon Hyuk Kang, Timothy Robertson

Faculty Publications

The non-existence and existence of the positive solution to the generalized elliptic model ∆u+g(u v) = 0 in Ω, ∆v+h(u, v) = 0 in Ω, u=v= 0 on∂Ω, were investigated.

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.

Characterization Of Rectifying And Sphere Curves In R^3, Yun Myung Oh, Julie Logan

Faculty Publications

Studies of curves in 3D-space have been developed by many geometers and it is known that any regular curve in 3D space is completely determined by its curvature and torsion, up to position. Many results have been found to characterize various types of space curves in terms of conditions on the ratio of torsion to curvature. Under an extracondition on the constant curvature, Y.L. Seo and Y. M. Oh found the series solution when the ratio of torsion to curvature is a linear function. Furthermore, this solution is known to be a rectifying curve by B. Y. Chen’s work. This …

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 …

Network Analytics For The Mirna Regulome And Mirna-Disease Interactions, Joseph Jayakar Nalluri

Theses and Dissertations

miRNAs are non-coding RNAs of approx. 22 nucleotides in length that inhibit gene expression at the post-transcriptional level. By virtue of this gene regulation mechanism, miRNAs play a critical role in several biological processes and patho-physiological conditions, including cancers. miRNA behavior is a result of a multi-level complex interaction network involving miRNA-mRNA, TF-miRNA-gene, and miRNA-chemical interactions; hence the precise patterns through which a miRNA regulates a certain disease(s) are still elusive. Herein, I have developed an integrative genomics methods/pipeline to (i) build a miRNA regulomics and data analytics repository, (ii) create/model these interactions into networks and use optimization techniques, motif …

A New Formulation Of Time Boundary Integral Equation For Acoustic Wave Scattering In The Presence Of A Uniform Mean Flow, Fang Q. Hu, Michelle E. Pizzo, Douglas M. Nark

Mathematics & Statistics Faculty Publications

It has been well-known that under the assumption of a constant uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation, in both the time domain and the frequency domain. Compared with solving partial differential equations, numerical methods based on the boundary integral equation have the advantage of a reduced spatial dimension and, hence, requiring only a surface mesh. However, the constant uniform mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the uniform mean flow. In …