Mathematics Commons^™

Weakly Horospherically Convex Hypersurfaces In Hyperbolic Space, Vincent Bonini, Jie Qing, Jingyong Zhu

Mathematics

In Bonini et al. (Adv Math 280:506–548, 2015), the authors develop a global correspondence between immersed weakly horospherically convex hypersurfaces ϕ:Mn→Hn+1 and a class of conformal metrics on domains of the round sphere Sn . Some of the key aspects of the correspondence and its consequences have dimensional restrictions n≥3 due to the reliance on an analytic proposition from Chang et al. (Int Math Res Not 2004(4):185–209, 2004) concerning the asymptotic behavior of conformal factors of conformal metrics on domains of Sn . In this paper, we prove a new lemma about the asymptotic behavior of a functional combining the …

Circumferences Of 3-Connected Claw-Free Graphs, Ii, Zhi-Hong Chen

Scholarship and Professional Work - LAS

For a graph H , the circumference of H , denoted by c ( H ) , is the length of a longest cycle in H . It is proved in Chen (2016) that if H is a 3-connected claw-free graph of order n with δ ≥ 8 , then c ( H ) ≥ min { 9 δ − 3 , n } . In Li (2006), Li conjectured that every 3-connected k -regular claw-free graph H of order n has c ( H ) ≥ min { 10 k − 4 , n } . Later, Li posed …

Time Varying Parameter Estimation Scheme For A Linear Stochastic Differential Equation, Olusegun Michael Otunuga

Mathematics Faculty Research

In this work, an attempt is made to estimate time varying parameters in a linear stochastic differential equation. By defining mk as the local admissible sample/data observation size at time tk, parameters and state at time tk are estimated using past data on interval [tk−mk+1, tk]. We show that the parameter estimates at each time tk converge in probability to the true value of the parameters being estimated. A numerical simulation is presented by applying the local lagged adapted generalized method of moments (LLGMM) method to the stochastic differential models governing prices of energy …

On ΤΣ-Quasinormal Subgroups Of Finite Groups, James C. Beidleman, Alexander N. Skiba

Mathematics Faculty Publications

Let σ = {σ_i ∣ i ∈ I} be a partition of the set of all primes P and G a finite group. A set H of subgroups of G is said to be a complete Hall σ-set of G if every member ≠ 1 of H is a Hall σ_i-subgroup of G for some i ∈ I and H contains exactly one Hall σ_i-subgroup of G for every i such that σ_i ∩ π(G) ≠ ∅.

Let τ_H(A) = {σ_i ∈ σ …

Morphogenesis And Growth Driven By Selection Of Dynamical Properties, Yuri Cantor

Dissertations, Theses, and Capstone Projects

Organisms are understood to be complex adaptive systems that evolved to thrive in hostile environments. Though widely studied, the phenomena of organism development and growth, and their relationship to organism dynamics is not well understood. Indeed, the large number of components, their interconnectivity, and complex system interactions all obscure our ability to see, describe, and understand the functioning of biological organisms.

Here we take a synthetic and computational approach to the problem, abstracting the organism as a cellular automaton. Such systems are discrete digital models of real-world environments, making them more accessible and easier to study then their physical world …

Ns-K-Nn: Neutrosophic Set-Based K-Nearest Neighbors Classifier, Florentin Smarandache, Yaman Akbulut, Abdulkadir Sengur, Yanhui Guo

Branch Mathematics and Statistics Faculty and Staff Publications

k-nearest neighbors (k-NN), which is known to be a simple and efficient approach, is a non-parametric supervised classifier. It aims to determine the class label of an unknown sample by its k-nearest neighbors that are stored in a training set. The k-nearest neighbors are determined based on some distance functions. Although k-NN produces successful results, there have been some extensions for improving its precision. The neutrosophic set (NS) defines three memberships namely T, I and F. T, I, and F shows the truth membership degree, the false membership degree, and the indeterminacy membership degree, respectively. In this paper, the NS …

An Efficient Image Segmentation Algorithm Using Neutrosophic Graph Cut, Florentin Smarandache, Yanhui Guo, Yaman Akbulut, Abdulkadir Sengur, Rong Xia

Branch Mathematics and Statistics Faculty and Staff Publications

Segmentation is considered as an important step in image processing and computer vision applications, which divides an input image into various non-overlapping homogenous regions and helps to interpret the image more conveniently. This paper presents an efficient image segmentation algorithm using neutrosophic graph cut (NGC). An image is presented in neutrosophic set, and an indeterminacy filter is constructed using the indeterminacy value of the input image, which is defined by combining the spatial information and intensity information. The indeterminacy filter reduces the indeterminacy of the spatial and intensity information. A graph is defined on the image and the weight for …

Some Metric Properties Of The Teichmüller Space Of A Closed Set In The Riemann Sphere, Nishan Chatterjee

Dissertations, Theses, and Capstone Projects

Let E be an infinite closed set in the Riemann sphere, and let T(E) denote its Teichmüller space. In this dissertation we study some metric properties of T(E). We prove Earle's form of Teichmüller contraction for T(E), holomorphic isometries from the open unit disk into T(E), extend Earle's form of Schwarz's lemma for classical Teichmüller spaces to T(E), and finally study complex geodesics and unique extremality for T(E).

Involute Analysis: Virtual Discourse, Memory Systems And Archive In The Involutes Of Thomas De Quincey, Kimberley A. Garcia

Dissertations, Theses, and Capstone Projects

Thomas De Quincey’s involutes inform metaphysical thought on memory and language, particularly concerning multiplicity and the virtual, repetition and difference. When co-opting the mathematic and mechanic involute in Suspiria de Profundis, De Quincey generates an interdisciplinary matrix for the semiotics underpinning his philosophy of language and theory of memory and experience. Involutes entangle and reproduce. De Quincey’s involute exposes the concrete and actual through which all experience accesses the abstract or virtual. The materiality of their informatics and technics provides a literary model and theoretical precursor to a combination of archive and systems theory. The textuality of involute system(s)—both …

A Weighted Möbius Function, Derek Garton

Mathematics and Statistics Faculty Publications and Presentations

Fix an odd prime ℓ and let G be the poset of isomorphism classes of finite abelian ℓ-groups, ordered by inclusion. If ξ:G→R^≥0 is a discrete probability distribution on G and A ∈ G, define the Ath moment of ξ to be . The question of determining conditions that ensure ξ is completely determined by its moments has been of recent interest in many problems of Cohen–Lenstra type. Furthermore, recovering ξ from its moments requires a new Möbius-type inversion formula on G. In this paper, we define this function, relate it to the classical Möbius …

Direct Computations Of Marangoni Driven Flows Using A Volume Of Fluid Method, Ivana Seric

Dissertations

The volume of fluid (VoF) interface tracking methods have been used for simulating a wide range of interfacial flows. An improved accuracy of the surface tension force computation has enabled the VoF method to become widely used for simulating flows driven by the surface tension force. A general methodology for the inclusion of variable surface tension coefficient into a VoF based Navier-Stokes solver is developed. This new numerical model provides a robust and accurate method for computing the surface gradients directly by finding the tangent directions on the interface using height functions. The implementation applies to both temperature and concentration …

Okcupid Data For Introductory Statistics And Data Science Courses, Albert Y. Kim, Adriana Escobedo-Land

Mathematics Sciences: Faculty Publications

We present a data set consisting of user profile data for 59,946 San Francisco OkCupid users (a free online dating website) from June 2012. The data set includes typical user information, lifestyle variables, and text responses to 10 essay questions. We present four example analyses suitable for use in undergraduate introductory probability and statistics and data science courses that use R. The statistical and data science concepts covered include basic data visualization, exploratory data analysis, multivariate relationships, text analysis, and logistic regression for prediction.

A Brief Introduction To Equi-Chordal And Equi-Isoclinic Tight Fusion Frames, Matthew C. Fickus, John Jasper, Dustin G. Mixon, Cody E. Watson

Faculty Publications

Equi-chordal and equi-isoclinic tight fusion frames (ECTFFs and EITFFs) are both types of optimal packings of subspaces in Euclidean spaces. In the special case where these subspaces are one-dimensional, ECTFFs and EITFFs both correspond to types of optimal packings of lines known as equiangular tight frames. In this brief note, we review some of the fundamental ideas and results concerning ECTFFs and EITFFs.

Split-Merge Model Of Workunit Replication In Distributed Computing, Alexander Rumyantsev, Srinivas R. Chakravarthy

Industrial & Manufacturing Engineering Presentations And Conference Materials

No abstract provided.

The Role Of Body Flexibility In Stroke Enhancements For Finite-Length Undulatory Swimmers In Viscoelastic Fluids, Becca Thomases, Robert D. Guy

Mathematics Sciences: Faculty Publications

The role of passive body dynamics on the kinematics of swimming micro-organisms in complex fluids is investigated. Asymptotic analysis of small-amplitude motions of a finite-length undulatory swimmer in a Stokes-Oldroyd-B fluid is used to predict shape changes that result as body elasticity and fluid elasticity are varied. Results from the analysis are compared with numerical simulations and the numerically simulated shape changes agree with the analysis at both small and large amplitudes, even for strongly elastic flows. We compute a stroke-induced swimming speed that accounts for the shape changes, but not additional effects of fluid elasticity. Elasticity-induced shape changes lead …

On Lower Bounds For S-Multiplicities, Lance Edward Miller, William D. Taylor

Mathematical Sciences Faculty Research

A recent continuous family of multiplicity functions on local rings was introduced by Taylor interpolating between Hilbert-Samuel and Hilbert-Kunz multiplicities. The obvious goal is to use this as a tool for deforming results from one to the other. The values in this family which do not match these classic variants however are not known yet to be well-behaved. This article explores lower bounds for these intermediate multiplicities as well as gives evidence for analogies of the Watanabe-Yoshida minimality conjectures for unmixed singular rings.

Solving Numerically Ermakov-Type Equation For Newtonian Cosmology Model With Vortex, Victor Christianto, Florentin Smarandache, Yunita Umniyati

Branch Mathematics and Statistics Faculty and Staff Publications

It has been known for long time that most of the existing cosmology models have singularity problem. Cosmological singularity has been a consequence of excessive symmetry of flow, such as “Hubble’s law”. More realistic one is suggested, based on Newtonian cosmology model but here we include the vertical-rotational effect of the whole Universe. We review a Riccati-type equation obtained by Nurgaliev, and solve the equation numerically with Mathematica. It is our hope that the new proposed method can be verified with observation data.

The Effects Of Gender And Ethnicity On Students' Perceptions Of Small-Group Learning In Collegiate Mathematics Courses, Layla Potts

Master's Theses and Doctoral Dissertations

Qualitative studies of students' perceptions on small-group work are limited, and few offer insights on the perceptions of women and minority students, for whom quantitative research suggests that small-group work is most beneficial. The aim of this research project is to conduct a qualitative analysis on the perceptions of women and minority students on their small-group learning experiences in collegiate mathematics courses. We conducted a Likert-scale survey of 114 Eastern Michigan University undergraduate students who were enrolled in a cross section of mathematics courses. The data were analyzed using statistical measures such as the frequency and modes of each response, …

Elliptic Solutions And Solitary Waves Of A Higher Order Kdv-Bbm Long Wave Equation, S.C. Mancas, Ronald Adams

Publications

We provide conditions for existence of hyperbolic, unbounded periodic and elliptic solutions in terms of Weierstrass ℘ functions of both third and fifth-order KdV–BBM (Korteweg-de Vries–Benjamin, Bona & Mahony) regularized long wave equation. An analysis for the initial value problem is developed together with a local and global well-posedness theory for the third-order KdV–BBM equation. Traveling wave reduction is used together with zero boundary conditions to yield solitons and periodic unbounded solutions, while for nonzero boundary conditions we find solutions in terms of Weierstrass elliptic ℘ functions. For the fifth-order KdV–BBM equation we show that a parameter γ = 1/12 …

It’S Déjà Vu All Over Again: A Classical Interpretation Of Syntropy And Precognitive Interdiction Based On Wheeler-Feynman’S Absorber Theory, Victor Christianto, Florentin Smarandache, Yunita Umniyati

Branch Mathematics and Statistics Faculty and Staff Publications

It has been known for long time that intuition plays significant role in many professions and human life, including in entrepreneurship, government, and also in detective or law enforcement activities. Even women are known to possess better intuitive feelings or “hunch” compared to men. Despite these examples, such a precognitive interdiction is hardly accepted in established science. In this paper, we discuss briefly the advanced solutions of Maxwell equations, and then make connection between syntropy and precognition from classical perspective. It is our hope that the new proposed method can be verified with experimental data. But we admit that our …