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2017

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Articles 181 - 210 of 1334

Full-Text Articles in Mathematics

Some Metric Properties Of The Teichmüller Space Of A Closed Set In The Riemann Sphere, Nishan Chatterjee Sep 2017

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).

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Ns-K-Nn: Neutrosophic Set-Based K-Nearest Neighbors Classifier, Florentin Smarandache, Yaman Akbulut, Abdulkadir Sengur, Yanhui Guo Sep 2017

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 …

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Direct Computations Of Marangoni Driven Flows Using A Volume Of Fluid Method, Ivana Seric Aug 2017

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 …

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A Brief Introduction To Equi-Chordal And Equi-Isoclinic Tight Fusion Frames, Matthew C. Fickus, John Jasper, Dustin G. Mixon, Cody E. Watson Aug 2017

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.

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Okcupid Data For Introductory Statistics And Data Science Courses, Albert Y. Kim, Adriana Escobedo-Land Aug 2017

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.

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Split-Merge Model Of Workunit Replication In Distributed Computing, Alexander Rumyantsev, Srinivas R. Chakravarthy Aug 2017

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

Industrial & Manufacturing Engineering Presentations And Conference Materials

No abstract provided.

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The Role Of Body Flexibility In Stroke Enhancements For Finite-Length Undulatory Swimmers In Viscoelastic Fluids, Becca Thomases, Robert D. Guy Aug 2017

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 …

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On Lower Bounds For S-Multiplicities, Lance Edward Miller, William D. Taylor Aug 2017

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.

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Solving Numerically Ermakov-Type Equation For Newtonian Cosmology Model With Vortex, Victor Christianto, Florentin Smarandache, Yunita Umniyati Aug 2017

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.

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The Effects Of Gender And Ethnicity On Students' Perceptions Of Small-Group Learning In Collegiate Mathematics Courses, Layla Potts Aug 2017

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, …

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Elliptic Solutions And Solitary Waves Of A Higher Order Kdv-Bbm Long Wave Equation, S.C. Mancas, Ronald Adams Aug 2017

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 …

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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 Aug 2017

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 …

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Frg: Collaborative Research: Homotopy Renormalization Of Topological Field Theories, Nathan Geer Aug 2017

Frg: Collaborative Research: Homotopy Renormalization Of Topological Field Theories, Nathan Geer

Funded Research Records

No abstract provided.

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A Finite Difference Method For Off-Fault Plasticity Throughout The Earthquake Cycle, Brittany A. Erickson, Eric M. Dunham, Arash Khosravifar Aug 2017

A Finite Difference Method For Off-Fault Plasticity Throughout The Earthquake Cycle, Brittany A. Erickson, Eric M. Dunham, Arash Khosravifar

Mathematics and Statistics Faculty Publications and Presentations

We have developed an efficient computational framework for simulating multiple earthquake cycles with off-fault plasticity. The method is developed for the classical antiplane problem of a vertical strike-slip fault governed by rate-and-state friction, with inertial effects captured through the radiationdamping approximation. Both rate-independent plasticity and viscoplasticity are considered, where stresses are constrained by a Drucker-Prager yield condition. The off-fault volume is discretized using finite differences and tectonic loading is imposed by displacing the remote side boundaries at a constant rate. Time-stepping combines an adaptive Runge-Kutta method with an incremental solution process which makes use of an elastoplastic tangent stiffness tensor …

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Improving The Accuracy For The Long-Term Hydrologic Impact Assessment (L-Thia) Model, Anqi Zhang, Lawrence Theller, Bernard A. Engel Aug 2017

Improving The Accuracy For The Long-Term Hydrologic Impact Assessment (L-Thia) Model, Anqi Zhang, Lawrence Theller, Bernard A. Engel

The Summer Undergraduate Research Fellowship (SURF) Symposium

Urbanization increases runoff by changing land use types from less impervious to impervious covers. Improving the accuracy of a runoff assessment model, the Long-Term Hydrologic Impact Assessment (L-THIA) Model, can help us to better evaluate the potential uses of Low Impact Development (LID) practices aimed at reducing runoff, as well as to identify appropriate runoff and water quality mitigation methods. Several versions of the model have been built over time, and inconsistencies have been introduced between the models. To improve the accuracy and consistency of the model, the equations and parameters (primarily curve numbers in the case of this model) …

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Predicting Locations Of Pollution Sources Using Convolutional Neural Networks, Yiheng Chi, Nickolas D. Winovich, Guang Lin Aug 2017

Predicting Locations Of Pollution Sources Using Convolutional Neural Networks, Yiheng Chi, Nickolas D. Winovich, Guang Lin

The Summer Undergraduate Research Fellowship (SURF) Symposium

Pollution is a severe problem today, and the main challenge in water and air pollution controls and eliminations is detecting and locating pollution sources. This research project aims to predict the locations of pollution sources given diffusion information of pollution in the form of array or image data. These predictions are done using machine learning. The relations between time, location, and pollution concentration are first formulated as pollution diffusion equations, which are partial differential equations (PDEs), and then deep convolutional neural networks are built and trained to solve these PDEs. The convolutional neural networks consist of convolutional layers, reLU layers …

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Problem Solving Practice With Problems From Fibonacci's "Liber Abbaci", Cynthia J. Huffman Ph.D. Aug 2017

Problem Solving Practice With Problems From Fibonacci's "Liber Abbaci", Cynthia J. Huffman Ph.D.

Open Educational Resources - Math

In this activity, problem solving skills are practiced using two well-known problems from Fibonacci's world-changing book "Liber Abbaci". Students are also asked to reflect on the differences and similarities between their solutions and those of Fibonacci. The two problems are the famous rabbit problem which led to what is now know as the Fibonacci sequence and the 30 birds for 30 denarii problem, which is not as well-known to the general public.

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Development And Implementation Of An Optimization Model To Improve Airport Security., Kassandra Guajardo, Angela Waterworth, Robert Brigantic Ph.D. Aug 2017

Development And Implementation Of An Optimization Model To Improve Airport Security., Kassandra Guajardo, Angela Waterworth, Robert Brigantic Ph.D.

STAR Program Research Presentations

What if airport security teams across the world could quantify and then minimize the amount of risk throughout areas of an airport? The Operations Research Team at the Pacific Northwest National Laboratory is developing and implementing an optimization model called ARAM (Airport Risk Analysis Model) for the Seattle-Tacoma International Airport. ARAM will provide a recommended optimal deployment of security assets to reduce risk in areas of an airport. The model is based on a risk equation that considers consequences, vulnerabilities, and threat magnitudes at airports. ARAM will also provide the estimated risk buy down percentage, which is how much risk …

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Efficient Parameter-Estimating Algorithms For Symmetry-Motivated Models: Econometrics And Beyond, Vladik Kreinovich, Anh H. Ly, Olga Kosheleva, Songsak Sriboonchitta Aug 2017

Efficient Parameter-Estimating Algorithms For Symmetry-Motivated Models: Econometrics And Beyond, Vladik Kreinovich, Anh H. Ly, Olga Kosheleva, Songsak Sriboonchitta

Departmental Technical Reports (CS)

It is known that symmetry ideas can explain the empirical success of many non-linear models. This explanation makes these models theoretically justified and thus, more reliable. However, the models remain non-linear and thus, identification or the model's parameters based on the observations remains a computationally expensive nonlinear optimization problem. In this paper, we show that symmetry ideas can not only help to select and justify a nonlinear model, they can also help us design computationally efficient almost-linear algorithms for identifying the model's parameters.

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Maximum Entropy Beyond Selecting Probability Distributions, Thach N. Nguyen, Olga Kosheleva, Vladik Kreinovich Aug 2017

Maximum Entropy Beyond Selecting Probability Distributions, Thach N. Nguyen, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditionally, the Maximum Entropy technique is used to select a probability distribution in situations when several different probability distributions are consistent with our knowledge. In this paper, we show that this technique can be extended beyond selecting probability distributions, to explain facts, numerical values, and even types of functional dependence.

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Almost All Diophantine Sets Are Undecidable, Vladik Kreinovich Aug 2017

Almost All Diophantine Sets Are Undecidable, Vladik Kreinovich

Departmental Technical Reports (CS)

The known 1970 solution to the 10th Hilbert problem says that no algorithm is possible that would decide whether a given Diophantine equation has a solution. In set terms, this means that not all Diophantine sets are decidable. In a posting to the Foundations of Mathematica mailing list, Timothy Y. Chow asked for possible formal justification for his impression that most Diophantine equations are not decidable. One such possible justification is presented in this paper.

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A Study On Traveling Wave Solutions In The Shallow-Water-Type System, Ting Luo Aug 2017

A Study On Traveling Wave Solutions In The Shallow-Water-Type System, Ting Luo

Mathematics Dissertations - Archive

The study of water waves reveals the physical principles of many phenomena of scientific and engineering interest. In this dissertation I consider three models: two-component Camassa-Holm system(2CH), generalized two-component Camassa-Holm equation(g2CH) and rotation-Camassa-Holm equation(R-CH). In the first part, we consider the stability of the Camassa-Holm peakons and antipeakons in the dynamics of the two-component Camassa-Holm system. The second part shows that the train of $N$-smooth traveling waves of this system is dynamically stable to perturbations in energy space with a range of parameters. In the third part, we formally derive the simplified phenomenological models with the Coriolis effect due to …

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Stability Study On Shear Flow And Vortices In Late Boundary Layer Transition, Jie Tang Aug 2017

Stability Study On Shear Flow And Vortices In Late Boundary Layer Transition, Jie Tang

Mathematics Dissertations - Archive

Turbulence is still an unsolved scientific problem, it has been regarded as “the most important unsolved problem of classical physics”. Dr. Liu proposed a new mechanism about turbulence generation and sustenance after decades of research on turbulence and transition. His new idea challenged the classical theorem in many aspects. One of them is the flow stability of transition. Dr. Liu believes that inside the flow field, shear (dominant in laminar) is very unstable while rotation (dominant in turbulence) is relative stable. This inherent property of flow creates the trend that non-vertical vorticity must transfer to vertical vorticity, and causes the …

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Image Reconstruction From Incomplete Radon Data And Generalized Principal Component Analysis, Sl Ghi Choi Aug 2017

Image Reconstruction From Incomplete Radon Data And Generalized Principal Component Analysis, Sl Ghi Choi

Mathematics Dissertations - Archive

Image reconstruction in various types of tomography requires inversion of the Radon transform and its generalizations. While there are many stable and robust algorithms for such inversions from reasonably well sampled data, most of these algorithms fail when applied to limited view data. In the dissertation we develop a new method of stable reconstruction from limited view data for functions, whose support is a union of finitely many circles. Such images, among other things, are good approximations of tomograms of certain types of tumors in lungs. Our method is based on a modified version of GPCA (General Principle Component Analysis) …

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Evoked And Spontaneous Neurotransmitter Releases For Independent Synaptic Currents: Mathematical Modeling And Analysis, Sat Byul Seo Aug 2017

Evoked And Spontaneous Neurotransmitter Releases For Independent Synaptic Currents: Mathematical Modeling And Analysis, Sat Byul Seo

Mathematics Dissertations - Archive

Synapses play a major role in neuron communications in the brain. The synapses act through a chemical process called synaptic fusion between pre-synaptic and post-synaptic terminals. Presynaptic terminals release neurotransmitters either in response to action potential or spontaneously independent of presynaptic activity. In the case of glutamate, released neurotransmitters acivate N-methyl-D-asparate (NMDA) receptors within a single postsynaptic site and give rise to miniature postsynaptic currents. In this dissertation, we develop a mathematical model in 3-D to emulate spontaneous and evoked neurotransmissions resulted from glutamate release within a single synapse. We propose numerical methods for solving piecewise continuous heat diffusion equation, …

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Simple Weight Modules Of The Lie Algebra Of Vector Fields Of C2, Andrew Cavaness Aug 2017

Simple Weight Modules Of The Lie Algebra Of Vector Fields Of C2, Andrew Cavaness

Mathematics Dissertations - Archive

Classification of the weight modules of the Lie algebra Wn of vector fields on C n has been a long-standing problem in the area of representation theory. In this thesis, a classification of all simple weight modules of W2 with a uniformly bounded set of weight multiplicities is provided, and much of the theory that will be needed to classify all simple weight modules of Wn with a uniformly bounded set of weight multiplicities will also be developed. To achieve this classification, a new family of generalized tensor Wn-modules is introduced, and a twisted localization functor is applied.

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Efficiently Representing The Integer Factorization Problem Using Binary Decision Diagrams, David Skidmore Aug 2017

Efficiently Representing The Integer Factorization Problem Using Binary Decision Diagrams, David Skidmore

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Let p be a prime positive integer and let α be a positive integer greater than 1. A method is given to reduce the problem of finding a nontrivial factorization of α to the problem of finding a solution to a system of modulo p polynomial congruences where each variable in the system is constrained to the set {0,...,p − 1}. In the case that p = 2 it is shown that each polynomial in the system can be represented by an ordered binary decision diagram with size less than 20.25log2(α)3 + 16.5log2(α)2 + …

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High Order Dns For Vortex Structure In Late Flow Transition, Yong Yang Aug 2017

High Order Dns For Vortex Structure In Late Flow Transition, Yong Yang

Mathematics Dissertations - Archive

Turbulence is still a world puzzle after over one hundred years research, and the current and classical theories brim with self-contradictions. C. Liu proposed a new theory on turbulence generation and structure after 28 years research, which are consistent without self-contradictions and well explain turbulence generation and structure. Based on this new theory, this dissertation (1) gives some mathematical explanations for new vortex identify method – Ω method; (2) analyzes the instability of shear layer by applying Chebyshev spectrum method to solve Orr-Sommerfeld eigenvalue equation; (3) investigates the vortex structure development in late flow transition; (4) utilizes the proper orthogonal …

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Characterizing College Algebra Students' Mathematical Problem Solving, R. Cavender Campbell Aug 2017

Characterizing College Algebra Students' Mathematical Problem Solving, R. Cavender Campbell

Mathematics Dissertations - Archive

This study examines the mathematical problem solving (MPS) practices of students enrolled in College Algebra at a large urban university in the southwestern United States. The primary research question explores how to characterize the MPS techniques, strategies or orientations used by College Algebra students. In addition, this study documents MPS approaches that appear to be most prevalent and examines how these approaches relate to student performance. A grounded theory approach is used to formulate a theory for characterizing the MPS of students in College Algebra. Data analysis shows that multiple student-held orientations identified in this theory correlate with improved performance …

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Mathematical Methods For Vortex Identification With Application On Shock Wave Vortex Ring Interaction, Yinlin Dong Aug 2017

Mathematical Methods For Vortex Identification With Application On Shock Wave Vortex Ring Interaction, Yinlin Dong

Mathematics Dissertations - Archive

Vortices are seen everywhere in nature, from smoke rings to tornadoes. Vortical structures play an essential role in the turbulence dynamics such as turbulence generation, kinetic energy production and dissipation, enhancement of transport of mass, heat and momentum and so on. In this dissertation, we present several vortex identification methods and compare them by the visualization of the examples studied by direct numerical simulation for flows with different speeds. The comparisons show the Omega method is much close to give vortex a mathematical definition and better visualization for vortical structures. We apply our method on the Micro Vortex Generator (MVG) …

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