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Articles 1 - 30 of 99
Full-Text Articles in Mathematics
Closed-Form Probability Distribution Of Number Of Infections At A Given Time In A Stochastic Sis Epidemic Model.Pdf, Michael Otunuga
Closed-Form Probability Distribution Of Number Of Infections At A Given Time In A Stochastic Sis Epidemic Model.Pdf, Michael Otunuga
Olusegun Michael Otunuga
A Comparison Of Machine Learning Techniques For Taxonomic Classification Of Teeth From The Family Bovidae, Gregory J. Matthews, Juliet K. Brophy, Maxwell Luetkemeier, Hongie Gu, George K. Thiruvathukal
A Comparison Of Machine Learning Techniques For Taxonomic Classification Of Teeth From The Family Bovidae, Gregory J. Matthews, Juliet K. Brophy, Maxwell Luetkemeier, Hongie Gu, George K. Thiruvathukal
George K. Thiruvathukal
This study explores the performance of machine learning algorithms on the classification of fossil teeth in the Family Bovidae. Isolated bovid teeth are typically the most common fossils found in southern Africa and they often constitute the basis for paleoenvironmental reconstructions. Taxonomic identification of fossil bovid teeth, however, is often imprecise and subjective. Using modern teeth with known taxons, machine learning algorithms can be trained to classify fossils. Previous work by Brophy et al. [Quantitative morphological analysis of bovid teeth and implications for paleoenvironmental reconstruction of plovers lake, Gauteng Province, South Africa, J. Archaeol. Sci. 41 (2014), pp. …
A Self-Contained Course In The Mathematical Theory Of Statistics For Scientists & Engineers With An Emphasis On Predictive Regression Modeling & Financial Applications., Tim Smith
Timothy Smith
Preface & Acknowledgments
This textbook is designed for a higher level undergraduate, perhaps even first year graduate, course for engineering or science students who are interested to gain knowledge of using data analysis to make predictive models. While there is no statistical perquisite knowledge required to read this book, due to the fact that the study is designed for the reader to truly understand the underlying theory rather than just learn how to read computer output, it would be best read with some familiarity of elementary statistics. The book is self-contained and the only true perquisite knowledge is a solid …
Almost Oscillatory Three Dimensional Dynamic Systems, Elvan Akin, Zuzana Dosla, Bonita Lawrence
Almost Oscillatory Three Dimensional Dynamic Systems, Elvan Akin, Zuzana Dosla, Bonita Lawrence
Bonita Lawrence
In this article, we investigate oscillation and asymptotic properties for 3D systems of dynamic equations. We show the role of nonlinearities and we apply our results to the adjoint dynamic systems.
Stochastic Modeling And Analysis Of Energy Commodity Spot Price Processes, Olusegun Michael Otunuga
Stochastic Modeling And Analysis Of Energy Commodity Spot Price Processes, Olusegun Michael Otunuga
Olusegun Michael Otunuga
Supply and demand in the World oil market are balanced through responses to price movement with considerable complexity in the evolution of underlying supply-demand
expectation process. In order to be able to understand the price balancing process, it is important to know the economic forces and the behavior of energy commodity spot price processes. The relationship between the different energy sources and its utility together with uncertainty also play a role in many important energy issues.
The qualitative and quantitative behavior of energy commodities in which the trend in price of one commodity coincides with the trend in price of …
Local Lagged Adapted Generalized Method Of Moments: An Innovative Estimation And Forecasting Approach And Its Applications.Pdf, Olusegun M. Otunuga
Local Lagged Adapted Generalized Method Of Moments: An Innovative Estimation And Forecasting Approach And Its Applications.Pdf, Olusegun M. Otunuga
Olusegun Michael Otunuga
A Math Research Project Inspired By Twin Motherhood, Tiffany N. Kolba
A Math Research Project Inspired By Twin Motherhood, Tiffany N. Kolba
Tiffany N Kolba
The phenomenon of twins, triplets, quadruplets, and other higher order multiples has fascinated humans for centuries and has even captured the attention of mathematicians who have sought to model the probabilities of multiple births. However, there has not been extensive research into the phenomenon of polyovulation, which is one of the biological mechanisms that produces multiple births. In this paper, I describe how my own experience becoming a mother to twins led me on a quest to better understand the scientific processes going on inside my own body and motivated me to conduct research on polyovulation frequencies. An overview of …
Excess Versions Of The Minkowski And Hölder Inequalities, Iosif Pinelis
Excess Versions Of The Minkowski And Hölder Inequalities, Iosif Pinelis
Iosif Pinelis
No abstract provided.
Global Stability For A 2n+1 Dimensional Hiv Aids Epidemic Model With Treatments, Olusegun M. Otunuga
Global Stability For A 2n+1 Dimensional Hiv Aids Epidemic Model With Treatments, Olusegun M. Otunuga
Olusegun Michael Otunuga
Inventing Around Edison’S Lamp Patent: The Role Of Patents In Stimulating Downstream Development And Competition, Ron D. Katznelson, John Howells
Inventing Around Edison’S Lamp Patent: The Role Of Patents In Stimulating Downstream Development And Competition, Ron D. Katznelson, John Howells
Ron D. Katznelson
We provide the first detailed empirical study of inventing around patent claims. The enforcement of Edison’s incandescent lamp patent in 1891-1894 stimulated a surge of patenting. Most of these later patents disclosed inventions around the Edison patent. Some of these patents introduced important new technology in their own right and became prior art for new fields, indicating that invention around patents contributes to dynamic efficiency. Contrary to widespread contemporary understanding, the Edison lamp patent did not suppress technological advance in electric lighting. The market position of General Electric (“GE”), the Edison patent-owner, weakened through the period of this patent’s enforcement.
Some Applications Of Sophisticated Mathematics To Randomized Computing, Ronald I. Greenberg
Some Applications Of Sophisticated Mathematics To Randomized Computing, Ronald I. Greenberg
Ronald Greenberg
No abstract provided.
Educational Magic Tricks Based On Error-Detection Schemes, Ronald I. Greenberg
Educational Magic Tricks Based On Error-Detection Schemes, Ronald I. Greenberg
Ronald Greenberg
Magic tricks based on computer science concepts help grab student attention and can motivate them to delve more deeply. Error detection ideas long used by computer scientists provide a rich basis for working magic; probably the most well known trick of this type is one included in the CS Unplugged activities. This paper shows that much more powerful variations of the trick can be performed, some in an unplugged environment and some with computer assistance. Some of the tricks also show off additional concepts in computer science and discrete mathematics.
Learning About Modeling In Teacher Preparation Programs, Hyunyi Jung, Eryn Stehr, Jia He, Sharon L. Senk
Learning About Modeling In Teacher Preparation Programs, Hyunyi Jung, Eryn Stehr, Jia He, Sharon L. Senk
Hyunyi Jung
This study explores opportunities that secondary mathematics teacher preparation programs provide to learn about modeling in algebra. Forty-eight course instructors and ten focus groups at five universities were interviewed to answer questions related to modeling. With the analysis of the interview transcripts and related course materials, we found few opportunities for PSTs to engage with the full modeling cycle. Examples of opportunities to learn about algebraic modeling and the participants’ perspectives on the opportunities can contribute to the study of modeling and algebra in teacher education.
Time Varying Parameter Estimation Scheme For A Linear Stochastic Differential Equation.Pdf, Michael Otunuga
Time Varying Parameter Estimation Scheme For A Linear Stochastic Differential Equation.Pdf, Michael Otunuga
Olusegun Michael Otunuga
Global Stability Of Nonlinear Stochastic Sei Epidemic Model With Fluctuations In Transmission Rate Of Disease, Olusegun M. Otunuga
Global Stability Of Nonlinear Stochastic Sei Epidemic Model With Fluctuations In Transmission Rate Of Disease, Olusegun M. Otunuga
Olusegun Michael Otunuga
Coarsening In High Order, Discrete, Ill-Posed Diffusion Equations, Catherine Kublik
Coarsening In High Order, Discrete, Ill-Posed Diffusion Equations, Catherine Kublik
Catherine Kublik
We study the discrete version of a family of ill-posed, nonlinear diffusion equations of order 2n. The fourth order (n=2) version of these equations constitutes our main motivation, as it appears prominently in image processing and computer vision literature. It was proposed by You and Kaveh as a model for denoising images while maintaining sharp object boundaries (edges). The second order equation (n=1) corresponds to another famous model from image processing, namely Perona and Malik's anisotropic diffusion, and was studied in earlier papers. The equations studied in this paper are high order analogues of the Perona-Malik equation, and like the …
Algorithms For Area Preserving Flows, Catherine Kublik, Selim Esedoglu, Jeffrey A. Fessler
Algorithms For Area Preserving Flows, Catherine Kublik, Selim Esedoglu, Jeffrey A. Fessler
Catherine Kublik
We propose efficient and accurate algorithms for computing certain area preserving geometric motions of curves in the plane, such as area preserving motion by curvature. These schemes are based on a new class of diffusion generated motion algorithms using signed distance functions. In particular, they alternate two very simple and fast operations, namely convolution with the Gaussian kernel and construction of the distance function, to generate the desired geometric flow in an unconditionally stable manner. We present applications of these area preserving flows to large scale simulations of coarsening.
An Implicit Interface Boundary Integral Method For Poisson’S Equation On Arbitrary Domains, Catherine Kublik, Nicolay M. Tanushev, Richard Tsai
An Implicit Interface Boundary Integral Method For Poisson’S Equation On Arbitrary Domains, Catherine Kublik, Nicolay M. Tanushev, Richard Tsai
Catherine Kublik
We propose a simple formulation for constructing boundary integral methods to solve Poisson’s equation on domains with smooth boundaries defined through their signed distance function. Our formulation is based on averaging a family of parameterizations of an integral equation defined on the boundary of the domain, where the integrations are carried out in the level set framework using an appropriate Jacobian. By the coarea formula, the algorithm operates in the Euclidean space and does not require any explicit parameterization of the boundaries. We present numerical results in two and three dimensions.
Lyapunov Functionals That Lead To Exponential Stability And Instability In Finite Delay Volterra Difference Equations, Catherine Kublik, Youssef Raffoul
Lyapunov Functionals That Lead To Exponential Stability And Instability In Finite Delay Volterra Difference Equations, Catherine Kublik, Youssef Raffoul
Catherine Kublik
We use Lyapunov functionals to obtain sufficient conditions that guarantee exponential stability of the zero solution of the finite delay Volterra difference equation. Also, by displaying a slightly different Lyapunov functional, we obtain conditions that guarantee the instability of the zero solution. The highlight of the paper is the relaxing of the condition |a(t)| < 1. Moreover, we provide examples in which we show that our theorems provide an improvement of some recent results.
A Note On Irreducibility And Weak Covering Properties, Joe Mashburn
A Note On Irreducibility And Weak Covering Properties, Joe Mashburn
Joe D. Mashburn
A space X is irreducible if every open cover of X has a minimal open refinement. Interest in irreducibility began when Arens and Dugendji used this property to show that metacompact countably compact spaces are compact. It was natural, then, to find out what other types of spaces would be irreducible and therefore compact in the presence of countable compactness or Lindelof in the presence of N1-compactness. … It is shown in this paper that T1 δθ -refinable spaces and T1 weakly δθ-refinable spaces are irreducible. Since examples of Lindelof spaces that are neither T1 nor irreducible can be easily …
Sobriety In Delta Not Sober, Joe Mashburn
Sobriety In Delta Not Sober, Joe Mashburn
Joe D. Mashburn
We will show that the space delta not sober defined by Coecke and Martin is sober in the Scott topology, but not in the weakly way below topology.
Dissertation: The Least Fixed Point Property For Ω-Chain Continuous Functions, Joe Mashburn
Dissertation: The Least Fixed Point Property For Ω-Chain Continuous Functions, Joe Mashburn
Joe D. Mashburn
The basic definitions are given in the first section, including those for ω-chain continuity, ω-chain completeness, and the least fixed point property for ω-chain continuous functions. Some of the relations between completeness and fixed point properties in partially ordered sets are stated and it is briefly shown how the question basic to the dissertation arises. In the second section, two examples are given showing that a partially ordered set need not be ω-chain complete to have the least fixed point property for ω-chain continuous functions. Retracts are discussed in section 3, where it is seen that they are not sufficient …
On The Decomposition Of Order-Separable Posets Of Countable Width Into Chains, Gary Gruenhage, Joe Mashburn
On The Decomposition Of Order-Separable Posets Of Countable Width Into Chains, Gary Gruenhage, Joe Mashburn
Joe D. Mashburn
partially ordered set X has countable width if and only if every collection of pairwise incomparable elements of X is countable. It is order-separable if and only if there is a countable subset D of X such that whenever p, q ∈ X and p < q, there is r ∈ D such that p ≤ r ≤ q. Can every order-separable poset of countable width be written as the union of a countable number of chains? We show that the answer to this question is "no" if there is a 2-entangled subset of IR, and "yes" under the Open Coloring …
The Least Fixed Point Property For Ω-Chain Continuous Functions, Joe Mashburn
The Least Fixed Point Property For Ω-Chain Continuous Functions, Joe Mashburn
Joe D. Mashburn
A partially ordered set P is ω-chain complete if every countable chain (including the empty set) in P has a supremum. … Notice that an ω-chain continuous function must preserve order. P has the (least) fixed point property for ω-chain continuous functions if every ω-chain continuous function from P to itself has (least) fixed point. It has been shown that a partially ordered set does not have to be ω-chain complete to have the least fixed point property for ω-chain continuous functions. This answers a question posed by G. Plotkin in 1978. I.I. Kolodner has shown that an ω-chain complete …
Oif Spaces, Zoltan Balogh, Harold Bennett, Dennis Burke, Gary Gruenhage, David Lutzer, Joe D. Mashburn
Oif Spaces, Zoltan Balogh, Harold Bennett, Dennis Burke, Gary Gruenhage, David Lutzer, Joe D. Mashburn
Joe D. Mashburn
A base β of a space X is called an OIF base when every element of B is a subset of only a finite number of other elements of β. We will explore the fundamental properties of spaces having such bases. In particular, we will show that in T2 spaces, strong OIF bases are the same as uniform bases, and that in T3 spaces where all subspaces have OIF bases, compactness, countable compactness, or local compactness will give metrizability.
A Spectral Order For Infinite Dimensional Quantum Spaces: A Preliminary Report, Joe Mashburn
A Spectral Order For Infinite Dimensional Quantum Spaces: A Preliminary Report, Joe Mashburn
Joe D. Mashburn
In 2002 Coecke and Martin created a Bayesian order for the finite dimensional spaces of classical states in physics and used this to define a similar order, the spectral order on the finite dimensional quantum states. These orders gave the spaces a structure similar to that of a domain. This allows for measuring information content of states and for determining which partial states are approximations of which pure states. In a previous paper the author extended the Bayesian order to infinite dimensional spaces of classical states. The order on infinite dimensional spaces retains many of the characteristics important to physics, …
Three Counterexamples Concerning Ω-Chain Continuous Functions And Fixed-Point Properties, Joe Mashburn
Three Counterexamples Concerning Ω-Chain Continuous Functions And Fixed-Point Properties, Joe Mashburn
Joe D. Mashburn
A partially ordered set is ω-chain complete if, for every countable chain, or ω-chain, in P, the least upper bound of C, denoted by sup C, exists. Notice that C could be empty, so an ω-chain complete partially ordered set has a least element, denoted by 0.
A Spectral Order For Infinite Dimensional Quantum Spaces, Joe Mashburn
A Spectral Order For Infinite Dimensional Quantum Spaces, Joe Mashburn
Joe D. Mashburn
In this paper we extend the spectral order of Coecke and Martin to infinite-dimensional quantum states. Many properties present in the finite-dimensional case are preserved, but some of the most important are lost. The order is constructed and its properties analysed. Most of the useful measurements of information content are lost. Shannon entropy is defined on only a part of the model, and that part is not a closed subset of the model. The finite parts of the lattices used by Birkhoff and von Neumann as models for classical and quantum logic appear as subsets of the models for infinite …
An Order Model For Infinite Classical States, Joe Mashburn
An Order Model For Infinite Classical States, Joe Mashburn
Joe D. Mashburn
In 2002 Coecke and Martin (Research Report PRG-RR-02-07, Oxford University Computing Laboratory,2002) created a model for the finite classical and quantum states in physics. This model is based on a type of ordered set which is standard in the study of information systems. It allows the information content of its elements to be compared and measured. Their work is extended to a model for the infinite classical states. These are the states which result when an observable is applied to a quantum system. When this extended order is restricted to a finite number of coordinates, the model of Coecke and …
A Note On Reordering Ordered Topological Spaces And The Existence Of Continuous, Strictly Increasing Functions, Joe Mashburn
A Note On Reordering Ordered Topological Spaces And The Existence Of Continuous, Strictly Increasing Functions, Joe Mashburn
Joe D. Mashburn
The origin of this paper is in a question that was asked of the author by Michael Wellman, a computer scientist who works in artificial intelligence at Wright Patterson Air Force Base in Dayton, Ohio. He wanted to know if, starting with Rn and its usual topology and product partial order, he could linearly reorder every finite subset and still obtain a continuous function from Rn into R that was strictly increasing with respect to the new order imposed on Rn. It is the purpose of this paper to explore the structural characteristics of ordered topological spaces which have this …