Mathematics Commons^™

Lefschetz Contact Manifolds And Odd Dimensional Symplectic Geometry, Yi Lin

Mathematical Sciences: Faculty Publications

In the literature, there are two different versions of Hard Lefschetz theorems for a compact Sasakian manifold. The first version, due to Kacimi-Alaoui, asserts that the basic cohomology groups of a compact Sasakian manifold satisfies the transverse Lefschetz property. The second version, established far more recently by Cappelletti-Montano, De Nicola, and Yudin, holds for the De Rham cohomology groups of a compact Sasakian manifold. In the current paper, using the formalism of odd dimensional symplectic geometry, we prove a Hard Lefschetz theorem for compact K-contact manifolds, which implies immediately that the two existing versions of Hard Lefschetz theorems are mathematically …

Noncrossing Partitions, Toggles, And Homomesies, David Einstein, Miriam Farber, Emily Gunawan, Michael Joseph, Matthew Macauley, James Propp, Simon Rubinstein-Salzedo

Publications

We introduce n(n−1)/2 natural involutions (“toggles”) on the set S of noncrossing partitions π of size n, along with certain composite operations obtained by composing these involutions. We show that for many operations T of this kind, a surprisingly large family of functions f on S (including the function that sends π to the number of blocks of π) exhibits the homomesy phenomenon: the average of f over the elements of a T -orbit is the same for all T -orbits. We can apply our method of proof more broadly to toggle operations back on the collection of independent sets …

The Ebb And Flow Of Official Calls In Water Polo, James Graham, John Mayberry

College of the Pacific Faculty Articles

Defensive fouls play an important role in elite men’s water polo generating over half of all goals. Despite their importance, little is known about the relationship between foul calling patterns and other game-state variables in the sport. Here we apply a sequence of hierarchical mixed logistic regression models on data from major tournaments in 2012–2014 to study such relationships and find a number of significant biases in foul calling rates. Offensive teams who are winning/tied are about 31% less likely to draw a defensive foul and 32% more likely to get called for an offensive foul than teams who are …

The Distribution Of The Number Of Clusters In The Arratia Flow, Vladimir Fomichov

Communications on Stochastic Analysis

No abstract provided.

Krawtchouk-Griffiths Systems I: Matrix Approach, Philip Feinsilver

Communications on Stochastic Analysis

No abstract provided.

Krawtchouk-Griffiths Systems Ii: As Bernoulli Systems, Philip Feinsilver

Communications on Stochastic Analysis

No abstract provided.

Ergodic Control Of Stochastic Navier-Stokes Equation With Lévy Noise, Manil T Mohan, Sivaguru S Sritharan

Communications on Stochastic Analysis

No abstract provided.

Exponential Convergence Of The Stochastic Micropolar And Magneto-Micropolar Fluid Systems, Kazuo Yamazaki

Communications on Stochastic Analysis

No abstract provided.

A General Itô Formula For Adapted And Instantly Independent Stochastic Processes, Chii-Ruey Hwang, Hui-Hsiung Kuo, Kimiaki Saitô, Jiayu Zhai

Communications on Stochastic Analysis

No abstract provided.

Path Functionals Of A Class Of Lévy Insurance Risk Processes, Ekaterina T Kolkovska, Ehyter M Martin-González

Communications on Stochastic Analysis

No abstract provided.

The Fourth Movement Of György Ligeti's Piano Concerto: Investigating The Musical-Mathematical Connection, Cynthia L. Wong

Dissertations, Theses, and Capstone Projects

This interdisciplinary study explores musical-mathematical analogies in the fourth movement of Ligeti’s Piano Concerto. Its aim is to connect musical analysis with the piece’s mathematical inspiration. For this purpose, the dissertation is divided into two sections. Part I (Chapters 1-2) provides musical and mathematical context, including an explanation of ideas related to Ligeti’s mathematical inspiration. Part II (Chapters 3-5) delves into an analysis of the rhythm, form, melody / motive, and harmony. Appendix A is a reduced score of the entire movement, labeled according to my analysis.

The Log-Logistic Weibull Distribution With Applications To Lifetime Data, Broderick O. Oluyede, Susan Foya, Gayan Warahena-Liyanage, Shujiao Huang

Mathematical Sciences: Faculty Publications

In this paper, a new generalized distribution called the log-logistic Weibull (LLoGW) distribution is developed and presented. This distribution contain the log-logistic Rayleigh (LLoGR), log-logistic exponential (LLoGE) and log-logistic (LLoG) distributions as special cases. The structural properties of the distribution including the hazard function, reverse hazard function, quantile function, probability weighted moments, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, distribution of order statistics, L-moments and Renyi entropy are derived. Method of maximum likelihood is used to estimate the parameters of this new distribution. A simulation study to examine the bias, mean square error of the maximum likelihood estimators …

Exploratory Modeling Of Tbi Data, Martin Zwick, Stephanie Kolakowsky-Hayner, Sadie Carney, Maya Balamane, Tracie Nettleton, D. Wright

Complex Systems Faculty Publications and Presentations

Most data analyses are confirmatory, but exploratory studies can find unexpected non-linear & many-variable interaction effects. The methodology of reconstructability analysis (RA) is explicitly designed for exploratory modeling. It analyzes both nominal and continuous (binned) variables, is easily interpretable, takes standard text input, is web-accessible, and is available for research use. This presentation reports some results of applying RA to data sets from Preece (auto accidents) and Wright (auto/motorcycle/bike accidents, hit pedestrians, and falls).

On The Geometry Of The Rotating Liquid Drop, Ivailo M. Mladenov, John Oprea

Mathematics and Statistics Faculty Publications

Here we consider the problem of a fluid body rotating with a constant angular velocity and subjected to surface tension. Determining the equilibrium configuration of this system turns out to be equivalent to the geometrical problem of determining the surface of revolution with a prescribed mean curvature. In the simply connected case, the equilibrium surface can be parameterized explicitly via elliptic integrals of the first and second kind. Here, we present two such parameterizations of the drops and we use the second of them to study finer details of the drop surfaces such as the existence of closed geodesics.

Another Generalized Transmuted Family Of Distributions: Properties And Applications, Faton Merovci, Morad Alizadeh, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce and study general mathematical properties of a new generator of continuous distributions with two extra parameters called the Another generalized transmuted family of distributions. We present some special models. We investigate the asymptotes and shapes. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. We obtain explicit expressions for the ordinary and incomplete moments and generating functions, Bonferroni and Lorenz curves, asymptotic distribution of the extreme values, Shannon and Renyi entropies and order statistics, which hold for any baseline model, certain characterisations are presented. Further, we …

Ultracoproduct Continua And Their Regular Subcontinua, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

We continue our study of ultracoproduct continua, focusing on the role played by the regular subcontinua—those subcontinua which are themselves ultracoproducts. Regular subcontinua help us in the analysis of intervals, composants, and noncut points of ultracoproduct continua. Also, by identifying two points when they are contained in the same regular subcontinua, we naturally generalize the partition of a standard subcontinuum of ℍ * into its layers.

Ermakov Equation And Camassa-Holm Waves, Haret C. Rosu, S.C. Mancas

Publications

From the works of authors of this article, it is known that the solution of the Ermakov equation is an important ingredient in the spectral problem of the Camassa-Holm equation. Here, we review this interesting issue and consider in addition more features of the Ermakov equation which have an impact on the behavior of the shallow water waves as described by the Camassa-Holm equation.

Cycle Structures Of Orthomorphisms Extending Partial Orthomorphisms Of Boolean Groups, Nichole Louise Schimanski, John S. Caughman Iv

Mathematics and Statistics Faculty Publications and Presentations

A partial orthomorphism of a group GG (with additive notation) is an injection π:S→G for some S⊆G such that π(x)−x ≠ π(y) for all distinct x,y∈S. We refer to |S| as the size of π, and if S=G, then π is an orthomorphism. Despite receiving a fair amount of attention in the research literature, many basic questions remain concerning the number of orthomorphisms of a given group, and what cycle types these permutations have.

It is known that conjugation by automorphisms of G forms a group action on the set of orthomorphisms of G. In this paper, we consider the …

Hamiltonian Bifurcations In Schrodinger Trimers, Casayndra H. Basarab

Dissertations

The phase space of the three-mode discrete NLS in the nonlinear regime with periodic boundary conditions is investigated by reducing the degree of freedom from three down to two. The families of standing waves are enumerated and normal forms are used to describe several families of relative periodic orbits whose topologies change due to Hamiltonian Hopf bifurcations and transcritical bifurcations. The Hamiltonian Hopf bifurcation occurs when eigenvalues on the imaginary axis collide and split and has two types: elliptic and hyperbolic. These two types arise in the DNLS problem, and the families of periodic orbits are discussed as a conserved …

Structural Exploration And Inference Of The Network, Ruihua Cheng

Dissertations

This dissertation consists of two parts. In the first part, a learning-based method for classification of online reviews that achieves better classification accuracy is extended. Automatic sentiment classification is becoming a popular and effective way to help online users or companies to process and make sense of customer reviews. The method combines two recent developments. First, valence shifters and individual opinion words are combined as bigrams to use in an ordinal margin classifier. Second, relational information between unigrams expressed in the form of a graph is used to constrain the parameters of the classifier. By combining these two components, it …