Mathematics Commons^™

05: Rats Grapher, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

RatsGrapher.nb graphs rational functions and labels all holes and asymptotes.

Temporal Order Of Alzheimer's Disease-Related Cognitive Marker Changes In Blsa And Wrap Longitudinal Studies, Murat Bilgel, Rebecca L. Koscik, Yang An, Jerry L. Prince, Susan M. Resnick, Sterling C. Johnson, Bruno Jedynak

Mathematics and Statistics Faculty Publications and Presentations

Investigation of the temporal trajectories of currently used neuropsychological tests is critical to identifying earliest changing measures on the path to dementia due to Alzheimer's disease (AD). We used the Progression Score (PS) method to characterize the temporal trajectories of measures of verbal memory, executive function, attention, processing speed, language, and mental state using data spanning normal cognition, mild cognitive impairment (MCI), and AD from 1661 participants with a total of 7839 visits (age at last visit 77.6 SD 9.2) in the Baltimore Longitudinal Study of Aging and 1542 participants with a total of 4467 visits (age at last visit …

Solving Fredholm Integral Equations Via A Piecewise Linear Maximum Entropy Method, Congming Jin, Jiu Ding

Faculty Publications

We propose a piecewise linear approximation method, based on the maximum entropy principle, to approximate a nonnegative solution of a Fredholm integral equation numerically. The theoretical analysis and numerical examples show that our method has a convergence rate of order 2, and it can get more accurate approximations with more moments used without ill-condition of the classic maximum entropy approach. The method can also be applied to solve Fredholm integral equations with singular kernels.

Trimethylamine N-Oxide And Mortality Risk In Patients With Peripheral Artery Disease, Vichai Senthong, Zeneng Wang, Yiying Fan, Yuping Wu, Stanley L. Hazen, W.H. Wilson Tang

Mathematics and Statistics Faculty Publications

Background: Production of the proatherogenic metabolite, trimethylamine N-oxide (TMAO), from dietary nutrients by intestinal microbiota enhances atherosclerosis development in animal models and is associated with atherosclerotic coronary artery disease in humans. The utility of studying plasma levels of TMAO to risk stratify in patients with peripheral artery disease (PAD) has not been reported. Methods and Results: We examined the relationship between fasting plasma TMAO and all-cause mortality (5-year), stratified by subtypes of PAD and presence of coronary artery disease in 935 patients with PAD who underwent elective angiography for cardiac evaluation at a tertiary care hospital. Median plasma TMAO was …

Faith Connections In The Math Classroom, Valorie L. Zonnefeld, Ryan G. Zonnefeld

Faculty Work Comprehensive List

Looking for ways to make faith connections in your math classroom? The Zonnefelds present a framework, developed in collaboration with local teachers, that synthesizes faith connections, the TfT framework, and Common Core standards.

Alan Turing: The Man Behind The Machine, Christopher D. Goff

College of the Pacific Faculty Presentations

No abstract provided.

A General Elliptic Nonlinear System Of Two Functions With Application, Timothy Robertson, Joon Hyuk Kang

Faculty Publications

The purpose of this paper is to give a sufficient condition for the existence and nonexistence of positive solutions to a rather general type of elliptic system of the Dirichlet problem on the bounded domain Ω in Rn. Also considered are the effects of perturbations on the coexistence state and uniqueness. The techniques used in this paper are upper-lower solutions, eigenvalues of operators, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations. These results yield an algebraically computable criterion for the positive coexistence of competing species of animals in many …

The Four Color Theorem: A Possible New Approach, Matthew Brady

All Student Theses and Dissertations

The goal of this thesis is to explore the topic of graph coloring and expand on existing ideas in the field of Graph Theory. These developments will then be used to provide a possible approach in proving the 4 – color theorem that was made famous by Guthrie in the 1800’s.

Since the theorem was presented, many proofs were presented and eventually disregarded for one reason or another. Today, the types of proofs that are considered correct all rely on a computer. The first of this kind was set forth by Appel and Haken in 1977. The driving idea behind …

Mapped Tent Pitching Schemes For Hyperbolic Systems, Jay Gopalakrishnan, Joachim Schöberl, C. Wintersteiger

Portland Institute for Computational Science Publications

A spacetime domain can be progressively meshed by tent shaped objects. Numerical methods for solving hyperbolic systems using such tent meshes to advance in time have been proposed previously. Such schemes have the ability to advance in time by different amounts at different spatial locations. This paper explores a technique by which standard discretizations, including explicit time stepping, can be used within tent-shaped spacetime domains. The technique transforms the equations within a spacetime tent to a domain where space and time are separable. After detailing techniques based on this mapping, several examples including the acoustic wave equation and the Euler …

Non-Commutative Automorphisms Of Bounded Non-Commutative Domains, John E. Mccarthy, Richard M. Timoney

Mathematics Faculty Research

We establish rigidity (or uniqueness) theorems for non-commutative (NC) automorphisms that are natural extensions of classical results of H. Cartan and are improvements of recent results. We apply our results to NC domains consisting of unit balls of rectangular matrices.

Inverse Laplace Transform And Post Inversion Formula, Qinmao Zhang

Mathematical Sciences Technical Reports (MSTR)

This paper is dedicated to a general numerical approach to inverse Laplace transforms based on the Post Inversion Formula, which is a theoretical equivalent to the inverse Laplace transform. Though most approaches are too computationally intensive to be of practical use, we introduce an efficient algorithm to compute it based on the Parker-Sochacki method (PSM). This paper also contains some example MATLAB code and algorithm analysis.

Some 2-Categorical Aspects In Physics, Arthur Parzygnat

Dissertations, Theses, and Capstone Projects

2-categories provide a useful transition point between ordinary category theory and infinity-category theory where one can perform concrete computations for applications in physics and at the same time provide rigorous formalism for mathematical structures appearing in physics. We survey three such broad instances. First, we describe two-dimensional algebra as a means of constructing non-abelian parallel transport along surfaces which can be used to describe strings charged under non-abelian gauge groups in string theory. Second, we formalize the notion of convex and cone categories, provide a preliminary categorical definition of entropy, and exhibit several examples. Thirdly, we provide a universal description …

A Geometric Model Of Twisted Differential K-Theory, Byung Do Park

Dissertations, Theses, and Capstone Projects

We construct a model of even twisted differential K-theory when the underlying topological twist represents a torsion class. We use smooth U(1)-gerbes with connection as differential twists and twisted vector bundles with connection as cycles. The model we construct satisfies the axioms of Kahle and Valentino, including functoriality, naturality of twists, and the hexagon diagram. We also construct an odd twisted Chern character of a twisted vector bundle with an automorphism. In addition to our geometric model of twisted differential K-theory, we introduce a smooth variant of the Hopkins-Singer model of differential K-theory. We prove that our model is naturally …

On The Free And G-Saturated Weight Monoids Of Smooth Affine Spherical Varieties For G=Sl(N), Won Geun Kim

Dissertations, Theses, and Capstone Projects

Let $X$ be an affine algebraic variety over $\mathbb{C}$ equipped with an action of a connected reductive group $G$. The weight monoid $\Gamma(X)$ of $X$ is the set of isomorphism classes of irreducible representations of $G$ that occur in the coordinate ring $\mathbb{C}[X]$ of $X$. Losev has shown that if $X$ is a smooth affine spherical variety, that is, if $X$ is smooth and $\mathbb{C}[X]$ is multiplicity-free as a representation of $G$, then $\Gamma(X)$ determines $X$ up to equivariant automorphism.

Pezzini and Van Steirteghem have recently obtained a combinatorial characterization of the weight monoids of smooth affine spherical varieties, using …

Explicit Formulae And Trace Formulae, Tian An Wong

Dissertations, Theses, and Capstone Projects

In this thesis, motivated by an observation of D. Hejhal, we show that the explicit formulae of A. Weil for sums over zeroes of Hecke L-functions, via the Maass-Selberg relation, occur in the continuous spectral terms in the Selberg trace formula over various number fields. In Part I, we discuss the relevant parts of the trace formulae classically and adelically, developing the necessary representation theoretic background. In Part II, we show how show the explicit formulae intervene, using the classical formulation of Weil; then we recast this in terms of Weil distributions and the adelic formulation of Weil. As an …

On Sums Of Binary Hermitian Forms, Cihan Karabulut

Dissertations, Theses, and Capstone Projects

In one of his papers, Zagier defined a family of functions as sums of powers of quadratic polynomials. He showed that these functions have many surprising properties and are related to modular forms of integral weight and half integral weight, certain values of Dedekind zeta functions, Diophantine approximation, continued fractions, and Dedekind sums. He used the theory of periods of modular forms to explain the behavior of these functions. We study a similar family of functions, defining them using binary Hermitian forms. We show that this family of functions also have similar properties.

On The Derivative Of 2-Holonomy For A Non-Abelian Gerbe, Cheyne J. Miller

Dissertations, Theses, and Capstone Projects

The local 2-holonomy for a non abelian gerbe with connection is first studied via a local zig-zag Hochschild complex. Next, by locally integrating the cocycle data for our gerbe with connection, and then glueing this data together, an explicit definition is offered for a global version of 2-holonomy. After showing this definition satisfies the desired properties for 2-holonomy, its derivative is calculated whereby the only interior information added is the integration of the 3-curvature. Finally, for the case when the surface being mapped into the manifold is a sphere, the derivative of 2-holonomy is extended to an equivariant closed form …

Explicit Reciprocity Laws For Higher Local Fields, Jorge Florez

Dissertations, Theses, and Capstone Projects

In this thesis we generalize to higher dimensional local fields the explicit reciprocity laws of Kolyvagin for the Kummer pairing associated to a formal group. The formulas obtained describe the values of the pairing in terms of multidimensional p-adic differentiation, the logarithm of the formal group, the generalized trace and the norm on Milnor K-groups.

Modeling And Methods Of Signal Separations With Applications In Spectroscopic Sensing, Yuanchang Sun

Mathematics Colloquium Series

Spectroscopic sensing is a powerful and a widely used family of techniques for detecting and identifying chemical and biological substances. For example, nuclear magnetic resonance (NMR) relies on the magnetic properties of the atomistic nucleus to determine the molecular structures. Raman spectroscopy (RS) uses laser light scattering and the resulting energy shift of photons to sense the vibrational modes of a sample. In remote sensing, hyperspectral imaging (HSI) makes use of hundreds of contiguous spectral bands to identify nearly invisible objects at subpixel level. Differential optical absorption spectroscopy (DOAS) is based on the light absorption property of matter to identify …

Mechanism Design For Land Acquisition., Soumendu Sarkar Dr.

Doctoral Theses

Conversion of land use from agriculture to industry is a typical feature of economic development in many densely populated countries. Large scale construction often requires industry or the government to acquire vast areas of land that are inhabited and often cultivated, by hundreds and even thousands of people. For some landowners, possession signifies power and status in society, while for others, it is the only means for earning a livelihood.Adamopoulos and Restuccia (2014) use data from World Census of Agriculture to show that average farm size in the poorest 20% of countries is 1.6 hectares, while that in the richest …