Mathematics Commons^™

Standards-Based Assessment In A Developmental Math Course, Valorie L. Zonnefeld, Michal Huizenga, Aaron Van Beek, Kate Van Weelden

Faculty Work Comprehensive List

Learn why we decided to try standards-based instruction in an undergraduate, developmental algebra course and what we learned in the process.

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 …

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.

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 …

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 …

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.

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 …

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 …

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 …

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 …

Identification Of Control Targets In Boolean Molecular Network Models Via Computational Algebra, David Murrugarra, Alan Veliz-Cuba, Boris Aguilar, Reinhard Laubenbacher

Mathematics Faculty Publications

Background: Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment. The identification of such strategies is typically based on a mathematical model of the process to be altered through targeted control inputs. This paper focuses on processes at the molecular level that determine the state of an individual cell, involving signaling or gene regulation. The mathematical model type …

Research On Formation Of Strategic Alliance And Its Effect On Container Lines’ Efficiency, Hyeonkuk Kang

World Maritime University Dissertations

No abstract provided.

Identification Of Control Targets In Boolean Molecular Network Models Via Computational Algebra, David Murrugarra, Alan Veliz-Cuba, Boris Aguilar, Reinhard Laubenbacher

Mathematics Faculty Publications

Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment. The identification of such strategies is typically based on a mathematical model of the process to be altered through targeted control inputs. This paper focuses on processes at the molecular level that determine the state of an individual cell, involving signaling or gene regulation. The mathematical model type considered …

Factors Analysis : Ghg Emissions From International Shipping, Weijia Cui

World Maritime University Dissertations

No abstract provided.

Economic Analysis On The 400k Dwt Vloc, Yongcheng Yang

World Maritime University Dissertations

No abstract provided.

The Economic Analysis Of Mega Containership, Tingyu Jiang

World Maritime University Dissertations

No abstract provided.

Research On Container Liner Company Marketing Strategy, Huayu Shi

World Maritime University Dissertations

No abstract provided.

The Research On The Volatility Of Vlcc Market, Yanwei Wang

World Maritime University Dissertations

No abstract provided.

Critical Groups Of Graphs With Dihedral Actions Ii, Darren B. Glass

Math Faculty Publications

In this paper we consider the critical group of finite connected graphs which admit harmonic actions by the dihedral group D_n, extending earlier work by the author and Criel Merino. In particular, we show that the critical group of such a graph can be decomposed in terms of the critical groups of the quotients of the graph by certain subgroups of the automorphism group. This is analogous to a theorem of Kani and Rosen which decomposes the Jacobians of algebraic curves with a D_n-action.

Temporal Network Analysis Of Small Group Discourse, Bernard P. Ricca, Michelle Jordan

Mathematical and Computing Sciences Faculty/Staff Publications

The analysis of school-age children engaged in engineering projects has proceeded by examining the conversations that take place among those children. The analysis of classroom discourse often considers a conversational turn to be the unit of analysis. In this study, small-group conversations among students engaged in a robotics project are analyzed by forming a dynamic network with the students as nodes and the utterances of each turn as edges. The data collected for this project contained more than 1000 turns for each group, with each group consisting of 4 students (and the occasional inclusion of a teacher or other interloper). …

State Space Analysis And Its Connection To The Classroom, Bernard P. Ricca, Kris H. Green

Mathematical and Computing Sciences Faculty/Staff Publications

Discrete dynamical systems have been used to theoretically model the complex dynamics of classrooms. While time-series analyses of these models has yielded some insights, state space analyses can yield additional insights; this paper will explore state space analyses and their application to classroom situations. One benefit of state space analysis is that it allows simultaneous exploration of multiple time-series, and so can more easily provide information about divergence and convergence of paths. Additionally, state space analysis, more easily than time-series analysis, can provide information about the existence of multiple paths leading toward a desired state. Further, state space analysis can …

Hyperplanes That Intersect Each Ray Of A Cone Once And A Banach Space Counterexample, Chris Mccarthy

Publications and Research

Suppose � is a cone contained in real vector space �. When does � contain a hyperplane � that intersects each of the 0-rays in �\{0} exactly once? We build on results found in Aliprantis, Tourky, and Klee Jr.’s work to give a partial answer to this question.We also present an example of a salient, closed Banach space cone � for which there does not exist a hyperplane that intersects each 0-ray in � \ {0} exactly once.

On A Multidimensional Spherically Invariant Extension Of The Rademacher-Gaussian Comparison, Iosif Pinelis

Department of Mathematical Sciences Publications

It is shown that P(ǁa₁U₁+ · · · +a_nU_nǁ > u) ≤ cP(aǁZ_dǁ> u) for all real u, where U₁, : : : , U_n are independent random vectors uniformly distributed on the unit sphere in R^d, a₁, : : : , a_n are any real numbers, a := √(a²₁ + · · · · + a²_n ) ∕ d, Z_d is a standard normal random vector in R^d, and c = 2e³ ∕ 9 …

Mathematical And Numerical Approaches To Cracked Euler-Bernoulli Beams, Jay Mayfield

Student Theses and Dissertations

We consider a nonlinear hyperbolic fourth order partial differential equation and ordinary differential equation mathematically and numerically that describe the motion of cracked Euler-Bernoulli beams. We assume that the endpoints of the beams are clamped and a crack in the beams is modeled by a set of natural boundary conditions. The effect of the crack on the beams increases in time, which is seen from the damage function. The beams will oscillate transversely in space until they break at the point of the crack. The midpoint rule is applied to a discretized time domain. Fully discrete numerical schemes are proposed …

Long Term Optimal Portfolio Selection Problem In Different Models, Bowen Hu

Mathematics Theses and Dissertations

In this project, we mainly focus on how to set up a complete methodology for finding the best investment portfolio which is meeting investor's risk preferences. In order to consider different aspects of their risk preferences, we use a combination of several risk and performance metrics in the ranking function. After applying this ranking system to select most suitable funds from a large pool, we use different models to optimize the portfolio. Past 5-10 years data set has been extracted from Bloomberg. We find out that the asymmetric multivariate t-distribution can dominate the multivariate normal distribution and the symmetric t-distribution …

Recurrence Relations For Orthogonal Polynomials For Pdes In Polar And Cylindrical Geometrics, Megan Richardson, James V. Lambers

Faculty Publications

This paper introduces two families of orthogonal polynomials on the interval (−1,1), with weight function w(x)=1. The first family satisfies the boundary condition p(1)=0, and the second one satisfies the boundary conditions p(-1)=p(1)=0. These boundary conditions arise naturally from PDEs defined on a disk with Dirichlet boundary conditions and the requirement of regularity in Cartesian coordinates. The families of orthogonal polynomials are obtained by orthogonalizing short linear combinations of Legendre polynomials that satisfy the same boundary conditions. Then, the three-term recurrence relations are derived. Finally, it is shown that from these recurrence relations, one can …

Maximizing H-Colorings Of Connected Graphs With Fixed Minimum Degree, John Engbers

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Grnsight: A Web Application And Service For Visualizing Models Of Small- To Medium-Scale Gene Regulatory Networks, Kam D. Dahlquist, John David N. Dionisio, Ben G. Fitzpatrick, Nicole A. Anguiano, Anindita Varshneya, Britain J. Southwick, Mihir Samdarshi

Biology Faculty Works

GRNsight is a web application and service for visualizing models of gene regulatory networks (GRNs). A gene regulatory network (GRN) consists of genes, transcription factors, and the regulatory connections between them which govern the level of expression of mRNA and protein from genes. The original motivation came from our efforts to perform parameter estimation and forward simulation of the dynamics of a differential equations model of a small GRN with 21 nodes and 31 edges. We wanted a quick and easy way to visualize the weight parameters from the model which represent the direction and magnitude of the influence of …