Mathematics Commons^™

Analysis On Strategies Of Competition And Cooperation Between Shanghai And Ningbo Port, Yuan Lu

World Maritime University Dissertations

No abstract provided.

Influencing Factors Of China Containerized Freight Index, Haishu Wang

World Maritime University Dissertations

No abstract provided.

Signal Space Cosamp For Sparse Recovery With Redundant Dictionaries, Mark A. Davenport, Deanna Needell, Michael B. Wakin

CMC Faculty Publications and Research

Compressive sensing (CS) has recently emerged as a powerful framework for acquiring sparse signals. The bulk of the CS literature has focused on the case where the acquired signal has a sparse or compressible representation in an orthonormal basis. In practice, however, there are many signals that cannot be sparsely represented or approximated using an orthonormal basis, but that do have sparse representations in a redundant dictionary. Standard results in CS can sometimes be extended to handle this case provided that the dictionary is sufficiently incoherent or well conditioned, but these approaches fail to address the case of a truly …

Algebraic Techniques In Designing Quantum Synchronizable Codes, Yuichiro Fujiwara, Vladimir Tonchev, Tony Wong

Department of Mathematical Sciences Publications

Quantum synchronizable codes are quantum error-correcting codes that can correct the effects of quantum noise as well as block synchronization errors. We improve the known general framework for designing quantum synchronizable codes through more extensive use of the theory of finite fields. This makes it possible to widen the range of tolerable magnitude of block synchronization errors while giving mathematical insight into the algebraic mechanism of synchronization recovery. Also given are families of quantum synchronizable codes based on punctured Reed-Muller codes and their ambient spaces.

On Cyclic Fixed Points Of Spectra, Marcel Bökstedt, Robert R. Bruner, Sverre Lunøe-Nielsen, John Rognes

Mathematics Faculty Research Publications

For a finite ��-group �� and a bounded below ��-spectrum �� of finite type mod ��, the ��-equivariant Segal conjecture for �� asserts that the canonical map ��^��→��^ℎ��, from ��-fixed points to ��-homotopy fixed points, is a ��-adic equivalence. Let ��_(��^��) be the cyclic group of order ��^��. We show that if the ��_��-equivariant Segal conjecture holds for a ��_(��^��)-spectrum ��, as well as for each of its geometric fixed point spectra Φ^(��_(��^��))(��) for 0<��<��, then the ��_(��^��)-equivariant Segal conjecture holds for ��. Similar results also hold for weaker forms of the Segal conjecture, asking only that the canonical map induces an equivalence in sufficiently high degrees, on homotopy groups with suitable finite coefficients.

A Class Of Univalent Convolutions Of Harmonic Mappings, Matthew Daniel Romney

Theses and Dissertations

A planar harmonic mapping is a complex-valued function ƒ : D → C of the form ƒ(x+iy) = u(x,y) + iv(x,y), where u and v are both real harmonic. Such a function can be written as ƒ = h+g where h and g are both analytic; the function w = g'/h' is called the dilatation of ƒ. This thesis considers the convolution or Hadamard product of planar harmonic mappings that are the vertical shears of the canonical half-plane mapping p;(z) = z/(1-z) with respective dilatations e^iθz and e^ipz, θ, p ∈ R. We prove that any such convolution is univalent. …

The Minimum Rank Problem For Outerplanar Graphs, John Henry Sinkovic

Theses and Dissertations

Given a simple graph G with vertex set V(G)={1,2,...,n} define S(G) to be the set of all real symmetric matrices A such that for all i not equal to j, the ijth entry of A is nonzero if and only if ij is in E(G). The range of the ranks of matrices in S(G) is of interest and can be determined by finding the minimum rank. The minimum rank of a graph, denoted mr(G), is the minimum rank achieved by a matrix in S(G). The maximum nullity of a graph, denoted M(G), is the maximum nullity achieved by a matrix …

Bounding The Norm Of Matrix Powers, Daniel Ammon Dowler

Theses and Dissertations

In this paper I investigate properties of square complex matrices of the form A^k, where A is also a complex matrix, and k is a nonnegative integer. I look at several ways of representing A^k. In particular, I present an identity expressing the k^th power of the Schur form T of A in terms of the elements of T, which can be used together with the Schur decomposition to provide an expression of A^k. I also explain bounds on the norm of A^k, including some based on the element-based expression of …

A Parabolic Equation Analysis Of The Underwater Noise Radiated By Impact Pile Driving, Nathan Laws

Dissertations and Theses

Impact pile driving can produce extremely high underwater sound levels, which are of increasing environmental concern due to their deleterious effects on marine wildlife. Prediction of underwater sound levels is important to the assessment and mitigation of the environmental impacts caused by pile driving. Current prediction methods are limited and do not account for the dynamic pile driving source, inhomogeneities in bathymetry and sediment, or physics-based sound wave propagation.

In this thesis, a computational model is presented that analyzes and predicts the underwater noise radiated by pile driving and is suitable for shallow, inhomogeneous environments and long propagation ranges. The …

Integral Traces Of Weak Maass Forms Of Genus Zero Odd Prime Level, Nathan Eric Green

Theses and Dissertations

Duke and Jenkins defined a family of linear maps from spaces of weakly holomorphic modular forms of negative integral weight and level 1 into spaces of weakly holomorphic modular forms of half integral weight and level 4 and showed that these lifts preserve the integrality of Fourier coefficients. We show that the generalization of these lifts to modular forms of genus 0 odd prime level also preserves the integrality of Fourier coefficients.

The Spacetime Geometry Of A Null Electromagnetic Field, Charles G. Torre

Presentations and Publications

We give a set of local geometric conditions on a spacetime metric which are necessary and sufficient for it to be a null electrovacuum, that is, the metric is part of a solution to the Einstein-Maxwell equations with a null electromagnetic field. These conditions are restrictions on a null congruence canonically constructed from the spacetime metric, and can involve up to five derivatives of the metric. The null electrovacuum conditions are counterparts of the Rainich conditions, which geometrically characterize non-null electrovacua. Given a spacetime satisfying the conditions for a null electrovacuum, a straightforward procedure builds the null electromagnetic field from …

A Mathematical Model And Numerical Method For Thermoelectric Dna Sequencing, Liwei Shi

Doctoral Dissertations

DNA sequencing is the process of determining the precise order of nucleotide bases, adenine, guanine, cytosine, and thymine within a DNA molecule. It includes any method or technology that is used to determine the order of the four bases in a strand of DNA. The advent of rapid DNA sequencing methods has greatly accelerated biological and medical research and discovery. Thermoelectric DNA sequencing is a novel method to sequence DNA by measuring the heat that is released when DNA polymerase inserts a deoxyribonucleoside triphosphate into a growing DNA strand. The thermoelectric device for this project is composed of four parts: …

Lattice Point Counting And Height Bounds Over Number Fields And Quaternion Algebras, Lenny Fukshansky, Glenn Henshaw

CMC Faculty Publications and Research

An important problem in analytic and geometric combinatorics is estimating the number of lattice points in a compact convex set in a Euclidean space. Such estimates have numerous applications throughout mathematics. In this note, we exhibit applications of a particular estimate of this sort to several counting problems in number theory: counting integral points and units of bounded height over number fields, counting points of bounded height over positive definite quaternion algebras, and counting points of bounded height with a fixed support over global function fields. Our arguments use a collection of height comparison inequalities for heights over a number …

Minimization Of Average Sensitivity As A Method Of Selecting Fuzzy Functions And Operations: Successes And Limitations, Riya George, Suresh Subramanian, Alejandro Vega, Olga Kosheleva

Departmental Technical Reports (CS)

Fuzzy logic is an extension of the standard 2-valued logic -- with two possible truth values 0 ("false") and ("true") -- to values (degrees of certainty) represented by arbitrary numbers from the interval [0,1]. One of the main challenges in fuzzy logic is that we need to extend the usual logical operations from the set {0,1} to the entire interval, and there are many possible extensions. One promising technique for selecting a reasonable extension is to take into account that the fuzzy degrees of certainty are themselves only known with uncertainty; so, it makes sense to select an operation which …

Developing Effective Mathematics Teachers Through National Science Foundation Funded Math And Science Partnership Grants, Ruth M. Heaton, Wendy M. Smith

The Mathematics Enthusiast

Every year the National Science Foundation (NSF) gathers together leadership teams of funded Math and Science Partnership programs (MSP) at a Learning Network Conference in Washington, D.C. The purpose of the annual conference is to bring together teams of MSP leaders who represent institution higher education (IHE) faculty from STEM disciplines, IHE education faculty, school partners, and project evaluators, to give them an opportunity to learn across projects, and provide opportunities for individual projects to reflect on their progress. For the last two years, 2011 and 2012, we were part of the conference’s organizing committee. During the two‐day conference, project …

Integrating Disciplinary Perspectives: The Poincaré Institute For Mathematics Education, Montserrat Teixidor-I-Bigas, Analúcia D. Schliemann, David W. Carraher

The Mathematics Enthusiast

We describe the development of the Poincaré Institute, an NSF‐MSP supported program developed through Tufts University Departments of Mathematics, Education, and Physics and by TERC, in partnership with nine school districts in Massachusetts, New Hampshire, and Maine. We focus on the challenges of developing an inter‐disciplinary program aimed at improving the teaching and learning of mathematics from grades 5 to 9, the choice of mathematical and educational content of the program, the course structure, and the progress of the first cohort of participant teachers. We also outline the changes we are implementing for future cohorts.

Developing Effective Mathematics Teaching: Assessing Content And Pedagogical Knowledge, Student-Centered Teaching, And Student Engagement, Serigne M. Gningue, Roger Peach, Barbara Schroder

The Mathematics Enthusiast

The Mathematics Teacher Transformation Institutes (MTTI) program attempts to develop math teacher leaders in part by providing content, inquiry and leadership courses aimed at making them more effective teachers. We assessed progress by observing teacher leaders’ teaching practices, and encouraging them to introduce or extend studentcentered pedagogy in their classrooms. We found there was little relationship between our measures of mathematics content knowledge and student‐centered pedagogy. But teachers who employed student‐centered pedagogy tended to have more highly‐engaged math students in their classrooms.

Making Explicit The Commonalities Of Msp Projects: Learning From Doing, Marilyn Strutchens, W. Gary Martin

The Mathematics Enthusiast

The seven projects discussed in the preceding articles are funded by the National Science Foundation (NSF) Math and Science Partnership (MSP) program (Hamos et al., 2009), which began in 2002. One of the main goals of the MSP program is to build capacity and integrate the work of higher education, especially its STEM disciplinary faculty, with that of K‐12 to strengthen and reform mathematics and science education (Hamos et al., 2009). Thus, the MSP program brought together three sets of people (disciplinary faculty, teacher educators, and school system personnel) who do not usually work together to reform the mathematics and …

Generalized Finite-Difference Time-Domain Schemes For Solving Nonlinear Schrödinger Equations, Frederick Ira Moxley Iii

Doctoral Dissertations

The nonlinear Schrödinger equation (NLSE) is one of the most widely applicable equations in physical science, and characterizes nonlinear dispersive waves, optics, water waves, and the dynamics of molecules. The NLSE satisfies many mathematical conservation laws. Moreover, due to the nonlinearity, the NLSE often requires a numerical solution, which also satisfies the conservation laws. Some of the more popular numerical methods for solving the NLSE include the finite difference, finite element, and spectral methods such as the pseudospectral, split-step with Fourier transform, and integrating factor coupled with a Fourier transform. With regard to the finite difference and finite element methods, …

Optimal Control Modeling And Simulation, With Application To Cholera Dynamics, Chairat Modnak

Mathematics & Statistics Theses & Dissertations

The theory of optimal control, a modern extension of the calculus of variations. has found many applications in a wide range of scientific fields, particularly in epidemiology with respect to disease prevention and intervention. In this dissertation. we conduct optimal control modeling, simulation and analysis to cholera dynamics. Cholera is a severe intestinal infectious disease that remains a serious public health threat in developing countries. Transmission of cholera involves complex interactions between the human host, the pathogen, and the environment. The worldwide cholera outbreaks and their increasing severity, frequency and duration in recent years underscore the gap between the complex …