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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
Algebraic Techniques In Designing Quantum Synchronizable Codes, Yuichiro Fujiwara, Vladimir Tonchev, Tony Wong
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.
Enumeration Of (16,4,16,4) Relative Difference Sets, David C. Clark, Vladimir Tonchev
Enumeration Of (16,4,16,4) Relative Difference Sets, David C. Clark, Vladimir Tonchev
Department of Mathematical Sciences Publications
A complete enumeration of relative difference sets (RDS) with parameters (16, 4, 16, 4) in a group of order 64 with a normal subgroup N of order 4 is given. If N = Z4 , three of the 11 abelian groups of order 64, and 23 of the 256 nonabelian groups of order 64 contain (16, 4, 16, 4) RDSs. If N = Z2 × Z2 , nine of the abelian groups and 194 of the non-abelian groups of order 64 contain (16, 4, 16, 4) RDSs.
Maximum Principle Preserving High Order Schemes For Convection-Dominated Diffusion Equations, Yi Jiang
Maximum Principle Preserving High Order Schemes For Convection-Dominated Diffusion Equations, Yi Jiang
Dissertations, Master's Theses and Master's Reports - Open
The maximum principle is an important property of solutions to PDE. Correspondingly, it's of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving(MPP) high order finite volume(FV) WENO scheme, and then propose a new parametrized MPP high order finite difference(FD) WENO framework, which is generalized from the one solving hyperbolic conservation laws. A formal analysis is presented to show that a third order finite difference scheme with this parametrized MPP flux limiters maintains …
Benson's Theorem For Partial Geometries, Ellen J. Kamischke
Benson's Theorem For Partial Geometries, Ellen J. Kamischke
Dissertations, Master's Theses and Master's Reports - Open
In 1970 Clark Benson published a theorem in the Journal of Algebra stating a congruence for generalized quadrangles. Since then this theorem has been expanded to other specific geometries. In this thesis the theorem for partial geometries is extended to develop new divisibility conditions for the existence of a partial geometry in Chapter 2. Then in Chapter 3 the theorem is applied to higher dimensional arcs resulting in parameter restrictions on geometries derived from these structures. In Chapter 4 we look at extending previous work with partial geometries with α = 2 to uncover potential partial geometries with higher values …
Dimension Reduction For Power System Modeling Using Pca Methods Considering Incomplete Data Readings, Ting Zhao
Dimension Reduction For Power System Modeling Using Pca Methods Considering Incomplete Data Readings, Ting Zhao
Dissertations, Master's Theses and Master's Reports - Open
Principal Component Analysis (PCA) is a popular method for dimension reduction that can be used in many fields including data compression, image processing, exploratory data analysis, etc. However, traditional PCA method has several drawbacks, since the traditional PCA method is not efficient for dealing with high dimensional data and cannot be effectively applied to compute accurate enough principal components when handling relatively large portion of missing data. In this report, we propose to use EM-PCA method for dimension reduction of power system measurement with missing data, and provide a comparative study of traditional PCA and EM-PCA methods. Our extensive experimental …
Three Hundred Years Of The St. Petersburg Paradox, Keguo Huang
Three Hundred Years Of The St. Petersburg Paradox, Keguo Huang
Dissertations, Master's Theses and Master's Reports - Open
The St. Petersburg Paradox was first presented by Nicholas Bernoulli in 1713. It is related to a gambling game whose mathematical expected payoff is infinite, but no reasonable person would pay more than $25 to play it. In the history, a number of ideas in different areas have been developed to solve this paradox, and this report will mainly focus on mathematical perspective of this paradox. Different ideas and papers will be reviewed, including both classical ones of 18th and 19th century and some latest developments. Each model will be evaluated by simulation using Mathematica.