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- BCH Codes (1)
- CCSD(T):MP2 (1)
- Computational Chemistry (1)
- Cooper's Philosophy (1)
- Cyclic Codes (1)
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- Df-MP2 (1)
- Fractals (1)
- General Error Locator Polynomials (1)
- Gröbner Bases (1)
- Handle Decomposition (1)
- Heegaard Splitting (1)
- Hydrodynamics (1)
- MP2 (1)
- Manifold (1)
- Pretzel Links; Fusion (1)
- Pretzel links (Mathematics); Forms (Mathematics) (1)
- Projective geometry (1)
- Relative Energy Comparison (1)
- Representation Theory (1)
- Tensor contraction (1)
- Tensor isomorphism (1)
- Trisection (1)
- Water (1)
- Water Cluster (1)
Articles 1 - 10 of 10
Full-Text Articles in Physical Sciences and Mathematics
A View Into Secondary Education Mathematics, Thomas Krieger Jr.
A View Into Secondary Education Mathematics, Thomas Krieger Jr.
Honors Theses
Teaching methods, and the effects they can have on students, are important to consider for a classroom because when teaching you should allow for every student to have an opportunity. Every student should feel encouraged in the classroom, however not every method may allow for that. An important task for a teacher is to find out how to reach their students in their classroom; be it adapting methods or choosing when to implement one item over another. This task differs with every student that enters the classroom as no student is the same. Every students’ differences stem from their academic …
A Fractal Geometry For Hydrodynamics, Jonah Mears
A Fractal Geometry For Hydrodynamics, Jonah Mears
Honors Theses
Experiments have shown that objects with uneven surfaces, such as golf balls, can have less drag than those with smooth surfaces. Since fractal surfaces appear naturally in other areas, it must be asked if they can produce less drag than a traditional surface and save energy. Little or no research has been conducted so far on this question. The purpose of this project is to see if fractal geometry can improve boat hull design by producing a hull with low friction.
Relative Energy Comparison For Various Water Clusters Using Mp2, Df-Mp2, And Ccsd(T):Mp2 Methods, Qihang Wang
Relative Energy Comparison For Various Water Clusters Using Mp2, Df-Mp2, And Ccsd(T):Mp2 Methods, Qihang Wang
Honors Theses
The study of water clusters is an important area of research in many disciplines, such as biology, physical chemistry, and environmental studies. However, due to the difficulty in studying larger water clusters, such as clathrate hydrates, it is beneficial to obtain accurate descriptions of smaller water clusters to use as models for larger systems via computational methods. By starting with small water clusters, such as (H2O)6, and moving into larger systems it is possible to build up data on various water structures that can determine the energetics of the various geometries within a certain number of water molecules. …
Classifying Pretzel Links Obtained By Strong Fusion, Jonathan Homan
Classifying Pretzel Links Obtained By Strong Fusion, Jonathan Homan
Honors Theses
A link is a collection of circles embedded into 3-dimensional space. Pretzel links are an important family of links which comprises those links that fit a general form that includes many of the most common links. The strong fusion of a link joins two components of the link via a band and adds an unknotted circle about the band [4]; this naturally arises in the study of concordance and has been used to model biological phenomena such as site specific recombination in DNA [2]. Here we present a complete and original classification of those pretzel links which can be obtained …
Gl(1|1) Graph Connections, Andrea Bourque
Opers On The Projective Line, Wronskian Relations, And The Bethe Ansatz, Ty J. Brinson
Opers On The Projective Line, Wronskian Relations, And The Bethe Ansatz, Ty J. Brinson
Honors Theses
No abstract provided.
Decomposing Manifolds In Low-Dimensions: From Heegaard Splittings To Trisections, Suixin "Cindy" Zhang
Decomposing Manifolds In Low-Dimensions: From Heegaard Splittings To Trisections, Suixin "Cindy" Zhang
Honors Theses
The decomposition of a topological space into smaller and simpler pieces is useful for understanding the space. In 1898, Poul Heegaard introduced the concept of a Heegaard splitting, which is a bisection of a 3-manifold. Heegaard diagrams, which describe Heegaard splittings combinatorially, have been recognized as a powerful tool for classifying 3-manifolds and producing important invariants of 3-manifolds. Handle decomposition, invented by Stephen Smale in 1962, describes how an n-manifold can be constructed by successively adding handles. In 2012, Gay and Kirby introduced trisections of 4-manifold, which are a four-dimensional analogues of Heegaard splittings in dimension three. Trisection diagrams give …
Representation Theory And Its Applications In Physics, Jakub Bystrický
Representation Theory And Its Applications In Physics, Jakub Bystrický
Honors Theses
Representation theory is a branch of mathematics that allows us to represent elements of a group as elements of a general linear group of a chosen vector space by means of a homomorphism. The group elements are mapped to linear operators and we can study the group using linear algebra. This ability is especially useful in physics where much of the theories are captured by linear algebra structures. This thesis reviews key concepts in representation theory of both finite and infinite groups. In the case of finite groups we discuss equivalence, orthogonality, characters, and group algebras. We discuss the importance …
Decoding Cyclic Codes Via Gröbner Bases, Eduardo Sosa
Decoding Cyclic Codes Via Gröbner Bases, Eduardo Sosa
Honors Theses
In this paper, we analyze the decoding of cyclic codes. First, we introduce linear and cyclic codes, standard decoding processes, and some standard theorems in coding theory. Then, we will introduce Gr¨obner Bases, and describe their connection to the decoding of cyclic codes. Finally, we go in-depth into how we decode cyclic codes using the key equation, and how a breakthrough by A. Brinton Cooper on decoding BCH codes using Gr¨obner Bases gave rise to the search for a polynomial-time algorithm that could someday decode any cyclic code. We discuss the different approaches taken toward developing such an algorithm and …
A Contraction Based Approach To Tensor Isomorphism, Anh Kieu
A Contraction Based Approach To Tensor Isomorphism, Anh Kieu
Honors Theses
Tensor isomorphism is a hard problem in computational complexity theory. Tensor isomorphism arises not just in mathematics, but also in other applied fields like Machine Learning, Cryptography, and Quantum Information Theory (QIT). In this thesis, we develop a new approach to testing (non)-isomorphism of tensors that uses local information from "contractions" of a tensor to detect differences in global structures. Specifically, we use projective geometry and tensor contractions to create a labelling data structure for a given tensor, which can be used to compare and distinguish tensors. This contraction labelling isomorphism test is quite general, and its practical potential remains …