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6 results on '"Dionne Ibarra"'

1. Logarithm-Based Methods for Interpolating Quaternion Time Series

Author

Joshua Parker, Dionne Ibarra, and David Ober

Subjects
quaternions, interpolation, rotations, Mathematics, QA1-939
Abstract

In this paper, we discuss a modified quaternion interpolation method based on interpolations performed on the logarithmic form. This builds on prior work that demonstrated this approach maintains C2 continuity for prescriptive rotation. However, we develop and extend this method to descriptive interpolation, i.e., interpolating an arbitrary quaternion time series. To accomplish this, we provide a robust method of taking the logarithm of a quaternion time series such that the variables θ and n^ have a consistent and continuous axis-angle representation. We then demonstrate how logarithmic quaternion interpolation out-performs Renormalized Quaternion Bezier interpolation by orders of magnitude.

Published
2023
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2. Schur multipliers and second quandle homology

Author

Takefumi Nosaka, Józef H. Przytycki, Rhea Palak Bakshi, Sujoy Mukherjee, and Dionne Ibarra

Subjects
Pure mathematics, Algebra and Number Theory, 010102 general mathematics, Primary: 19C09, Secondary: 20J06, 57M27, Geometric Topology (math.GT), K-Theory and Homology (math.KT), Group Theory (math.GR), Homology (mathematics), Mathematics::Algebraic Topology, Mathematics::Geometric Topology, 01 natural sciences, Mathematics - Geometric Topology, Mathematics - K-Theory and Homology, 0103 physical sciences, FOS: Mathematics, 010307 mathematical physics, 0101 mathematics, Mathematics - Group Theory, Schur multiplier, Mathematics
Abstract

We define a map from second quandle homology to the Schur multiplier and examine its properties. Furthermore, we express the second homology of Alexander quandles in terms of exterior algebras. Additionally, we present a self-contained proof of its structure and provide some computational examples., 16 pages

Published
2020

3. Lectures in Knot Theory : An Exploration of Contemporary Topics

Author

Józef H. Przytycki, Rhea Palak Bakshi, Dionne Ibarra, Gabriel Montoya-Vega, Deborah Weeks, Józef H. Przytycki, Rhea Palak Bakshi, Dionne Ibarra, Gabriel Montoya-Vega, and Deborah Weeks

Subjects
Manifolds (Mathematics), Discrete mathematics, Associative rings, Associative algebras
Abstract

This text is based on lectures delivered by the first author on various, often nonstandard, parts of knot theory and related subjects. By exploring contemporary topics in knot theory including those that have become mainstream, such as skein modules, Khovanov homology and Gram determinants motivated by knots, this book offers an innovative extension to the existing literature. Each lecture begins with a historical overview of a topic and gives motivation for the development of that subject. Understanding of most of the material in the book requires only a basic knowledge of topology and abstract algebra. The intended audience is beginning and advanced graduate students, advanced undergraduate students, and researchers interested in knot theory and its relations with other disciplines within mathematics, physics, biology, and chemistry.Inclusion of many exercises, open problems, and conjectures enables the reader to enhance their understanding of the subject. The use of this text for the classroom is versatile and depends on the course level and choices made by the instructor. Suggestions for variations in course coverage are included in the Preface. The lecture style and array of topical coverage are hoped to inspire independent research and applications of the methods described in the book to other disciplines of science. An introduction to the topology of 3-dimensional manifolds is included in Appendices A and B. Lastly, Appendix C includes a Table of Knots.

Published
2024

4. On framings of links in 3-manifolds

Author

Gabriel Montoya-Vega, Dionne Ibarra, Rhea Palak Bakshi, Deborah Weeks, and Józef H. Przytycki

Subjects
Pure mathematics, General Mathematics, 010102 general mathematics, Geometric Topology (math.GT), 01 natural sciences, Mathematics::Geometric Topology, Mathematics - Geometric Topology, Primary: 57M27. Secondary: 55A25, 57M25, 0103 physical sciences, FOS: Mathematics, Algebraic Topology (math.AT), 010307 mathematical physics, Mathematics - Algebraic Topology, 0101 mathematics, Mathematics::Symplectic Geometry, Mathematics
Abstract

We show that the only way of changing the framing of a link by ambient isotopy in an oriented $3$-manifold is when the manifold has a properly embedded non-separating $S^2$. This change of framing is given by the Dirac trick, also known as the light bulb trick. The main tool we use is based on McCullough's work on the mapping class groups of $3$-manifolds. We also relate our results to the theory of skein modules., Comment: 12 pages, 9 figures

Published
2020
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5. A generalization of the Gram determinant of type A

Author

Sujoy Mukherjee, Józef H. Przytycki, Rhea Palak Bakshi, and Dionne Ibarra

Subjects
Conjecture, Generalization, 010102 general mathematics, Geometric Topology (math.GT), Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing), Annulus (mathematics), Bilinear form, Type (model theory), Mathematics::Geometric Topology, 01 natural sciences, 010101 applied mathematics, Combinatorics, Mathematics - Geometric Topology, Primary: 57M27. Secondary: 57M25, 05A19, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Geometry and Topology, 0101 mathematics, Klein bottle, Mathematics, Gram
Abstract

The Gram determinant of type $A$ was introduced by Lickorish in his work on invariants of 3 - manifolds. We generalize the theory of the Gram determinant of type $A$ by evaluating, in the annulus, a bilinear form of non-intersecting connections in the disc. The main result provides a closed formula for this Gram determinant. We conclude the paper by discussing Chen's conjecture about the Gram determinant of type $Mb$ evaluated in the Klein bottle., Comment: 17 pages, 19 figures

Published
2021

6. On a state model for the SO(2n) Kauffman polynomial

Author

Carmen Caprau, Dionne Ibarra, and David Heywood

Subjects
State model, Polynomial, General Mathematics, Geometric Topology (math.GT), Mathematics::Geometric Topology, Planar graph, Combinatorics, Mathematics - Geometric Topology, symbols.namesake, Mathematics::Quantum Algebra, Kauffman polynomial, FOS: Mathematics, 57M27, 57M15, symbols, Invariant (mathematics), Mathematics::Representation Theory, Mathematics
Abstract

F. Jaeger presented the two-variable Kauffman polynomial of an unoriented link L as a weighted sum of HOMFLY-PT polynomials of oriented links associated with L. Murakami, Ohtsuki and Yamada (MOY) used planar graphs and a recursive evaluation of these graphs to construct a state model for the sl(n)-link invariant (a one-variable specialization of the HOMFLY-PT polynomial). We apply the MOY framework to Jaeger's work, and construct a state summation model for the SO(2n) Kauffman polynomial., Comment: 14 pages, many figures

Published
2014

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