Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Algebra (4)
- Artificial Intelligence and Robotics (2)
- Computer Engineering (2)
- Computer Sciences (2)
- Engineering (2)
-
- Applied Mathematics (1)
- Business (1)
- Categorical Data Analysis (1)
- Computer and Systems Architecture (1)
- Data Science (1)
- Data Storage Systems (1)
- Databases and Information Systems (1)
- Dynamics and Dynamical Systems (1)
- Engineering Science and Materials (1)
- Logic and Foundations (1)
- Management Information Systems (1)
- Numerical Analysis and Computation (1)
- Numerical Analysis and Scientific Computing (1)
- Other Engineering (1)
- Programming Languages and Compilers (1)
- Software Engineering (1)
- Sports Management (1)
- Statistical Models (1)
- Statistics and Probability (1)
- Technology and Innovation (1)
- Keyword
-
- Algebraic Geometry (2)
- Commutative Algebra (2)
- Arc spaces (1)
- Artificial Intelligence (1)
- Ascending HNN extensions (1)
-
- Computer Vision (1)
- Data Visualization (1)
- Derivations (1)
- Endomorphisms (1)
- Free groups (1)
- Geometric group theory (1)
- Gromov's question (1)
- Hilbert Function (1)
- Innovations (1)
- Jet schemes (1)
- Machine Learning (1)
- Mapping torus (1)
- Mathematical sciences (1)
- Rees Algebra (1)
- Scalable solvers (1)
- Soccer (1)
- Sports Analytics (1)
- University of Arkansas (1)
- Virtual conference (1)
- Publication
- Publication Type
Articles 1 - 9 of 9
Full-Text Articles in Algebraic Geometry
Some Interpolation Problems In The Projective Plane, Lilah Estes
Some Interpolation Problems In The Projective Plane, Lilah Estes
Mathematical Sciences Undergraduate Honors Theses
Given some set of r general points in the projective plane, we want to better understand: what is the smallest degree of any polynomial passing through the points m times? How many linearly independent equations of this degree pass through the points m times? The investigation of these questions, particularly for the case of m=3 and r< 16, motivates the development of several results. We translate Terracini's inductive argument, a tool for evaluating the expectedness of certain sets of double points, into a version which can be used for triple points, and prove that the argument holds. We compute the minimal graded free resolutions for the ideals corresponding to up to 15 points, for m up to 6, and we conjecture a connection between the expectedness of these ideals and what their resolutions look like. Further, we prove that this conjecture holds when m=1, and we either fully or partially prove that these ideals are …
Computer Vision In Soccer: Yolov11 Analytics Engine For Quantifying Game Strategy, Connor S. Maurer
Computer Vision In Soccer: Yolov11 Analytics Engine For Quantifying Game Strategy, Connor S. Maurer
Data Science Undergraduate Honors Theses
Single-shot object detection capabilities significantly reduce computational overhead for real-time computer vision in sports analytics at 60 FPS. YOLO11’s lightweight CNN gives promising accuracy while meeting the low-latency demand of dynamic soccer matches. As data-driven approaches take over the sport of soccer, efficient player tracking systems become critical for informing coach’s strategies. I prototype the ETL (Extract, Transform, Load) process of data collected from a single- shot detection program and evaluate its viability for estimating player fatigue. YOLO11 detects players, the ball, and other characteristics, with the output transformed by homography to estimate the positions in the real world. These …
Derived Jet Schemes And Arc Spaces, And Arithmetic Arc Space Representability, C. Eric Overton-Walker
Derived Jet Schemes And Arc Spaces, And Arithmetic Arc Space Representability, C. Eric Overton-Walker
Graduate Theses and Dissertations
Associated to a given scheme X one can define geometric and arithmetic notions of jet schemes and arc spaces. We develop a construction of the geometric jets and arcs in the setting of derived schemes and explore consequences thereof. In particular, we prove an analogous theorem to that of one by Tommaso de Fernex and Roi Docampo concerning the cotangent sheaves of geometric jets and arcs. Our version then produces many subsequent results which allow us to prove stronger versions of results concerning geometric jets and arcs by removing unnecessary hypotheses. Separately, we explore evidence as to why, in contrast …
Interpolation Problems And The Characterization Of The Hilbert Function, Bryant Xie
Interpolation Problems And The Characterization Of The Hilbert Function, Bryant Xie
Mathematical Sciences Undergraduate Honors Theses
In mathematics, it is often useful to approximate the values of functions that are either too awkward and difficult to evaluate or not readily differentiable or integrable. To approximate its values, we attempt to replace such functions with more well-behaving examples such as polynomials or trigonometric functions. Over the algebraically closed field C, a polynomial passing through r distinct points with multiplicities m1, ..., mr on the affine complex line in one variable is determined by its zeros and the vanishing conditions up to its mi − 1 derivative for each point. A natural question would then be to consider …
Lecture 00: Opening Remarks: 46th Spring Lecture Series, Tulin Kaman
Lecture 00: Opening Remarks: 46th Spring Lecture Series, Tulin Kaman
Mathematical Sciences Spring Lecture Series
Opening remarks for the 46th Annual Mathematical Sciences Spring Lecture Series at the University of Arkansas, Fayetteville.
Hyperbolic Endomorphisms Of Free Groups, Jean Pierre Mutanguha
Hyperbolic Endomorphisms Of Free Groups, Jean Pierre Mutanguha
Graduate Theses and Dissertations
We prove that ascending HNN extensions of free groups are word-hyperbolic if and only if they have no Baumslag-Solitar subgroups. This extends Brinkmann's theorem that free-by-cyclic groups are word-hyperbolic if and only if they have no Z2 subgroups. To get started on our main theorem, we first prove a structure theorem for injective but nonsurjective endomorphisms of free groups. With the decomposition of the free group given by this structure theorem, we (more or less) construct representatives for nonsurjective endomorphisms that are expanding immersions relative to a homotopy equivalence. This structure theorem initializes the development of (relative) train track theory …
Equations Of Multi-Rees Algebras, Babak Jabbar Nezhad
Equations Of Multi-Rees Algebras, Babak Jabbar Nezhad
Graduate Theses and Dissertations
In this thesis we describe the defining equations of certain multi-Rees algebras. First, we determine the defining equations of the multi-Rees algebra $R[I^{a_1}t_1,\dots,I^{a_r}t_r]$ over a Noetherian ring $R$ when $I$ is an ideal of linear type. This generalizes a result of Ribbe and recent work of Lin-Polini and Sosa. Second, we describe the equations defining the multi-Rees algebra $R[I_1^{a_1}t_1,\dots,I_r^{a_r}t_r]$, where $R$ is a Noetherian ring containing a field and the ideals are generated by a subset of a fixed regular sequence.
Early Investigations In Conformal And Differential Geometry, Raymond T. Walter
Early Investigations In Conformal And Differential Geometry, Raymond T. Walter
Inquiry: The University of Arkansas Undergraduate Research Journal
The present article introduces fundamental notions of conformal and differential geometry, especially where such notions are useful in mathematical physics applications. Its primary achievement is a nontraditional proof of the classic result of Liouville that the only conformal transformations in Euclidean space of dimension greater than two are Möbius transformations. The proof is nontraditional in the sense that it uses the standard Dirac operator on Euclidean space and is based on a representation of Möbius transformations using 2x2 matrices over a Clifford algebra. Clifford algebras and the Dirac operator are important in other applications of pure mathematics and mathematical physics, …
Where Does It All End? Boundaries Beyond Euclidean Space, Jonathan Thompson
Where Does It All End? Boundaries Beyond Euclidean Space, Jonathan Thompson
Inquiry: The University of Arkansas Undergraduate Research Journal
No abstract provided.