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Articles 1  30 of 214
FullText Articles in Algebraic Geometry
Topology And Dynamics Of Gene Regulatory Networks: A MetaAnalysis, Claus Kadelka
Topology And Dynamics Of Gene Regulatory Networks: A MetaAnalysis, Claus Kadelka
Biology and Medicine Through Mathematics Conference
No abstract provided.
Unifications Of Pythagorean Triple Schema, Emily Hammes
Unifications Of Pythagorean Triple Schema, Emily Hammes
Undergraduate Honors Theses
Euclid’s Method of finding Pythagorean triples is a commonly accepted and applied technique. This study focuses on a myriad of other methods behind finding such Pythagorean triples. Specifically, we discover whether or not other ways of finding triples are special cases of Euclid’s Method.
On The Complexity Of Computing Galois Groups Of Differential Equations, Mengxiao Sun
On The Complexity Of Computing Galois Groups Of Differential Equations, Mengxiao Sun
All Dissertations, Theses, and Capstone Projects
The differential Galois group is an analogue for a linear differential equation of the classical Galois group for a polynomial equation. An important application of the differential Galois group is that a linear differential equation can be solved by integrals, exponentials and algebraic functions if and only if the connected component of its differential Galois group is solvable. Computing the differential Galois groups would help us determine the existence of the solutions expressed in terms of elementary functions (integrals, exponentials and algebraic functions) and understand the algebraic relations among the solutions.
Hrushovski first proposed an algorithm for computing the differential ...
Data Parsing For Optimized Molecular Geometry Calculations, Luke Rens
Data Parsing For Optimized Molecular Geometry Calculations, Luke Rens
Undergraduate Research Conference
The purpose of this project is to optimize and streamline to process of using ADF and ReaxFF. There is no efficient way to effectively add constraints to a compound and run it through ADF, take the ADF output and create a file that can be run through Reaxff, then take that Reaxff output and come to conclusions on it. To streamline this process, scripts were developed using Python to parse information out of data generated by ADF.
Enhanced Koszulity In Galois Cohomology, Marina Palaisti
Enhanced Koszulity In Galois Cohomology, Marina Palaisti
Electronic Thesis and Dissertation Repository
Despite their central role in Galois theory, absolute Galois groups remain rather mysterious; and one of the main problems of modern Galois theory is to characterize which profinite groups are realizable as absolute Galois groups over a prescribed field. Obtaining detailed knowledge of Galois cohomology is an important step to answering this problem. In our work we study various forms of enhanced Koszulity for quadratic algebras. Each has its own importance, but the common ground is that they all imply Koszulity. Applying this to Galois cohomology, we prove that, in all known cases of finitely generated pro$p$groups, Galois ...
Dense Geometry Of Music And Visual Arts: Vanishing Points, Continuous Tonnetz, And Theremin Performance, Maria Mannone, Irene Iaccarino, Rosanna Iembo
Dense Geometry Of Music And Visual Arts: Vanishing Points, Continuous Tonnetz, And Theremin Performance, Maria Mannone, Irene Iaccarino, Rosanna Iembo
The STEAM Journal
The dualism between continuous and discrete is relevant in music theory as well as in performance practice of musical instruments. Geometry has been used since longtime to represent relationships between notes and chords in tonal system. Moreover, in the field of mathematics itself, it has been shown that the continuity of real numbers can arise from geometrical observations and reasoning. Here, we consider a geometrical approach to generalize representations used in music theory introducing continuous pitch. Such a theoretical framework can be applied to instrument playing where continuous pitch can be naturally performed. Geometry and visual representations of concepts of ...
Umsl Faculty Expertise
Adrian Clingher
Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg
Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg
All Graduate Plan B and other Reports
Lie algebra cohomology is an important tool in many branches of mathematics. It is used in the Topology of homogeneous spaces, Deformation theory, and Extension theory. There exists extensive theory for calculating the cohomology of semi simple Lie algebras, but more tools are needed for calculating the cohomology of general Lie algebras. To calculate the cohomology of general Lie algebras, I used the symbolic software program called Maple. I wrote software to calculate the cohomology in several different ways. I wrote several programs to calculate the cohomology directly. This proved to be computationally expensive as the number of differential forms ...
The Influence Of Canalization On The Robustness Of Finite Dynamical Systems, Claus Kadelka
The Influence Of Canalization On The Robustness Of Finite Dynamical Systems, Claus Kadelka
Annual Symposium on Biomathematics and Ecology: Education and Research
No abstract provided.
Dual Perspectives On Desargues' Theorem, Carl Lienert
Galois Groups Of Differential Equations And Representing Algebraic Sets, Eli Amzallag
Galois Groups Of Differential Equations And Representing Algebraic Sets, Eli Amzallag
All Dissertations, Theses, and Capstone Projects
The algebraic framework for capturing properties of solution sets of differential equations was formally introduced by Ritt and Kolchin. As a parallel to the classical Galois groups of polynomial equations, they devised the notion of a differential Galois group for a linear differential equation. Just as solvability of a polynomial equation by radicals is linked to the equation’s Galois group, so too is the ability to express the solution to a linear differential equation in "closed form" linked to the equation’s differential Galois group. It is thus useful even outside of mathematics to be able to compute and ...
Webwork Problems For Linear Algebra, Hashim Saber, Beata Hebda
Webwork Problems For Linear Algebra, Hashim Saber, Beata Hebda
Mathematics Ancillary Materials
This set of problems for Linear Algebra in the opensource WeBWorK mathematics platform was created under a Round Eleven MiniGrant for Ancillary Materials Creation. The problems were created for an implementation of the CCBY Lyrix open textbook A First Course in Linear Algebra. Also included as an additional file are the selected and modified Lyryx Class Notes for the textbook.
Topics covered include:
 Linear Independence
 Linear Transformations
 Matrix of a Transformation
 Isomorphisms
 Eigenvalues and Eigenvectors
 Diagonalization
 Orthogonality
Constructing Surfaces With (1/(K2)^2)(1,K3) Singularities, Liam Patrick Keenan
Constructing Surfaces With (1/(K2)^2)(1,K3) Singularities, Liam Patrick Keenan
Lawrence University Honors Projects
We develop a procedure to construct complex algebraic surfaces which are stable, minimal, and of general type, possessing a Tsingularity of the form (1/(k2)^{2})(1,k3).
Mixed Categories Of Sheaves On Toric Varieties, Sean Michael Taylor
Mixed Categories Of Sheaves On Toric Varieties, Sean Michael Taylor
LSU Doctoral Dissertations
In [BGS96], Beilinson, Ginzburg, and Soergel introduced the notion of mixed categories. This idea often underlies many interesting "Koszul dualities." In this paper, we produce a mixed derived category of constructible complexes (in the sense of [BGS96]) for any toric variety associated to a fan. Furthermore, we show that it comes equipped with a tstructure whose heart is a mixed version of the category of perverse sheaves. In chapters 2 and 3, we provide the necessary background. Chapter 2 concerns the categorical preliminaries, while chapter 3 gives the background geometry. This concerns both some basics of toric varieties as well ...
The Average Measure Of A KDimensional Simplex In An NCube, John A. Carter
The Average Measure Of A KDimensional Simplex In An NCube, John A. Carter
MSU Graduate Theses
Within an ndimensional unit cube, a number of kdimensional simplices can be formed whose vertices are the vertices of the ncube. In this thesis, we analyze the average measure of a ksimplex in the ncube. We develop exact equations for the average measure when k = 1, 2, and 3. Then we generate data for these cases and conjecture that their averages appear to approach n^{k/2} times some constant. Using the convergence of Bernstein polynomials and a ksimplex Bernstein generalization, we prove the conjecture is true for the 1simplex and 2simplex cases. We then develop a generalized formula for ...
Determinantal Representations Of Elliptic Curves Via Weierstrass Elliptic Functions, MaoTing Chien, Hiroshi Nakazato
Determinantal Representations Of Elliptic Curves Via Weierstrass Elliptic Functions, MaoTing Chien, Hiroshi Nakazato
Electronic Journal of Linear Algebra
Helton and Vinnikov proved that every hyperbolic ternary form admits a symmetric derminantal representation via Riemann theta functions. In the case the algebraic curve of the hyperbolic ternary form is elliptic, the determinantal representation of the ternary form is formulated by using Weierstrass $\wp$functions in place of Riemann theta functions. An example of this approach is given.
Dalton State College Apex Calculus, Thomas Gonzalez, Michael Hilgemann, Jason Schmurr
Dalton State College Apex Calculus, Thomas Gonzalez, Michael Hilgemann, Jason Schmurr
Mathematics Open Textbooks
This text for Analytic Geometry and Calculus I, II, and III is a Dalton State College remix of APEX Calculus 3.0. The text was created through a Round Six ALG Textbook Transformation Grant.
Topics covered in this text include:
 Limits
 Derivatives
 Integration
 Antidifferentiation
 Sequences
 Vectors
Files can also be downloaded on the Dalton State College GitHub:
https://github.com/DaltonStateCollege/calculustext/blob/master/Calculus.pdf
Analytic Geometry And Calculus I, Ii, & Iii (Dalton), Thomas Gonzalez, Michael Hilgemann, Jason Schmurr
Analytic Geometry And Calculus I, Ii, & Iii (Dalton), Thomas Gonzalez, Michael Hilgemann, Jason Schmurr
Mathematics Grants Collections
This Grants Collection for Analytic Geometry and Calculus I, II, & III was created under a Round Six ALG Textbook Transformation Grant.
Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.
Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:
 Linked Syllabus
 Initial Proposal
 Final Report
Branching Matrices For The Automorphism Group Lattice Of A Riemann Surface, Sean A. Broughton
Branching Matrices For The Automorphism Group Lattice Of A Riemann Surface, Sean A. Broughton
Mathematical Sciences Technical Reports (MSTR)
Let S be a Riemann surface and G a large subgroup of Aut(S) (Aut(S) may be unknown). We are particularly interested in regular ngonal surfaces, i.e., the quotient surface S/G (and hence S/Aut(S)) has genus zero. For various H the ramification information of the branched coverings S/K > S/H may be captured in a matrix. The ramification information, in particular strong branching, may be then be used in analyzing the structure of Aut(S). The ramification information is conjugation invariant so the matrix's rows and columns may be indexed by conjugacy ...
Schubert Polynomial Multiplication, Sara Amato
Schubert Polynomial Multiplication, Sara Amato
Honors Theses
Schur polynomials are a fundamental object in the field of algebraic combinatorics. The product of two Schur polynomials can be written as a sum of Schur polynomials using nonnegative integer coefficients. A simple combinatorial algorithm for generating these coefficients is called the LittlewoodRichardson Rule. Schubert polynomials are generalizations of the Schur polynomials. Schubert polynomials also appear in many contexts, such as in algebraic combinatorics and algebraic geometry. It is known from algebraic geometry that the product of two Schubert polynomials can be written as a sum of Schubert polynomials using nonnegative integer coefficients. However, a simple combinatorial algorithm for generating ...
Centroidal Voronoi Tessellations With Few Generator Points, Kirill Shakhnovskiy
Centroidal Voronoi Tessellations With Few Generator Points, Kirill Shakhnovskiy
Senior Projects Spring 2018
A Voronoi tessellation with $n$ generator points is the partitioning of a bounded region in $\rr^2$ into polygons such that every point in a given polygon is closer to its generator point than to any other generator point. A centroidal Voronoi tessellation (CVT) is a Voronoi tessellation where each polygon’s generator point is also its center of mass. In this project I will demonstrate what kinds of CVTs can exists within specific parameters, such as a square or rectangular region, and a set number generator points. I will also prove that the examples I present are the only ...
On The Landscape Of Random Tropical Polynomials, Christopher Hoyt
On The Landscape Of Random Tropical Polynomials, Christopher Hoyt
HMC Senior Theses
Tropical polynomials are similar to classical polynomials, however addition and multiplication are replaced with tropical addition (minimums) and tropical multiplication (addition). Within this new construction, polynomials become piecewise linear curves with interesting behavior. All tropical polynomials are piecewise linear curves, and each linear component uniquely corresponds to a particular monomial. In addition, certain monomial in the tropical polynomial can be trivial due to the fact that tropical addition is the minimum operator. Therefore, it makes sense to consider a graph of connectivity of the monomials for any given tropical polynomial. We investigate tropical polynomials where all coefficients are chosen from ...
An Incidence Approach To The Distinct Distances Problem, Bryce Mclaughlin
An Incidence Approach To The Distinct Distances Problem, Bryce Mclaughlin
HMC Senior Theses
In 1946, Erdös posed the distinct distances problem, which asks for the minimum number of distinct distances that any set of n points in the real plane must realize. Erdös showed that any point set must realize at least &Omega(n^{1/2}) distances, but could only provide a construction which offered &Omega(n/&radic(log(n)))$ distances. He conjectured that the actual minimum number of distances was &Omega(n^{1&epsilon}) for any &epsilon > 0, but that sublinear constructions were possible. This lower bound has been improved over the years, but Erdös' conjecture seemed to hold until in 2010 ...
Geometric Serendipity, Dakota Becker
Geometric Serendipity, Dakota Becker
Auctus: The Journal of Undergraduate Research and Creative Scholarship
The central focus of my practice is the serendipitous exploration into geometry, symmetry, design, and color. I have found more and more that the affinity I have for hardedge geometric abstraction is a deeper reflection of the way in which I process my thoughts and surroundings. In the past year, I have sought to challenge myself by questioning the core of my practice and pushing it to go beyond its individual elements. In this way, I seek to create work that is more than its parts. As a result, I have become more purposeful with my designs and push both ...
Framed Sheaves On A Quadric Surface, Nguyen Thuc Huy Le
Framed Sheaves On A Quadric Surface, Nguyen Thuc Huy Le
Doctoral Dissertations
We study framed sheaves on a smooth quadric surface and conjecture that the moduli of such framed sheaves admits a twistor deformation similar to one studied in the paper "BrillNoether duality for moduli spaces of sheaves on K3 surfaces" by Markman.
On Representations Of The Jacobi Group And Differential Equations, Benjamin Webster
On Representations Of The Jacobi Group And Differential Equations, Benjamin Webster
UNF Graduate Theses and Dissertations
In PDEs with nontrivial Lie symmetry algebras, the Lie symmetry naturally yield Fourier and Laplace transforms of fundamental solutions. Applying this fact we discuss the semidirect product of the metaplectic group and the Heisenberg group, then induce a representation our group and use it to investigate the invariant solutions of a general differential equation of the form .
A Journey To The Adic World, Fayadh Kadhem
A Journey To The Adic World, Fayadh Kadhem
Electronic Theses and Dissertations
The first idea of this research was to study a topic that is related to both Algebra and Topology and explore a tool that connects them together. That was the entrance for me to the “adic world”. What was needed were some important concepts from Algebra and Topology, and so they are treated in the first two chapters.
The reader is assumed to be familiar with Abstract Algebra and Topology, especially with Ring theory and basics of Pointset Topology.
The thesis consists of a motivation and four chapters, the third and the fourth being the main ones. In the third ...
Ideal Containments Under Flat Extensions And Interpolation On Linear Systems In P^{2}, Solomon Akesseh
Ideal Containments Under Flat Extensions And Interpolation On Linear Systems In P2, Solomon Akesseh
Dissertations, Theses, and Student Research Papers in Mathematics
Fat points and their ideals have stimulated a lot of research but this dissertation concerns itself with aspects of only two of them, broadly categorized here as, the ideal containments and polynomial interpolation problems.
EinLazarsfeldSmith and HochsterHuneke cumulatively showed that for all ideals I in k[P^{n}], I^{(mn)} ⊆ I^{m} for all m ∈ N. Over the projective plane, we obtain I^{(4)}< ⊆ I^{2}. Huneke asked whether it was the case that I^{(3)} ⊆ I^{2}. Dumnicki, Szemberg and TutajGasinska show that if I is the saturated homogeneous radical ideal of the 12 points of the Hesse configuration, then ...
Descartes Comes Out Of The Closet, Nora E. Culik
Descartes Comes Out Of The Closet, Nora E. Culik
Journal of Humanistic Mathematics
While “Descartes Comes Out of the Closet” is ostensibly about a young woman’s journey to Paris, the descriptive detail borrows language and images from Cartesian coordinate geometry, dualistic philosophy, neuroanatomy (the pineal), and projections of three dimensions onto planes. This mathematical universe is counterpointed in the natural language of the suppressed love story that locates the real in the human. Thus, at the heart of the story is the tension between competing notions of mathematics, i.e., as either an independent realm apart from history or as a culturally produced and historical set of practices. Of course, the central ...
College Algebra, Trigonometry, And Precalculus (Clayton), Chaogui Zhang, Scott Bailey, Billie May, Jelinda Spotorno, Kara Mullen
College Algebra, Trigonometry, And Precalculus (Clayton), Chaogui Zhang, Scott Bailey, Billie May, Jelinda Spotorno, Kara Mullen
Mathematics Grants Collections
This Grants Collection for College Algebra, Trigonometry, and Precalculus was created under a Round Five ALG Textbook Transformation Grant.
Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.
Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:
 Linked Syllabus
 Initial Proposal
 Final Report