Topology And Dynamics Of Gene Regulatory Networks: A Meta-Analysis, 2019 Iowa State University

#### Topology And Dynamics Of Gene Regulatory Networks: A Meta-Analysis, Claus Kadelka

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Unifications Of Pythagorean Triple Schema, 2019 East Tennessee State University

#### 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, 2019 The Graduate Center, City University of New York

#### 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, 2019 Stephen F Austin State University

#### 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, 2019 The University of Western Ontario

#### 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, 2019 Independent researcher, Palermo, Italy

#### 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, 2018 Selected Works

#### Umsl Faculty Expertise

*Adrian Clingher*

Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, 2018 Utah State University

#### 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, 2018 Illinois State University

#### 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, 2018 Ursinus College

Galois Groups Of Differential Equations And Representing Algebraic Sets, 2018 The Graduate Center, City University of New York

#### 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, 2018 University of North Georgia

#### Webwork Problems For Linear Algebra, Hashim Saber, Beata Hebda

*Mathematics Ancillary Materials*

This set of problems for Linear Algebra in the open-source WeBWorK mathematics platform was created under a Round Eleven Mini-Grant for Ancillary Materials Creation. The problems were created for an implementation of the CC-BY 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/(K-2)^2)(1,K-3) Singularities, 2018 Lawrence University

#### Constructing Surfaces With (1/(K-2)^2)(1,K-3) 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 T-singularity of the form (1/(k-2)^{2})(1,k-3).

Mixed Categories Of Sheaves On Toric Varieties, 2018 Louisiana State University and Agricultural and Mechanical College

#### 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 t-structure 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 K-Dimensional Simplex In An N-Cube, 2018 Missouri State University

#### The Average Measure Of A K-Dimensional Simplex In An N-Cube, John A. Carter

*MSU Graduate Theses*

Within an n-dimensional unit cube, a number of k-dimensional simplices can be formed whose vertices are the vertices of the n-cube. In this thesis, we analyze the average measure of a k-simplex in the n-cube. 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 k-simplex Bernstein generalization, we prove the conjecture is true for the 1-simplex and 2-simplex cases. We then develop a generalized formula for ...

Determinantal Representations Of Elliptic Curves Via Weierstrass Elliptic Functions, 2018 Soochow University

#### Determinantal Representations Of Elliptic Curves Via Weierstrass Elliptic Functions, Mao-Ting 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.

Analytic Geometry And Calculus I, Ii, & Iii (Dalton), 2018 Dalton State College

#### 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

Dalton State College Apex Calculus, 2018 Dalton State College

#### 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/calculus-text/blob/master/Calculus.pdf

Branching Matrices For The Automorphism Group Lattice Of A Riemann Surface, 2018 Rose-Hulman Institute of Technology

#### 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 *n*-gonal 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, 2018 Assumption College

#### 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 non-negative integer coefficients. A simple combinatorial algorithm for generating these coefficients is called the Littlewood-Richardson 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 non-negative integer coefficients. However, a simple combinatorial algorithm for generating ...