Algebraic Geometry Commons^™

Radiation Effect On Mixed Convection Flow Of Nanofluid Between Two Concentric Cylinders With Hall And Ion-Slip Effects, Md. Shafeeurrahman, D. Srinivasacharya

Applications and Applied Mathematics: An International Journal (AAM)

This paper analyzes the effects of thermal radiation, Hall and ion slip parameter on mixed convective nanofluid flow in an annuli between two concentric cylinders in the existence of strong magnetic field. The nonlinear governing equations are non-dimensionalized and then solved by using homotopy analysis method. The influence of radiation, magnetic, Hall and ion slip parameters on the velocity, temperature, nanoparticle concentration, Nusselt number and nanoparticle Sherwood number are investigated and represented graphically.

Taking A Canon To The Adjunction Formula, Paul M. Harrelson

Electronic Theses and Dissertations

In this paper, we show how the canonical divisor of a graph is related to the canonical divisor of its subgraph. The use of chip firing and the adjunction formula for graphs ex- plains said relation and even completes it. We go on to show the difference between the formula for full subgraphs and that of non-full subgraphs. Examples are used to simplify these results and to see the adjunction formula in action. Finally, we show that though the adjunction formula seems simple at first glance, it is somewhat complex and rather useful.

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 …

Application And Evaluation Of Lighthouse Technology For Precision Motion Capture, Soumitra Sitole

Masters Theses

This thesis presents the development towards a system that can capture and quantify motion for applications in biomechanical and medical fields demanding precision motion tracking using the lighthouse technology. Commercially known as SteamVR tracking, the lighthouse technology is a motion tracking system developed for virtual reality applications that makes use of patterned infrared light sources to highlight trackers (objects embedded with photodiodes) to obtain their pose or spatial position and orientation. Current motion capture systems such as the camera-based motion capture are expensive and not readily available outside of research labs. This thesis provides a case for low-cost motion capture …

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

Geometry

No abstract provided.

Galois Groups Of Differential Equations And Representing Algebraic Sets, Eli Amzallag

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 represent these …

Optimization For Lng Terminals Routing In North China, Shuting Wang

World Maritime University Dissertations

No abstract provided.

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.

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, 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, 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, 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 …

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

Some Studies On Algebraic Integers In Q(I,√3) By Using Coset Diagram, Florentin Smarandache, Saima Anis, Seok-Zun Song, Young Bae Jun

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we studied the action of Picard modular group PSL(2,Z[i])

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

Accessible files with optical character recognition (OCR) and auto-tagging provided by the Center for Inclusive Design and Innovation.

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 classes of subgroups. The only required …

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 "Brill-Noether duality for moduli spaces of sheaves on K3 surfaces" by Markman.

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 …

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 Larry Guth and Nets Hawk Katz …