Rendering Hypercomplex Fractals, 2018 Rhode Island College

#### Rendering Hypercomplex Fractals, Anthony Atella

*Honors Projects Overview*

Fractal mathematics and geometry are useful for applications in science, engineering, and art, but acquiring the tools to explore and graph fractals can be frustrating. Tools available online have limited fractals, rendering methods, and shaders. They often fail to abstract these concepts in a reusable way. This means that multiple programs and interfaces must be learned and used to fully explore the topic. Chaos is an abstract fractal geometry rendering program created to solve this problem. This application builds off previous work done by myself and others [1] to create an extensible, abstract solution to rendering fractals. This paper covers ...

Self-Assembly Of Dna Graphs And Postman Tours, 2018 University of North Florida

#### Self-Assembly Of Dna Graphs And Postman Tours, Katie Bakewell

*UNF Graduate Theses and Dissertations*

DNA graph structures can self-assemble from branched junction molecules to yield solutions to computational problems. Self-assembly of graphs have previously been shown to give polynomial time solutions to hard computational problems such as 3-SAT and k-colorability problems. Jonoska et al. have proposed studying self-assembly of graphs topologically, considering the boundary components of their thickened graphs, which allows for reading the solutions to computational problems through reporter strands. We discuss weighting algorithms and consider applications of self-assembly of graphs and the boundary components of their thickened graphs to problems involving minimal weight Eulerian walks such as the Chinese Postman Problem and ...

On Spectral Theorem, 2018 Colby College

#### On Spectral Theorem, Muyuan Zhang

*Honors Theses*

There are many instances where the theory of eigenvalues and eigenvectors has its applications. However, Matrix theory, which usually deals with vector spaces with finite dimensions, also has its constraints. Spectral theory, on the other hand, generalizes the ideas of eigenvalues and eigenvectors and applies them to vector spaces with arbitrary dimensions. In the following chapters, we will learn the basics of spectral theory and in particular, we will focus on one of the most important theorems in spectral theory, namely the spectral theorem. There are many different formulations of the spectral theorem and they convey the "same" idea. In ...

International Students’ Expectations Of Information Literacy Instruction, 2018 Edith Cowan University

#### International Students’ Expectations Of Information Literacy Instruction, Nicole Johnston, Meggan Houlihan, Jodi Neindorf

*ECU Publications Post 2013*

This paper presents the findings of a case study that investigated international university students’ expectations and experiences of information literacy across two countries. The results from this case study provide insights that can be utilized by librarians working with international students, to plan and develop their information literacy instruction classes and programs. Armed with an awareness of what international students’ expectations and experiences with information literacy programs are, librarians can develop more meaningful instruction that better meets the information needs of international students. Moving beyond the pilot survey, the researchers aim to improve the survey instrument and collaborate with librarians ...

Optimal Supply Delivery Under Military Specific Constraints, 2018 Georgia Southern University

#### Optimal Supply Delivery Under Military Specific Constraints, Talena Fletcher

*Electronic Theses and Dissertations*

Through-out military history, the need to safely and effectively allocate resources to various military operations was a task of extreme importance. Satisfying the needs of multiple consumers by optimally pairing with appropriate suppliers falls into the category of vehicle routing problems (VRP), which has been intensively studied over the years. In general, finding the optimal solution to VRP is known to be NP-hard. The proposed solutions rely on mathematical programming and the size of the problems that can be optimally solved is typically limited. In military settings, balancing the needs of multiple consumers with the current operational environment has always ...

Can Addressing Language Skills For Fifth Grade Ells In A Multiplication Curriculum Help Address The Achievement Gap In Math? A Multiplication Workbook For Big Kids, 2017 The University of San Francisco

#### Can Addressing Language Skills For Fifth Grade Ells In A Multiplication Curriculum Help Address The Achievement Gap In Math? A Multiplication Workbook For Big Kids, Michelle Douglas

*Master's Projects and Capstones*

Currently, the state of California has 1,332,405 students from grades k-12 who speak a language other than English at home (Caledfacts, 2016). When I started my first year teaching fifth grade with 95% of my students being English language learners (ELLs), I was surprised to see an achievement gap of two to three years in my student’s reading and math skills. I found that my student’s developmental language and math skills contributed to a lack of engagement during math time. Upon further research, I found that these three factors play a role in the wide achievement ...

Facing The Sun, 2017 Dublin Institute of Technology

#### Facing The Sun, Frank Prendergast, Muiris O'Sullivan, Ken Williams, Gabriel Cooney

*Articles*

December 2017 marked 50 years since archaeologist Michael J. O’Kelly first observed the solar illumination of the burial chamber in the Neolithic passage tomb at Newgrange during the period of the winter solstice. O’Kelly subsequently recorded direct sunlight entering Newgrange through the ‘especially contrived slit which lies under the roof-box at the outer end of the passage roof’ on 21 December 1969. The discovery of this historic phenomenon, dating back over 5,000 years, captured the public interest and imagination at that time and ever since. In this major article published in the Winter 2017 edition of *Archaeology ...*

The Calculus War: The Ultimate Clash Of Genius, 2017 University of Tennessee, Knoxville

#### The Calculus War: The Ultimate Clash Of Genius, Walker Briles Bussey-Spencer

*Chancellor’s Honors Program Projects*

No abstract provided.

Making Models With Bayes, 2017 California State University, San Bernardino

#### Making Models With Bayes, Pilar Olid

*Electronic Theses, Projects, and Dissertations*

Bayesian statistics is an important approach to modern statistical analyses. It allows us to use our prior knowledge of the unknown parameters to construct a model for our data set. The foundation of Bayesian analysis is Bayes' Rule, which in its proportional form indicates that the posterior is proportional to the prior times the likelihood. We will demonstrate how we can apply Bayesian statistical techniques to fit a linear regression model and a hierarchical linear regression model to a data set. We will show how to apply different distributions to Bayesian analyses and how the use of a prior affects ...

Essential Sets For Random Operators Constructed From An Arratia Flow, 2017 Institute of Mathematics, National Academy of Sciences of Ukraine

#### Essential Sets For Random Operators Constructed From An Arratia Flow, Andrey A. Dorogovtsev, Ia. A. Korenovska

*Communications on Stochastic Analysis*

No abstract provided.

The Moments Of Lévy's Area Using A Sticky Shuffle Hopf Algebra, 2017 Loughborough University

#### The Moments Of Lévy's Area Using A Sticky Shuffle Hopf Algebra, Robin Hudson, Uwe Schauz, Yue Wu

*Communications on Stochastic Analysis*

No abstract provided.

A Note On Time-Dependent Additive Functionals, 2017 ENSTA ParisTech

#### A Note On Time-Dependent Additive Functionals, Adrien Barrasso, Francesco Russo

*Communications on Stochastic Analysis*

No abstract provided.

Perpetual Integral Functionals Of Brownian Motion And Blowup Of Semilinear Systems Of Spdes, 2017 Centro de Investigación en Matemáticas, Guanajuato

#### Perpetual Integral Functionals Of Brownian Motion And Blowup Of Semilinear Systems Of Spdes, Eugenio Guerrero, José Alfredo López-Mindela

*Communications on Stochastic Analysis*

No abstract provided.

One Dimensional Complex Ornstein-Uhlenbeck Operator, 2017 Jiangxi Normal University

#### One Dimensional Complex Ornstein-Uhlenbeck Operator, Yong Chen

*Communications on Stochastic Analysis*

No abstract provided.

Gaussian Guesswork: Infinite Sequences And The Arithmetic-Geometric Mean, 2017 Colorado State University-Pueblo

#### Gaussian Guesswork: Infinite Sequences And The Arithmetic-Geometric Mean, Janet Heine Barnett

*Calculus*

No abstract provided.

Evolution Of Superoscillations For Schrödinger Equation In A Uniform Magnetic Field, 2017 Politecnico di Milano

#### Evolution Of Superoscillations For Schrödinger Equation In A Uniform Magnetic Field, Fabrizio Colombo, Jonathan Gantner, Daniele C. Struppa

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

Aharonov-Berry superoscillations are band-limited functions that oscillate faster than their fastest Fourier component. Superoscillations appear in several fields of science and technology, such as Aharonov’s weak measurement in quantum mechanics, in optics, and in signal processing. An important issue is the study of the evolution of superoscillations using the Schrödinger equation when the initial datum is a weak value. Some superoscillatory functions are not square integrable, but they are real analytic functions that can be extended to entire holomorphic functions. This fact leads to the study of the continuity of a class of convolution operators acting on suitable spaces ...

Ar(1) Sequence With Random Coefficients:Regenerative Properties And Its Application, 2017 Iowa State University

#### Ar(1) Sequence With Random Coefficients:Regenerative Properties And Its Application, Krishna B. Athreya, Koushik Saha, Radhendushka Srivastava

*Communications on Stochastic Analysis*

No abstract provided.

Constructing A Square An Ancient Indian Way Activity, 2017 Pittsburg State University

#### Constructing A Square An Ancient Indian Way Activity, Cynthia J. Huffman Ph.D.

*Open Educational Resources - Math*

In this activity students use string to model one of the ways that was used in ancient India for constructing a square. The construction was used in building a temporary fire altar. The activity is based on a translation by Sen and Bag of the Baudhāyana-śulba-sūtra.

Constructing A Square Indian Fire Altar Activity, 2017 Pittsburg State University

#### Constructing A Square Indian Fire Altar Activity, Cynthia J. Huffman Ph.D.

*Open Educational Resources - Math*

In this activity, we will model constructing a square fire altar with a method similar to one used by people in ancient India. The fire altars, which were made of bricks, had various shapes. Instructions for building the altars were in Vedic texts called *Śulba-sūtras*. We will follow instructions for constructing a square *gārhapatya *fire altar* *from the *Baudhāyana-śulba-sūtra*, which was written during the Middle Vedic period, about 800-500 BC.

Splittings Of Relatively Hyperbolic Groups And Classifications Of 1-Dimensional Boundaries, 2017 University of Wisconsin-Milwaukee

#### Splittings Of Relatively Hyperbolic Groups And Classifications Of 1-Dimensional Boundaries, Matthew Haulmark

*Theses and Dissertations*

In the first part of this dissertation, we show that the existence of non-parabolic local cut point in the relative (or Bowditch) boundary, $\relbndry$, of a relatively hyperbolic group $(\Gamma,\bbp)$ implies that $\Gamma$ splits over a $2$-ended subgroup. As a consequence we classify the homeomorphism type of the Bowditch boundary for the special case when the Bowditch boundary $\relbndry$ is one-dimensional and has no global cut points.

In the second part of this dissertation, We study local cut points in the boundary of CAT(0) groups with isolated flats. In particular the relationship between local cut points in ...