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.

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.

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.

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.

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 ...

Extending Difference Of Votes Rules On Three Voting Models., 2017 University of Louisville

#### Extending Difference Of Votes Rules On Three Voting Models., Sarah Schulz King

*Electronic Theses and Dissertations*

In a voting situation where there are only two competing alternatives, simple majority rule outputs the alternatives with the most votes or declares a tie if both alternatives receive the same number of votes. For any non-negative integer *k*, the difference of votes rule M_{k} outputs the alternative that beats the competing alternative by more than *k* votes. Llamazares (2006) gives a characterization of the difference of votes rules in terms of five axioms. In this thesis, we extend Llamazares' result by completely describing the class of voting rules that satisfy only two out of his five axioms. In ...

Residuated Maps, The Way-Below Relation, And Contractions On Probabilistic Metric Spaces., 2017 University of Louisville

#### Residuated Maps, The Way-Below Relation, And Contractions On Probabilistic Metric Spaces., M. Ryan Luke

*Electronic Theses and Dissertations*

In this dissertation, we will examine residuated mappings on a function lattice and how they behave with respect to the way-below relation. In particular, which residuated $\phi$ has the property that $F$ is way-below $\phi(F)$ for $F$ in appropriate sets. We show the way-below relation describes the separation of two functions and how this corresponds to contraction mappings on probabilistic metric spaces. A new definition for contractions is considered using the way-below relation.

Dependence Structures In Lévy-Type Markov Processes, 2017 University of Tennessee, Knoxville

#### Dependence Structures In Lévy-Type Markov Processes, Eddie Brendan Tu

*Doctoral Dissertations*

In this dissertation, we examine the positive and negative dependence of infinitely divisible distributions and Lévy-type Markov processes. Examples of infinitely divisible distributions include Poissonian distributions like compound Poisson and α-stable distributions. Examples of Lévy-type Markov processes include Lévy processes and Feller processes, which include a class of jump-diffusions, certain stochastic differential equations with Lévy noise, and subordinated Markov processes. Other examples of Lévy-type Markov processes are time-inhomogeneous Feller evolution systems (FES), which include additive processes. We will provide a tour of various forms of positive dependence, which include association, positive supermodular association (PSA), positive supermodular dependence (PSD), and positive ...

Π-Operators In Clifford Analysis And Its Applications, 2017 University of Arkansas, Fayetteville

#### Π-Operators In Clifford Analysis And Its Applications, Wanqing Cheng

*Theses and Dissertations*

In this dissertation, we studies Π-operators in different spaces using Clifford algebras. This approach generalizes the Π-operator theory on the complex plane to higher dimensional spaces. It also allows us to investigate the existence of the solutions to Beltrami equations in different spaces.

Motivated by the form of the Π-operator on the complex plane, we first construct a Π-operator on a general Clifford-Hilbert module. It is shown that this operator is an L^2 isometry. Further, this can also be used for solving certain Beltrami equations when the Hilbert space is the L^2 space of a measure space. This ...

Vertex Weighted Spectral Clustering, 2017 East Tennessee State University

#### Vertex Weighted Spectral Clustering, Mohammad Masum

*Electronic Theses and Dissertations*

Spectral clustering is often used to partition a data set into a specified number of clusters. Both the unweighted and the vertex-weighted approaches use eigenvectors of the Laplacian matrix of a graph. Our focus is on using vertex-weighted methods to refine clustering of observations. An eigenvector corresponding with the second smallest eigenvalue of the Laplacian matrix of a graph is called a Fiedler vector. Coefficients of a Fiedler vector are used to partition vertices of a given graph into two clusters. A vertex of a graph is classified as unassociated if the Fiedler coefficient of the vertex is close to ...

Cayley Graphs Of Groups And Their Applications, 2017 Missouri State University

#### Cayley Graphs Of Groups And Their Applications, Anna Tripi

*MSU Graduate Theses*

Cayley graphs are graphs associated to a group and a set of generators for that group (there is also an associated directed graph). The purpose of this study was to examine multiple examples of Cayley graphs through group theory, graph theory, and applications. We gave background material on groups and graphs and gave numerous examples of Cayley graphs and digraphs. This helped investigate the conjecture that the Cayley graph of any group (except Z_2) is hamiltonian. We found the conjecture to still be open. We found Cayley graphs and hamiltonian cycles could be applied to campanology (in particular, to the ...

Efficiently Representing The Integer Factorization Problem Using Binary Decision Diagrams, 2017 Utah State University

#### Efficiently Representing The Integer Factorization Problem Using Binary Decision Diagrams, David Skidmore

*All Graduate Plan B and other Reports*

Let p be a prime positive integer and let α be a positive integer greater than 1. A method is given to reduce the problem of finding a nontrivial factorization of α to the problem of finding a solution to a system of modulo p polynomial congruences where each variable in the system is constrained to the set {0,...,p − 1}. In the case that p = 2 it is shown that each polynomial in the system can be represented by an ordered binary decision diagram with size less than 20.25log_{2}(α)^{3} + 16.5log_{2}(α)^{2} + 6log ...

Disciple, 2017 Pacific Lutheran University

#### Disciple, Jessica K. Sklar

*Journal of Humanistic Mathematics*

This is a love poem for mathematics.

Discrete And Continuous: A Fundamental Dichotomy In Mathematics, 2017 University of New South Wales

#### Discrete And Continuous: A Fundamental Dichotomy In Mathematics, James Franklin

*Journal of Humanistic Mathematics*

The distinction between the discrete and the continuous lies at the heart of mathematics. Discrete mathematics (arithmetic, algebra, combinatorics, graph theory, cryptography, logic) has a set of concepts, techniques, and application areas largely distinct from continuous mathematics (traditional geometry, calculus, most of functional analysis, differential equations, topology). The interaction between the two – for example in computer models of continuous systems such as fluid flow – is a central issue in the applicable mathematics of the last hundred years. This article explains the distinction and why it has proved to be one of the great organizing themes of mathematics.

Some Thoughts On The Epicurean Critique Of Mathematics, 2017 American University of Kuwait

#### Some Thoughts On The Epicurean Critique Of Mathematics, Michael Aristidou

*Journal of Humanistic Mathematics*

In this paper, we give a comprehensive summary of the discussion on the Epicurean critique of mathematics and in particular of Euclid's geometry. We examine the methodological critique of the Epicureans on mathematics and we assess whether a 'mathematical atomism' was proposed, and its implications. Finally, we examine the Epicurean philosophical stance on mathematics and evaluate whether it was on target or not.