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.

Quantitative Literacy In The Affective Domain: Computational Geology Students’ Reactions To Devlin’S The Math Instinct, 2017 University of South Florida

#### Quantitative Literacy In The Affective Domain: Computational Geology Students’ Reactions To Devlin’S The Math Instinct, Victor J. Ricchezza, H. L. Vacher

*Numeracy*

Building on suggestions from alumni from a recent interview project, students in Computational Geology at the University of South Florida were tasked with reading a popular non-fiction book on mathematics and writing about the book and their feelings about math. The book, *The Math Instinct* by Keith Devlin, was chosen because we believed it would give the students something interesting to write about and not because we had any expectations in particular about what it might reveal about or do for their math anxiety. The nature of the responses received from the students led to the performance of a post-hoc ...

Figures And First Years: An Analysis Of Calculus Students' Use Of Figures In Technical Reports, 2017 Ithaca College

#### Figures And First Years: An Analysis Of Calculus Students' Use Of Figures In Technical Reports, Nathan J. Antonacci, Michael Rogers, Thomas J. Pfaff, Jason G. Hamilton

*Numeracy*

This three-year study focused on first-year Calculus I students and their abilities to incorporate figures in technical reports. In each year, these calculus students wrote a technical report as part of the Polar Bear Module, an educational unit developed for use in partner courses in biology, computer science, mathematics, and physics as part of the Multidisciplinary Sustainability Education (MSE) project at Ithaca College. In the first year of the project, students received basic technical report guidelines. In year two, the report guidelines changed to include explicit language on how to incorporate figures. In year three, a grading rubric was added ...

An Optimal Execution Problem With S-Shaped Market Impact Functions, 2017 Association of Mathematical Finance Laboratory

#### An Optimal Execution Problem With S-Shaped Market Impact Functions, Takashi Kato

*Communications on Stochastic Analysis*

No abstract provided.

Shrinkage Function And Its Applications In Matrix Approximation, 2017 University of Florida, Gainesville

#### Shrinkage Function And Its Applications In Matrix Approximation, Toby Boas, Aritra Dutta, Xin Li, Katie Mercier, Eric Niderman

*Electronic Journal of Linear Algebra*

The shrinkage function is widely used in matrix low-rank approximation, compressive sensing, and statistical estimation. In this article, an elementary derivation of the shrinkage function is given. In addition, applications of the shrinkage function are demonstrated in solving several well-known problems, together with a new result in matrix approximation.

Rainbow Copies Of C4 In Edge-Colored Hypercubes, 2017 University of Illinois at Urbana-Champaign

#### Rainbow Copies Of C4 In Edge-Colored Hypercubes, József Balogh, Michelle Delcourt, Bernard Lidicky, Cory Palmer

*Bernard Lidický*

For positive integers k and d such that 4 <= k < d and k not equal 5, we determine the maximum number of rainbow colored copies of C-4 in a k-edge-coloring of the d-dimensional hypercube Q(d). Interestingly, the k-edge-colorings of Q(d) yielding the maximum number of rainbow copies of C-4 also have the property that every copy of C-4 which is not rainbow is monochromatic.

Spatial Ergodicity Of The Harris Flows, 2017 Institute of Mathematics NAS of Ukraine

#### Spatial Ergodicity Of The Harris Flows, E.V. Glinyanaya

*Communications on Stochastic Analysis*

No abstract provided.

Entropy In Topological Groups, Part 2, 2017 University of Udine

#### Entropy In Topological Groups, Part 2, Dikran Dikranjan

*Summer Conference on Topology and Its Applications*

Entropy was introduced first in thermodynamics and statistical mechanics, as well as information theory. In the last sixty years entropy made its way also in topology, ergodic theory, as well as other branches of mathematics as algebra, geometry and number theory where dynamical systems appear in one way or another.

Roughly speaking, entropy is a non-negative real number or infinity assigned to a "selfmap" T of a "space" X, where the "space" X can be a topological or uniform space, a measure space, an abstract or topological group (or vector space) or just a set. The "selfmap" T can be ...

Statistical Analysis Of The Non-Ergodic Fractional Ornstein–Uhlenbeck Process Of The Second Kind, 2017 Cadi Ayyad University

#### Statistical Analysis Of The Non-Ergodic Fractional Ornstein–Uhlenbeck Process Of The Second Kind, Brahim El Onsy, Khalifa Es-Sebaiy, Ciprian A. Tudor

*Communications on Stochastic Analysis*

No abstract provided.

Mixed Strategies For Deterministic Differential Games, 2017 Brown University

#### Mixed Strategies For Deterministic Differential Games, Wendell H. Fleming, Daniel Hernandez-Hernandez

*Communications on Stochastic Analysis*

No abstract provided.

Stationary Solutions Of Stochastic Partial Differential Equations In The Space Of Tempered Distributions, 2017 Tata Institute of Fundamental Research

#### Stationary Solutions Of Stochastic Partial Differential Equations In The Space Of Tempered Distributions, Suprio Bhar

*Communications on Stochastic Analysis*

No abstract provided.

Poisson Approximation Of Rademacher Functionals By The Chen-Stein Method And Malliavin Calculus, 2017 Ruhr University Bochum

#### Poisson Approximation Of Rademacher Functionals By The Chen-Stein Method And Malliavin Calculus, Kai Kronkowski

*Communications on Stochastic Analysis*

No abstract provided.

Fractal Behavior Of Multivariate Operator-Self-Similar Stable Random Fields, 2017 Heinrich-Heine-Universität Düsseldorf

#### Fractal Behavior Of Multivariate Operator-Self-Similar Stable Random Fields, Ercan Sönmez

*Communications on Stochastic Analysis*

No abstract provided.

A Note On Evolution Systems Of Measures Of Stochastic Differential Equations In Infinite Dimensional Hilbert Spaces, 2017 University of Quynhon

#### A Note On Evolution Systems Of Measures Of Stochastic Differential Equations In Infinite Dimensional Hilbert Spaces, Thanh Tan Mai

*Communications on Stochastic Analysis*

No abstract provided.

On Infinite Stochastic And Related Matrices, 2017 Volterra Center, Roma

#### On Infinite Stochastic And Related Matrices, Andreas Boukas, Philip Feinsilver, Anargyros Fellouris

*Communications on Stochastic Analysis*

No abstract provided.

Revolution In Ideology: Crafting A Holistic Scientific Dialectic, 2017 Abilene Christian University

#### Revolution In Ideology: Crafting A Holistic Scientific Dialectic, Nathan Neill

*Dialogue & Nexus*

**Ideology drives scientific research far more than is acknowledged. Since science itself is conducted by individuals, each scientist has a biased conception of themselves and their surroundings relative to the rest of the universe, even if it is never explicated. This sense of relation to the greater universe is what defines the ideology of the individual. It is this sense of relation and self that creates the individual, who goes on to investigate the natural world by the scientific method. In this paper I will examine extant scientific ideology, particularly in Western science, and propose changes that could be helpful.**

Asymptotic Expansion Of The L^2-Norm Of A Solution Of The Strongly Damped Wave Equation, 2017 University of Wisconsin-Milwaukee

#### Asymptotic Expansion Of The L^2-Norm Of A Solution Of The Strongly Damped Wave Equation, Joseph Silvio Barrera

*Theses and Dissertations*

The Fourier transform, F, on R^N (N≥1) transforms the Cauchy problem for the strongly damped wave equation u_tt(t,x) - Δu_t(t,x) - Δu(t,x) = 0 to an ordinary differential equation in time t. We let u(t,x) be the solution of the problem given by the Fourier transform, and v(t,ƺ) be the asymptotic profile of F(u)(t,ƺ) = û(t,ƺ) found by Ikehata in [4].

In this thesis we study the asymptotic expansions of the squared L^2-norms of u(t,x), û(t,ƺ) - v(t,ƺ), and v(t ...

On Some One-Complex Dimensional Slices Of The Boundedness Locus Of A Multi-Parameter Rational Family, 2017 University of Wisconsin-Milwaukee

#### On Some One-Complex Dimensional Slices Of The Boundedness Locus Of A Multi-Parameter Rational Family, Matthew Hoeppner

*Theses and Dissertations*

Complex dynamics involves the study of the behavior of complex-valued functions when they are composed with themselves repeatedly. We observe the orbits of a function by passing starting values through the function iteratively. Of particular interest are the orbits of any critical points of the function, called critical orbits. The behavior of a family of functions can be determined by examining the change in the critical orbit(s) of the functions as the values of the associated parameters vary. These behaviors are often separated into two categories: parameter values where one or more critical orbits remain bounded, and parameter values ...

Cocompact Cubulations Of Mixed 3-Manifolds, 2017 University of Wisconsin-Milwaukee

#### Cocompact Cubulations Of Mixed 3-Manifolds, Joseph Dixon Tidmore

*Theses and Dissertations*

In this dissertation, we complete the classification of which compact 3-manifolds have a virtually compact special fundamental group by addressing the case of mixed 3-manifolds. A compact aspherical 3-manifold M is mixed if its JSJ decomposition has at least one JSJ torus and at least one hyperbolic block. We show the fundamental group of M is virtually compact special iff M is chargeless, i.e. each interior Seifert fibered block has a trivial Euler number relative to the fibers of adjacent blocks.