Physical Sciences and Mathematics Commons^™

Strategies For Photochemical And Thermal Modification Of Materials, Sara Ghiassian

Electronic Thesis and Dissertation Repository

The modification of materials/surfaces is central to numerous applications ranging from opto-electronic devices to biomedical implants and drug delivery. Thus, there exists a high motivation for improving the methodologies which can be employed in order to modify surfaces in a selective and efficient fashion. One of the major goals of surface engineering is to control the chemical composition at the material interface. The fine control of the surface properties is a field of intense research as the performance of functional materials is strongly related to the processes and interactions that are occurring at the materials’ interface.

In general, the modification …

The Topology Of Absence, Nora E. Culik

Journal of Humanistic Mathematics

“The Topology of Absence” literalizes triangulations, hyperbeloids, and the concept of the limit in the story of “locating” a lost mother. This story, like “The Physicist’s Basement” in the July 2014 issue, is part of a series that worries about competing notions of mathematics, i.e., mathematics as some sort of disembodied configuration or as emergent in the material reality of human life.

Music And Mathematics, Robert J. Boucher

Journal of Humanistic Mathematics

Mathematics has forever been.

Geometry Of Life, Janice Dykacz

Journal of Humanistic Mathematics

Relationships in life can be expressed through geometric curves

Mathematical Double Dactyls, Tristan Miller

Journal of Humanistic Mathematics

No abstract provided.

Robin Chapman On (Her) Mathematics Education, Robin Chapman

Journal of Humanistic Mathematics

No abstract provided.

On Mathematicians' Eccentricity, Robert Haas

Journal of Humanistic Mathematics

Eccentricity, though not inevitable, happens. Lightheartedly classifying examples, the author traces it back to factors, like creativity and absorption, essential to mathematical success, and recommends an attitude of amused tolerance towards others as well as to ourselves.

A System Of Equations: Mathematics Lessons In Classical Literature, Valery F. Ochkov, Andreas Look

Journal of Humanistic Mathematics

The aim of this paper is to showcase a handful of mathematical challenges found in classical literature and to offer possible ways of integrating classical literature in mathematics lessons. We analyze works from a range of authors such as Jules Verne, Anton Chekhov, and others. We also propose ideas for further tasks. Most of the problems can be restated in terms of simple mathematical equations, and they can often be solved without a computer. Nevertheless, we use the computer program Mathcad to solve the problems and to illustrate the solutions to enhance the reader’s mathematical experience.

Mathematics: What Has It To Do With Me?, Man Keung Siu

Journal of Humanistic Mathematics

Mathematics teachers must have encountered the following question raised by students: “What is the use of mathematics?” Although the value of mathematics is not to be determined solely by its applications, to the general public this is a more important and more convincing facet of the subject. Nevertheless, this also brings up the corresponding query: is this subject being properly used? Does mathematics play a role in moral education?

On Similarities And Differences Between Proving And Problem Solving, Milos Savic

Journal of Humanistic Mathematics

A link between proving and problem solving has been established in the literature [5, 21]. In this paper, I discuss similarities and differences between proving and problem solving using the Multidimensional Problem-Solving Framework created by Carlson and Bloom [2] with Livescribepen data from a previous study [13]. I focus on two participants’ proving processes: Dr. G, a topologist, and L, a mathematics graduate student. Many similarities between the framework and the proving processes of Dr. G and L were revealed, but there were also some differences. In addition, there were some distinct differences between the proving actions of the …

Counting The Angels And Devils In Escher's Circle Limit Iv, John Choi, Nicholas Pippenger

Journal of Humanistic Mathematics

We derive the rational generating function that enumerates the angels and devils in M. C. Escher's Circle Limit IV according to their combinatorial distance from the six creatures whose feet meet at the center of the disk. This result shows that the base of the exponential rate of growth is 1.582... (the largest root of the polynomial 1 - z^2 - 2z^3 - z^4 + z^6).

Sobriety In Delta Not Sober, Joe Mashburn

Joe D. Mashburn

We will show that the space delta not sober defined by Coecke and Martin is sober in the Scott topology, but not in the weakly way below topology.

Dissertation: The Least Fixed Point Property For Ω-Chain Continuous Functions, Joe Mashburn

Joe D. Mashburn

The basic definitions are given in the first section, including those for ω-chain continuity, ω-chain completeness, and the least fixed point property for ω-chain continuous functions. Some of the relations between completeness and fixed point properties in partially ordered sets are stated and it is briefly shown how the question basic to the dissertation arises. In the second section, two examples are given showing that a partially ordered set need not be ω-chain complete to have the least fixed point property for ω-chain continuous functions. Retracts are discussed in section 3, where it is seen that they are not sufficient …

On The Decomposition Of Order-Separable Posets Of Countable Width Into Chains, Gary Gruenhage, Joe Mashburn

Joe D. Mashburn

partially ordered set X has countable width if and only if every collection of pairwise incomparable elements of X is countable. It is order-separable if and only if there is a countable subset D of X such that whenever p, q ∈ X and p < q, there is r ∈ D such that p ≤ r ≤ q. Can every order-separable poset of countable width be written as the union of a countable number of chains? We show that the answer to this question is "no" if there is a 2-entangled subset of IR, and "yes" under the Open Coloring …

The Least Fixed Point Property For Ω-Chain Continuous Functions, Joe Mashburn

Joe D. Mashburn

A partially ordered set P is ω-chain complete if every countable chain (including the empty set) in P has a supremum. … Notice that an ω-chain continuous function must preserve order. P has the (least) fixed point property for ω-chain continuous functions if every ω-chain continuous function from P to itself has (least) fixed point. It has been shown that a partially ordered set does not have to be ω-chain complete to have the least fixed point property for ω-chain continuous functions. This answers a question posed by G. Plotkin in 1978. I.I. Kolodner has shown that an ω-chain complete …

Oif Spaces, Zoltan Balogh, Harold Bennett, Dennis Burke, Gary Gruenhage, David Lutzer, Joe D. Mashburn

Joe D. Mashburn

A base β of a space X is called an OIF base when every element of B is a subset of only a finite number of other elements of β. We will explore the fundamental properties of spaces having such bases. In particular, we will show that in T2 spaces, strong OIF bases are the same as uniform bases, and that in T3 spaces where all subspaces have OIF bases, compactness, countable compactness, or local compactness will give metrizability.

Linearly Ordered Topological Spaces And Weak Domain Representability, Joe Mashburn

Joe D. Mashburn

It is well known that domain representable spaces, that is topological spaces that are homeomorphic to the space of maximal elements of some domain, must be Baire. In this paper it is shown that every linearly ordered topological space (LOTS) is homeomorphic to an open dense subset of a weak domain representable space. This means that weak domain representable spaces need not be Baire.

A Spectral Order For Infinite Dimensional Quantum Spaces: A Preliminary Report, Joe Mashburn

Joe D. Mashburn

In 2002 Coecke and Martin created a Bayesian order for the finite dimensional spaces of classical states in physics and used this to define a similar order, the spectral order on the finite dimensional quantum states. These orders gave the spaces a structure similar to that of a domain. This allows for measuring information content of states and for determining which partial states are approximations of which pure states. In a previous paper the author extended the Bayesian order to infinite dimensional spaces of classical states. The order on infinite dimensional spaces retains many of the characteristics important to physics, …

Three Counterexamples Concerning Ω-Chain Continuous Functions And Fixed-Point Properties, Joe Mashburn

Joe D. Mashburn

A partially ordered set is ω-chain complete if, for every countable chain, or ω-chain, in P, the least upper bound of C, denoted by sup C, exists. Notice that C could be empty, so an ω-chain complete partially ordered set has a least element, denoted by 0.

U.S. Drought Monitor, July 28, 2015, Richard R. Heim Jr.

United States Agricultural Commodities in Drought Archive

Drought map of U.S. for July 28, 2015 (7/28/15) plus: U.S. crop areas experiencing drought (map), Approximate percentage of crop located in drought, by state (bar graph), Percent of crop area located in drought, past 52 weeks (line graph) for: Corn, Soybeans, Hay, Cattle, Winter wheat.

Long-Time Dynamics Of 2d Double-Diffusive Convection: Analysis And/Of Numerics, Florentina Tone, Xiaoming Wang, Djoko Wirosoetisno

Mathematics and Statistics Faculty Research & Creative Works

We consider a two-dimensional model of double-diffusive convection and its time discretisation using a second-order scheme (based on backward differentiation formula for the time derivative) which treats the non-linear term explicitly. Uniform bounds on the solutions of both the continuous and discrete models are derived (under a timestep restriction for the discrete model), proving the existence of attractors and invariant measures supported on them. as a consequence, the convergence of the attractors and longtime statistical properties of the discrete model to those of the continuous one in the limit of vanishing timestep can be obtained following established methods.

Quantifying Measurement Error In Digital Instruments, William B. Laing Iii, Sean Bryant

Faculty Works

A first lab experiment clearly illustrates that a glucose meter is actually an excellent source of both random and systematic error, much to the surprise to students and physicians alike. A histogram is constructed and the utility of the standard deviation and standard error to quantify the uncertainty in each measurement and in the mean value, respectively, is demonstrated. From the first lab on, students are challenged to express and interpret confidence intervals in order to form quantitative conclusions. Assessments reveal that many students find this to be surprisingly challenging.

The Physics Of Human Performance: An Ideal Lab, William B. Laing Iii, Harold Mayer

Faculty Works

Physics lab goes to the gymnasium, where students calculate the mechanical power required to walk on an inclined treadmill in watts and convert to units power used to measure human performance: VO2, and METs. Students learn how to use two linear regression models: the ACSM "walking equation" to estimate the actual power expenditure of walking and the Rockport 1 mile test to estimate their own VO2max. Students use models to prescribe exercise parameters for themselves and for two cases. The IDEAL lab collaboration is developing labs that are open, applied to life, and rigorously quantitative.

Maybe I Could Use This Again! Two Ideal Labs Introducing Instrumentation, Sean Bryant, William B. Laing Iii

Faculty Works

Physics lab students are introduced to custom instrumentation using Arduino-like microcontrollers which have allowed us to implement two labs of particular utility for life-science majors. Constructing a fluid circuit using the sponge-resistor model, flow sensors and an LCD display show the current through each section of pipe. The instrument can simultaneously measure and record 18 voltages, which enables us to record high-frequency “snap shots” of a signal generated on an RC-circuit model of an axon. The IDEAL lab collaboration is developing labs that are open, applied to life, and rigorously quantitative.

New Potential Energy Surface For The Hcs⁺-He System And Inelastic Rate Coefficients, Marie-Lise Dubernet, Ernesto Quintas-Sánchez, Philip Tuckey

Chemistry Faculty Research & Creative Works

A new high quality potential energy surface is calculated at a coupled-cluster single double triple level with an aug-cc-pV5Z basis set for the HCS⁺-He system. This potential energy surface is used in low energy quantum scattering calculations to provide a set of (de)-excitation cross sections and rate coefficients among the first 20 rotational levels of HCS⁺ by He in the range of temperature from 5 K to 100 K. The paper discusses the impact of the new ab initio potential energy surface on the cross sections at low energy and provides a comparison with the HCO^{+ …}

Foreland-Directedpropagation Of High-Grade Tectonism In The Deep Roots Of A Paleoproterozoic Collisionalorogen, Sw Montana, Usa, Cailey B. Condit, Kevin H. Mahan, Alexis K. Ault, Rebecca M. Flowers

Geosciences Faculty Publications

The study of deeply exhumed ancient collisional belts offers important constraints on geologic processes and properties complementary to inaccessible portions of the crustal column in active orogens. The ca. 1.8−1.7 Ga Big Sky orogeny in southwest Montana is a major convergent belt associated with the Proterozoic amalgamation of Laurentia. New structural, petrologic, and geochronologic data from the Northern Madison Range, crossing the NE-SW trend of the belt, record key information about the internal dynamics of the orogen. At least two phases of Big Sky−related deformation are preserved, both nearly coeval with peak metamorphic conditions of ∼0.9−0.8 GPa and >700 °C. …

Wavelet Analysis On Local Fields Of Positive Characteristic., Quiser Jahan Dr.

Doctoral Theses

In this chapter, we will give a brief history of wavelet analysis on R. We will also list some bask results on local felds which will be used in subvequent chapters.1.1 Wavelets on RWe fiest start with a brief history of wavelets und some basic defnitions and results conceming the orthonormal wavekts on R.1.1.1 A brief historyIn the last few decades vaveler theory has growa extensively and has drawn great atlention sot only in mathematies bu also in engineering, pitysics, computer science and many other fields. In signal and image processing, wavelets play a very important role.In 1910, A. Haar …

Euler Class Groups Of Polynomial And Sub Integral Extensions Of A Noetherian Ring., Md. Ali Zinna Dr.

Doctoral Theses

ObjectiveThe main objectives of this thesis are the following:(i) To investigate the behaviour of the Euler class groups under integral and subintegral extensions. More precisely, given a subintegral (or integral) extension R+ S of Noetherian rings, we are interested in finding out the relationship between the Euler class group of R and the Euler class group of S.(ii) To develop a theory (namely, an extension of the theory of Euler class group to the Euler class group of R[T) relative to a projective R[T|-module L of rank 1) in order to detect the precise obstruction for a projective R[T]-module P …

Complete And Partial Ordering Approaches In The Context Of Poverty Ordering And On The Impacts Of Growth And Inequality On Poverty., Sandip Sarkar Dr.

Doctoral Theses

No abstract provided.

Advances In Fetal Heart Rate Monitoring Using Smart Phones, Chang Su Lee, Martin Masek, Chiou Peng Lam, Keng Tiong Tan

Martin Masek

It has been shown that the rate of preterm birth in remote and rural populations in Australia is more than twice of those in the metropolitan population, and that increased access to quality antenatal care in such communities leads to a significant improvement. This paper describes a system that supports remote fetal heart rate monitoring, thus providing a technique that addresses this need for better remote antenatal care. The application involves a smart phone, a portable Doppler ultrasound device, a remote back-end server and network connectivity provided by the global system for mobile communications (GSM) and general packet radio service …