Physical Sciences and Mathematics Commons^™

Investigating The Links Between Ozone And Organic Aerosol Chemistry In A Biomass Burning Plume From A Prescribed Fire In California Chaparral, M. J. Alvarado, C. R. Lonsdale, Robert Yokelson, S. K. Akagi, H. Coe, J. S. Craven, E. V. Fischer, G. R. Mcmeeking, J. H. Seinfeld, T. Soni, J. W. Taylor, D. R. Weise, C. E. Wold

Chemistry and Biochemistry Faculty Publications

Within minutes after emission, rapid, complex photochemistry within a biomass burning smoke plume can cause large changes in the concentrations of ozone (O₃) and organic aerosol (OA). Being able to understand and simulate this rapid chemical evolution under a wide variety of conditions is a critical part of forecasting the impact of these fires on air quality, atmospheric composition, and climate. Here we use version 2.1 of the Aerosol Simulation Program (ASP) to simulate the evolution of O₃ and secondary organic aerosol (SOA) within a young biomass burning smoke plume from the Williams prescribed burn in chaparral, …

Spectral Evolution Of Energetic Neutral Atom Emissions At The Heliospheric Poles As Measured By Ibex During Its First Three Yeras, M. Dayeh, F. Allegrini, R. Demajistre, M. I. Desai, R. W. Ebert, S. A. Fuselier, Paul H. Janzen, G. Livadiotis, D. J. Mccomas, Daniel B. Reisenfeld, N. A. Schwadron, M. Siewert

Physics and Astronomy Faculty Publications

The Interstellar Boundary Explorer (IBEX) mission continues to measure energetic neutral atom (ENA) emissions produced by charge exchange between solar wind (SW) protons and interstellar neutrals at the edge of our heliosphere. Using the first 3 yr of IBEX-Hi ENA measurements (2009-2011), we examined the spectral evolution of ~0.5-6 keV ENAs at the polar regions (above 60°). We found the following: (1) pixels with a characteristic "ankle" spectra (lower spectral index at higher energies) increase by ~5% in 2010 and ~10% in 2011 compared to 2009. (2) The averaged spectral index in 2011 is smaller than that of 2009. (3) …

Reasoning-And-Proving Within Ireland’S Reform-Oriented National Syllabi, Jon Davis

The Mathematics Enthusiast

As educational systems around the world attempt to reform their mathematics programs to increase students’ opportunities to engage in processes central to the practice of mathematics such as proof, it is important to understand how this mathematical act is portrayed in national curriculum documents that drive that change. This study examined the presence of reasoning-and-proving (RP) in Ireland’s national reform-oriented secondary syllabi for junior cycle (ages 12-15) and senior cycle (ages 15-18) students. The analyses reveal that there were no differences among direct and indirect RP learning outcomes within each syllabus, but statistically significant differences did exist across syllabi in …

Flow Dynamics Of Byrd Glacier, East Antarctica, C. J. Van Der Veen, L. A. Stearns, Jesse Johnson, B. Csatho

Computer Science Faculty Publications

Force-balance calculations on Byrd Glacier, East Antarctica, reveal large spatial variations in the along-flow component of driving stress with corresponding sticky spots that are stationary over time. On the large scale, flow resistance is partitioned between basal (�80%) and lateral (�20%) drag. Ice flow is due mostly to basal sliding and concentrated vertical shear in the basal ice layers, indicating the bed is at or close to the pressure-melting temperature. There is a significant component of driving stress in the across-flow direction resulting in nonzero basal drag in that direction. This is an unrealistic result and we propose that there …

Generalizing Cantor-Schroeder-Bernstein: Counterexamples In Standard Settings, Tien Chih

The Mathematics Enthusiast

The Cantor-Schroeder-Bernstein theorem states that any two sets that have injections into each other have the same cardinality, i.e. there is a bijection between them. Another way to phrase this is if two sets A;B have monomorphisms from A to B and B to A, then they are isomorphic in the setting of sets. One naturally wonders if this may be extended to other commonly studied systems of sets with structure and functions which preserve that structure. Given two objects with injective structure preserving maps between them are the structures of these objects the same? In other words, would these …

Editorial: Is Every Tme Issue Special?, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

Bhaskara’S Approximation For The Sine, Karel Stroethoff

The Mathematics Enthusiast

The 7th century Indian mathematician Bhaskara (c.600 – c.680) obtained a remarkable approximation for the sine function. Many subsequent ancient authors have given versions of this rule, but none provided a proof or described how the result was obtained. Grover [1] provides a possible explanation, but I think the rule can be explained more clearly. Rather than give the rule first, we will derive it, and then discuss its accuracy, and explore some alternative approximations. Our derivation is simply an exercise in modeling.

Pursuing Coherence Among Proportionality, Linearity, And Similarity: Two Pathways From Preservice Teachers’ Geometric Representations, Hyung Sook Lee, Jaehoon Yim

The Mathematics Enthusiast

The importance of using multiple representations of a mathematical concept and connecting the representations has been discussed in learning and teaching mathematics. The Common Core State Standards further the discussion with an emphasis on focus and coherence in teaching mathematical concepts across grades. Preservice teachers in our problem solving class were asked to use geometric representations to solve a problem that required proportional reasoning. They were also asked to sequence the works of their peers as well as their own from a developmental perspective. Sequencing geometric representations with various levels was challenging because it required showing a coherent understanding of …

The Development Of Calculus In The Kerala School, Phoebe Webb

The Mathematics Enthusiast

The Kerala School of mathematics, founded by Madhava in Southern India, produced many great works in the area of trigonometry during the fifteenth through eighteenth centuries. This paper focuses on Madhava's derivation of the power series for sine and cosine, as well as a series similar to the well-known Taylor Series. The derivations use many calculus related concepts such as summation, rate of change, and interpolation, which suggests that Indian mathematicians had a solid understanding of the basics of calculus long before it was developed in Europe. Other evidence from Indian mathematics up to this point such as interest in …

Development Of The Binary Number System And The Foundations Of Computer Science, Daniel R. Lande

The Mathematics Enthusiast

This paper discusses the formalization of the binary number system and the groundwork that was laid for the future of digital circuitry, computers, and the field of computer science. The goal of this paper is to show how Gottfried Leibniz formalized the binary number system and solidified his thoughts through an analysis of the Chinese I Ching. In addition, Leib-niz’s work in logic and with computing machines is presented. This work laid the foundation for Boolean algebra and digital circuitry which was continued by George Boole, Augustus De Mor-gan, and Claude Shannon in the centuries following. Some have coined Leibniz …

Numerically Integrating Irregularly-Spaced (X, Y) Data, B. Cameron Reed

The Mathematics Enthusiast

This article describes a computer program for numerically integrating under a y(x) curve of experimental data where the abscissa values are not equally-spaced. This technique is based on fitting parabolas to successive groups of three data points, and may be regarded as a generalization of Simpson’s rule.

Difficulties In Solving Context-Based Pisa Mathematics Tasks: An Analysis Of Students’ Errors, Ariyadi Wijaya, Marja Van Den Heuvel-Panhuizen, Michiel Doorman, Alexander Robitzsch

The Mathematics Enthusiast

The intention of this study was to clarify students’ difficulties in solving context-based mathematics tasks as used in the Programme for International Student Assessment (PISA). The study was carried out with 362 Indonesian ninth- and tenth-grade students. In the study we used 34 released PISA mathematics tasks including three task types: reproduction, connection, and reflection. Students’ difficulties were identified by using Newman’s error categories, which were connected to the modeling process described by Blum and Leiss and to the PISA stages of mathematization, including (1) comprehending a task, (2) transforming the task into a mathematical problem, (3) processing mathematical procedures, …

Math As A Tool Of Anti-Semitism, Jay Egenhoff

The Mathematics Enthusiast

At Moscow State University’s Department of Mathematics during the 1970’s and 1980’s, there was rampant discrimination against Jewish and other unwanted students. The professors at the math department made a strong effort to keep Jewish students out of the department. They designed "killer" or "coffin" problems and Jewish students had to answer them during an oral exam. These problems have simple solutions, but require a clever strategy to solve them. This paper explores some of the context of this episode and provides several problems with detailed solutions.

The Miracle Of Applied Mathematics, Frank Blume

The Mathematics Enthusiast

We provide an outline of a college-level lecture on systems of differential equations that is intended to offer an alternative, integrative view of the subject. Particular emphasis is placed on the fact that very elementary concepts and insights can be employed to gain access to a very wide range of important applications, including the Schr¨odinger equation, the Klein-Gordon equation, the Laplace equation, and the Poisson equation.

A Study On Malaysian Mathematicians’ Way Of Knowing, Lim Chap Sam

The Mathematics Enthusiast

“Can you name me a mathematician?” “Einstein??”

“Do you wish to become a mathematician one day?”

If these questions were asked to the public or any school students, the most likely answer to both questions might be a big ‘No!’. Why is this so?

The director of the Public Understanding of Mathematics Forum, Gene Kloz (1996) claims that the mathematics profession is the most misunderstood in all of academia. According to him, the public thinks that mathematicians contemplate ancient proofs and work as lonely recluses. Moreover, the most common public image of a mathematician has been furnished by a physicist …

An Examination Of Pre-Service Secondary Mathematics Teachers’ Conceptions Of Angles, Melike Yigit

The Mathematics Enthusiast

The concept of angles is one of the foundational concepts to develop of geometric knowledge, but it remains a difficult concept for students and teachers to grasp. Exiting studies claimed that students’ difficulties in learning of the concept of angles are based on learning of the multiple definitions of an angle, describing angles measuring the size of angles, and conceiving different types of angles such as 0-line angles, 1- line angles, and 2-line angles. This study was designed to gain better insight into pre-service secondary mathematics teachers’ (PSMTs) mental constructions of the concept of angles from the perspective of Action-Process-Object-Schema …

Common Sense About The Common Core, Alan H. Schoenfeld

The Mathematics Enthusiast

Is the Common Core the best thing since sliced bread, or the work of the devil? Is it brand new, or a rehash of old ideas? Is it anything more than a brand name, or is there substance? Can it work, given the implementation challenges in our political and school systems? Opinions about the Common Core are everywhere, but the op-eds I’ve seen are often short on facts, and equally short on common sense. A mathematician by training, I’ve worked for nearly 40 years as an education researcher, curriculum materials developer, test developer, standards writer, and teacher. What follows is …

Book Review Of The Tower Of Hanoi: Myths And Maths (Birkhäuser), Cory Palmer

The Mathematics Enthusiast

As the title of the book suggests, the central topic of “The Tower of Hanoi – Myths and Maths” by Hinz, Klavˇzar, Milutinovi´c, and Petr is the famous puzzle of the same name. The classic Tower of Hanoi puzzle along with a number of its variations and related puzzles are examined in a rigorous mathematical framework.

Scholastic Standards In The United States – The Discussion Concerning The ‘Common Core’, Alan H. Schoenfeld, Günter Törner

The Mathematics Enthusiast

Preface: This article has been developed based on a personal discussion between the German author Günter Törner and Alan Schoenfeld, who is an expert in the field of mathematical didactics. Basically there are three reasons for us to share our insights with the public:

(1) Readers, having subscribed to Jerry Becker’s e-mail information network, have received numerous messages over the past few months; what do we need to know about this fact in Germany?

(2) Scholastic standards – a keyword that sounds very familiar to us in terms of educational policy… But it is also a hot topic in other …

Tme Volume 11, Number 3

The Mathematics Enthusiast

No abstract provided.

Ion Composition In Interchange Injection Events In Saturn's Magnetosphere, M. F. Thomsen, Daniel B. Reisenfeld, R. J. Wilson, M. Andriopoulou, F. J. Crary, G. B. Hospodarsky, C. M. Jackman, X. Jia, K. K. Khurana, C. Paranicas, E. Roussos, N. Sergis, R. L. Tokar

Physics and Astronomy Faculty Publications

Interchange injection events are commonly observed by the Cassini spacecraft in the region between about 6 and 12 R_s (1 R_s = 60,268 km) and even frequently beyond. In this study, 13 examples of interchange injection events are identified in Cassini-Cassini Plasma Spectrometer data under special conditions such that time-of-flight (TOF) mass spectra could be obtained from entirely within the events. Using the TOF data to separate the main ion species H⁺, H₂⁺, and W⁺, approximate densities of each species are calculated under the assumption that all distributions were isotropic. The …

Cold Magnetically Trapped 2DG Scandium Atoms. I. Interaction Potential, Tijs Karman, Xi Chu, Gerrit C. Groenenboom

Chemistry and Biochemistry Faculty Publications

We present a first principles description of the interaction of two ground-state scandium atoms. Scandium has a ²D_g ground state. Thirty molecular states correlate to the lowest dissociation limit of the dimer. In the short range, potential energy curves are calculated using second-order n-electron valence state perturbation theory. The first-order long-range interaction is calculated at the complete active space self-consistent field level. We determine the second-order long-range dispersion interaction from atomic dynamic polarizabilities at imaginary frequencies. These polarizabilities are calculated using time-dependent density functional theory. We merge the short-range approach with the long-range model to obtain a physical …

Separation Of The Ribbon From Globally Distributed Energetic Neutral Atom Flux Using The First Five Years Of Ibex Observations, N. A. Schwadron, E. Moebius, S. A. Fuselier, D. J. Mccomas, H. O. Funsten, Paul H. Janzen, Daniel B. Reisenfeld, H. Kucharek, M. A. Lee, K. Fairchild, F. Allegrini, M. Dayeh, G. Livadiotis, M. Reno, M. Bzowski, J. M. Sokol, M. A. Kubiak, E. R. Christian, R. Demajistre, P. Frisch, A. Galli, P. Wurz, M. Gruntman

Physics and Astronomy Faculty Publications

The Interstellar Boundary Explorer (IBEX) observes the IBEX ribbon, which stretches across much of the sky observed in energetic neutral atoms (ENAs). The ribbon covers a narrow (∼20^◦–50^◦) region that is believed to be roughly perpendicular to the interstellar magnetic field. Superimposed on the IBEX ribbon is the globally distributed flux that is controlled by the processes and properties of the heliosheath. This is a second study that utilizes a previously developed technique to separate ENA emissions in the ribbon from the globally distributed flux. A transparency mask is applied over the ribbon and …

A Regional Look At Hanpp: Human Consumption Is Increasing, Npp Is Not, Steven W. Running

Ecosystem and Conservation Sciences Faculty Publications

Abdi et al (2014 Environ. Res. Lett. 9 094003), have adapted the concept of comparing supply and demand of annual plant production known as human appropriation of net primary production (HANPP) to a region of the Sahel with rapid population growth. They found that HANPP more than doubled over the study period of 2000–2010, from 19% to 41%, suggesting increasing vulnerability of these populations to food insecurity.

Ecogeomorphic Feedbacks And Flood Loss Of Riparian Tree Seedlings In Meandering Channel Experiments, Li Kui, John C. Stella, Anne Lightbody, Andrew C. Wilcox

Geosciences Faculty Publications

During floods, fluvial forces interact with riparian plants to influence evolution of river morphology and floodplain plant community development. Understanding of these interactions, however, is constrained by insufficient precision and control of drivers in field settings, and insufficient realism in laboratory studies. We completed a novel set of flume experiments using woody seedlings planted on a sandbar within an outdoor meandering stream channel. We quantified effects on local sedimentation and seedling loss to scour and burial across realistic ranges of woody plant morphologies (Populus versus Tamarix species), densities (240 plants m^-2 versus 24 m^-2), and sediment …

Aerosol Emissions From Prescribed Fires In The United States: A Synthesis Of Laboratory And Aircraft Measurements, A. A. May, G. R. Mcmeeking, T. Lee, J. W. Taylor, J. S. Craven, I. R. Burling, A. P. Sullivan, Sheryl Kashi Akagi, J. L. Collett Jr., M. Flynn, H. Coe, S. P. Urbanski, J. H. Seinfeld, Robert Yokelson, S. M. Kreidenweis

Chemistry and Biochemistry Faculty Publications

Aerosol emissions from prescribed fires can affect air quality on regional scales. Accurate representation of these emissions in models requires information regarding the amount and composition of the emitted species.Wemeasured a suite of submicron particulatematter species in young plumes emitted from prescribed fires (chaparral and montane ecosystems in California; coastal plain ecosystem in South Carolina) and from open burning of over 15 individual plant species in the laboratory. We report emission ratios and emission factors for refractory black carbon (rBC) and submicron nonrefractory aerosol and compare field and laboratory measurements to assess the representativeness of our laboratory-measured emissions. Laboratory measurements …

Airborne Characterization Of Smoke Marker Ratios From Prescribed Burning, A. P. Sullivan, A. A. May, T. Lee, G. R. Mcmeeking, S. M. Kreidenweis, S. K. Akagi, Robert Yokelson, S. P. Urbanski, J. L. Collett Jr.

Chemistry and Biochemistry Faculty Publications

A Particle-Into-Liquid Sampler – Total Organic Carbon (PILS-TOC) and fraction collector system was flown aboard a Twin Otter aircraft sampling prescribed burning emissions in South Carolina in November 2011 to obtain smoke marker measurements. The fraction collector provided 2 min time-integrated offline samples for carbohydrate (i.e., smoke markers levoglucosan, mannosan, and galactosan) analysis by high-performance anion-exchange chromatography with pulsed amperometric detection. Each fire location appeared to have a unique 1levoglucosan /1water-soluble organic carbon (WSOC) ratio (RF01/RF02/RF03/RF05 = 0.163± 0.007 μg C μg−1 C, RF08 = 0.115 ± 0.011 μg C μg−1 C, RF09A = 0.072 ± 0.028 μgC μg−1 C, …

Theoretical Analysis Of Steady State Genetic Algorithms, Alexandru Agapie, Alden H. Wright

Computer Science Faculty Publications

Evolutionary Algorithms, also known as Genetic Algorithms in a former terminology, are probabilistic algorithms for optimization, which mimic operators from natural selection and genetics. The paper analyses the convergence of the heuristic associated to a special type of Genetic Algorithm, namely the Steady State Genetic Algorithm (SSGA), considered as a discrete-time dynamical system non-generational model. Inspired by the Markov chain results in finite Evolutionary Algorithms, conditions are given under which the SSGA heuristic converges to the population consisting of copies of the best chromosome.

Trace Gas Emissions From Combustion Of Peat, Crop Residue, Domestic Biofuels, Grasses, And Other Fuels: Configuration And Fourier Transform Infrared (Ftir) Component Of The Fourth Fire Lab At Missoula Experiment (Flame-4), C. E. Stockwell, R. J. Yokelson, S. M. Kreidenweis, A. L. Robinson, P. J. Demott, R. C. Sullivan, J. Reardon, K. C. Ryan, D. W.T. Griffith, L. Stevens

Chemistry and Biochemistry Faculty Publications

During the fourth Fire Lab at Missoula Experiment (FLAME-4, October-November 2012) a large variety of regionally and globally significant biomass fuels was burned at the US Forest Service Fire Sciences Laboratory in Missoula, Montana. The particle emissions were characterized by an extensive suite of instrumentation that measured aerosol chemistry, size distribution, optical properties, and cloud-nucleating properties. The trace gas measurements included high-resolution mass spectrometry, one-and two-dimensional gas chromatography, and open-path Fourier transform infrared (OP-FTIR) spectroscopy. This paper summarizes the overall experimental design for FLAME-4-including the fuel properties, the nature of the burn simulations, and the instrumentation employed-and then focuses on …

Identification And Quantification Of Gaseous Organic Compounds Emitted From Biomass Burning Using Two-Dimensional Gas Chromatography/Time-Of-Flight Mass Spectrometry, L. E. Hatch, W. Luo, J. F. Pankow, Robert Yokelson, C. Stockwell, K. C. Barsanti

Chemistry and Biochemistry Faculty Publications

The current understanding of secondary organic aerosol (SOA) formation within biomass burning (BB) plumes is limited by the incomplete identification and quantification of the non-methane organic compounds (NMOCs) emitted from such fires. Gaseous organic compounds were collected on sorbent cartridges during laboratory burns as part of the fourth Fire Lab at Missoula Experiment (FLAME-4), with analysis by two-dimensional gas chromatography/time-of-flight mass spectrometry (GC×GC/TOFMS). The sensitivity and resolving power of GC×GC/TOFMS allowed the acquisition of the most extensive data set of BB NMOCs to date, with measure ments for 722 positively or tentatively identified compounds. Estimated emission factors (EFs) are presented …