Physical Sciences and Mathematics Commons^™

Tme Volume 12, Numbers 1, 2, And 3

The Mathematics Enthusiast

No abstract provided.

Students’ Language Repertoires For Prediction, David Wagner, Joseph Dicks, Paula Kristmanson

The Mathematics Enthusiast

Communication about prediction is complex in a number of ways. First, language is by nature recursive — language is an indicator of meaning as well as a force that shapes meaning. Second, the same language used to communicate prediction in uncertain environments is used for other purposes. In this article, we describe how the recursive nature of language impacted the choices we made in a cross-sectional longitudinal study aimed at gaining insight into children’s language repertoires relating to conjecture. We then explore some Grade 6 students’ communication about prediction to develop insight into their meaning and meaning-making with prediction language. …

A Conversation With Herbert Tate: Mathematics Educator And Builder, Christian Genest

The Mathematics Enthusiast

Herbert Tate was a Professor of Mathematics at McGill University (Montréal, Canada) from 1921 to 1964. As the author of four textbooks, and in his capacity as Chairman of the Department of Mathematics from 1948 to 1960, he played a key role in structuring the institution’s research and study programs in mathematics during an important period of growth. McGill’s current position as a hub of mathematical research owes much to him. In this interview given shortly after his retirement, Herbert Tate describes his career and shares some of his views about mathematics and related topics. Beyond its archival value, this …

Mathematical Creativity: The Unexpected Links, Amine El-Sahili, Nour Al-Sharif, Sahar Khanafer

The Mathematics Enthusiast

Creativity in mathematics is identified in many forms or we can say is made up of many components. One of these components is The Unexpected Links where one tries to solve a mathematical problem in a nontraditional manner that requires the formation of hidden bridges between distinct mathematical domains or even between seemingly far ideas within the same domain. In this article, we design problems that express unexpected links in mathematics and suit students of intermediate and secondary levels. We prove their feasibility through teachers’ testimonies and through introducing them in classrooms and collecting students’ attitudes with respect to understanding …

A Dialectical Invariant For Research In Mathematics Education, Mauro García Pupo, Juan E. Nápoles Valdes

The Mathematics Enthusiast

Many current problems in research in mathematics education emerge from pairs of contradictory dialectical categories. In effect, these pairs characterize the problems. When an epistemological study is made to determine the object of research in which a problem is immersed, it is possible to find essential pairs of dialectical categories that become more profound and thus provide enough elements for the determination of appropriate didactic actions to solve the problem under research.

What Can Education Learn From Real-World Communication Of Risk And Uncertainty?, David Spiegelhalter, Jenny Gage

The Mathematics Enthusiast

Probability is a difficult topic to teach, not least because it is rather unclear what it actually means. Modern risk communication has tackled general public incomprehension of probability statements by using the metaphor of ‘expected frequencies’ – for example, “of 100 people like you, we would expect 10 to have a heart attack or stroke in the next 10 years.” We show how these ideas can be taken into the classroom as the basis for teaching probability, using frequency tree diagrams as the fundamental representation. Empirical frequency trees can be used to summarise a series of classroom experiments, and then …

Judgment Of Association Between Potential Factors And Associated Risk In 2x2 Tables: A Study With Psychology Students, Carmen Batanero, Gustavo R. Cañadas, Carmen Díaz, Maria M. Gea

The Mathematics Enthusiast

This study was aimed to evaluate the accuracy and strategies used in the estimation of association between potential factors and associated risks when data are presented in 2x2 tables. A sample of 414 undergraduate Psychology students from three different Spanish universities was given three different tasks (direct and inverse association and perfect independence) where they had to estimate such association. Most participants judged association in the task where there was perfect independence, but the data contradicted the students’ previous expectations. The estimation of association was consistent with the perception of association and the accuracy of estimates increased with correct strategies. …

Making Decisions About Gambling: The Influence Of Risk On Children’S Arguments, Annie Savard

The Mathematics Enthusiast

This article presents results from a study on decision-making towards eventual participation to gambling activities by grade 4 students. For this study, six learning situations were proposed in a fourth grade classroom. The researcher, who was also the teacher, proposed some extra activities in order to define gambling. Students learned about probability and developed, at the same time, the ability to think critically about gambling. She then proposed three fictional situations of gambling to the students, and asked them if and why they would (or would not) participate in the situation. By studying the arguments that students provided, she explored …

Guest Editorial: Risk – Mathematical Or Otherwise, Egan J. Chernoff

The Mathematics Enthusiast

No abstract provided.

Risk Education: A Worldview Analysis Of What Is Present And Could Be, Gale L. Russell

The Mathematics Enthusiast

Risk, risk analysis, risk management and risk-based decision-making are ubiquitous ideas in the modern world. Consequently, risk education is emerging as a new field of research. However, just as the defining of risk and what it entails is a contested topic, so too is the field of risk education research open to many possible approaches. In this paper notions of risk, particularly as they play out in research on risk education, are analyzed (within an ethical space) using a theoretical framework based on the Traditional Western and an Indigenous worldview. Through this analysis, along with the identification of the kinds …

Adults’ Perceptions Of Risk In The Big Data Era, Theodosia Prodromou

The Mathematics Enthusiast

The present digital era has seen rapid growth in the availability of big data; we were curious about whether such availability of data changes perceptions and assessments of risk. In this paper, we investigate adults’ (35-63 years old) perceptions of risk in the big-data era and how it figures in their everyday life. We developed decision-making scenarios for socio-economic, environmental and health topics that involve modelling with personal value systems alongside Gapminder word map data. Going beyond the idea of risk in statistical theory, we attempt to gain an understanding of the processes by which adults assess risks.

Hydrodynamic Analogues Of Hamiltonian Systems, Francisco J. Jauffred

Graduate Masters Theses

A one-dimensional Hamiltonian system can be modeled and understood as a two-dimensional incompressible fluid in phase space. In this sense, the chaotic behavior of one-dimensional time dependent Hamiltonians corresponds to the mixing of two-dimensional fluids. Amey (2012) studied the characteristic values of one such system and found a scaling law governing them. We explain this scaling law as a diffusion process occurring in an elliptical region with very low eccentricity. We prove that for such a scaling law to occur, it is necessary for a vorticity field to be present. Furthermore, we show that a conformal mapping of an incompressible …

Repcoin: A Market-Based Approach To Reputation, Stephen D. Malina

Dartmouth College Undergraduate Theses

Individuals use measures of reputation as heuristics for determining how much interest and trust they should place in other individuals. Clear measures of reputation save time and increase efficiency because they prevent individuals from having to go through the traditional process of determining reputation, especially in cases where these traditional measures no longer suffice. Repcoin aimed to give experts in different areas a platform for highlighting their expertise, provide an avenue for users to find credible experts in different areas, and a place for users to try and predict whose reputation will increase and thereby prove their ability to identify …

Advances In Understanding Carboxysome Assembly In Prochlorococcus And Synechococcus Implicate Csos2 As A Critical Component, Fei Cai, Zhicheng Dou, Susan L. Bernstein, Ryan Leverenz, Eric B. Williams, Sabine Heinhorst, Jessup M. Shively, Gordon C. Cannon, Cheryl A. Kerfeld

Faculty Publications

The marine Synechococcus and Prochlorococcus are the numerically dominant cyanobacteria in the ocean and important in global carbon fixation. They have evolved a CO₂-concentrating-mechanism, of which the central component is the carboxysome, a self-assembling proteinaceous organelle. Two types of carboxysome, α and β, encapsulating form IA and form IB d-ribulose-1,5-bisphosphate carboxylase/oxygenase, respectively, differ in gene organization and associated proteins. In contrast to the β-carboxysome, the assembly process of the α-carboxysome is enigmatic. Moreover, an absolutely conserved α-carboxysome protein, CsoS2, is of unknown function and has proven recalcitrant to crystallization. Here, we present studies on the CsoS2 protein in …

Hydrogen And Syngas Production From Gasification Of Lignocellulosic Biomass In Supercritical Water Media, Jun-Ki Choi, Abtin Ataei, Ahmad Tavasoli, Farid Safari

Mechanical and Aerospace Engineering Faculty Publications

Novel biomass-processing technologies have been recently used for conversion of organic wastes into valuable biofuels like bio-hydrogen. Agricultural wastes are available and renewable energy resources to supply energy demand of the future. The purpose of this study is to investigate the production of hydrogen-rich syngas from wheat straw, walnut shell, and almond shell.

Exponential Type Product Estimator For Finite Population Mean With Information On Auxiliary Attribute, Monika Saini, Ashish Kumar

Applications and Applied Mathematics: An International Journal (AAM)

The main objective of the present study is to develop a new modified unbiased exponential type product estimator for the estimation of the population mean. The proposed estimator possesses the characteristic of a bi-serial negative correlation between the study variable and its auxiliary attribute. Efficiency comparison has been carried out between the proposed estimator and the existing estimators theoretically and numerically.

On Factorization Of A Special Type Of Vandermonde Rhotrix, P. L. Sharma, Satish Kumar, Mansi Rehan

Applications and Applied Mathematics: An International Journal (AAM)

Vandermonde matrices have important role in many branches of applied mathematics such as combinatorics, coding theory and cryptography. Some authors discuss the Vandermonde rhotrices in the literature for its mathematical enrichment. Here, we introduce a special type of Vandermonde rhotrix and obtain its LR factorization namely left and right triangular factorization, which is further used to obtain the inverse of the rhotrix.

Magnetic Flux Circulation In The Rotationally Driven Giant Magnetospheres, P. A. Delamere, A. Otto, X. Ma, F. Bagenal, R. J. Wilson

Publications

The giant‐planet magnetodiscs are shaped by the radial transport of plasma originating in the inner magnetosphere. Magnetic flux transport is a key aspect of the stretched magnetic field configuration of the magnetodisc. While net mass transport is outward (ultimately lost to the solar wind), magnetic flux conservation requires a balanced two‐way transport process. Magnetic reconnection is a critical aspect of the balanced flux transport. We present a comprehensive analysis of current sheet crossings in Saturn's magnetosphere using Cassini magnetometer data from 2004 to 2012 in an attempt to quantify the circulation of magnetic flux, emphasizing local time dependence. A key …

Modeling Of Humoral Immune Response To Repeated Influenza A Virus Infections, Abbiana Arenas, Safiyah Muhammad, Ly Nguyen, Samita Andreansky, Evan Haskell

Mathematics Faculty Proceedings, Presentations, Speeches, Lectures

Seasonal infections by Influenza A virus (IAV) causes hundreds of thousands of deaths worldwide each year, with most individuals being infected multiple times throughout their lifetimes. The relative impact of the components of the host immune system in controlling the severity and duration of repeated challenges from an IAV infection remains unclear. In particular, the differential contribution of the humoral immune response in primary and secondary challenges from IAV are relatively little explored. We develop a parsimonious mathematical model of the humoral immune response to IAV infection with biologically meaningful and identifiable parameters. We show the relative sensitivity of the …

On Spectra Of Composition Operators, Valentin Matache

Mathematics Faculty Publications

In this paper we consider composition operators Cφ on the Hilbert Hardy space over the unit disc, induced by analytic selfmaps φ. We use the fact that the operator C∗φCφ is asymptotically Toeplitz to obtain information on the essential spectrum and spectrum of Cϕ, which we are able to describe in select cases (including the case of some hypercyclic composition operators or that of composition operators with the property that the asymptotic symbol of C∗φCφ is constant a.e.). One of our tools is the Nikodym derivative of the pull-back measure induced by φ. An alternative formula for the essential norm …

Iowa Waste Reduction Center Newsletter, June 2015, University Of Northern Iowa. Iowa Waste Reduction Center.

Iowa Waste Reduction Center Newsletter

Inside this Issue:

--- Food Waste Compost Training
--- 12 Month Rolling Log Available to Download
--- EMS in Depth Workshop
--- Industry News

Hyers-Ulam And Hyers-Ulam-Aoki-Rassias Stability For Linear Ordinary Differential Equations, A. N. Mohapatra

Applications and Applied Mathematics: An International Journal (AAM)

Here we prove the Hyers-Ulam stability and Hyers-Ulam-Aoki-Rassias stability of the n-th order ordinary linear differential equation with smooth coefficients on compact and semi-bounded intervals using successive integration by parts. Keywords:

Application Of Reduced Differential Transform Method For Solving Nonlinear Reaction-Diffusion-Convection Problems, A. Taghavi, A. Babaei, A.` Mohammadpour

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, Reduced differential transform method is presented for solving nonlinear reactiondiffusion- convection initial value problems. The methodology with some known techniques shows that the present approach is simple and effective.To show the efficiency of the present method, four interesting examples is given.

Mathematical Modeling And Analysis Of Leukemia: Effect Of External Engineered T Cells Infusion, Manju Agarwal, Archana S. Bhadauria

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a nonlinear model is proposed and analyzed to study the spread of Leukemia by considering the effect of genetically engineered patients T cells to attack cancer cells. The model is governed by four dependent variables namely; naive or susceptible blood cells, infected or dysfunctional blood cells, cancer cells and immune cells. The model is analyzed by using the stability theory of differential equations and numerical simulation. We have observed that the system is stable in the local and global sense if antigenicity rate or rate of stimulation of immune cells is greater than a threshold value dependent …

Unsteady Boundary Layer Flow Of Thermophoretic Mhd Nanofluid Past A Stretching Sheet With Space And Time Dependent Internal Heat Source/Sink, N. Sandeep, C. Sulochana, C. S. K. Raju, M. J. Babu, V. Sugunamma

Applications and Applied Mathematics: An International Journal (AAM)

In this study we analyze the boundary layer flow of a thermophoretic magnetohydrodynamic dissipative nanofluid over an unsteady stretching sheet in a porous medium with space and time dependent internal heat source/sink. The governing equations are transformed to ordinary differential equations by using similarity transformation. Numerical solutions of these equations are obtained by using the Shooting Technique. The effects of non-dimensional governing parameters on the velocity, temperature, concentration profiles, friction factor, Nusselt and Sherwood numbers are discussed and presented through graphs and tables. Accuracy of the results compared with the existing ones. Excellent agreement is found with earlier studies.

On Some Optimal Multiple Root-Finding Methods And Their Dynamics, Munish Kansal, V. Kanwar, Saurabh Bhatia

Applications and Applied Mathematics: An International Journal (AAM)

Finding multiple zeros of nonlinear functions pose many difficulties for many of the iterative methods. In this paper, we present an improved optimal class of higher-order methods for multiple roots having quartic convergence. The present approach of deriving an optimal class is based on weight function approach. In terms of computational cost, all the proposed methods require three functional evaluations per full iteration, so that their efficiency indices are 1.587 and, are optimal in the sense of Kung-Traub conjecture. It is found by way of illustrations that they are useful in high precision computing enviroments. Moreover, basins of attraction of …

Solution Of Fractional Drinfeld-Sokolov-Wilson Equation Using Homotopy Perturbation Transform Method, P. K. Singh, K. Vishal, T. Som

Applications and Applied Mathematics: An International Journal (AAM)

In this article, the approximate solutions of the non-linear Drinfeld-Sokolov-Wilson equation with fractional time derivative have been obtained. The fractional derivative is described in the Caputo sense. He’s polynomial is used to tackle the nonlinearity which arise in our considered problems. A time fractional nonlinear partial differential equation has been computed numerically. The numerical procedures illustrate the effectiveness and reliability of the method. Effects of fractional order time derivatives on the solutions for different particular cases are presented through graphs.

E-Super Vertex Magic Labelling Of Graphs And Some Open Problems, G. Marimuthu, B. Suganya, S. Kalaivani, M. Balakrishnan

Applications and Applied Mathematics: An International Journal (AAM)

Let G be a finite graph with p vertices and q edges. A vertex magic total labelling is a bijection from the union of the vertex set and the edge set to the consecutive integers 1, 2, 3, . . . , p + q with the property that for every u in the vertex set, the sum of the label of u and the label of the edges incident with u is equal to k for some constant k. Such a labelling is E-super, if the labels of the edge set is the set {1, 2, 3, . . …

Thermal Stresses In Functionally Graded Hollow Sphere Due To Non-Uniform Internal Heat Generation, S. P. Pawar, K. C. Deshmukh, G. D. Kedar

Applications and Applied Mathematics: An International Journal (AAM)

In this article, the thermal stresses in a hollow thick sphere of functionally graded material subjected to non-uniform internal heat generation are obtained as a function of radius to an exact solution by using the theory of elasticity. Material properties and heat generation are assumed as a function of radius of sphere and Poisson’s ratio as constant. The distribution of thermal stresses for different values of the powers of the module of elasticity and varying power law index of heat generation is studied. The results are illustrated numerically and graphically.

A Super Non-Dominated Point For Multi-Objective Transportation Problem, Abbas S. Bander, Vahid Morovati, Hadi Basirzadeh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper a method to obtain a non-dominated point for the multi-objective transportation problem is presented. The superiority of this method over the other existing methods is that the presented non-dominated point is the closest solution to the ideal solution of that problem. The presented method does not need to have the ideal point and other parameters to find this solution. Also, the calculative load of this method is less than other methods in the literature.