Mathematics | Open Access Articles | Digital Commons Network™

How To Create A Jordan Algebra, Ian M. Anderson, Thomas J. Apedaile

How to... in 10 minutes or less

We show how to create a Jordan algebra in Maple using the commands AlgebraLibraryData and AlgebraData.

How To Create The Quaternion & Octonion Algebras, Ian M. Anderson, Thomas J. Apedaile

How to... in 10 minutes or less

We show how to create the quaternion and octonion algebras with the DifferentialGeometry software. For each algebra, there is a split-form also available.

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The Ideal Free Strategy With Weak Allee Effect, Daniel Munther

Mathematics and Statistics Faculty Publications

This paper examines the interplay between optimal movement strategies and the weak Allee effect within the context of two competing species in a spatially heterogenous environment. When both species have the same populations dynamics, previous studies identified an ‘ideal free’ strategy which is able to exclude any other competitor playing a ‘non-ideal free’ strategy. We find that if the ideal free disperser is subject to a weak Allee effect, a competing species utilizing very weak or very strong advection will still be excluded despite having superior population dynamics. However, for intermediate advection rates, such a competitor can invade the ideal …

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Usefulness Of Cardiac Biomarker Score For Risk Stratification In Stable Patients Undergoing Elective Cardiac Evaluation Across Glycemic Status, W.H. Wilson Tang, Naveed Iqbal, Yuping Wu, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

Several clinically available cardiac biomarkers have established their prognostic value in patients with acute coronary syndromes. However, their relative prognostic significance in stable subjects has not been prospectively validated, either individually or in combination. The aim of this study was to evaluate the extent to which B-type natriuretic peptide, myeloperoxidase, and high-sensitivity C-reactive protein alone or together could be prognostic biomarkers in 3,635 consecutive stable patients without acute coronary syndrome who underwent elective diagnostic coronary angiography. After adjusting for traditional risk factors and renal function, each of the markers monitored was a significant predictor of incident major adverse cardiovascular events …

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New Results For Oscillatory Behavior Of Even-Order Half-Linear Delay Differential Equations, Chenghui Zhang, Ravi P. Agarwal, Martin Bohner, Tongxing Li

Mathematics and Statistics Faculty Research & Creative Works

Some new oscillation results are presented that improve those reported in [C. Zhang, T. Li, B. Sun, and E. Thandapani, On the oscillation of higher-order half-linear delay differential equations, Appl. Math. Lett. 24 (2011) 1618-1621]. © 2012 Elsevier Ltd. All rights reserved.

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Use Of Grothendieck Inequality In Interval Computations: Quadratic Terms Are Estimated Accurately Modulo A Constant Factor, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main problems of interval computations is to compute the range of a given function f over given intervals. For a linear function, we can feasibly estimate its range, but for quadratic (and for more complex) functions, the problem of computing the exact range is NP-hard. So, if we limit ourselves to feasible algorithms, we have to compute enclosures instead of the actual ranges. It is known that asymptotically the smallest possible excess width of these enclosures is O(Δ²), where Δ is the largest half-width of the input intervals. This asymptotics is attained for the Mean …

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Checking Monotonicity Is Np-Hard Even For Cubic Polynomials, Andrzej Pownuk, Luc Longpre, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main problems of interval computations is to compute the range of a given function over given intervals. In general, this problem is computationally intractable (NP-hard) -- that is why we usually compute an enclosure and not the exact range. However, there are cases when it is possible to feasibly compute the exact range; one of these cases is when the function is monotonic with respect to each of its variables. The monotonicity assumption holds when the derivatives at a midpoint are different from 0 and the intervals are sufficiently narrow; because of this, monotonicity-based estimates are often …

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Why Complex-Valued Fuzzy? Why Complex Values In General? A Computational Explanation, Olga Kosheleva, Vladik Kreinovich, Thavatchai Ngamsantivong

Departmental Technical Reports (CS)

In the traditional fuzzy logic, as truth values, we take all real numbers from the interval [0,1]. In some situations, this set is not fully adequate for describing expert uncertainty, so a more general set is needed. From the mathematical viewpoint, a natural extension of real numbers is the set of complex numbers. Complex-valued fuzzy sets have indeed been successfully used in applications of fuzzy techniques. This practical success leaves us with a puzzling question: why complex-valued degree of belief, degrees which do not seem to have a direct intuitive meaning, have been so successful? In this paper, we use …

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An Exploration Of Metacognition And Its Effect On Mathematical Performance In Differential Equations, Mary Jarratt Smith

Mathematics Faculty Publications and Presentations

Research suggests that students who are “metacognitively aware learners” demonstrate better academic performance (Shraw & Dennison, 1994; Md. Yunus & Ali, 2008). In this research, the metacognitive levels for two classes of differential equations students were studied. Students completed a survey adapted from the Metacognitive Awareness Inventory (MAI) (Shraw & Dennison, 1994) at the start of the course. The questions chosen from the MAI were aimed at three components concerning the students’ knowledge about their cognition: declarative knowledge, procedural knowledge, and conditional knowledge. Analysis shows student performance, as measured by the course grade, cannot be predicted by metacognitive awareness levels.

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A High-Order Kernel Method For Diffusion And Reaction-Diffusion Equations On Surfaces, Edward J. Fuselier, Grady B. Wright

Mathematics Faculty Publications and Presentations

In this paper we present a high-order kernel method for numerically solving diffusion and reaction-diffusion partial differential equations (PDEs) on smooth, closed surfaces embedded in R^d . For two-dimensional surfaces embedded in R³ , these types of problems have received growing interest in biology, chemistry, and computer graphics to model such things as diffusion of chemicals on biological cells or membranes, pattern formations in biology, nonlinear chemical oscillators in excitable media, and texture mappings. Our kernel method is based on radial basis functions and uses a semi-discrete approach (or the method-of-lines) in which the surface derivative operators that …

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The Performance Of Mlem For Dynamic Imaging From Simulated Few-View, Multi-Pinhole Spect, Dan Ma, Paul Arthur Wolf, Anne V. Clough, Taly Gilat Schmidt

Mathematics, Statistics and Computer Science Faculty Research and Publications

Stationary small-animal SPECT systems are being developed for rapid dynamic imaging from limited angular views. This work quantified, through simulations, the performance of Maximum Likelihood Expectation Maximization (MLEM) for reconstructing a time-activity curve (TAC) with uptake duration of a few seconds from a stationary, three-camera multi-pinhole SPECT system. The study also quantified the benefits of a heuristic method of initializing the reconstruction with a prior image reconstructed from a conventional number of views, for example from data acquired during the late-study portion of the dynamic TAC. We refer to MLEM reconstruction initialized by a prior-image initial guess (IG) as MLEM …

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A Spectral Order For Infinite Dimensional Quantum Spaces, Joe Mashburn

Mathematics Faculty Publications

In this paper we extend the spectral order of Coecke and Martin to infinite-dimensional quantum states. Many properties present in the finite-dimensional case are preserved, but some of the most important are lost. The order is constructed and its properties analysed. Most of the useful measurements of information content are lost. Shannon entropy is defined on only a part of the model, and that part is not a closed subset of the model. The finite parts of the lattices used by Birkhoff and von Neumann as models for classical and quantum logic appear as subsets of the models for infinite …

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3e: Energy-Efficient Elastic Scheduling For Independent Tasks In Heterogeneous Computing Systems, Xiaomin Zhu, Rong Ge, Jinguang Sun, Chuan He

Mathematics, Statistics and Computer Science Faculty Research and Publications

Reducing energy consumption is a major design constraint for modern heterogeneous computing systems to minimize electricity cost, improve system reliability and protect environment. Conventional energy-efficient scheduling strategies developed on these systems do not sufficiently exploit the system elasticity and adaptability for maximum energy savings, and do not simultaneously take account of user expected finish time. In this paper, we develop a novel scheduling strategy named energy-efficient elastic (3E) scheduling for aperiodic, independent and non-real-time tasks with user expected finish times on DVFS-enabled heterogeneous computing systems. The 3E strategy adjusts processors’ supply voltages and frequencies according to the system workload, and …

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Some Minor-Closed Classes Of Signed Graphs, Dan Slilaty, Xiangqian Zhou

Mathematics and Statistics Faculty Publications

We define four minor-closed classes of signed graphs in terms of embeddability in the annulus, projective plane, torus, and Klein bottle. We give the full list of 20 excluded minors for the smallest class and make a conjecture about the largest class.

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Generalizing Tanisaki's Ideal Via Ideals Of Truncated Symmetric Functions, Aba Mbirika, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

Abstract. We define a family of ideals I_h in the polynomial ring Z[_{x1, . . . , xn}] that are parametrized by Hessenberg functions h (equivalently Dyck paths or ample partitions). The ideals I_h generalize algebraically a family of ideals called the Tanisaki ideal, which is used in a geometric construction of permutation representations called Springer theory. To define I_h, we use polynomials in a proper subset of the variables {_{x1, . . . , xn}} that are symmetric under the corresponding permutation subgroup. We call these polynomials truncated symmetric functions and …

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Parametric Catalan Numbers And Catalan Triangles, Tian-Xiao He

Scholarship

Here presented a generalization of Catalan numbers and Catalan triangles associated with two parameters based on the sequence characterization of Bell-type Riordan arrays. Among the generalized Catalan numbers, a class of large generalized Catalan numbers and a class of small generalized Catalan numbers are defined, which can be considered as an extension of large Schroder numbers and small Schroder numbers, respectively. Using the characterization sequences of Bell-type Riordan arrays, some properties and expressions including the Taylor expansions of generalized Catalan numbers are given. A few combinatorial interpretations of the generalized Catalan numbers are also provided. Finally, a generalized Motzkin numbers …

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Sum Formula Of Multiple Hurwitz-Zeta Values, Jianqiang Zhao

Mathematical Sciences: Faculty Publications

Let s1,⋯,sd be d positive integers and define the multiple t-values of depth d byt(s1,⋯,sd)=∑n1>⋯>nd≥11(2n1−1)s1⋯(2nd−1)sd,which is equal to the multiple Hurwitz-zeta value 2−wζ(s1,⋯,sd;−12,⋯,−12) where w=s1+⋯+sd is called the weight. For d≤n, let T(2n,d) be the sum of all multiple t-values with even arguments whose weight is 2n and whose depth is d. In 2011, Shen and Cai gave formulas for T(2n,d) for d≤5 in terms of t(2n), t(2)t(2n−2) and t(4)t(2n−4). In this short note we generalize their results to arbitrary depth by using the theory of symmetric functions established by Hoffman (2012).

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Modeling Cell Proliferation In A Perfusion Tissue Engineering Bioreactor, Jeffrey Vincent Pohlmeyer

Dissertations

In this dissertation we develop a comprehensive model to simulate a tissue engineering experiment. The experiment takes place in a bioreactor in which a cell seeded porous scaffold is placed, and the scaffold experiences a perfused flow of a nutrient-rich culture medium. The goal of the model is to assist experimentalists in evaluation of different parameter scenarios as the time needed to simulate an experiment is significantly less than the time needed for the experiment itself. We provide the full two-dimensional model development, as well as investigation into possible variations of specific model choices, and we demonstrate the robustness and …

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The Goodness-Of-Fit Tests For Geometric Models, Feiyan Chen

Dissertations

We propose two types of goodness-of-fit tests for geometric distribution and for a bivariate geometric distribution called BGD(B&D), based on their probability generating function (PGF). The first type is a special-case application of the general testing procedure for discrete distributions proposed by Kocherlakota and Kocherlakota (1986). The second type utilizes the supremum of the absolute value of the standardized difference between the PGF’s maximum likelihood estimator (MLE) and its empirical counterpart as the test statistic. We verify the asymptotic properties of the test statistics for the first type of test and explore the asymptotic behaviors of the test statistics for …

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Some Contributions To The Sociology Of Numbers, Robert Dawson

Journal of Humanistic Mathematics

Those who work with numbers eventually realize that they all have different personalities (the word "numbers" can of course be replaced by any number of other nouns here.) Here is one view of the issue.

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How To Cook Up A Math Poem In N Easy Steps, Caleb Emmons

Journal of Humanistic Mathematics

A mathematical poem attempts to distill a mathematical concept and present it in a literary or visually compelling way. This paper presents an outline of my own personal method of composing such poetry. The outline is elucidated via an extended meditation on the composition of one particular poem.

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On Contemplation In Mathematics, Frank Lucas Wolcott

Journal of Humanistic Mathematics

In a section about research, we make the case that intentional, structured reflection on the mathematical research process, by mathematical researchers themselves, would result in better mathematicians doing better mathematics. As supporting evidence, we describe the Flavors and Seasons project. In a section about teaching, we describe the contemplative education movement and share personal experiences using meditation in the math classroom. We conclude with an explicit proposal for elucidating the experiential context of mathematics, in both research and teaching environments.

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Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz

Journal of Humanistic Mathematics

The narrative about the nineteenth century favored by many philosophers of mathematics strongly influenced by either logic or algebra, is that geometric intuition led real and complex analysis astray until Cauchy and Kronecker in one sense and Dedekind in another guided mathematicians out of the labyrinth through the arithmetization of analysis. Yet the use of geometry in most cases in nineteenth century mathematics was not misleading and was often key to important developments. Thus the geometrization of complex numbers was essential to their acceptance and to the development of complex analysis; geometry provided the canonical examples that led to the …

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The Lesson Of Grace In Teaching, Francis Su

All HMC Faculty Publications and Research

I want to talk about the biggest life lesson that I have learned, and that I continue to learn over and over again. It is deep and profound. It has changed the way I relate with people. It has reshaped my academic life. And it continually renovates the way I approach my students.

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On Mountain Pass Type Algorithms, James Bisgard

All Faculty Scholarship for the College of the Sciences

We consider constructive proofs of the mountain pass lemma, the saddle point theorem and a linking type theorem. In each, an initial “path” is deformed by pushing it downhill using a (pseudo) gradient flow, and, at each step, a high point on the deformed path is selected. Using these high points, a Palais–Smale sequence is constructed, and the classical minimax theorems are recovered. Because the sequence of high points is more accessible from a numerical point of view, we investigate the behavior of this sequence in the final two sections. We show that if the functional satisfies the Palais–Smale condition …

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Brown, James Monroe, 1800-1886 (Sc 806), Manuscripts & Folklife Archives

Manuscript Collection Finding Aids

Finding aid only for Manuscripts Small Collection 806. Ciphering book, 1822-1827 (40 p.), of James M. Brown, Butler County, Kentucky, which also contains a few pages of account entries and other various notations, (806a). Photocopy of ciphering book is also included. Also letter, 1989, from donor relating family data.

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Discontinuous Parameter Estimates With Least Squares Estimators, J. L. Mead

Mathematics Faculty Publications and Presentations

We discuss weighted least squares estimates of ill-conditioned linear inverse problems where weights are chosen to be inverse error covariance matrices. Least squares estimators are the maximum likelihood estimate for normally distributed data and parameters, but here we do not assume particular probability distributions. Weights for the estimator are found by ensuring its minimum follows a χ² distribution. Previous work with this approach has shown that it is competitive with regularization methods such as the L-curve and Generalized Cross Validation (GCV) [20]. In this work we extend the method to find diagonal weighting matrices, rather than a scalar regularization …

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Open Access: What We're Doing And How It Helps You, Sandra G. Yee, Joshua Neds-Fox, Michael Priehs, Nancy A. Wilmes

Library Scholarly Publications

Presentation to faculty in Wayne State University's (WSU) Department of Mathematics about Open Access Initiatives at WSU, and how to participate in Green OA as a matter of course in research and publication.

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From Solute Transport To Chemical Weathering, Allen Hunt, Thomas E. Skinner

Physics Seminars

A theory for conservative solute transport, based on concepts from percolation theory, is applied directly to reactive solute transport. Chemical reactions are assumed to have reached equilibrium at the scale of an individual pore, but at larger length scales, equilibration is limited by solute transport velocities, which are not the same as fluid velocities! The results of this theory already predicted observed dispersivity values for conservative solute transport over ten orders of magnitude of length scale as well as the variation of solute arrival time distributions with medium saturation. We now show that the solute velocity predicts the time-dependence of …

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04. Botany, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

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Full-Text Articles in Mathematics

How To Create A Jordan Algebra, Ian M. Anderson, Thomas J. Apedaile

How to... in 10 minutes or less

How To Create The Quaternion & Octonion Algebras, Ian M. Anderson, Thomas J. Apedaile

How to... in 10 minutes or less

The Ideal Free Strategy With Weak Allee Effect, Daniel Munther

Mathematics and Statistics Faculty Publications

Usefulness Of Cardiac Biomarker Score For Risk Stratification In Stable Patients Undergoing Elective Cardiac Evaluation Across Glycemic Status, W.H. Wilson Tang, Naveed Iqbal, Yuping Wu, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

New Results For Oscillatory Behavior Of Even-Order Half-Linear Delay Differential Equations, Chenghui Zhang, Ravi P. Agarwal, Martin Bohner, Tongxing Li

Mathematics and Statistics Faculty Research & Creative Works

Use Of Grothendieck Inequality In Interval Computations: Quadratic Terms Are Estimated Accurately Modulo A Constant Factor, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Checking Monotonicity Is Np-Hard Even For Cubic Polynomials, Andrzej Pownuk, Luc Longpre, Vladik Kreinovich

Departmental Technical Reports (CS)

Why Complex-Valued Fuzzy? Why Complex Values In General? A Computational Explanation, Olga Kosheleva, Vladik Kreinovich, Thavatchai Ngamsantivong

Departmental Technical Reports (CS)

An Exploration Of Metacognition And Its Effect On Mathematical Performance In Differential Equations, Mary Jarratt Smith

Mathematics Faculty Publications and Presentations

A High-Order Kernel Method For Diffusion And Reaction-Diffusion Equations On Surfaces, Edward J. Fuselier, Grady B. Wright

Mathematics Faculty Publications and Presentations

The Performance Of Mlem For Dynamic Imaging From Simulated Few-View, Multi-Pinhole Spect, Dan Ma, Paul Arthur Wolf, Anne V. Clough, Taly Gilat Schmidt

Mathematics, Statistics and Computer Science Faculty Research and Publications

A Spectral Order For Infinite Dimensional Quantum Spaces, Joe Mashburn

Mathematics Faculty Publications

3e: Energy-Efficient Elastic Scheduling For Independent Tasks In Heterogeneous Computing Systems, Xiaomin Zhu, Rong Ge, Jinguang Sun, Chuan He

Mathematics, Statistics and Computer Science Faculty Research and Publications

Some Minor-Closed Classes Of Signed Graphs, Dan Slilaty, Xiangqian Zhou

Mathematics and Statistics Faculty Publications

Generalizing Tanisaki's Ideal Via Ideals Of Truncated Symmetric Functions, Aba Mbirika, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

Parametric Catalan Numbers And Catalan Triangles, Tian-Xiao He

Scholarship

Sum Formula Of Multiple Hurwitz-Zeta Values, Jianqiang Zhao

Mathematical Sciences: Faculty Publications

Modeling Cell Proliferation In A Perfusion Tissue Engineering Bioreactor, Jeffrey Vincent Pohlmeyer

Dissertations

The Goodness-Of-Fit Tests For Geometric Models, Feiyan Chen

Dissertations

Some Contributions To The Sociology Of Numbers, Robert Dawson

Journal of Humanistic Mathematics

How To Cook Up A Math Poem In N Easy Steps, Caleb Emmons

Journal of Humanistic Mathematics

On Contemplation In Mathematics, Frank Lucas Wolcott

Journal of Humanistic Mathematics

Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz

Journal of Humanistic Mathematics

The Lesson Of Grace In Teaching, Francis Su

All HMC Faculty Publications and Research

On Mountain Pass Type Algorithms, James Bisgard

All Faculty Scholarship for the College of the Sciences

Brown, James Monroe, 1800-1886 (Sc 806), Manuscripts & Folklife Archives

Manuscript Collection Finding Aids

Discontinuous Parameter Estimates With Least Squares Estimators, J. L. Mead

Mathematics Faculty Publications and Presentations

Open Access: What We're Doing And How It Helps You, Sandra G. Yee, Joshua Neds-Fox, Michael Priehs, Nancy A. Wilmes

Library Scholarly Publications

From Solute Transport To Chemical Weathering, Allen Hunt, Thomas E. Skinner

Physics Seminars

04. Botany, University Of Central Oklahoma

Oklahoma Research Day Abstracts