Diagonalization Of 1-D Differential Operators With Piecewise Constant Coefficients Using The Uncertainty Principle,
2019
University of Southern Mississippi
Diagonalization Of 1-D Differential Operators With Piecewise Constant Coefficients Using The Uncertainty Principle, Sarah D. Long, Somayyeh Sheikholeslami, James V. Lambers, Carley Walker
Faculty Publications
A highly accurate and efficient numerical method is presented for computing the solution of a 1-D time-dependent partial differential equation in which the spatial differential operator features a piecewise constant coefficient defined on n" role="presentation"> pieces, in either self-adjoint and non-self-adjoint form, on a finite interval with periodic boundary conditions. The Uncertainty Principle is used to estimate the eigenvalues of the operator. Then, these estimates are used to construct a basis of eigenfunctions for use with a spectral method. The solution is presented as a truncated eigenfunction expansion, where each eigenfunction is a wave function that changes frequencies at the …
Differential Invariants Of Non-Degenerate Surfaces,
2019
Karadeniz Technical University
Differential Invariants Of Non-Degenerate Surfaces, Yasemin Sağıroğlu, Djavvat Khadjiev, Uğur Gözütok
Applications and Applied Mathematics: An International Journal (AAM)
This paper aims to prove that the set {g_{ij}(x), L_{ij} (x), i, j = 1, 2} is a complete system of the SM(3)- invariants of a nondegenerate surface in R3, where {g_{ij}(x)} and {L_{ij}(x)}, 1, j = 1, 2 are the sets of all coefficients of the first and second fundamental forms of a surface x in R3. A similar result was obtained for the group M(3).
Birkhoff’S Ergodic Theorem For Weighted Variable Exponent Amalgam Spaces,
2019
Sinop University
Birkhoff’S Ergodic Theorem For Weighted Variable Exponent Amalgam Spaces, Ismail Aydın, Cihan Unal
Applications and Applied Mathematics: An International Journal (AAM)
In this study, we consider some properties of weighted variable exponent Lebesgue and amalgam spaces. It is known these spaces are considerably used in harmonic and time-frequency analysis including elastic mechanics, electrorheological fluids, image processing, etc. Ergodic theory investigates the long-term averaging properties of measure preserving dynamical systems. This theory has also several applications and problems of statistical physics and mechanics. Moreover, it has influence on many areas of mathematics, especially probability theory and dynamical systems as well as Fourier analysis, functional analysis, and group theory. Therefore, we investigate Ergodic theorem for unweighted variable exponent Lebesgue spaces and also an …
Some Midpoint Type Inequalities For Riemann Liouville Fractional Integrals,
2019
Karadeniz Technical University
Some Midpoint Type Inequalities For Riemann Liouville Fractional Integrals, Zeynep Şanli
Applications and Applied Mathematics: An International Journal (AAM)
In the literature, there are a lot of studies about midpoint type inequalities for Riemann Liouville Fractional Integrals. But for most of them, the right and left fractional integrals are used together. In this paper, we give three new Riemann-Liouville fractional midpoint type identities for differentiable functions by using only the right or the left fractional integral. From these identities, we obtain some new midpoint type inequalities for harmonically convex functions by applying power mean and Hölder inequalities.
Schur Rings Over Infinite Groups,
2019
Brigham Young University
Schur Rings Over Infinite Groups, Cache Porter Dexter
Theses and Dissertations
A Schur ring is a subring of the group algebra with a basis that is formed by a partition of the group. These subrings were initially used to study finite permutation groups, and classifications of Schur rings over various finite groups have been studied. Here we investigate Schur rings over various infinite groups, including free groups. We classify Schur rings over the infinite cyclic group.
Factors That Influence Mathematical Creativity,
2019
Utah State University
Factors That Influence Mathematical Creativity, Joseph S. Kozlowski, Scott A. Chamberlin, Eric Mann
Mathematics and Statistics Faculty Publications
Creativity is a psychological construct that has gained research popularity (Akgul & Kaveci, 2016), however it remains a challenging one to define. The variety of definitions promulgated to understand creativity hints at the complexity of the mental process. Furthermore, as a subset of creativity, domain-specific mathematical creativity has also garnered a variety of definitions. The transdisciplinary research on creativity (Sriraman & Haavold, 2017) is seminal in this world of fast-paced innovation, invention, solution, and synthesis. Considering every human being with at least average cognitive abilities possesses the ability to think creatively (Baran, 2011), developing students’ creative talents and abilities must …
Conformality And Q-Harmonicity In Sub-Riemannian Manifolds,
2019
Worcester Polytechnic Institute
Conformality And Q-Harmonicity In Sub-Riemannian Manifolds, Luca Capogna, Giovanna Citti, Enrico Le Donne, Alessandro Ottazzi
Mathematics Sciences: Faculty Publications
We establish regularity of conformal maps between sub-Riemannian manifolds from regularity of Q-harmonic functions, and in particular we prove a Liouville-type theorem, i.e., 1-quasiconformal maps are smooth in all contact sub-Riemannian manifolds. Together with the recent results in [15], our work yields a new proof of the smoothness of boundary extensions of biholomorphims between strictly pseudoconvex smooth domains [29].
Analysis Of Feast Spectral Approximations Using The Dpg Discretization,
2019
Portland State University
Analysis Of Feast Spectral Approximations Using The Dpg Discretization, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall, Benjamin Quanah Parker
Mathematics and Statistics Faculty Publications and Presentations
A filtered subspace iteration for computing a cluster of eigenvalues and its accompanying eigenspace, known as “FEAST”, has gained considerable attention in recent years. This work studies issues that arise when FEAST is applied to compute part of the spectrum of an unbounded partial differential operator. Specifically, when the resolvent of the partial differential operator is approximated by the discontinuous Petrov Galerkin (DPG) method, it is shown that there is no spectral pollution. The theory also provides bounds on the discretization errors in the spectral approximations. Numerical experiments for simple operators illustrate the theory and also indicate the value of …
Special Issue Call For Papers: Creativity In Mathematics,
2019
University of Oklahoma
Special Issue Call For Papers: Creativity In Mathematics, Milos Savic, Emily Cilli-Turner, Gail Tang, Gulden Karakok, Houssein El Turkey
Journal of Humanistic Mathematics
The Journal of Humanistic Mathematics is pleased to announce a call for papers for a special issue on Creativity in Mathematics. Please send your abstract submissions via email to the guest editors by March 1, 2019. Initial submission of complete manuscripts is due August 1, 2019. The issue is currently scheduled to appear in July 2020.
What The Wasp Said,
2019
Independent scholar
What The Wasp Said, Hugh C. Culik
Journal of Humanistic Mathematics
On a bright spring day, the ancient building housing the English and Logic Departments begins to slowly collapse on itself, trapping McMann (an inept English professor) and Lucy Curt (a logician) in the office they share. As the Fibonacci repetitions of the building’s brickwork slowly peel away, McMann seizes the moment to tell Lucy stories about skunks, stories whose recurrent pattern finally leads to the unrecognized connection between a “message” burned into his ear by a wasp and the orderly universe for which he cannot find a language. At last, he looks up only to see Lucy descending a ladder, …
An 1883 Faery Tale,
2019
Claremont Colleges
An 1883 Faery Tale, Scott W. Williams
Journal of Humanistic Mathematics
A poem about the construction of Georg Cantor's famous set.
Irrational Infinity,
2019
Claremont Colleges
Irrational Infinity, Ricky Chen
Journal of Humanistic Mathematics
A short whimsical poem on the cardinality of irrational numbers.
Cosmology,
2019
Edinboro University
A Mathematician's Travel Memories,
2019
University of Pikeville
A Mathematician's Travel Memories, Michael Holcomb
Journal of Humanistic Mathematics
No abstract provided.
Geometry Of Night,
2019
The Ohio State University
Geometry Of Night, Jenny Patton
Journal of Humanistic Mathematics
No abstract provided.
Ecstatic Syllabi: Four Poems,
2019
Claremont Colleges
Ecstatic Syllabi: Four Poems, Mary Peelen
Journal of Humanistic Mathematics
Four poems with mathematical themes. Poems are entitled: Algebra I, Algebra II, Plane Geometry, Number Theory.
A Selection Of Poems From Ode To Numbers,
2019
Department of Mathematics, University of Connecticut
A Selection Of Poems From Ode To Numbers, Sarah Glaz
Journal of Humanistic Mathematics
My first poetry collection, Ode to Numbers, was published by Antrim House in September 2017 (http://www.antrimhousebooks.com/glaz.html). The book contains poems written over a quarter of a century and inspired by mathematics and my life as a mathematician. The poems in this folder are a small selection from the book—a series of seven poems focusing on events from the history of mathematics.
Book Review: Ode To Numbers: Poems By Sarah Glaz,
2019
Glasgow Caledonian University (retired)
Book Review: Ode To Numbers: Poems By Sarah Glaz, Eveline Pye
Journal of Humanistic Mathematics
This review explores the issues surrounding mathematics poetry and its role in challenging stereotypes about mathematics and mathematicians. In Ode to Numbers Sarah Glaz takes us from her childhood in Romania to her work as a professor at the University of Connecticut in the USA, with the constant thread of her love of mathematics. It is an intense emotional journey through time and place, arriving at mature reflection. The reader will encounter a wide range of poetic forms; some traditional, others inspired by mathematics. Glaz writes with originality, courage, insight, and generosity and this collection secures her reputation as an …
Teaching History Of Mathematics: A Dialogue,
2019
University of Kentucky
Teaching History Of Mathematics: A Dialogue, Benjamin Braun, Eric Kahn
Journal of Humanistic Mathematics
Many colleges and universities offer a course in the history of mathematics. While the potential benefits for students taking such a course might be apparent, it is often less clear how teaching a history of mathematics course can be a transformational experience for faculty. We present a dialogue between the authors regarding their experiences teaching history of mathematics courses, including their motivation for doing so, the impact these experiences have had on their classroom practices and assessment methods, and the opportunities history of mathematics courses offer for incorporating social justice, equity, and inclusion into the study of mathematics. Our goal …
Finding Teaching Inspiration From Gorgias: Mathematics Lessons From A Sophist,
2019
Bowling Green State University
Finding Teaching Inspiration From Gorgias: Mathematics Lessons From A Sophist, Ann L. Von Mehren
Journal of Humanistic Mathematics
The logos or rational language of the fifth-century BCE teacher, Gorgias, as contained in the fragment On the Nonexistent, challenges a reader to understand the relationship between the existent and the nonexistent; yet the text also offers an accessible idea of logos. Inspired by William M. Priestley's approach to the study of logos through ratios, and by Ivor Grattan-Guinness's recommendation to broaden the study of historical texts in the history of mathematics and mathematics education, and pursue their significance in a heritage sense, this article suggests that this ancient non-mathematics text by Gorgias may inspire and refresh elementary mathematics educators' …
