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Articles 751 - 780 of 1389
Full-Text Articles in Mathematics
Singular Ramsey And Turán Numbers, Yair Caro, Zsolt Tuza
Singular Ramsey And Turán Numbers, Yair Caro, Zsolt Tuza
Theory & Applications of Graphs
We say that a subgraph F of a graph G is singular if the degrees dG(v) are all equal or all distinct for the vertices v ∈ V (F). The singular Ramsey number Rs(F) is the smallest positive integer n such that, for every m at least n, in every edge 2-coloring of Km, at least one of the color classes contains F as a singular subgraph. In a similar flavor, the singular Turán number Ts(n,F) is defined as the maximum number of edges in a graph of order n, …
Decision Theory Explains "Telescoping Effect" -- That Our Time Perception Is Biased, Laxman Bokati, Vladik Kreinovich
Decision Theory Explains "Telescoping Effect" -- That Our Time Perception Is Biased, Laxman Bokati, Vladik Kreinovich
Departmental Technical Reports (CS)
People usually underestimate time passed since distant events, and overestimate time passed since recent events. There are several explanations for this "telescoping effect", but most current explanations utilize specific features of human memory and/or human perception. We show that the telescoping effect can be explained on a much basic level of decision theory, without the need to invoke any specific ways we perceive and process time.
Hypersurfaces With Nonnegative Ricci Curvature In Hyperbolic Space, Vincent Bonini, Shiguang Ma, Jie Qing
Hypersurfaces With Nonnegative Ricci Curvature In Hyperbolic Space, Vincent Bonini, Shiguang Ma, Jie Qing
Mathematics
Based on properties of n-subharmonic functions we show that a complete, noncompact, properly embedded hypersurface with nonnegative Ricci curvature in hyperbolic space has an asymptotic boundary at infinity of at most two points. Moreover, the presence of two points in the asymptotic boundary is a rigidity condition that forces the hypersurface to be an equidistant hypersurface about a geodesic line in hyperbolic space. This gives an affirmative answer to the question raised by Alexander and Currier (Proc Symp Pure Math 54(3):37–44, 1993).
Diagonal Sums Of Doubly Substochastic Matrices, Lei Cao, Zhi Chen, Xuefeng Duan, Selcuk Koyuncu, Huilan Li
Diagonal Sums Of Doubly Substochastic Matrices, Lei Cao, Zhi Chen, Xuefeng Duan, Selcuk Koyuncu, Huilan Li
Mathematics Faculty Articles
Let Ωn denote the convex polytope of all n x n doubly stochastic matrices, and ωn denote the convex polytope of all n x n doubly substochastic matrices. For a matrix A ϵ ωn, define the sub-defect of A to be the smallest integer k such that there exists an (n + k) x (n + k) doubly stochastic matrix containing A as a submatrix. Let ωn,k denote the subset of ωn which contains all doubly substochastic matrices with sub-defect k. For π a permutation of symmetric group of degree …
How To Generate "Nice" Cubic Polynomials -- With Rational Coefficients, Rational Zeros And Rational Extrema: A Fast Algorithm, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich
How To Generate "Nice" Cubic Polynomials -- With Rational Coefficients, Rational Zeros And Rational Extrema: A Fast Algorithm, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Students feel more comfortable with rational numbers than with irrational ones. Thus, when teaching the beginning of calculus, it is desirable to have examples of simple problems for which both zeros and extrema point are rational. Recently, an algorithm was proposed for generating cubic polynomials with this property. However, from the computational viewpoint, the existing algorithm is not the most efficient one: in addition to applying explicit formulas, it also uses trial-and-error exhaustive search. In this paper, we propose a computationally efficient algorithm for generating all such polynomials: namely, an algorithm that uses only explicit formulas.
When Revolutions Happen: Algebraic Explanation, Julio Urenda, Vladik Kreinovich
When Revolutions Happen: Algebraic Explanation, Julio Urenda, Vladik Kreinovich
Departmental Technical Reports (CS)
At first glance, it may seem that revolutions happen when life becomes really intolerable. However, historical analysis shows a different story: that revolutions happen not when life becomes intolerable, but when a reasonably prosperous level of living suddenly worsens. This empirical observation seems to contradict traditional decision theory ideas, according to which, in general, people's happiness monotonically depends on their level of living. A more detailed model of human behavior, however, takes into account not only the current level of living, but also future expectations. In this paper, we show that if we properly take these future expectations into account, …
Estimating The Density Of The Abundant Numbers, Dominic Klyve, Melissa Pidde, Kathryn E. Temple
Estimating The Density Of The Abundant Numbers, Dominic Klyve, Melissa Pidde, Kathryn E. Temple
Mathematics Faculty Scholarship
Mathematicians have been interested in properties of abundant numbers – those which are smaller than the sum of their proper factors – for over 2,000 years. During the last century, one line of research has focused in particular on determining the density of abundant numbers in the integers. Current estimates have brought the upper and lower bounds on this density to within about 10−4, with a value of K ≈ 0.2476, but more precise values seem difficult to obtain. In this paper, we employ computational data and tools from inferential statistics to get more insight into this value. We also …
Differential Invariants Of Non-Degenerate Surfaces, Yasemin Sağıroğlu, Djavvat Khadjiev, Uğur Gözütok
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).
Some Midpoint Type Inequalities For Riemann Liouville Fractional Integrals, Zeynep Şanli
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.
Diagonalization Of 1-D Differential Operators With Piecewise Constant Coefficients Using The Uncertainty Principle, Sarah D. Long, Somayyeh Sheikholeslami, James V. Lambers, Carley Walker
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 …
Schur Rings Over Infinite Groups, Cache Porter Dexter
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.
Birkhoff’S Ergodic Theorem For Weighted Variable Exponent Amalgam Spaces, Ismail Aydın, Cihan Unal
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 …
Proper Orthogonal Decomposition (Pod) Of The Flow Dynamics For A Viscoelastic Fluid In A Four-Roll Mill Geometry At The Stokes Limit, Paloma Gutierrez-Castillo, Becca Thomases
Proper Orthogonal Decomposition (Pod) Of The Flow Dynamics For A Viscoelastic Fluid In A Four-Roll Mill Geometry At The Stokes Limit, Paloma Gutierrez-Castillo, Becca Thomases
Mathematics Sciences: Faculty Publications
Numerical simulations of viscoelastic fluids in the Stokes limit with a four-roll mill background force were performed at a range of Weissenberg number (non-dimensional relaxation time). For small Weissenberg number the flow is steady and symmetric but upon increasing the Weissenberg number (corresponding to increased elasticity or flow memory time), the flow becomes unstable leading to a variety of temporal evolutions to different periodic and aperiodic solutions. These dynamics were analyzed using a Proper Orthogonal Decomposition (POD) that extracted elastic modes in terms of their contribution to the energy of the system. The temporal behavior of the system, captured by …
Springer Fibers And Schubert Points, Martha Precup, Julianna Tymoczko
Springer Fibers And Schubert Points, Martha Precup, Julianna Tymoczko
Mathematics Sciences: Faculty Publications
Springer fibers are subvarieties of the flag variety parametrized by partitions; they are central objects of study in geometric representation theory. Schubert varieties are subvarieties of the flag variety that induce a well-known basis for the cohomology of the flag variety. This paper relates these two varieties combinatorially. We prove that the Betti numbers of the Springer fiber associated to a partition with at most three rows or two columns are equal to the Betti numbers of a specific union of Schubert varieties.
Conformality And Q-Harmonicity In Sub-Riemannian Manifolds, Luca Capogna, Giovanna Citti, Enrico Le Donne, Alessandro Ottazzi
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].
Factors That Influence Mathematical Creativity, Joseph S. Kozlowski, Scott A. Chamberlin, Eric Mann
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 …
Analysis Of Feast Spectral Approximations Using The Dpg Discretization, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall, Benjamin Quanah Parker
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 …
A Re-Emergent Analysis Of Early Algebraic Learning, Steven Boyce, Diana Moss
A Re-Emergent Analysis Of Early Algebraic Learning, Steven Boyce, Diana Moss
Extension Research
In this paper, we discuss a novel approach for collaborative retrospective analysis. One researcher was directly involved in a classroom teaching experiment, adopting an emergent perspective as an interpreter-witness of classroom interactions during a four-week algebra instructional unit with sixth-grade students. The other researcher experienced and analyzed the data in reverse chronological order. We describe how this re-emergent perspective revealed aspects of students’ early algebraic reasoning.
Special Issue Call For Papers: Creativity In Mathematics, Milos Savic, Emily Cilli-Turner, Gail Tang, Gulden Karakok, Houssein El Turkey
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, Hugh C. Culik
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, Scott W. Williams
An 1883 Faery Tale, Scott W. Williams
Journal of Humanistic Mathematics
A poem about the construction of Georg Cantor's famous set.
Irrational Infinity, Ricky Chen
Irrational Infinity, Ricky Chen
Journal of Humanistic Mathematics
A short whimsical poem on the cardinality of irrational numbers.
Cosmology, Craig W. Steele
A Mathematician's Travel Memories, Michael Holcomb
A Mathematician's Travel Memories, Michael Holcomb
Journal of Humanistic Mathematics
No abstract provided.
Geometry Of Night, Jenny Patton
Geometry Of Night, Jenny Patton
Journal of Humanistic Mathematics
No abstract provided.
Ecstatic Syllabi: Four Poems, Mary Peelen
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, Sarah Glaz
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, Eveline Pye
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, Benjamin Braun, Eric Kahn
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, Ann L. Von Mehren
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' …