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16,898 full-text articles. Page 12 of 488.

Singular Ramsey And Turán Numbers, Yair Caro, Zsolt Tuza 2019 University of Haifa-Oranim

Singular Ramsey And Turán Numbers, Yair Caro, Zsolt Tuza

Theory and Applications of Graphs

We say that a subgraph F of a graph G is singular if the degrees d_G(v) are all equal or all distinct for the vertices v of 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 K_m, 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, which does not contain F as a ...


Solving The Sylvester Equation Ax-Xb=C When $\Sigma(A)\Cap\Sigma(B)\Neq\Emptyset$, Nebojša Č. Dinčić 2019 Faculty of Sciences and Mathematics, University of Niš

Solving The Sylvester Equation Ax-Xb=C When $\Sigma(A)\Cap\Sigma(B)\Neq\Emptyset$, Nebojša Č. Dinčić

Electronic Journal of Linear Algebra

The method for solving the Sylvester equation $AX-XB=C$ in complex matrix case, when $\sigma(A)\cap\sigma(B)\neq \emptyset$, by using Jordan normal form is given. Also, the approach via Schur decomposition is presented.


When Revolutions Happen: Algebraic Explanation, Julio Urenda, Vladik Kreinovich 2019 University of Texas at El Paso

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 ...


Hypersurfaces With Nonnegative Ricci Curvature In Hyperbolic Space, Vincent Bonini, Shiguang Ma, Jie Qing 2019 California Polytechnic State University - San Luis Obispo

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).


Decision Theory Explains "Telescoping Effect" -- That Our Time Perception Is Biased, Laxman Bokati, Vladik Kreinovich 2019 University of Texas at El Paso

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.


How To Generate "Nice" Cubic Polynomials -- With Rational Coefficients, Rational Zeros And Rational Extrema: A Fast Algorithm, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich 2019 University of Texas at El Paso

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.


Analysis Of Feast Spectral Approximations Using The Dpg Discretization, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall, Benjamin Q. Parker 2019 Portland State University

Analysis Of Feast Spectral Approximations Using The Dpg Discretization, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall, Benjamin Q. 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, Milos Savic, Emily Cilli-Turner, Gail Tang, Gulden Karakok, Houssein El Turkey 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, Hugh C. Culik 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 ...


An 1883 Faery Tale, Scott W. Williams 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, Ricky Chen 2019 Claremont Colleges

Irrational Infinity, Ricky Chen

Journal of Humanistic Mathematics

A short whimsical poem on the cardinality of irrational numbers.


Cosmology, Craig W. Steele 2019 Edinboro University

Cosmology, Craig W. Steele

Journal of Humanistic Mathematics

No abstract provided.


A Mathematician's Travel Memories, Michael Holcomb 2019 University of Pikeville

A Mathematician's Travel Memories, Michael Holcomb

Journal of Humanistic Mathematics

No abstract provided.


Geometry Of Night, Jenny Patton 2019 The Ohio State University

Geometry Of Night, Jenny Patton

Journal of Humanistic Mathematics

No abstract provided.


Ecstatic Syllabi: Four Poems, Mary Peelen 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, Sarah Glaz 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, Eveline Pye 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, Benjamin Braun, Eric Kahn 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, Ann L. von Mehren 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 ...


On Mathematical Conjectures And Counterexamples, Ali Barahmand 2019 Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran

On Mathematical Conjectures And Counterexamples, Ali Barahmand

Journal of Humanistic Mathematics

This article provides an overview of the limitations of checking out a few cases to prove conjectures in mathematics. To that end, I present a purposeful collection of number-theoretic conjectures where extensive checking of cases has found counterexamples, with emphasis on the historical backgrounds. Historical examples of long-term attempts to prove or disprove such conjectures could help individuals to realize more deeply that a limited number of observations does not guarantee the correctness of a conjecture, even though there may be many examples in its favor.


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