How To Calculate Pi: Buffon's Needle (Non-Calculus Version), 2019 Central Washington University

#### How To Calculate Pi: Buffon's Needle (Non-Calculus Version), Dominic Klyve

*Pre-calculus and Trigonometry*

No abstract provided.

Greatest Common Divisor: Algorithm And Proof, 2019 University of St. Thomas - Houston

#### Greatest Common Divisor: Algorithm And Proof, Mary K. Flagg

*Number Theory*

No abstract provided.

Brauer's Theorem And Nonnegative Matrices With Prescribed Diagonal Entries, 2019 Universidad Católica del Norte

#### Brauer's Theorem And Nonnegative Matrices With Prescribed Diagonal Entries, Ricardo L. Soto, Ana I. Julio, Macarena A. Collao

*Electronic Journal of Linear Algebra*

The problem of the existence and construction of nonnegative matrices with prescribed eigenvalues and diagonal entries is an important inverse problem, interesting by itself, but also necessary to apply a perturbation result, which has played an important role in the study of certain nonnegative inverse spectral problems. A number of partial results about the problem have been published by several authors, mainly by H. \v{S}migoc. In this paper, the relevance of a Brauer's result, and its implication for the nonnegative inverse eigenvalue problem with prescribed diagonal entries is emphasized. As a consequence, given a list of complex ...

Diagonal Sums Of Doubly Substochastic Matrices, 2019 Georgian Court University

#### Diagonal Sums Of Doubly Substochastic Matrices, Lei Cao, Zhi Chen, Xuefeng Duan, Selcuk Koyuncu, Huilan Li

*Electronic Journal of Linear Algebra*

Let $\Omega_n$ denote the convex polytope of all $n\times n$ doubly stochastic matrices, and $\omega_{n}$ denote the convex polytope of all $n\times n$ doubly substochastic matrices. For a matrix $A\in\omega_n$, define the sub-defect of $A$ to be the smallest integer $k$ such that there exists an $(n+k)\times(n+k)$ doubly stochastic matrix containing $A$ as a submatrix. Let $\omega_{n,k}$ denote the subset of $\omega_n$ which contains all doubly substochastic matrices with sub-defect $k$. For $\pi$ a permutation of symmetric group of degree $n$, the sequence of elements $a_{1\pi(1 ...

In-Sphere Property And Reverse Inequalities For Matrix Means, 2019 Ton Duc Thang University

#### In-Sphere Property And Reverse Inequalities For Matrix Means, Trung Hoa Dinh, Tin-Yau Tam, Bich Khue T Vo

*Electronic Journal of Linear Algebra*

The in-sphere property for matrix means is studied. It is proved that the matrix power mean satisfies in-sphere property with respect to the Hilbert-Schmidt norm. A new characterization of the matrix arithmetic mean is provided. Some reverse AGM inequalities involving unitarily invariant norms and operator monotone functions are also obtained.

Surjective Additive Rank-1 Preservers On Hessenberg Matrices, 2019 Walailak University

#### Surjective Additive Rank-1 Preservers On Hessenberg Matrices, Prathomjit Khachorncharoenkul, Sajee Pianskool

*Electronic Journal of Linear Algebra*

Let $H_{n}(\mathbb{F})$ be the space of all $n\times n$ upper Hessenberg matrices over a field~$\mathbb{F}$, where $n$ is a positive integer greater than two. In this paper, surjective additive maps preserving rank-$1$ on $H_{n}(\mathbb{F})$ are characterized.

Role Of Combinatorial Complexity In Genetic Networks, 2019 Southern Methodist University

#### Role Of Combinatorial Complexity In Genetic Networks, Sharon Yang

*SMU Journal of Undergraduate Research*

A common motif found in genetic networks is the formation of large complexes. One difficulty in modeling this motif is the large number of possible intermediate complexes that can form. For instance, if a complex could contain up to 10 different proteins, 210 possible intermediate complexes can form. Keeping track of all complexes is difficult and often ignored in mathematical models. Here we present an algorithm to code ordinary differential equations (ODEs) to model genetic networks with combinatorial complexity. In these routines, the general binding rules, which counts for the majority of the reactions, are implemented automatically, thus the users ...

Singular Ramsey And Turán Numbers, 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 $\Sigma(A)\Cap\Sigma(B)\Neq\Emptyset$, 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.

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 ...

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 ...