The median is a way of measuring the center of a set of data that is robust to outlying values. However, the concept of a median for three-dimensional rotation data has been largely nonexistent. Although there are already ways to measure the center of three-dimensional rotation data using the idea of a “mean rotation”, the median estimator developed here is shown to be less influenced by outlying data points. A simulation study that investigates scenarios under which the median is an improvement over the mean will be discussed. An application to a three-dimensional data set in the area of human motion will be considered.

In this paper, we study numerically the existence and stability of the steady state solutions of the reaction-diffusion equation, $u_t-a{u}_{xx}-u+u^3=0$, and the Klein–Gordon equation, $u_{tt}+c{u}_t-a{u}_{xx}-u+u^3=0$, with the boundary conditions: $u\left(-1\right)=u\left(1\right)=0$. We show that as $a$ varies, the number of steady state solutions and their stability change.

We consider a family of simple graphs known as PS ear-decomposable graphs. These graphs are one-dimensional specializations of the more general class of PS ear-decomposable simplicial complexes, which were by Chari as a means of understanding matroid simplicial complexes. We outline a shifting algorithm for PS ear-decomposable graphs that allows us to explicitly show that the $h$-vector of a PS ear-decomposable graph is a pure $\mathcal{O}$-sequence.

This work deals with estimation of parameters of a zero-inflated Poisson (ZIP) distribution as well as using it to model some natural calamities’ data. First, we compare the maximum likelihood estimators (MLEs) and the method of moments estimators (MMEs) in terms of standardized bias (SBias) and standardized mean squared error (SMSE). We then proceed to show how datasets from some recent natural disasters can be modeled by the ZIP distribution.

Let $R$ be a unital ring and let $X\in M_n\left(R\right)$ be any upper triangular matrix of trace zero. Then there exist matrices $A$ and $B$ in $M_n\left(R\right)$ such that $X=\left[A,B\right]$.

Our main result is the proof of the recently conjectured nonexistence of cubic Legendre multiplier sequences. We also give an alternative proof of the nonexistence of linear Legendre multiplier sequences using a method that will allow for a more methodical treatment of sequences interpolated by higher degree polynomials.

We exhibit a combinatorial model based on seating rearrangements, motivated by some problems proposed in the 1990s by Kennedy, Cooper, and Honsberger. We provide a simpler interpretation of their results on rectangular grids, and then generalize the model to arbitrary graphs. This generalization allows us to pose a variety of well-motivated counting problems on other frequently studied families of graphs.

In this paper we will fully characterize all types of winning moves in the “take-away” game of Fibonacci Nim. We prove the known winning algorithm as a corollary of the general winning algorithm and then show that no other winning algorithms exist. As a by-product of our investigation of the game, we will develop useful properties of Fibonacci numbers. We conclude with an exploration of the probability that unskilled player may beat a skilled player and show that as the number of tokens increase, this probability goes to zero exponentially.