作者：Samantha Davies , Chenxiao Xue , Carl Yerger 来源：[J].Involve, a Journal of Mathematics, 2017, Vol.10 (5), pp.721-734MSP 摘要：A knight's tour is a sequence of knight's moves such that each squareon theboard is visited exactly once.An Aztec diamond is a square board of size $2n$ where triangularregions of side length $n-1$ have been removed from all four corners.We show that the existence of knight's tou...
 作者：Hala Al-Khalil , Catherine Brennan , Robert Decker ... 来源：[J].Involve, a Journal of Mathematics, 2017, Vol.10 (5), pp.857-879MSP 摘要：This paper presents the steady-state solutions and traveling wavesolutions for a spatially distributed PDE version of the sprucebudworm model. The ODE (undistributed) model has been used inpractical scenarios to model the outbreaks of the spruce budwormin forest environments, alo...
 作者：David Sykes , Jan Rychtář 来源：[J].Involve, a Journal of Mathematics, 2017, Vol.10 (5), pp.735-747MSP 摘要：\vspace*{-5pt}We have created and analyzed a model for kleptoparasitic interactionswhen individuals decide on the level of aggression in which they wantto engage in the contest over a resource item.The more aggressive each individual is relative to an opponent, thehigher are the ...
 作者：Jill Cochran , Terry Henderson , Aaron Ostrander ... 来源：[J].Involve, a Journal of Mathematics, 2017, Vol.10 (5), pp.749-766MSP 摘要：We provide results for the exponential dominating numbers andtotal exponential dominating numbers of a family of triangular grid graphs. Wethen prove inequalities for these numbers and compare them with inequalitiesthat hold more generally for exponential dominating numbers of gr...
 作者：Wanda Boyer , Gary MacGillivray , Laura Morrison ... 来源：[J].Involve, a Journal of Mathematics, 2017, Vol.10 (5), pp.881-892MSP 摘要：For a given integer $k$, general necessary and sufficient conditionsfor the existence of integer solutions to an equation of the form$x^{2}+y^{2}=z^{2}-k$ are given. It is shown that when there is asolution, there are infinitely many solutions. An elementary methodforfinding the ...
 作者：Geoffrey Buhl , Elijah Cronk , Rosa Moreno ... 来源：[J].Involve, a Journal of Mathematics, 2017, Vol.10 (5), pp.781-799MSP 摘要：A matrix completion problem asks whether a partial matrix composed ofspecified and unspecified entries can be completed to satisfy a givenproperty. This work focuses on determining which patterns of specifiedand unspecified entries correspond to partial matrices that can becomple...
 作者：Chenthuran Abeyakaran 来源：[J].Involve, a Journal of Mathematics, 2017, Vol.10 (5), pp.893-900MSP 摘要：In a recent paper, Frechette and Locus examined and found expressionsfor the infinite product $D_m(q):= \prod_{t=1}^{\infty}(1-q^{mt})/(1-q^t)$ in terms of productsof $q$-series of the Rogers--Ramanujan type coming from Hall--Littlewoodpolynomials, when $m\equiv 0,1,2\pmod{4}$. T...
 作者：Yunjiao Wang , Bamidele Omidiran , Franklin Kigwe ... 来源：[J].Involve, a Journal of Mathematics, 2017, Vol.10 (5), pp.813-831MSP 摘要：Boolean (BL) systems and coupled ordinary differential equations(ODEs) are popular models for studying biological networks. BLsystems can be set up without detailed reaction mechanisms and rateconstants and provide qualitatively useful information, but theycannot capture the cont...
 作者：Chassidy Bozeman , Minerva Catral , Brendan Cook ... 来源：[J].Involve, a Journal of Mathematics, 2017, Vol.10 (5), pp.767-779MSP 摘要：Given a graph $G$, the tree cover number of the graph,denoted $T(G)$, is the minimum number of vertex disjoint simpletrees occurring as induced subgraphs that cover all the vertices of G.This graph parameter was introduced in 2011 as a tool for studyingthe maximum positive semide...
 作者：Christopher Grimm , John A. Gemmer 来源：[J].Involve, a Journal of Mathematics, 2017, Vol.10 (5), pp.833-856MSP 摘要：In this paper we study the brachistochrone problem in an inverse-squaregravitational field on the unit disk. We show that the time-optimalsolutions consist of either smooth strong solutions to the Euler--Lagrangeequation or weak solutions formed by appropriately patched together ...