作者：Ksenia Frolova , Polina Grigoreva , Konstantin Lezhnev ... 来源：[J].Mathematics and Mechanics of Complex Systems, 2019, Vol.7 (2), pp.175-187MSP 摘要：\advance\leftskip5pt\advance\rightskip5ptProppant flowback control is one of the main issues in hydraulic fracturemodeling since the propping agent maintains the crack in an open stateand therefore provides oil inflow to the wellbore. The main objective ofthis paper is to determi...
 作者：Mikhail Guzev , Gurami Tsitsiashvili , Marina Osipova 来源：[J].Mathematics and Mechanics of Complex Systems, 2019, Vol.7 (2), pp.189-201MSP 摘要：The problem of object detection by autonomous apparatus is considered. Theprobabilistic formulation of the problem is proposed by means of a reductionto the classical Buffon problem. The latter naturally arises when theproblem is formulated in the coordinate system associated wit...
 作者：Brandon Bate , Kyle Craft , Jonathon Yuly 来源：[J].Involve, a Journal of Mathematics, 2019, Vol.12 (6), pp.969-994MSP 摘要：In her Ph.D.\ thesis, Jacqueline Anderson identified a nonarchimedean setsimilar in spirit to the Mandelbrot set which appears toexhibit a fractal-like boundary.We continue this research by presenting algorithms for determining whenrational points lie in this set.We then prove th...
 作者：Connor Olson , Marshall Mueller , Sigurd B. Angenent 来源：[J].Involve, a Journal of Mathematics, 2019, Vol.12 (6), pp.1015-1034MSP 摘要：\advance\leftskip2pt\advance\rightskip2ptWe give an existence proof for distribution solutions to a scalar reactiondiffusion equation, with the aim of illustrating both the differencesand thecommon ingredients of the nonstandard and standard approaches.In particular,our proof sho...
 作者：Bjarni Jens Kristinsson , Henning Ulfarsson 来源：[J].Involve, a Journal of Mathematics, 2019, Vol.12 (6), pp.901-918MSP 摘要：We define the occurrence graph $G_{\mkern-2mu p}(\pi)$ of a pattern $p$ in apermutation $\pi$ as the graph whose vertices are the occurrences of $p$ in $\pi$,with edges between thevertices if the occurrences differ by exactlyone element. We then study properties of these graphs. ...
 作者：Suzanne Craig , Naiche Downey , Lucas Goad ... 来源：[J].Involve, a Journal of Mathematics, 2019, Vol.12 (6), pp.941-959MSP 摘要：\advance\leftskip-1pt\advance\rightskip-1ptWe show that nonisomorphic effective linear circleactions yield nondiffeomorphicdifferential structures on the correspondingorbit spaces.
 作者：Alan Veliz-Cuba , Lauren Geiser 来源：[J].Involve, a Journal of Mathematics, 2019, Vol.12 (6), pp.1051-1068MSP 摘要：AND-OR networks are Boolean networks where each coordinate function iseither the AND or OR logical operator. We study the number of fixed pointsof these Boolean networks in the case that they have a wiring diagram withchain topology. We find closed formulas for subclasses of thes...
 作者：Yixuan Huang , Michael Tait , Robert Won 来源：[J].Involve, a Journal of Mathematics, 2019, Vol.12 (6), pp.995-1003MSP 摘要：For each natural number $d$, we introduce the concept of a $d$-cap in$\mathbb{F}_3^n$. A set of points in $\mathbb{F}_3^n$ is called a $d$-cap if,for each $k = 1, 2, \dots, d$, no $k+2$ of the points lie on a $k$-dimensionalflat. This generalizes the notion of a cap in $\mathbb{F...  作者：Ethan Gwaltney , Paul Hagelstein , Daniel Herden ... 来源：[J].Involve, a Journal of Mathematics, 2019, Vol.12 (6), pp.961-968MSP 摘要：In 1935, Besicovitch proved a remarkable theorem indicating that anintegrable function$f$on$\mathbb{R}^2$is strongly differentiable ifand only if its associated strong maximal function$M_S f$is finite a.e.We consider analogues of Besicovitch's result in the context of ergod...  作者：Ryan Coopergard , Marju Purin 来源：[J].Involve, a Journal of Mathematics, 2019, Vol.12 (6), pp.919-940MSP 摘要：We investigate a class of truncated path algebras in which the Betti numbersof a simple module satisfy a polynomial of arbitrarily large degree.We produce truncated path algebras where the$i$-th Betti number of asimple module$S$is$\beta_i(S)=i^k$for$2\leq k\leq 4\$ and provi...