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A model of the proppant flowback: setup of the theoretical framework
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...
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    The object detection by autonomous apparatus as a solution of the Buffon needle problem
    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...
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      Algorithms for classifying points in a 2-adic Mandelbrot set
      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...
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        Nonstandard existence proofs for reaction diffusion equations
        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...
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          Occurrence graphs of patterns in permutations
          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. ...
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            Orbit spaces of linear circle actions
            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.
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              The number of fixed points of AND-OR networks with chain topology
              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...
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                Sidon sets and 2-caps in 𝔽3n
                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...
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                  On a theorem of Besicovitch and a problem in ergodic theory
                  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...
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                    Truncated path algebras and Betti numbers of polynomial growth
                    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...
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