Search

Recently, metapopulation models for rock-paper-scissors games have been presented. Each subpopulation is represented by a node on a graph. An individual is either rock (R), scissors (S) or paper (P); it randomly migrates among subpopulations. In the present paper, we assume victory rates differ in different subpopulations. To investigate the dynamic state of each subpopulation (node), we numerically obtain the solutions of reaction-diffusion equations on the graphs with two and three nodes. In the case of homogeneous victory rates, we find each subpopulation has a periodic solution with neutral stability. However, when victory rates between subpopulations are heterogeneous, the solution approaches stable focuses. The heterogeneity of victory rates promotes the coexistence of species.

Migration paths of animals are rarely the same. The paths may change according to seasonal and circadian rhythms. We study the effect of temporal migration on population dynamics of rock-paper-scissors (RPS) games with mutation by using the metapopulation dynamic model with two patches. Via mutation, an individual R changes to S with rate μ. All agents move by random walk between two patches and the RPS game is performed in each patch. The migration path between two patches is switched on or off periodically. The dynamics are represented by the reaction-diffusion equations with time-dependent diffusion coefficients in diffusively coupled reactors. We obtain the solutions of time-dependent reaction-diffusion equations numerically and analytically. The time-varying migration path induces complex behavior for the RPS dynamics, depending on the frequency of the periodical path. We find that the phase transitions occur by varying mutation rate μ. The phase transition depends highly on the frequency.

In a recent paper referred to in the title, the author used the concept of quasi self-adjointness to obtain conservation laws for a system of the ( 2 + 1 ) -dimensional Bogoyavlensky–Konopelchenko equation. Apart from the adjoint system of equations, all the results on the quasi self-adjointness and the subsequent conservation laws obtained are inaccurate. In this comment, we clarify these inaccuracies and also generate conservation laws for a potential form of the underlying equation through Noether theorem.

In this corrigendum we correct an error in our paper [T. Caraballo, R. Colucci, J. Lopez-de-la-Cruz and A. Rapaport. A way to model stochastic perturbations in population dynamics models with bounded realizations, Commun Nonlinear Sci Numer Simulat, 77(2019) 239–257]. We present a correct way to model real noisy perturbations by considering a slightly different stochastic process based, as in the original paper, on the Ornstein-Uhlenbeck process. Namely, we correct the formulae that generates the noisy realizations to ensure the boundedness property to be satisfied with probability one (which turns out not to be true in our original paper even though it was observed in all the simulations).

We propose a new concept which is a generalization of fuzzy soft subset and fuzzy soft equal. Using such notions, we will be able to consider the distributive law of fuzzy soft sets. Using the distributive law of fuzzy soft sets, we point out that the distributive law of trapezoidal fuzzy soft sets as proposed by Xiao et al. (2012) is not true. The correction will further improve further extensions of the results of Xiao et al. (2012). We will also establish the generalized distributive law of trapezoidal fuzzy soft sets along with illustrative examples.

Corrugated paper is produced by gluing three types of papers of the same breadth. Given a set of orders, we first assign each order to one of the standard breadths, and then sequence those assigned to each standard breadth so that they are continuously manufactured from the three rolls of the specified standard breadth equipped in the machine called corrugator. Here we are asked to achieve multi-goals of minimizing total length of roll papers, total loss of papers caused by the differences between standard breadths and real breadths of the orders, and the number of machine stops needed during production. We use integer programming to assign orders to standard breadths, and then develop a special purpose algorithm to sequence the orders assigned to each standard breadth. This is a first attempt to handle scheduling problems of the corrugator machine.

A controllability analysis of a paper machine forming zone in a newsprint mill was performed to determine the maximum allowable variability of the pulp furnished to the process. The goal was to keep the output variables, basis weight and first-pass retention between certain limits in spite of disturbances and paper grade changes. The results indicate that the process is more disturbed at high frequencies, and that the two output variables may be maintained within the interval ±1% of their nominal values if the maximum variability in the consistency and fines content of the thick-stock is kept lower than ±1 and ±2%, respectively.

Rock-paper-scissors games metaphorically model cyclic dominance in ecology and microbiology. In a static environment, these models are characterized by fixation probabilities obeying two different "laws" in large and small well-mixed populations. Here, we investigate the evolution of these three-species models subject to a randomly switching carrying capacity modeling the endless change between states of resources scarcity and abundance. Focusing mainly on the zero-sum rock-paper-scissors game, equivalent to the cyclic Lotka-Volterra model, we study how the ${\it coupling}$ of demographic and environmental noise influences the fixation properties. More specifically, we investigate which species is the most likely to prevail in a population of fluctuating size and how the outcome depends on the environmental variability. We show that demographic noise coupled with environmental randomness "levels the field" of cyclic competition by balancing the effect of selection. In particular, we show that fast switching effectively reduces the selection intensity proportionally to the variance of the carrying capacity. We determine the conditions under which new fixation scenarios arise, where the most likely species to prevail changes with the rate of switching and the variance of the carrying capacity. Random switching has a limited effect on the mean fixation time that scales linearly with the average population size. Hence, environmental randomness makes the cyclic competition more egalitarian, but does not prolong the species coexistence. We also show how the fixation probabilities of close-to-zero-sum rock-paper-scissors games can be obtained from those of the zero-sum model by rescaling the selection intensity., 31 pages, 15 figures: Main text (18 pages, 9 figures) followed by Supplementary Material (13 pages, 6 figures). Supplementary Information and resources available at https://doi.org/10.6084/m9.figshare.8858273.v1

We highlight some problems in this paper. They lead to question the model itself.

We analyze the multiauthorship matrix M, defined as the matrix where a cell M (j, @k) denotes the number of times authors with j publications are ranked as the @k^t^h author of an article. We prove that if the distribution of the number of authors per paper follows a power law, then the author rank distribution is approximately equal to this power law (more precisely, equal in Landau's big O sense). We further determine the author rank distribution in the case where authors can be characterized through a seed number; this is the probability of preceding a fixed author in the byline of an article. Such a seed is determined for alphabetical ranking of authors using the standard western alphabet.

This paper presents a new method to calculate the feedback control gain for a class of multivariable bilinear system, and also applied this method on the control of two sections of paper-making process with disturbance. The robust H∞ control problem is to design a state feedback controller such that the robust stability and a prescribed H∞ performance of the resulting closed-loop system are ensured. The controller turns out to be robust with respect to the disturbance in the plant. Utilizing the Schur complement and some variable transformations, the stability conditions of the multivariable bilinear systems are formulated in terms of Lyapunov function via the form of linear matrix inequality (LMI). The gain of controller will be calculated via LMI. Finally, the application examples of a headbox section and a dryer section of paper-making process are used to illustrate the applicability of the proposed method.

The most representative papers of M. V. Keldysh (10.02.1911-24.06.1978) in the field of mechanics and applied mathematics concerned with aircraft construction, shipbuilding and explosion theory are reviewed. Formulations of problems with their substantiation, the methods of solving them, which he used, and the main results obtained are given.

We introduce an algorithm for approximating a 2-manifold 3D mesh by a set of developable surfaces. Each developable surface is a generalized cylinder represented as a strip of triangles not necessarily taken from the original mesh. Our algorithm is automatic, creates easy-to-assemble pieces, and provides L"@K global error bounds. The algorithm consists of three stages. In the first stage, the mesh is segmented into meaningful components. The second stage approximates each of the mesh components in 3D by a set of triangle strips with smooth (non-jagged) boundaries that guarantee a maximal user-defined error relative to the original mesh. Finally, these strips are unfolded to the plane, resulting in flat patterns, which may be cut and assembled from paper. The approximation quality is controlled by a user-supplied parameter specifying the allowed Hausdorff distance between the input mesh and its piecewise-developable approximation. The strips generated by our algorithm may be parameterized to conform with the parameterization of the original mesh, if given, to facilitate texture mapping. We demonstrate this by physically assembling paper-craft models from the strips generated by our algorithm when run on several polygonal 3D mesh data sets.

In this paper, a finite element procedure is used to study the dynamic behaviour of a paper web in a free span between two rollers, including effects of transport velocity and surrounding air. The paper web is modelled as a three-dimensional orthotropic structure. The influence of air is accounted for by utilizing fluid-solid interaction analyses based on acoustic theory. The contribution of transport velocity is included through gyroscopic matrices and forces. The structural response on harmonic excitations has been studied using linear and non-linear models. Results show that air significantly reduces eigenfrequencies of the web. So called ''edge-flutter'' is nothing but the result of skew tension profile. Excessive web vibration can be eliminated by adjusting the web tension.

In this note, we point out an error in the recently published article [R.K. Mohanty, M.K. Jain, D. Dhall, A cubic spline approximation and application of TAGE iterative method for the solution of two-point boundary value problems with forcing function in integral form, Appl. Math. Model. 35 (2011) 3036–3047] and then correct it.

In a recent paper (Computer Aided Geometric Design 23 (3), 243-260), Yang presented a novel kind of nonlinear and geometry driven subdivision scheme for curve interpolation. The author declared that this scheme was shape preserving when all free parameters were explicitly selected by some specific rules. In this note, we demonstrate that the author (a) ignored the consistency of the definition to straight edges, and also (b) did not give a perfect scheme and proof for the shape preserving subdivision.

Yang (the second author of this paper) et al. (2009) [3] established the distributive law of interval-valued fuzzy soft sets. In this article, it is pointed that it is not true in general. But, in order to establish the distributive law of interval-valued fuzzy soft sets, more general notions than interval-valued fuzzy soft sets and interval-valued fuzzy soft equal are considered. Using such notions, the generalized distributive law of interval-valued fuzzy soft sets is established.

The paper addresses ranking of factors with a use of the pairwise comparison method in sense of the analytic hierarchy process (AHP). The aim of this study is to show that the logarithmic least squares method used to approximate judgement matrix in order to calculate the ranking of factors does not cause the reduction of weight of a new alternative as the eigenvector method does.

Ahn, Lee, Park and Yoo proved that the best constrained degree reduction of a polynomial f in L"2-norm equals the best weighted Euclidean approximation of the Bernstein-Bezier coefficients of f in a paper, published in the journal, Computer Aided Geometric Design 21 (2) (2004) 181-191. In this note, we point out an error in their paper and give the correct result.

In a recently published article in EJOR, Christofides et al. (CAT) present a depth-first search, branch-and-bound solution procedure for the multiple-resource constrained, single project scheduling problem. While there are many important contributions in this paper, we show by counterexample that if the branching strategy described by the authors is used, the optimal solution might not result. Computational experience on a set of test problems appearing in the open literature is reported both with the original branching strategy suggested by the authors and a modified branching strategy that we propose. The modified strategy guarantees the determination of the optimal solution in all instances of the problem at the expense of an increase in node evaluations and average CPU time. Computational results using the revised procedure and a hybrid, breadth-first search procedure also investigated by CAT are reported.

The problem of finding the inverse of the Eshelby tensor, which relates, in particular, the stresses in a spheroidal rigid inclusion contained in an isotropic elastic space to the stresses at infinity, is considered. Components of the tensor are found in closed form for spheroidal inclusions.

In recent years, many results on oscillation criteria of second-order nonlinear neutral delay differential equations with distributed deviating argument have been obtained, but some of these criteria are incorrect due to a mistake in a crucial auxiliary result. We give two counterexamples.

A nonoscillation criterion for a second-order linear difference equation is established correcting a result in [1].

Asymptotic expressions for deflections of the order of e −1 ( e → 0) are constructed in the thermoelastic problem for a non-uniform plate (e is the characteristic dimension of the periodicity cell). These expressions are then used to obtain the governing equations for the corresponding forces and moments so that the results obtained agreed with the classical results.

In a recent paper, Little et al. point out that certain terms in the eigenvector expansion of a nonsymmetric stochastic matrix are unbounded. This appears to throw doubt on the usual assumption that only terms associated with the largest eigenvalues contribute significantly to high powers of the matrix. In this note we show that although individual terms can be unbounded, their sum is always well behaved, and since this is the relevant quantity, the eigenvalue criterion is still valid. An explicit bound on the sum is obtained for a 3 × 3 case, and for the general N × N case it is shown that the factors causing the unboundedness cancel.

The exact solutions given in [1] are generalized to the case of cylindrical and spherical sectors rotating about the azimuth relative to the coordinate origin either at a uniform rate or with uniform acceleration (or deceleration). The class of equations of motion of the boundaries of the half-space (in the Cartesian coordinates) which lead to exact solutions of the Fourier equation defined in these domains, is enlarged.

Two augmentation block triangular preconditioners were introduced by Shen et?al. (2012) for the regularized saddle point problem. However, the spectral analysis of the preconditioner based on the augmentation of the ( 2 , 2 ) block was not throughly derived there. In this short paper, we give a detailed spectral analysis on this preconditioner. A numerical example is employed to validate the efficiency of the presented theoretical results.

To safeguard analytical tractability and the concavity of objective functions, the vast majority of models belonging to oligopoly theory relies on the restrictive assumption of linear demand functions. Here we lay out the analytical solution of a differential Cournot game with hyperbolic inverse demand, where firms accumulate capacity over time à la Ramsey. The subgame perfect equilibrium is characterized via the Hamilton–Jacobi–Bellman equations solved in closed form both on infinite and on finite horizon setups. To illustrate the applicability of our model and its implications, we analyze the feasibility of horizontal mergers in both static and dynamic settings, and find appropriate conditions for their profitability under both circumstances. Static profitability of a merger implies dynamic profitability of the same merger. It appears that such a demand structure makes mergers more likely to occur than they would on the basis of the standard linear inverse demand.