A mathematical model for fungal development in heterogeneous environments

A mathematical model for the development of fungal mycelia in heterogeneous environmental conditions is presented. The validity of this model is tested by comparison of numerical simulations with experimental observations.     

On condensations of -spaces onto compacta

A condensation is a one-to-one onto mapping. It is established that, for each -compact metrizable space , the space of real-valued continuous functions on in the topology of pointwise convergence condenses onto a metrizable compactum. Note that not every Tychonoff space condenses onto a compactum.

     

The development of a cellular automaton-finite volume model for dendritic growth

A cellular automaton to track the solid–liquid interface movement is linked to finite volume computations of solute diffusion to simulate the behavior of dendritic structures in binary alloys during solidification. A significant problem encountered in the CA formulation has been the presence of artificial anisotropy in growth kinetics introduced by a Cartesian CA grid. A new technique to track the interface movement is proposed to model dendritic growth in different crystallographic orientations while reducing the anisotropy due to grid orientation. The model stability with respect to the numerical parameters (cell size and time step) for various operating conditions is examined. A method for generating an operating window in Δt and Δx has been identified, in which the model gives a grid-independent set of results for calculated dendrite tip radius and tip undercooling. Finally, the model is compared to published experimental and analytical results for both directional and equiaxed growth conditions.     

Co-constructive development of a green chemistry-based model for the assessment of nanoparticles synthesis

Nanomaterials (materials at the nanoscale, ${10}^{?9}$ meters) are extensively used in several industry sectors due to the improved properties they empower commercial products with. There is a pressing need to produce these materials more sustainably. This paper proposes a Multiple Criteria Decision Aiding (MCDA) approach to assess the implementation of green chemistry principles as applied to the protocols for nanoparticles synthesis. In the presence of multiple green and environmentally oriented criteria, decision aiding is performed with a synergy of ordinal regression methods; preference information in the form of desired assignment for a subset of reference protocols is accepted. The classification models, indirectly derived from such information, are composed of an additive value function and a vector of thresholds separating the pre-defined and ordered classes. The method delivers a single representative model that is used to assess the relative importance of the criteria, identify the possible gains with improvement of the protocol’s evaluations and classify the non-reference protocols. Such precise recommendation is validated against the outcomes of robustness analysis exploiting the sets of all classification models compatible with all maximal subsets of consistent assignment examples. The introduced approach is used with real-world data concerning silver nanoparticles. It is proven to effectively resolve inconsistency in the assignment examples, tolerate ordinal and cardinal measurement scales, differentiate between inter- and intra-criteria attractiveness and deliver easily interpretable scores and class assignments. This work thoroughly discusses the learning insights that MCDA provided during the co-constructive development of the classification model.     

Peer‐coaching as a component of a professional development model for biology teachers

To increase the likelihood for continuous growth and improvement, professional development for high school biology teachers should include long‐term, targeted instruction with an accompanying peer‐coaching component. This study examined the views of biology teachers who were engaged in a two‐year professional development program, which included a strong peer‐coaching component. With an overall goal of enhancing the teachers’ instructional practices, the peer‐coaches and teachers collaborated to increase the amount of inquiry in the science classroom. Data were collected using focus groups and researcher notes. Emergent themes included the significance of relationships, importance of teacher commitment, and resulting change and growth in educators.     

Further development of the mathematical model of a snakeboard

This paper gives the further development for the mathematical model of a derivative of a skateboard known as the snakeboard. As against to the model, proposed by Lewis et al. [1] and investigated by various methods in [1–13], our model takes into account an opportunity that platforms of a snakeboard can rotate independently from each other. This assumption has been made earlier only by Golubev [13]. Equations of motion of the model are derived in the Gibbs-Appell form. Analytical and numerical investigations of these equations are fulfilled assuming harmonic excitations of the rotor and platforms angles. The basic snakeboard gaits are analyzed and shown to result from certain resonances in the rotor and platforms angle frequencies. All the obtained theoretical results are confirmed by numerical experiments.      

A MIP flow model for crop-rotation planning in a context of forest sustainable development

We propose a Mixed-Integer Linear Programming model for a class of multi-period crop rotation optimization problems with demand constraints and incompatibility constraints between cultivation and fallow state on a land plot. This model is applied to a case study on Madagascan farms in the scope of a sustainable development campain against deforestation, where the objective is to better control agricultural space while covering seasonal needs of farmer. We propose an efficient upper bound computation and study the variation of the minimum number of plots and total space needed in function of the unitary surface area of a plot. Numerical results associated with the Madagascan case are reported.     

Linguistic fuzzy consensus model for collaborative development of fuzzy cognitive maps: a case study in software development risks

Fuzzy cognitive maps (FCMs) have been widely used in several domains for information processing, such as, data fusion, decision making. Although several methods to automatically learn FCMs are recognized from the scientific literature, the most used approach to build an FCM relies on a collaborative task involving single person or, more suitably, group of experts. Collaborative development increases reliability and robustness of the resulting FCM, but rises some problems in terms of group decision making to aggregate different perspectives of the problem representation. This paper proposes to support collaborative development of FCMs introducing knowledge engineering process that relies on Linguistic Fuzzy Consensus Model. In the proposed approach, each expert builds the own version of the FCM. When all different versions are available, a Group Decision Making process is activated in order to reach the consensus on conflictual modeling opinions. The result is a unique final version of the FCM that is not a simple aggregation of the versions provided by the experts but is the result of a well-suited mathematical model. In addition, this work adopts consensus model with incomplete preference relations scheme to address knowledge harmonization issues. Finally, advantages and the limitations of the proposed framework are argued.     

A field scale model for the spread of fungal diseases in crops: the example of a powdery mildew epidemic over a large vineyard

The aim of this article is to derive an asymptotic two‐scale model for the propagation of a fungal disease over a large vineyard. The original model is based on a singularly perturbed system of two linear reaction‐diffusion equations coupled with a set of nonlinear ordinary differential equations in a highly heterogeneous medium. We prove the well‐posedness of the asymptotic model and obtain a convergence result confirmed by numerical simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

函数在一点处的限教学设计

本文探究了函数在一点处极限的教学设计.从实际案例出发,抽象出函数在一点处极限的数学表达形式.从数形结合角度,解释本节课的难点,即ε和δ的关系.通过给出函数在一点处极限的定义,探索和思考用定义进行计算的关键问题.最后,结合课程思政,将课程落脚到育人.     

Analysis of dynamical model for resource-based industry sustainable development

This paper aims at the sustainable development of resource-based industry. First, one-dimensional discrete dynamic model is formulated by considering exploitation and protection of renewable resource simultaneously, and then it is extended to two-dimensional dynamic model by assuming that government carries on the dynamic management to the exploitation speed of resource. The conditions of the existence and local stability of positive equilibrium are derived. The threshold of output is given which ensures the resource is stabilized at a fixed value. The global analysis of both models is represented by determining the feasible domain of attractor. The stability of positive fixed point at flip bifurcation and Neimark-Sacker bifurcation is respectively investigated with center manifold theorem and normal form. We also verify the given conclusions by the method of numerical analysis. In the end, we argued that if the government implements the dynamic quota management for resource exploitation, not only can we maintain a certain stock of resources so that people can get more resources permanently but also we can ensure a higher and wider output to meet the development of the industry.     

Some Geometric Inequalities for a Tangent Point Simplex

The tangent point simplex of a simplex is the pedal simplex of the incenter of . In this paper we obtain some geometric inequalities between and .     

Regularity Near a Contact Point for Flame Propagation

In this paper we study a free boundary problem, arising from a model for the propagation of laminar flames. Consider a cylindrical region S in ? ⁿ , and the following free boundary problem with Dirichlet data on ? S: u _t  = Δ u in {u > 0} ∩ S, |? u|=1 on ? {u > 0} ∩ S and u = 0 on ? S. We show that if there is a contact point of the free boundary {u = 0, |? u|=1} with ? S, then the free boundary approaches ? S tangentially and it turns out to be a graph of C ^{1+α, α} function near the contact point. In particular, the space normal is Hölder continuous.     

Inequalities for a Simplex and an Interior Point

We establish some inequalities for the inradius, circumradius and distances between an interior point and facets of an n-simplex, and prove a recursion inequality for the radii of the circumscribed spheres of an n-simplex and its facets.     

Experiences during development of a dynamic crash response automobile model

A finite element automobile model for use in crash safety studies was developed through reverse engineering. The model was designed for calculating the response of the automobile structure during full frontal, offset frontal, or side impacts. The reverse engineering process involves the digitization of component surfaces as the vehicle is dismantled, the meshing and reassembly of these components into a complete finite element model, and the measurement of stiffness properties for structural materials. Quasi-static component tests and full-vehicle crash tests were used to validate the model, which will become part of a finite element vehicle fleet.     

Eigenfunction Statistics for a Point Scatterer on a Three-Dimensional Torus

In this paper, we study eigenfunction statistics for a point scatterer (the Laplacian perturbed by a delta-potential) on a three-dimensional flat torus. The eigenfunctions of this operator are the eigenfunctions of the Laplacian which vanish at the scatterer, together with a set of new eigenfunctions (perturbed eigenfunctions). We first show that for a point scatterer on the standard torus all of the perturbed eigenfunctions are uniformly distributed in configuration space. Then we investigate the same problem for a point scatterer on a flat torus with some irrationality conditions, and show uniform distribution in configuration space for almost all of the perturbed eigenfunctions.