Opportunity to learn problem solving in Dutch primary school mathematics textbooks

In the Netherlands, mathematics textbooks are a decisive influence on the enacted curriculum. About a decade ago, Dutch primary school mathematics textbooks provided hardly any opportunities to learn problem solving. In this study we investigated whether this provision has changed. In order to do so, we carried out a textbook analysis in which we established to what degree current textbooks provide non-routine problem-solving tasks for which students do not immediately have a particular solution strategy at their disposal. We also analyzed to what degree textbooks provide ‘gray-area’ tasks, which are not really non-routine problems, but are also not straightforwardly solvable. In addition, we inventoried other ways in which present textbooks facilitate the opportunity to learn problem solving. Finally, we researched how inclusive these textbooks are with respect to offering opportunities to learn problem solving for students with varying mathematical abilities. The results of our study show that the opportunities that the currently most widely used Dutch textbooks offer to learn problem solving are very limited, and these opportunities are mainly offered in materials meant for more able students. In this regard, Dutch mainstream textbooks have not changed compared to the situation a decade ago. A textbook that is the Dutch edition of a Singapore mathematics textbook stands out in offering the highest number of problem-solving tasks, and in offering these in the materials meant for all students. However, in the ways this textbook facilitates the opportunity to learn problem solving, sometimes a tension occurs concerning the creative character of genuine problem solving.     

Beta Variables as Times Spent in [0, {infty}[ by Certain Perturbed Brownian Motions

The paper shows that the times spent in [0, +) by certain processesY which are defined by perturbations of Brownian motion involvingreflection at maxima and minima are beta distributed. This resultrelies heavily on Ray–Knight theorems for such perturbedBrownian motions.     

Unstable attractors induce perpetual synchronization and desynchronization

Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which unstable attractors arise naturally. From random initial conditions, groups of synchronized oscillators (clusters) are formed that send pulses alternately, resulting in a periodic dynamics of the network. Under the influence of arbitrarily weak noise, this synchronization is followed by a desynchronization of clusters, a phenomenon induced by attractors that are unstable. Perpetual synchronization and desynchronization lead to a switching among attractors. This is explained by the geometrical fact, that these unstable attractors are surrounded by basins of attraction of other attractors, whereas the full measure of their own basin is located remote from the attractor. Unstable attractors do not only exist in these systems, but moreover dominate the dynamics for large networks and a wide range of parameters.     

On realistic terrains

We study worst-case complexities of visibility and distance structures on terrains under realistic assumptions on edge length ratios and the angles of the triangles, and a more general low-density assumption. We show that the visibility map of a point for a realistic terrain with n triangles has complexity . We also prove that the shortest path between two points p and q on a realistic terrain passes through triangles, and that the bisector of p and q has complexity . We use these results to show that the shortest path map for any point on a realistic terrain has complexity , and that the Voronoi diagram for any set of m points on a realistic terrain has complexity and . Our results immediately imply more efficient algorithms for computing the various structures on realistic terrains.     

Lifetime maximization in wireless directional sensor network

This paper addresses two versions of a lifetime maximization problem for target coverage with wireless directional sensor networks. The sensors used in these networks have a maximum sensing range and a limited sensing angle. In the first problem version, predefined sensing directions are assumed to be given, whereas sensing directions can be freely devised in the second problem version. In that case, a polynomial-time algorithm is provided for building sensing directions that allow to maximize the network lifetime. A column generation algorithm is proposed for both problem versions, the subproblem being addressed with a hybrid approach based on a genetic algorithm, and an integer linear programming formulation. Numerical results show that addressing the second problem version allows for significant improvements in terms of network lifetime while the computational effort is comparable for both problem versions.     

Pencils on separating (M-2)-curves

A separating ( \(M-2\) )-curve is a smooth geometrically irreducible real projective curve \(X\) such that \(X(\mathbb{R })\) has \(g-1\) connected components and \(X(\mathbb{C })\setminus X(\mathbb{R })\) is disconnected. Let \(T_g\) be a Teichmüller space of separating ( \(M-2\) )-curves of genus g. We consider two partitions of \(T_g\) , one by means of a concept of special type, the other one by means of the separating gonality. We show that those two partitions are very closely related to each other. As an application, we obtain the existence of real curves having isolated real linear systems \(g^1_{g-1}\) for all \(g\ge 4\) .     

Magnesium‐Catalyzed Hydroboration of Terminal and Internal Alkynes

A magnesium‐catalyzed hydroboration of alkynes providing good yields and selectivities for a wide range of terminal and symmetrical and unsymmetrical internal alkynes has been developed. The compatibility with many functional groups makes this magnesium catalyzed procedure attractive for late stage functionalization. Experimental mechanistic investigations and DFT calculations reveal insights into the reaction mechanism of the magnesium catalyzed protocol.     

A fluidized bed process for electron sterilization of powders

A small capacity (100 g.s⁻¹) pilot system is described for presentation of powders and fine aggregates at high velocity, to an electron beam. Electron beam dose rate is continuously monitored in real time, while the thickness of the fluidized bed used to pneumatically transport the product can be monitored and controlled using beta-gauge techniques. Using electron paramagnetic resonance (EPR) techniques, alanine power mixed with the product is used for precise determination of dose delivered to the powder stream. Thin film dosimeters transported in the bed are also used for dose determination. Results with a variety of products are presented using both dose rate and velocity as the independent variables. Lethality data for the bioburdens present in several powdered foodstuffs are discussed.     

Gadolinium chelate coated gold nanoparticles as contrast agents for both X-ray computed tomography and magnetic resonance imaging

Functionalized gold nanoparticles were applied as contrast agents for both in vivo X-ray and magnetic resonance imaging. These particles were obtained by encapsulating gold cores within a multilayered organic shell which is composed of gadolinium chelates bound to each other through disulfide bonds. The contrast enhancement in MRI stems from the presence of gadolinium ions which are entrapped in the organic shell, whereas the gold core provides a strong X-ray absorption. This study revealed that these particles suited for dual modality imaging freely circulate in the blood vessels without undesirable accumulation in the lungs, spleen, and liver.