Self‐Healing Polymers via Supramolecular Forces

As polymers and polymeric materials are “the” smart invention and technological driving force of the 20th century, the quest for self‐healing or self‐repairing polymers is strong. The concept of supramolecular self‐healing materials relies on the use of noncovalent, transient bonds to generate networks, which are able to heal the damaged site, putting aspects of reversibility and dynamics of a network as crucial factors for the understanding and design of such self‐healing materials. This Review describes recent examples and concepts of supramolecular polymers based on hydrogen bonding, π–π interactions, ionomers, and coordinative bonds, thus convincingly discussing the advantages and versatility of these supramolecular forces for the design and realization of self‐healing polymers.     

Density functional study on formation of A and B rings in conversion of 2,3-oxidosqualene to lanosterol

A density functional computational study has been performed on a model system for the formation of the A and B rings in the oxidosqulene cyclase pathway for the cyclization of squalene to lanosterol. Unlike what had previously been found for the squalene hopene cyclase pathway, the formation of the A and B rings was found not to be concerted. Two intermediates were located on the reaction pathway during the formation of the B ring, though they were found to be very shallow minima on a quite flat part of the potential surface. It is unlikely that in the enzymatic pathway these intermediates would play an important role, if indeed they exist at all.     

Ensemble Steering, Weak Self-Duality, and the Structure of Probabilistic Theories

In any probabilistic theory, we say that a bipartite state ω on a composite system AB steers its marginal state ω ^B if, for any decomposition of ω ^B as a mixture ω ^B =∑ _i p _i β _i of states β _i on B, there exists an observable {a _i } on A such that the conditional states $\omega_{B|a_{i}}$ are exactly the states β _i . This is always so for pure bipartite states in quantum mechanics, a fact first observed by Schrödinger in 1935. Here, we show that, for weakly self-dual state spaces (those isomorphic, but perhaps not canonically isomorphic, to their dual spaces), the assumption that every state of a system A is steered by some bipartite state of a composite AA consisting of two copies of A, amounts to the homogeneity of the state cone. If the state space is actually self-dual, and not just weakly so, this implies (via the Koecher-Vinberg Theorem) that it is the self-adjoint part of a formally real Jordan algebra, and hence, quite close to being quantum mechanical.     

Torsion-free,Divisible, and Mittag-Leffler Modules

We study (relative) 𝒦-Mittag–Leffler modules, with emphasis on the class 𝒦 of absolutely pure modules. A final goal is to describe the 𝒦-Mittag–Leffler abelian groups as those that are, modulo their torsion part, ?₁-free. Several more general results of independent interest are derived on the way. In particular, every flat 𝒦-Mittag–Leffler module (for 𝒦 as before) is Mittag–Leffler. A question about the definable subcategories generated by the divisible modules and the torsion-free modules, resp., has been left open.     

Coarse-Grid-CFD for a Wire Wrapped Fuel Assembly

Computational fluid dynamics (CFD) simulations of complete nuclear reactor core geometries requires exceedingly large computational resources. However, in most cases there are repetitive geometry- and flow patterns allowing the general approach of creating a parameterized model for one segment and composing many of these reduced models to obtain the entire reactor simulation. Traditionally, this approach lead to so-called subchannel analysis codes that are relying heavily on transport models based on experimental and empirical correlations. With our method, the Coarse-Grid-CFD (CGCFD), we intend to replace the experimental or empirical input with CFD data. Our method is based on detailed and well-resolved CFD simulations of representative segments. From these simulations we extract and tabulate volumetric source terms. Parameterized data is used to close an otherwise strongly under resolved, coarsely meshed model of a complete reactor setup. In the previous formulation only forces created internally in the fluid are accounted for. The Anisotropic Porosity (AP) formulation wich is subject of the present investigation adresses other influences, like obstruction and flow guidance through spacers and in particular geometric details which are under resolved or ignored by the coarse mesh. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

‘Negative of my money,positive of her money’: secondary students’ ways of relating equations to a debt context

We interviewed 40 students each in grades 7 and 11 to investigate their integer-related reasoning. In one task, the students were asked to write and interpret equations related to a story problem about borrowing money from a friend. All the students solved the story problem correctly. However, they reasoned about the problem in different ways. Many students represented the situation numerically without invoking negative numbers, whereas others wrote equations involving negative numbers. When asked to interpret equations involving negative numbers in relation to the story, students did so in two ways. Their responses reflect distinct perspectives concerning the relationship between arithmetic equations and borrowing/owing. We discuss these findings and their implications regarding the role of contexts in integer instruction.     

Automata on ordinals and automaticity of linear orders

We investigate structures recognizable by finite state automata with an input tape of length a limit ordinal. At limits, the set of states which appear unboundedly often before the limit are mapped to a limit state. We describe a method for proving non-automaticity and apply this to determine the optimal bounds for the ranks of linear orders recognized by such automata.     

Measuring the Stability of Results From Supervised Statistical Learning

Stability is a major requirement to draw reliable conclusions when interpreting results from supervised statistical learning. In this article, we present a general framework for assessing and comparing the stability of results, which can be used in real-world statistical learning applications as well as in simulation and benchmark studies. We use the framework to show that stability is a property of both the algorithm and the data-generating process. In particular, we demonstrate that unstable algorithms (such as recursive partitioning) can produce stable results when the functional form of the relationship between the predictors and the response matches the algorithm. Typical uses of the framework in practical data analysis would be to compare the stability of results generated by different candidate algorithms for a dataset at hand or to assess the stability of algorithms in a benchmark study. Code to perform the stability analyses is provided in the form of an R package. Supplementary material for this article is available online.