Large collections of curves pairwise intersecting exactly once

Let \(\Omega =(\omega _{j})_{j\in I}\) be a maximum size collection of pairwise non-isotopic simple closed curves on the closed, orientable, genus \(g\) surface \(S_{g}\) , such that \(\omega _{i}\) and \(\omega _{j}\) intersect exactly once for \(i\ne j\) . We show that for \(g\ge 3\) , there exists atleast two such collections up to the action of the mapping class group, answering a question posed by Malestein, Rivin and Theran. As a consequence, we show that the automorphism group of the systole graph for \(S_{g}, g\ge 3\) (whose vertices are isotopy classes of simple closed curves, and whose edges correspond to pairs of curve intersecting once) does not act transitively on maximal complete subgraphs.     

Surface plasmons reveal spin crossover in nanometric layers

Nano-objects and thin films displaying molecular spin-crossover phenomena have recently attracted much attention. However, the investigation of spin crossover at reduced sizes is still a big challenge. Here we demonstrate that surface plasmon polariton waves propagating along the interface between a metal and a dielectric layer can be used to detect the spin-state changes in the latter with high sensitivity, even at the nanometer scale.     

Mechanically Driven Activation of Polyaniline into Its Conductive Form

Mechanical treatment of polymers produces surface cations and anions which, as demonstrated here for the first time, can drive chemical reactions. In particular, it is shown that such a mechanical treatment transforms nonconductive polyaniline into its conductive form. These results provide a mechanical means of patterning conductive polymers and also coating small polymer objects with conductive polyaniline films preventing accumulation of static electricity.     

A new steroid from the Red Sea soft coral Lobophytum lobophytum

Chemical investigation of the soft coral Lobophytum lobophytum collected from the Red Sea led to the isolation of a new compound gorgostan-5,25-dien-3β-ol (1), and two known compounds gorgosterol (2), and alismol (3). Structures were elucidated by employing extensive NMR and HR-ESI-MS experiments.     

Gradient Estimates for Solutions of Ultraparabolic Equations

We establish a priori estimates for solutions to ultraparabolic equations which play a crucial role in the solvability of the initial value problem. A class of these equations came from population dynamics, namely from a fish larvae model.      

Synthesis conditions of europium tetrakis dibenzoylmethide triethylammonium crystals

Europium tetrakis dibenzoylmethide triethylammonium crystals are highly triboluminescent, indicating possible use in structural health monitoring. This work investigates the effect of synthesis conditions on crystalline yield and morphology of this material. Less solvent yields more material, but may cause striations in crystal faces. No statistical effect on triboluminescent yield was recorded. Scanning electron microscopy shows crystal size varies from 30–400 μm based on synthesis conditions.     

What really drives chemical reactions on contact charged surfaces?

Although it is known that contact-electrified polymers can drive chemical reactions, the origin of this phenomenon remains poorly understood. To date, it has been accepted that this effect is due to excess electrons developed on negatively charged surfaces and to the subsequent transfer of these electrons to the reactants in solution. The present study demonstrates that this view is incorrect and, in reality, the reactions are driven by mechanoradicals created during polymer-polymer contact.     

A Tsallis’ statistics based neural network model for novel word learning

We invoke the Tsallis entropy formalism, a nonextensive entropy measure, to include some degree of non-locality in a neural network that is used for simulation of novel word learning in adults. A generalization of the gradient descent dynamics, realized via nonextensive cost functions, is used as a learning rule in a simple perceptron. The model is first investigated for general properties, and then tested against the empirical data, gathered from simple memorization experiments involving two populations of linguistically different subjects. Numerical solutions of the model equations corresponded to the measured performance states of human learners. In particular, we found that the memorization tasks were executed with rather small but population-specific amounts of nonextensivity, quantified by the entropic index q. Our findings raise the possibility of using entropic nonextensivity as a means of characterizing the degree of complexity of learning in both natural and artificial systems.