Mobility of water molecules in Li+, Na+ and Cs+ ionic forms of Nafion membrane studied by NMR

Correlation times and diffusion coefficients of water molecules were measured for the first time by ¹H spin relaxation and pulsed field gradient NMR in Li⁺, Na⁺ and Cs⁺ ionic forms of Nafion 117 membrane. Hydration numbers of Li⁺, Na⁺ and Cs⁺ cations were calculated. It was shown that at high humidity macroscopic transfer is controlled by the local translational motion of water molecules.     

Catalytic Nitrene Transfer by an FeIV-Imido Complex Generated by a Comproportionation Process

Nitrene transfer reactions have emerged as one of the most powerful and versatile ways to insert an amine function to various kinds of hydrocarbon substrates. However, the mechanisms of nitrene generation have not been studied in depth albeit their formation is taken for granted in most cases without definitive evidence of their occurrence. In the present work, we compare the generation of tosylimido iron species and NTs transfer from Fe^II and Fe^III precursors where the metal is embedded in a tetracarbene macrocycle. Catalytic nitrene transfer to reference substrates (thioanisole, styrene, ethylbenzene and cyclohexane) revealed that the same active species was at play, irrespective of the ferrous versus ferric nature of the precursor. Through combination of spectroscopic (UV-visible, Mössbauer), ESI-MS and DFT studies, an Fe^IV tosylimido species was identified as the catalytically active species and was characterized spectroscopically and computationally. Whereas its formation from the Fe^II precursor was expected by a two-electron oxidative addition, its formation from an Fe^III precursor was unprecedented. Thanks to a combination of spectroscopic (UV-visible, EPR, Hyscore and Mössbauer), ESI-MS and DFT studies, we found that, when starting from the Fe^III precursor, an Fe^III tosyliodinane adduct was formed and decomposed into an Fe^V tosylimido species which generated the catalytically active Fe^IV tosylimide through a comproportionation process with the Fe^III precursor.     

Synthesis and optical properties of new chalcones containing 4-[bis(2-hydroxyethyl)amino]phenyl fragment

New chalcones with 4-[bis(2-hydroxyethyl)amino] phenyl fragment were obtained from 4-[bis(2-acetoxyethyl) amino]- benzaldehyde by the Claisen–Schmidt reaction. From their UV-VIS absorption and emission spectra, optical band gap values were calculated based on the Stokes shifts as well as the molar absorption coefficients and fluorescence quantum yields were estimated. The dependence of the absorption and emission maxima on solvent polarity and pH was evaluated.     

Global existence and time decay of the non-cutoff Boltzmann equation with hard potential

This paper is concerned with the Cauchy problem on the Boltzmann equation without angular cutoff assumption for hard potential in the whole space. When the initial data is a small perturbation of a global Maxwellian, the global existence of solution to this problem is proved in unweighted Sobolev spaces $H^N\left({\mathbb{R}}_{x,v}^6\right)$ with $N\ge 2$. But if we want to obtain the optimal temporal decay estimates, we need to add the velocity weight function, in this case the global existence and the optimal temporal decay estimate of the Boltzmann equation are all established. Meanwhile, we further gain a more accurate energy estimate, which can guarantee the validity of the assumption in Chen et al. (0000).     

Hyperparameter on-line learning of stochastic resonance based threshold networks

Aiming at training the feed-forward threshold neural network consisting of nondifferentiable activation functions, the approach of noise injection forms a stochastic resonance based threshold network that can be optimized by various gradient-based optimizers. The introduction of injected noise extends the noise level into the parameter space of the designed threshold network, but leads to a highly non-convex optimization landscape of the loss function. Thus, the hyperparameter on-line learning procedure with respective to network weights and noise levels becomes of challenge. It is shown that the Adam optimizer, as an adaptive variant of stochastic gradient descent, manifests its superior learning ability in training the stochastic resonance based threshold network effectively. Experimental results demonstrate the significant improvement of performance of the designed threshold network trained by the Adam optimizer for function approximation and image classification.     

On pointwise decay rates of time‐periodic solutions to the Navier–Stokes equation

We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution $\{u,p\}$ of the Navier–Stokes equation such that $|{?}^j{u(t,x)|=O(|x|}^{1?n?j})$ and $|{?}^j{p(t,x)|=O(|x|}^{?n?j})(j=0,1,\dots )$ uniformly in $t\in \mathbb{R}$ as $|x|\to \infty$. Our solution decays faster than the time‐periodic Stokes fundamental solution and the faster decay of its spatial derivatives of higher order is also described.     

Differentiable spaces that are subcartesian

We show that the differential structure of the orbit space of a proper action of a Lie group on a smooth manifold is weakly reflexive. This implies that the orbit space is a differentiable space in the sense of Smith, which ensures that the orbit space has an exterior algebra of differential forms, that satisfies Smith’s version of de Rham’s theorem. Because the orbit space is a locally closed subcartesian space, it has vector fields and their flows.     

Regularity of optimal sets for some functional involving eigenvalues of an operator in divergence form

In this paper we consider minimizers of the functional$\min \{{\lambda }_1(\mathrm{\Omega })+\cdots +{\lambda }_k(\mathrm{\Omega })+\mathrm{\Lambda }|\mathrm{\Omega }|,:\mathrm{\Omega }\subset D\text{ open}\}$ where $D\subset {\mathbb{R}}^d$ is a bounded open set and where $0<{\lambda }_1(\mathrm{\Omega })\le \cdots \le {\lambda }_k(\mathrm{\Omega })$ are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets ${\mathrm{\Omega }}^{⁎}$ have finite perimeter and that their free boundary $\partial {\mathrm{\Omega }}^{⁎}\cap D$ is composed of a regular part, which is locally the graph of a $C^{1,\alpha }$-regular function, and a singular part, which is empty if $d<d^{⁎}$, discrete if $d=d^{⁎}$ and of Hausdorff dimension at most $d-d^{⁎}$ if $d>d^{⁎}$, for some $d^{⁎}\in \{5,6,7\}$.