On dual molecules and convolution-dominated operators

We show that sampling or interpolation formulas in reproducing kernel Hilbert spaces can be obtained by reproducing kernels whose dual systems form molecules, ensuring that the size profile of a function is fully reflected by the size profile of its sampled values. The main tool is a local holomorphic calculus for convolution-dominated operators, valid for groups with possibly non-polynomial growth. Applied to the matrix coefficients of a group representation, our methods improve on classical results on atomic decompositions and bridge a gap between abstract and concrete methods.     

Sparse dimension reduction based on energy and ball statistics

Advances in Data Analysis and Classification - Two new methods for sparse dimension reduction are introduced, based on martingale difference divergence and ball covariance, respectively. These...     

A combined Mössbauer spectroscopy and x-ray diffraction operando study of Sn-based composite anode materials for Li-ion accumulators

The reaction mechanisms of Li with Sn/BPO₄ composites to be used as negative electrode materials for Li-ion batteries were studied during electrochemical cycling by operando Mössbauer spectroscopy and X-ray diffraction using a specifically conceived in situ electrochemical cell. The starting composites consist of three main components: β-Sn particles as the electrochemically active species, an inactive matrix of BPO₄ and an amorphous Sn^II-borophosphate interfacial phase linking the two former components and improving the cohesion of the composite. During the first discharge, the latter Sn(II) species are first reduced to zerovalent tin forming Li-poor Li–Sn alloys. After its complete reduction, the reaction of Li continues with β-Sn leading to Li–Sn alloys increasingly rich in Li, with a final composition between those of Li₇Sn₂ and Li₁₃Sn₅. X-ray diffraction shows a progressive loss of long range order of the composites with the suppression of the diffraction peaks of the initial β-Sn and the formation of an ill-defined mixture of Li–Sn alloys. The evolution of this mechanism is investigated on going from a reference Sn/BPO₄ composite prepared by conventional ceramic methods with common micrometric BPO₄ to a new improved material prepared by carbothermal synthesis starting from nanometric BPO₄. With the new composite prepared by carbothermal synthesis, a significant improvement of the reversible capacity at the first cycle is obtained together with a slight improvement of the cycling behaviour. An additional improvement can be obtained by increasing the rate of the first discharge, and thus hampering the formation of the thermodynamically stable LiSn intermetallic.     

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Total Synthesis of Aspidosperma and Strychnos Alkaloids through Indole Dearomatization

Monoterpenoid indole alkaloids are the major class of tryptamine-derived alkaloids found in nature. Together with their structural complexity, this has attracted great interest from synthetic organic chemists. In this Review, the syntheses of Aspidosperma and Strychnos alkaloids through dearomatization of indoles are discussed.     

The response of clamped-clamped microbeams under mechanical shock

We present modeling, simulation, and characterization for the dynamic response of clamped-clamped microbeams under mechanical shock. A Galerkin-based reduced-order model is utilized and its results are verified by comparing to finite-element results. The results indicate that the response of a microbeam to mechanical shock is inherently non-linear because of the dominating effect of mid-plane stretching. The effect of the shock pulse shape is investigated. It is concluded that the shape of the shock pulse can result in significant dynamic amplification in the response of the microbeam even in cases where the shock load is considered quasi-static.The combined effect of the electrostatic force and mechanical shock is investigated. The results show that this combined effect can lead to early instability in microelectromechanical systems (MEMS) devices through dynamic pull-in. This could explain some of the reported experimental evidences for the existence of strange modes of failure of MEMS devices under mechanical shock and impact. These failures are characterized by overlaps between moving microstructures and stationary electrodes, which cause electrical shorts. The shock-electrostatic interaction is shown to be promising to design smart MEMS switches triggered at predetermined level of shock and acceleration. Finally, the mechanical shock combined with the packaging effect of MEMS devices is analyzed. A single-degree-of-freedom model representing the motion of the package, which is mounted over a printed circuit board, coupled with the continuous beam model is utilized. Our results reveal that neglecting the effect of the package motion on the response of microbeams can overestimate or underestimate their response. It is concluded that a poor design of the package may result in severe amplification of the shock effect leading to a device failure.     

Non-Kinetic Effects Convolute Activity and Tafel Analysis for the Alkaline Oxygen Evolution Reaction on NiFeOOH Electrocatalysts

A large variety of nickel-based catalysts has been investigated for the oxygen evolution reaction (OER) in alkaline media. However, their reported activity, as well as Tafel slope values, vary greatly. To understand this variation, we studied electrodeposited Ni₈₀Fe₂₀OOH catalysts with different loadings at varying rotation rates, hydroxide concentrations, with or without sonication. We show that, at low current density (<5 mA cm⁻²), the Tafel slope value is ≈30 mV dec⁻¹ for Ni₈₀Fe₂₀OOH. At higher polarization, the Tafel slope continuously increases and is dependent on rotation rate, loading, hydroxide concentration and sonication. These Tafel slope values are convoluted by non-kinetic effects, such as bubbles, potential-dependent changes in ohmic resistance and (internal) OH⁻ gradients. As best practise, we suggest that Tafel slopes should be plotted vs. current or potential. In such a plot, it can be appreciated if there is a kinetic Tafel slope or if the observed Tafel slope is influenced by non-kinetic effects.     

Product detection of the CH radical reaction with acetaldehyde

The reaction of the methylidyne radical (CH) with acetaldehyde (CH(3)CHO) is studied at room temperature and at a pressure of 4 Torr (533.3 Pa) using a multiplexed photoionization mass spectrometer coupled to the tunable vacuum ultraviolet synchrotron radiation of the Advanced Light Source at Lawrence Berkeley National Laboratory. The CH radicals are generated by 248 nm multiphoton photolysis of CHBr(3) and react with acetaldehyde in an excess of helium and nitrogen gas flow. Five reaction exit channels are observed corresponding to elimination of methylene (CH(2)), elimination of a formyl radical (HCO), elimination of carbon monoxide (CO), elimination of a methyl radical (CH(3)), and elimination of a hydrogen atom. Analysis of the photoionization yields versus photon energy for the reaction of CH and CD radicals with acetaldehyde and CH radical with partially deuterated acetaldehyde (CD(3)CHO) provides fine details about the reaction mechanism. The CH(2) elimination channel is found to preferentially form the acetyl radical by removal of the aldehydic hydrogen. The insertion of the CH radical into a C-H bond of the methyl group of acetaldehyde is likely to lead to a C(3)H(5)O reaction intermediate that can isomerize by β-hydrogen transfer of the aldehydic hydrogen atom and dissociate to form acrolein + H or ketene + CH(3), which are observed directly. Cycloaddition of the radical onto the carbonyl group is likely to lead to the formation of the observed products, methylketene, methyleneoxirane, and acrolein.     

The determination of some trace elements in rainwater by neutron activation analysis

A routine method for the determination of 12 elements in small rain water samples is presented. Instrumental neutron activation analysis is applied for the determination of Mn, Na, Cl, V and Al. Bromine and iodine are isolated by isotope exchange between the irradiated water and a solution of Br₂ resp. I₂ in CCl₄. Extraction with APDC/MIBK is used for the separation of the shortlived isotopes of Co, V, Cr, Zn and In.