Direct Structural Identification of Gas Induced Gate‐Opening Coupled with Commensurate Adsorption in a Microporous Metal–Organic Framework

Gate‐opening is a unique and interesting phenomenon commonly observed in flexible porous frameworks, where the pore characteristics and/or crystal structures change in response to external stimuli such as adding or removing guest molecules. For gate‐opening that is induced by gas adsorption, the pore‐opening pressure often varies for different adsorbate molecules and, thus, can be applied to selectively separate a gas mixture. The detailed understanding of this phenomenon is of fundamental importance to the design of industrially applicable gas‐selective sorbents, which remains under investigated due to the lack of direct structural evidence for such systems. We report a mechanistic study of gas‐induced gate‐opening process of a microporous metal–organic framework, [Mn(ina)₂] (ina=isonicotinate) associated with commensurate adsorption, by a combination of several analytical techniques including single crystal X‐ray diffraction, in situ powder X‐ray diffraction coupled with differential scanning calorimetry (XRD‐DSC), and gas adsorption–desorption methods. Our study reveals that the pronounced and reversible gate opening/closing phenomena observed in [Mn(ina)₂] are coupled with a structural transition that involves rotation of the organic linker molecules as a result of interaction of the framework with adsorbed gas molecules including carbon dioxide and propane. The onset pressure to open the gate correlates with the extent of such interaction.     

Numerical stability of biorthogonal wavelet transforms

Biorthogonal wavelets are essential tools for numerous practical applications. It is very important that wavelet transforms work numerically stable in floating point arithmetic. This paper presents new results on the worst-case analysis of roundoff errors occurring in floating point computation of periodic biorthogonal wavelet transforms, i.e. multilevel wavelet decompositions and reconstructions. Both of these wavelet algorithms can be realized by matrix–vector products with sparse structured matrices. It is shown that under certain conditions the wavelet algorithms can be remarkably stable. Numerous tests demonstrate the performance of the results.      

Prony's Method for Multivariate Signals

The problem of recovering translates and corresponding amplitudes of sparse sums of Gaussians out of sampling values as well as reconstructing sparse sums of exponentials are nonlinear inverse problems that can be solved for example by Prony's method. Here, we want to demonstrate a new extension to multivariate input data. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Poly[(μ4‐adamantane‐1,3‐dicarboxylato‐κ5O1:O1′:O3,O3′:O3′)(μ3‐adamantane‐1,3‐dicarboxylato‐κ5O1,O1′:O3,O3′:O3′)dimagnesium]: a layered coordination polymer

The title compound, [Mg₂(C₁₂H₁₄O₄)₂]_n, is the first example of an s‐block metal adamantanedicarboxylate coordination polymer. The asymmetric unit comprises two crystallographically unique Mg^II centers and two adamantane‐1,3‐dicarboxylate ligands. The compound is constructed from a combination of chains of corner‐sharing magnesium‐centered polyhedra, parallel to the a axis, connected by organic linkers to form a layered polymer. The two Mg^II centers are present in distorted tetrahedral and octahedral coordination environments derived from carboxylate O atoms. Tetrahedrally coordinated Mg^II centers have been reported in organometallic compounds, but this is the first time that such coordination has been observed in a magnesium‐based coordination polymer. The bond valance sums of the two Mg^II centers are 2.05 and 2.11 valence units, matching well with the expected value of 2.     

Experimental Investigation into the Low-Molecular-Weight Fluoropolymer for the Storage of Ultracold Neutrons

The experimental setup for examining the low-molecular-weight CF₃(CF₂)₃–O–CF₂–O–(CF₂)₃CF₃ fluoropolymer, which is a promising coating material for the walls of storage chambers for ultracold neutrons, is described. The results are detailed. The measurement data are interpreted in the model of a multilayer complex quantum-mechanical potential of the chamber walls.     

On the kinetic interpretation of post-irradiation decay of trapped electrons

The post-irradiation decay of electrons trapped in low-temperature glasses has been analyzed either in terms of tunnelling models which invoke direct transfer of electrons from initial solvent traps to acceptors or in terms of a first order reaction with a time-dependent rate constant of the form , O<1. This particular form of time-dependent rate constant was believed to be unique for the CTRW model of MONTROLL and WEISS. It is shown that the time-dependent rate constant calculated from the tunnelling models can be adequately approximated by this particular form with O<0.1.     

Application of the AAK theory and Prony-like Methods for sparse approximation of exponential sums

We derive a new method for optimal ℓ²-approximation of discrete signals on ℓ²(ℕ₀) whose entries can be represented as an exponential sum of finite length. Our approach employs Prony's method in a first step to recover the exponential sum that is determined by the signal. In the second step we use the theory of Adamjan, Arov and Krein (AAK) to derive an algorithm for computing a shorter exponential sum that approximates the original signal in the ℓ²-norm well. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Uniform spherical grids via equal area projection from the cube to the sphere

We construct an area preserving map from a cube to the unit sphere S², both centered at the origin. More precisely, each face F_i of the cube is first projected to a curved square S_i of the same area, and then each S_i is projected onto the sphere by inverse Lambert azimuthal equal area projection, with respect to the points situated at the intersection of the coordinate axes with S². This map is then used to construct uniform and refinable grids on a sphere, starting from any grid on a square.