On Dual Gabor Frame Pairs Generated by Polynomials

We provide explicit constructions of particularly convenient dual pairs of Gabor frames. We prove that arbitrary polynomials restricted to sufficiently large intervals will generate Gabor frames, at least for small modulation parameters. Unfortunately, no similar function can generate a dual Gabor frame, but we prove that almost any such frame has a dual generated by a B-spline. Finally, for frames generated by any compactly supported function φ whose integer-translates form a partition of unity, e.g., a B-spline, we construct a class of dual frame generators, formed by linear combinations of translates of φ. This allows us to chose a dual generator with special properties, for example, the one with shortest support, or a symmetric one in case the frame itself is generated by a symmetric function. One of these dual generators has the property of being constant on the support of the frame generator.     

Computing Approximating Automata for a Class of Hybrid Systems

This paper presents a new algorithm for generating finite-state automata models of hybrid systems in which the continuous-state dynamics can be switched when the continuous-state trajectory generates threshold events. The automata state transitions correspond to threshold events and the automata states correspond to portions of the threshold surfaces in the continuous state space. The hybrid system dynamics are approximated by the automata models in the sense that the languages of threshold event sequences generated by the automata contain the threshold event language for the hybrid system. Properties of the algorithm for constructing and refining the approximating automata are demonstrated and the application of approximating automata for system verification is illustrated for a switching controller for an inverted pendulum. Relationships to other approaches to hybrid system synthesis and verification are also discussed.     

Body fitted link-cell algorithm for particulate flow simulation in curved pipeline domain

The link-cell (LC) algorithm is widely used in discrete element method (DEM) simulation, in order to increase computational efficiency. The common way is to divide the entire computational domain into a series of square sub-cells. A huge index matrix, Ω$\Omega$, is required to store the information of particles located in each of these sub-cells. However, most of these sub-cells are always empty for some anomalistic computational domain, such as particulate flow in a pipeline. These empty sub-cells also consume the limited memory bandwidth and lower the computational power. In order to reduce the size of the index matrix, a body fitted link-cell (BFLC) algorithm is established to identify the neighbors quickly. Furthermore, a simplified algorithm for simulation of two dimensional particulate flow in curved pipelines is presented. Lastly, an example is presented to validate the BFLC algorithm.     

Computational Prediction of 1H and 13C NMR Chemical Shifts for Protonated Alkylpyrroles: Electron Correlation and Not Solvation is the Salvation

Prediction of chemical shifts in organic cations is known to be a challenge. In this article we meet this challenge for α-protonated alkylpyrroles, a class of compounds not yet studied in this context, and present a combined experimental and theoretical study of the ¹³C and ¹H chemical shifts in three selected pyrroles. We have investigated the importance of the solvation model, basis set, and quantum chemical method with the goal of developing a simple computational protocol, which allows prediction of ¹³C and ¹H chemical shifts with sufficient accuracy for identifying such compounds in mixtures. We find that density functional theory with the B3LYP functional is not sufficient for reproducing all ¹³C chemical shifts, whereas already the simplest correlated wave function model, Møller–Plesset perturbation theory (MP2), leads to almost perfect agreement with the experimental data. Treatment of solvent effects generally improves the agreement with experiment to some extent and can in most cases be accomplished by a simple polarizable continuum model. The only exception is the NH proton, which requires inclusion of explicit solvent molecules in the calculation.     

Rate coefficients for reactions of OH radicals with CH3D,CH2D2, CHD3, and CD4

Fourier transform infrared (FTIR) smog chamber techniques were used to investigate the atmospheric chemistry of the isotopologues of methane. Relative rate measurements were performed to determine the kinetics of the reaction of the isotopologues of methane with OH radicals in cm³ molecule⁻¹ s⁻¹ units: k(CH₃D + OH) = (5.19 ± 0.90) × 10⁻¹⁵, k(CH₂D₂ + OH) = (4.11 ± 0.74) × 10⁻¹⁵, k(CHD₃ + OH) = (2.14 ± 0.43) × 10⁻¹⁵, and k(CD₄ + OH) = (1.17 ± 0.19) × 10⁻¹⁵ in 700 Torr of air diluent at 296 ± 2 K. Using the determined OH rate coefficients, the atmospheric lifetimes for CH_4–xD_x (x = 1–4) were estimated to be 6.1, 7.7, 14.8, and 27.0 years, respectively. The results are discussed in relation to previous measurements of these rate coefficients.     

Shape morphing and topology optimization of fluid channels by explicit boundary tracking

An integrated shape morphing and topology optimization approach based on the deformable simplicial complex methodology is developed to address Stokes and Navier‐Stokes flow problems. The optimized geometry is interpreted by a set of piecewise linear curves embedded in a well‐formed triangular mesh, resulting in a physically well‐defined interface between fluid and impermeable regions. The shape evolution is realized by deforming the curves while maintaining a high‐quality mesh through adaption of the mesh near the structural boundary, rather than performing global remeshing. Topological changes are allowed through hole merging or splitting of islands. The finite element discretization used provides smooth and stable optimized boundaries for simple energy dissipation objectives. However, for more advanced problems, boundary oscillations are observed due to conflicts between the objective function and the minimum length scale imposed by the meshing algorithm. A surface regularization scheme is introduced to circumvent this issue, which is specifically tailored for the deformable simplicial complex approach. In contrast to other filter‐based regularization techniques, the scheme does not introduce additional control variables, and at the same time, it is based on a rigorous sensitivity analysis. Several numerical examples are presented to demonstrate the applicability of the approach.     

Compressing a Non-Planar Aromatic Heterocyclic [7]Helicene to a Planar Hetero[8]Circulene

This work describes a synthetic approach where a non-planar aromatic heterocyclic [7]helicene is compressed to yield a hetero[8]circulene containing an inner antiaromatic cyclooctatetraene (COT) core. This [8]circulene consists of four benzene rings and four heterocyclic rings, and it is the first heterocyclic [8]circulene containing three different heteroatoms. The synthetic pathway proceeds via a the flattened dehydro-hetero[7]helicene, which is partially a helicene and partially a circulene: it is non-planar and helically chiral as helicenes, and contains a COT motif like [8]circulenes. The antiaromaticity of the COT core is confirmed by nucleus independent chemical shift (NICS) calculations. The planarization from a helically π-conjugated [7]helicene to a fully planar heterocyclic [8]circulene significantly alters the spectroscopic properties of the molecules. Post-functionalization of the [7]helicenes and the [8]circulenes by oxygenation of the thiophene rings to the corresponding thiophene-sulfones allows an almost complete fluorescence emission coverage of the visible region of the optical spectrum (400–700 nm).     

Determination of ivermectin and transformation products in environmental waters using hollow fibre-supported liquid membrane extraction and liquid chromatography-mass spectrometry/mass spectrometry

A simple and easy-to-use extraction method for aqueous samples based on hollow fibre-supported liquid membrane (HF-SLM) followed by liquid chromatography-mass spectrometry/mass spectrometry (LC-MS/MS) was developed to determine ivermectin and transformation products, the monosaccharide (TP1) and the aglycon of ivermectin (TP2). The proposed method attained enrichment factors up to 80, after optimising parameters, such as fibre length, organic solvent, stirring speed, salt level, pH in samples/fibre, extraction time and fibre emptying technique. Method validation with tap and lake water samples provided good linearity and detection limits of 0.2, 1.6 and 0.9 microg/l for ivermectin, TP1 and TP2 in lake water with RSD below 15%.     

Synthesis, structure and catalytic activity of a bimacrocylic NHC palladium allyl complex

The preparation of a bimacrocyclic NHC palladium allyl complex 4 is described. The complex was obtained by transmetalation with allyl palladium chloride dimer from the NHC silver complex 2 in 85% yield. Complex 4 was fully characterized by spectroscopic methods and by single-crystal X-ray analysis. In a preliminary catalytic study, complex 4 showed high activity in the Suzuki-Miyaura cross-coupling of unactivated aryl chlorides and bromides with 1-naphthalene-boronic acid at low catalyst loading. Good results were also obtained in the Mizoroki-Heck reaction of aryl bromides with styrene, but a decrease in yield was observed when aryl chlorides were used.