Minireview: Advances in Germanium Isotope Analysis by Multiple Collector–Inductively Coupled Plasma–Mass Spectrometry

The advent of multiple collector–inductively coupled plasma–mass spectrometry (MC-ICP-MS) has made the high-precision determination of Ge isotopes possible, which leads to the widespread application of Ge isotopes in earth, ocean, and cosmochemistry fields. This paper reviews the history of Ge isotope analysis, chemical dissolution and purification, and mass spectrometry measurements. Concentrated HNO₃ is sufficient to dissolve nearly all types of samples and HF is also involved for Si-rich samples. Low-temperature ashing prior to dissolution is an alternative way to preconcentrate Ge in organic-rich samples. For different matrices, Ge isotopes can be determined by MC-ICP-MS coupled with a traditional nebulizer system or hydride generation system after two-step separation, one step cation/anion-exchange separation, or Mg/Fe co-precipitation protocols. Ion-exchange column methods are suitable for samples with elevated matrix and Ge content such as sulfides, iron oxides, silicate rocks, and coals, whereas Mg or Fe coprecipitation methods are particularly suitable for all kinds of water. Hydride generation systems are improved over traditional nebulizer system due to the smaller sample quantity and fewer matrix-related interferences. Sample-standard bracketing, double spike, and external Ga isotope normalization are used to mass bias correction and yield consistent results. Analytical methods involving Ge-poor samples and Ge isotope analyses based on different Ge species or specific Ge compound in natural environment will be important prospects in the further study. For further applications of Ge isotopes in mineral deposits such as sulfide and iron oxide deposits, sulfides, and iron oxides reference materials should be developed in the future.     

A Brylinski filtration for affine Kac–Moody algebras

Braverman and Finkelberg have recently proposed a conjectural analogue of the geometric Satake isomorphism for untwisted affine Kac–Moody groups. As part of their model, they conjecture that (at dominant weights) Lusztig's q-analog of weight multiplicity is equal to the Poincare series of the principal nilpotent filtration of the weight space, as occurs in the finite-dimensional case. We show that the conjectured equality holds for all affine Kac–Moody algebras if the principal nilpotent filtration is replaced by the principal Heisenberg filtration. The main body of the proof is a Lie algebra cohomology vanishing result. We also give an example to show that the Poincare series of the principal nilpotent filtration is not always equal to the q-analog of weight multiplicity. Finally, we give some partial results for indefinite Kac–Moody algebras.     

Construction of Helical Structures with Multiple Fused Anthracenes: Structures and Properties of Long Expanded Helicenes

Polycyclic aromatic compounds consisting of four or five fused anthracene units were synthesized by PtCl₂-catalyzed cycloisomerization as novel long expanded helicenes. These compounds have helical structures with significant stacking of the terminal anthracene moieties at 0.33 nm interlayer distance. In the UV-vis and fluorescence spectra, the absorption and emission bands were red-shifted as the number of fused anthracene units was increased. The characteristic broad and long-lived emission bands of the long analogues are explained by the excimer-like stabilization of the excited state. These photophysical data as well as their cyclic voltammetric data are discussed on the basis of the π-conjugation and interlayer π⋅⋅⋅π interactions in the molecular structures and the molecular orbitals. The barrier and mechanism of helical inversion are also reported.     

A computational framework for the form-finding and design of tensegrity structures

A new computational framework is proposed for the form-finding and design of tensegrity structures with or without super-stability. The form-finding of tensegrities is formulated as two unconstrained minimisation problems where their objective functions are defined based on eigenvalues of a modified force density matrix. The Nelder–Mead simplex method is then used to solve the minimisation problems. Furthermore, another efficient method is suggested for the interactive form-finding and design of tensegrities with geometrical and force constraints. Examples of the form-finding of tensegrities are presented and the results obtained are compared and contrasted with those analytical results documented in the literature, to verify the accuracy and efficiency of the developed methods.     

Ultra-High Performance Liquid Chromatography with Electrospray Ionization Tandem Mass Spectrometry for the Determination of Caffeine in Energy Drinks

A simple and highly sensitive method for the determination of caffeine in energy beverages was developed and validated. Sample preparation utilizing solid-phase extraction (SPE) was simple and reliable. Separation by isocratic ultra-high performance liquid chromatography (UPLC) with a reversed-phase C₁₈ column was performed within 6 min. The use of SPE with UPLC coupled with electrospray ionization-multiple tandem mass spectrometry detection (ESI-MSⁿ) was accurate, reproducible, and validated for the determination of caffeine in energy drink matrices. The limit of quantification for caffeine was approximately 2.1 ng mL^?1. The intra-day and inter-day precisions were less than 4%, and the accuracy of the measurements was between 85.1% and 93.2%. Results for caffeine concentrations in eighteen beverages were compared to the values on the labels. This paper describes the first use of the UPLC–ESI-ion trap MSⁿ technique for quality-control purposes of caffeine present in energy drinks.     

A two dimensional Euler–Lagrangian model of wood gasification in a charcoal bed—Part II: Parameter influence and comparison

A Euler–Lagrangian simulation was employed for a comprehensive parameter study of wood gasification in a fluidized charcoal bed. The parameters that were varied include the initial bed temperature, fuel mass flow rate, inert tar fraction, and kinetic energy losses caused by particle–particle and particle–wall collisions. The results of each parameter variation are compared with a base scenario, previously described in detail in Part I of this study (Gerber & Oevermann, 2014). The results are interpreted by comparing the reactor outlet temperature, averaged particle temperature, overall wood mass, overall charcoal mass, concentrations of several gaseous species, and axial barycenter data for particles obtained with different sets of parameters. The inert tar fraction and fuel mass flow rate are the most sensitive parameter, while the particle–particle and particle–wall contact parameters have only a small impact on the results. Increasing the reactive tar components by 19% almost doubled the amount of reactive tars at the reactor outlet, while decreasing the restitution coefficients of the particle collisions by 0.2 results in higher overall gas production but almost no change in bed height. Herein, our numerical results are discussed in detail while assessing the model restrictions.     

Continuous segregation of binary heterogeneous solids in a fast-fluidized bed

Continuous segregation of binary heterogeneous solids (different density mixtures) is carried out in a gas–solid fluidized bed to study the effects of gas velocity, solids feed rate, feed composition and density difference of solids on the separation factor (recovery of flotsam at top outlet) and the quality of the product (purity of flotsam at top outlet) in a continuous fast-fluidized bed. The holdup of the bed material is obtained in each experimental run. It is observed that the separation factor decreases with increase in solids feed rate or density difference of solids, and increases with gas velocity or proportion of flotsam in the feed. The quality of the product decreases with increase in gas velocity or solids flow rate, and increases with feed composition or density difference of solids. The experimental results show that the separation factor and the quality of the product are more sensitive to gas velocity than to other operating parameters. Empirical correlations for predicting the separation factor and quality of the product are proposed based on the Richards model for individual flotsam mass fraction in the feed, and the predictions agree satisfactorily with the present experimental data.     

A simultaneous canonical form of a pair of matrices and applications involving the weighted Moore–Penrose inverse

In this paper, a simultaneous canonical form of a pair of rectangular complex matrices is developed. Using this new tool we give a necessary and sufficient condition to assure that the reverse order law is valid for the weighted Moore–Penrose inverse. Additionally, we characterize matrices ordered by the weighted star partial order and adjacent matrices as applications.     

Convenient In-Flow Preparation of Cr(II) Chloride for Nozaki–Hiyama–Kishi Reaction

A flow preparation of chromous chloride has been introduced as a viable alternative to the batch protocol. Activity of the prepared reagent has been demonstrated in the traditional Nozaki–Hiyama–Kishi reaction.