Metal Oxide Assisted Preparation of Core–Shell Beads with Dense Metal–Organic Framework Coatings for the Enhanced Extraction of Organic Pollutants

Dense and homogeneous metal–organic framework (MOF) coatings on functional bead surfaces are easily prepared by using intermediate sacrificial metal oxide coatings containing the metal precursor of the MOF. Polystyrene (PS) beads are coated with a ZnO layer to give ZnO@PS core–shell beads. The ZnO@PS beads are reactive in the presence of 2‐methylimidazole to transform part of the ZnO coating into a porous zeolitic imidazolate framework‐8 (ZIF‐8) external shell positioned above the internal ZnO precursor shell. The obtained ZIF‐8@ZnO@PS beads can be easily packed in column format for flow‐through applications, such as the solid‐phase extraction of trace priority‐listed environmental pollutants. The prepared material shows an excellent permeance to flow when packed as a column to give high enrichment factors, facile regeneration, and excellent reusability for the extraction of the pollutant bisphenol A. It also shows an outstanding performance for the simultaneous enrichment of mixtures of endocrine disrupting chemicals (bisphenol A, 4‐tert‐octylphenol and 4‐n‐nonylphenol), facilitating their analysis when present at very low levels (<1 μg L^?1) in drinking waters. For the extraction of the pollutant bisphenol A, the prepared ZIF‐8@ZnO@PS beads also show a superior extraction and preconcentration capacity to that of the PS beads used as precursors and the composite materials obtained by the direct growth of ZIF‐8 on the surface of the PS beads in the absence of metal oxide intermediate coatings.     

Finite tchebycheff transformations of generalized functions

By using Hilbert space techniques, the finite Tchebycheff transformations of the first and the second kind are defined on appropriate spaces of generalized functions. The inversion theorems are established and some operation transform formulas are obtained. These results are applied in solving certain distributional differential equations.     

Regioselective Hydration of Alkynes by Iron(III) Lewis/Brønsted Catalysis

The triflimide iron(III) salt [Fe(NTf₂)₃] promotes the direct hydration of terminal and internal alkynes with very good Markovnikov regioselectivities and high yields. The enhanced carbophilic Lewis acidity of the Fe^III cation mediated by the weakly‐coordinating triflimide anion is crucial for the catalytic activity. The iron(III) metal salt can be recycled in the form of the OPPh₃/[Fe(NTf₂)₃] system with similar activity and selectivity. However, spectroscopic and kinetic studies show that [Fe(NTf₂)₃] hydrolyzes under the reaction conditions and that catalytically less active Brønsted species are formed, which points to a Lewis/Brønsted co‐catalysis. This triflimide‐based catalytic system is regioselective for the hydration of internal aryl‐alkynes and opens the door to a new synthetic route to alkyl ketophenones. As a proof of concept, the synthesis of two antipsychotics Haloperidol and Melperone, with general butyrophenone‐like structure, is shown.     

Strategies for spectrum slicing based on restarted Lanczos methods

In the context of symmetric-definite generalized eigenvalue problems, it is often required to compute all eigenvalues contained in a prescribed interval. For large-scale problems, the method of choice is the so-called spectrum slicing technique: a shift-and-invert Lanczos method combined with a dynamic shift selection that sweeps the interval in a smart way. This kind of strategies were proposed initially in the context of unrestarted Lanczos methods, back in the 1990’s. We propose variations that try to incorporate recent developments in the field of Krylov methods, including thick restarting in the Lanczos solver and a rational Krylov update when moving from one shift to the next. We discuss a parallel implementation in the SLEPc library and provide performance results.     

Economic lot scheduling with deliberated and controlled coproduction

This paper presents an algorithm to define the optimal parameters for deliberated and controlled coproduction in an economic lot scheduling problem setting (DCCELSP). Coproduction is said to be deliberated and controlled because it is possible to decide whether or not to coproduce when all the parameters associated with the process are known. The aim is to determine how to produce two products most economically where deliberated coproduction is an option. For this purpose, a procedure for defining optimal lot periods is introduced. Two models are proposed for this procedure and a numerical illustration is provided to gain insight into their dynamics. The cost advantages of coproduction were found to depend on the relationship between setup and holding costs, production rates, and demand for products. The more similar these system parameters are and the higher the machine usage ratio is, the more favourable coproduction is. Additionally, if coproduction is not deliberated appropriately, costs soar.     

Asymptotics of Higher Order Ospt-Functions for Overpartitions

In this paper we obtain asymptotic formulas for positive crank and rank moments for overpartitions. Moreover, we show that crank and rank moments are asymptotically equal while the difference is asymptotically positive. This indicates that there exist analogous higher ospt-functions for overpartitions, which we define.