Single‐cell fourth‐order difference approximations for $${\font\twelvesl=cmsl10\partial {\sl\bf u}\over\partial {\sl\bf x}},{\partial \sl\bf u\over\partial\sl\bf y}$$ , and $${\font\twelvesl=cmsl10\partial {\sl\bf u}\over\partial{\sl\bf z}}$$ of the three‐dimensional quasi‐linear elliptic equation

Finite difference methods of O(h⁴) are proposed for obtaining estimates of first‐order partial derivatives of the solution of three‐dimensional quasi‐linear elliptic equation with mixed derivative terms subject to Dirichlet boundary conditions on a uniform cubic grid. In all the cases, we use a single computational cell and the methods are applicable to the problems both in cartesian and polar coordinates. The utility of the new methods is shown by testing the methods on three‐dimensional poisson solvers in polar coordinates. Some numerical examples are provided to demonstrate the accuracy and efficiency of the methods discussed. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 417–425, 2000     

Enhanced visible light absorption in layered Cs3Bi2Br9 through mixed-valence Sn(ii)/Sn(iv) doping

Lead-free halides with perovskite-related structures, such as the vacancy-ordered perovskite Cs₃Bi₂Br₉, are of interest for photovoltaic and optoelectronic applications. We find that addition of SnBr₂ to the solution-phase synthesis of Cs₃Bi₂Br₉ leads to substitution of up to 7% of the Bi(iii) ions by equal quantities of Sn(ii) and Sn(iv). The nature of the substitutional defects was studied by X-ray diffraction, ¹³³Cs and ¹¹⁹Sn solid state NMR, X-ray photoelectron spectroscopy and density functional theory calculations. The resulting mixed-valence compounds show intense visible and near infrared absorption due to intervalence charge transfer, as well as electronic transitions to and from localised Sn-based states within the band gap. Sn(ii) and Sn(iv) defects preferentially occupy neighbouring B-cation sites, forming a double-substitution complex. Unusually for a Sn(ii) compound, the material shows minimal changes in optical and structural properties after 12 months storage in air. Our calculations suggest the stabilisation of Sn(ii) within the double substitution complex contributes to this unusual stability. These results expand upon research on inorganic mixed-valent halides to a new, layered structure, and offer insights into the tuning, doping mechanisms, and structure–property relationships of lead-free vacancy-ordered perovskite structures.

Mixed valence Sn doping of Cs₃Bi₂Br₉ leads to broad visible light absorption.     

Branch-and-bound solves random binary IPs in poly(n)-time

Mathematical Programming - Branch-and-bound is the workhorse of all state-of-the-art mixed integer linear programming (MILP) solvers. These implementations of branch-and-bound typically use...     

Hyperpolarized 13C NMR Spectroscopy of Urine Samples at Natural Abundance by Quantitative Dissolution Dynamic Nuclear Polarization

Hyperpolarized nuclear magnetic resonance (NMR) offers an ensemble of methods that remarkably address the sensitivity issues of conventional NMR. Dissolution Dynamic Nuclear Polarization (d-DNP) provides a unique and general way to detect ¹³C NMR signals with a sensitivity enhanced by several orders of magnitude. The expanding application scope of d-DNP now encompasses the analysis of complex mixtures at natural ¹³C abundance. However, the application of d-DNP in this area has been limited to metabolite extracts. Here, we report the first d-DNP-enhanced ¹³C NMR analysis of a biofluid -urine- at natural abundance, offering unprecedented resolution and sensitivity for this challenging type of sample. We also show that accurate quantitative information on multiple targeted metabolites can be retrieved through a standard addition procedure.     

Solving sparse principal component analysis with global support

Mathematical Programming - Sparse principal component analysis with global support (SPCAgs), is the problem of finding the top-r leading principal components such that all these principal...     

Thermo-Kinetic Study of Piperazine Immobilized Silica Surface

In the present study, the degradation process of piperazine (PP) immobilized silica gel (SiPP) is investigated under dynamic conditions. The degradation of SiPP is studied with thermogravimetric analyzer (TGA). The kinetics of degradation process is analyzed by Kissinger method, Flynn–Wall–Ozawa's (FWO) method, and Deconvolution method. It is found that degradation of SiPP can be described by parallel independent two-portion process model, which includes two processing state of the system (marked by processes 1 and 2), where process 1 and 2 can be attributed to decomposition processes of organic moiety attached on silica surface. The apparent activation energy (E_a) is calculated by Flynn–Wall–Ozawa's (FWO) method and deconvolution method.     

Thermoelectricity in a Quasiperiodic Lattice Beyond Nearest-Neighbor Electron Hopping

A new route to obtain a large figure of merit (>1) is reported, for the first time, by considering a one-dimensional quasiperiodic lattice where an electron can hop beyond usual nearest-neighbor sites. A finite positional correlation is imposed among the constituent lattice sites, following the well-known Aubry-André-Harper (AAH) form. In the presence of second-neighbor hopping, the AAH lattice exhibits energy dependent mobility edge which plays the central role for efficient energy conversion. Employing a tight-binding framework, all the thermoelectric quantities are computed based on the standard nonequilibrium Green's function formalism. The analysis can be utilized to investigate thermoelectric phenomena in similar kinds of other aperiodic systems possessing higher order electron hopping.     

Advancement and future challenges of metal–organic coordination polymers: A case study of optical sensor for the detection of the environmental contaminants

Fast industrialization, increasing population, rapid urbanization, and the greediness of creamy layer in the society without the issues of caring the sustainability of ecosystem are the main out of many reasons behind the environmental catastrophe. The ecological balance is disturbed with the noxious materials generated from the uncontrolled use of modern science and technology and also unscientific and unsystematic societal growths. To save the modern civilization, a fast-track task is the monitoring of the toxic materials for the maintenance of sustainable ecological health and their utilization in a circular economy. Accordingly, optical methods are employed for the detection and estimation of environmental contaminants for immediate monitoring. The stability and structural tunability of the coordination polymeric (CPs) materials make them promising optical sensors for easy, low cost, reliable, selective, and sensitive detection of toxic ions/molecules. The crystallinity, thermal, mechanical, magnetic, and optical stability and flexibility of the CPs play a beneficial role for the accurate and stress-free recognition of the toxicants. In this review, the recent developments as well as the outlook on the sensing of pollutants at a very low concentration level using CPs as selective and specific sensors by spectro-fluorometric method are summarized. The progresses and challenges in the fabrication of hybrid materials and understanding their structure property correlations are described with an aim to motivate and facilitate the future researchers to perform research in the area.