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This is an active area of research, for example, homogeneous Dirichlet BCs were studied in [3 10], homogeneous Robin BCs in [7, 9, 10], nonlocal BCs of Dirichlet type in [1, 11 19] and nonlocal BCs of Robin type in [16, 19 23].
The authors in [34] localized the interval on the existence of three solutions of equations of p-Laplace type with various boundary conditions (for example, homogeneous Dirichlet and inhomogeneous Robin problems) which were inspired by the study of Arcoya and Carmona [38].
For example, homogeneous water-soluble Rh-based catalysts were successfully used for PHIP-based hyperpolarization of C-labeled contrast agents intended for in vivo MRI applications.
For example, homogeneous samples can enhance the precision of estimates of treatment effects, but they also reduce the extent to which findings can be generalised to the wider population of interest, i.e. people who do not fit restrictive inclusion/exclusion criteria.
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Here, by optimizing enzyme solubility in ionic liquids, we have discovered solvent-induced substrate promiscuity of glucosidase, demonstrating an unprecedented example of homogeneous enzyme bioprocessing of cellulose.
As an illustrative and industrially relevant example, the homogeneous catalytic exothermic N-oxidation of alkylpyridines is investigated using a jacketed CSTR model.
Sulfuric acid used as a catalyst for the formation of diethyl ether from ethyl alcohol is an example of homogeneous catalysis in the liquid phase (when the products, water and ether, are continuously removed by distillation); by this method, considerable quantities of alcohol can be converted to ether with a single charge of sulfuric acid.
Taking the NIR band as an example, for homogeneous regions the prediction of the ESTARFM is slightly better than the STARFM (average absolute difference [AAD] 0.0106 vs. 0.0129 reflectance units).
Nagel, himself, took as a paradigm example of homogeneous reduction, the reduction of the Galilean laws of falling bodies to Newtonian mechanics.
For example, the homogeneous and disordered assembly of densely packed nanoparticles can result in bulk transparent film-like objects through gradually evaporating the high-quality homogeneous nanoparticle colloid [12, 13].
However, by varying the order of addition of these reagents [34] it is possible to prepare nanoparticles that exhibit core shell structures and examples of these are given in Fig. 1 together with an example of homogeneous Au Pd alloy nanoparticles.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com