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It is shown that there exist a finite number of discrete well defined periodic solutions for the lateral buckling problem of a straight pipeline under constant pressure and temperature.
I explain why this proof is not entirely convincing and show how, by restricting the notion of function in terms of discrete well defined processes, we are led to the non algorithmic enumerability of the computable functions, but also through Church's thesis to the algorithmic enumerability of partial computable functions.
Coating technologies, drug delivery systems, cleaning and personal care formulations all rely on discrete well controlled physical properties at several distance scales in order to derive the desired product performance, and are reliant on an in-depth knowledge of the surface of interest.
The diagnosis of sarcoidosis was made if the patient's lung biopsy (transbronchial biopsy (n = 59, 82%) and surgical biopsy (n = 13, 18%)) showed discrete, well formed, non-necrotizing granulomas without evidence of infection or inorganic material to account for the pulmonary granulomatous reaction.
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Strategic, discrete, well-planned, original (in its time), the Stonewall march is the pure manifestation of how social movements succeed.
Light sources that are capable of primarily emitting radiation with discrete, well-defined frequencies are also widely used in spectroscopy.
The new work, by contrast, geared to a much larger gallery space, is bright but a bit tame, a collection of discrete, well-made things, rather than a cohesive installation.
The scanning electron microscopy (SEM) image showed that C-nZVI is approximately discrete, well-dispersed and an almost spherical shape.
Foveolitis is characterized by a discrete, well-defined yellow-orange subretinal lesions in the fovea, which usually corresponds to disruption of the outer neurosensory retina and the inner segment/outer segment (IS/OS) junction.
Observation of discrete well-defined conformations in this large RNA that are stable on the seconds timescale at low [Mg2+] (<0.1 mM) suggests that even at low ionic strength, with a tremendous number of possible (weak) interactions, a few critical interactions may produce deep energy wells that allow for rapid averaging of motions within each well, and yield kinetics that are relatively simple.
Only discrete, well-separated structures were counted.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com