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If one invokes prior structural knowledge, usually that the crystal is composed of discrete atoms of known atomic numbers, then the observed magnitudes are, in general, sufficient to determine the positions of the atoms, that is, the crystal structure.
The underlying physical descriptions can also vary with scale: first, the quantum mechanical treatment of degrees of freedom at (sub- atomic sub- atomicond, the clascales represecondion of discretheatoms, moleclassicalgrepresentationules at intermediate scales, and third, the mesofcopic or continuum treatment of entire molecular systems.
If the analyte consists of discrete atoms (which exist only in the gaseous state), the method is termed atomic absorption spectrophotometry.
According to this approach, "space is made of discrete atoms each of which carries a very tiny unit of volume".
So how can Achilles ever catch up with the tortoise (see figure)? Zeno's paradoxes may also be interpreted as showing that space and time are not made up of discrete atoms but are substances which are infinitely divisible.
Underlying this dispute was a perceived basic dichotomy, not confined to mathematics but pervading all nature: is the universe made up of discrete atoms (as the philosopher Democritus believed) which hence can be counted, or does it consist of one or more continuous substances (as Thales of Miletus is reputed to have believed) and thus can only be measured?
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The electronic properties of the metal oxide are effected by particle size of material, the quantum size or confinement effects are produced in nanostructured materials which essentially arise from the presence of discrete, atom-like electronic states (Marcos and Rodriguez 2007), and also nanosized material is observed to have small band gap in its lattice.
The radiation that is emitted in this environment is usually a mixture of discrete atomic lines that come from the relaxation of the atoms to lower energy states and continuum radiation resulting from closely spaced lines that have been broadened by collisions with other atoms and the electrons.
Another reflection of quantum size effect is the emergence of discrete atomic separated energy state due to the presence of smaller atoms [35].
The results of Onsager's approach are independently confirmed with those of the Discrete Atom Method, a Monte Carlo technique predicated upon the combination of statistical mechanics and linear elasticity.
What was so remarkable about Riemann's zeta function was that it somehow took a question about prime numbers -- those discrete atoms of simple arithmetic, things easy to imagine -- and put it in terms of a far larger and more esoteric class of numbers known as complex numbers.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com