As mentioned, the dimensional change was relatively mild in this experiment, perhaps, it could be due to the fact that the thermal energy is relatively high at 700 °C and the DA was small with 2 nm and thus the resulting NPs are small.
One can derive a one-dimensional wave equation from the above mentioned one-dimensional model and extend it to the following two-dimensional wave equation.
In this study, a field enhancement factor of the order of 103 was obtained for fractal-like a-C nanotips consisting of several branches, each branch similar in shape to the previously mentioned one-dimensional nanotips.
As we mentioned before, dimensionality reduction is made explicit by TCMC, since optimization takes place over a smaller dimensional vector v, instead of the higher dimensional vector κ specified by the model.
But cells are vastly more complicated than that, not to mention three-dimensional.
In spite of this, the above-mentioned dimensional reduction can lead to counterintuitive results.
As mentioned before, one-dimensional graph entropy can only represent global information rather than the property of its spatial relationships.
In the Williams tube or electrostatic memory, previously mentioned, a two-dimensional rectangular array of binary digits was stored on the face of a commercially-available cathode ray tube.
In Section 3, we apply the modified Fan sub-equation method to solve the above mentioned two high-dimensional nonlinear equations, and more new exact traveling wave solutions are explicitly obtained.
In 1913, Riesz [516], in one of the first books on operator theory on infinite dimensional spaces, mentioned residues of poles of ((z-A)^{-1}) could be studied and, in 1930, he noted [517] in the Hilbert space case that decompositions of the spectrum into disjoint closed sets induced a decomposition of the space.
All the dilemmas mentioned are therefore two-dimensional.
