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The two rightmost columns indicate which irreducible representations describe the symmetry transformations of the three Cartesian coordinates (x, y and z), rotations about those three coordinates (R x, R y and R z), and functions of the quadratic terms of the coordinates(x 2, y 2, z 2, xy, xz, and yz).
Ammonia solution, also known as ammonia water, ammonium hydroxide, ammoniacal liquor, ammonia liquor, aqua ammonia, aqueous ammonia, or (inaccurately) ammonia, is a solution of ammonia in water. It can be denoted by the symbols NH 3 (aq). Although the name ammonium hydroxide suggests a salt with the composition [NH + 4][OH −
The irreducible complex characters of a finite group form a character table which encodes much useful information about the group G in a concise form. Each row is labelled by an irreducible character and the entries in the row are the values of that character on any representative of the respective conjugacy class of G (because characters are class functions).
Ammonia is used in numerous different industrial applications requiring carbon or stainless steel storage vessels. Ammonia with at least 0.2% by weight water content is not corrosive to carbon steel. NH 3 carbon steel construction storage tanks with 0.2% by weight or more of water could last more than 50 years in service. [141]
Reducible representation. ... Page information; Cite this page; Get shortened URL; Download QR code; Wikidata item; Print/export Download as PDF; Printable version;
Cite this page; Get shortened URL; Download QR code; Print/export Download as PDF; Printable version; In other projects ... 11.61 kPa: 8.91: 32.88 kPa: 11.07 kPa: 11.57:
For n = 3 the obvious analogue of the (n − 1)-dimensional representation is reducible – the permutation representation coincides with the regular representation, and thus breaks up into the three one-dimensional representations, as A 3 ≅ C 3 is abelian; see the discrete Fourier transform for representation theory of cyclic groups.
Example of a linear molecule. N atoms in a molecule have 3N degrees of freedom which constitute translations, rotations, and vibrations.For non-linear molecules, there are 3 degrees of freedom for translational (motion along the x, y, and z directions) and 3 degrees of freedom for rotational motion (rotations in R x, R y, and R z directions) for each atom.