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The 2-adic integers, with selected corresponding characters on their Pontryagin dual group. In mathematics, Pontryagin duality is a duality between locally compact abelian groups that allows generalizing Fourier transform to all such groups, which include the circle group (the multiplicative group of complex numbers of modulus one), the finite abelian groups (with the discrete topology), and ...
R group may refer to: In chemistry: Pendant group or side group; Side chain; Substituent; In mathematics: Tempered representation This page was last edited on ...
In organic chemistry, a carboxylic acid is an organic acid that contains a carboxyl group (−C(=O)−OH) [1] attached to an R-group. The general formula of a carboxylic acid is often written as R−COOH or R−CO 2 H, sometimes as R−C(O)OH with R referring to an organyl group (e.g., alkyl, alkenyl, aryl), or hydrogen, or other groups ...
For example, the dihedral group D 8 of order sixteen can be generated by a rotation, r, of order 8; and a flip, f, of order 2; and certainly any element of D 8 is a product of r ' s and f ' s. However, we have, for example, rfr = f −1, r 7 = r −1, etc., so such products are not unique in D 8. Each such product equivalence can be expressed ...
In organic chemistry and biochemistry, a side chain is a chemical group that is attached to a core part of the molecule called the "main chain" or backbone.The side chain is a hydrocarbon branching element of a molecule that is attached to a larger hydrocarbon backbone.
COOH, R, NH 2 and H (where R is the side-chain) are arranged around the chiral center carbon atom. With the hydrogen atom away from the viewer, if the arrangement of the CO→R→N groups around the carbon atom as center is counter-clockwise, then it is the L form. [14] If the arrangement is clockwise, it is the D form. As usual, if the ...
R rhombohedral A reflection plane m within the point groups can be replaced by a glide plane , labeled as a , b , or c depending on which axis the glide is along. There is also the n glide, which is a glide along the half of a diagonal of a face, and the d glide, which is along a quarter of either a face or space diagonal of the unit cell.
The group (H, τ r) is not a Lie group. While the map exp : h → (H, τ r) is an analytic bijection, its inverse is not continuous. That is, if U ⊂ h corresponds to a small open interval −ε < θ < ε, there is no open V ⊂ (H, τ r) with log(V) ⊂ U due to the appearance of the sets V. However, with the group topology τ g, (H, τ g) is ...