Cross Patte

Again, let the Perfect Pyramid be laid flat so the sides splay into a Cross Patte. The area of a circle inscribed within the Cross Patte is ... 

With the Cross Patte, medieval mathematicians found an... 

Pyramid, make it into a Cross Patte and inscribe a circle. The area of the circle is twice that of the square base of the pyramid. Using a square made from the diagonal of the base of the pyramid rather than the base of the pyramid itself, the twice factor disappears. This is because the diagonal measures sV2. The area of such a square is 2.s. Thus the esoteric solution from the Perfect Pyramid is ... 

Paul, F., Patt, J., Hartwig, J. F. Palladium-catalyzed formation of carbon-nitrogen bonds. Reaction intermediates and catalyst improvements in the hetero cross-coupling of aryl halides and tin amides. J. Am. Chem. Soc. 1994,116, 5969-5970. 

To address the solvent dynamic range problem, one or multiple signals from the solvent are selectively suppressed in the NMR spectrum. Solvent suppression is not a perfect solution. Compound peaks that are proximal to the solvent are also completely or partially suppressed. Similarly, hydrogens that readily exchange with water are also equally suppressed with the water solvent peak. Additionally, solvent suppression causes artifacts and streaking in 2D NMR spectra. This streaking may obscure cross peaks that fall near the solvent chemical shift in either spectral dimension. The commonly used solvent suppression NMR techniques, such as, PRESAT, WET (Smallcombe and Patt,... 

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