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Showing posts with the label ELEMENTARY EUCLIDEAN SPACE

Cosmic Chemistry Unveiled - The Genesis of Methyl Cations in Protoplanetary Disk Photochemistry

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Forty years ago it was proposed that gas phase organic chemistry in the interstellar medium can be initiated by the methyl cation CH 3 +  ( 1–3 ), but hitherto it has not been observed outside the Solar System ( 4, 5 ). Alternative routes involving processes on grain surfaces have been invoked ( 6, 7 ). Here we report JWST observations of CH+3CH3+ in a protoplanetary disk in the Orion star forming region. We find that gas-phase organic chemistry is activated by UV irradiation. Introduction : In the realm of cosmic evolution, protoplanetary disks serve as the cradles of new star systems and planetary bodies. These disks, composed of gas and dust, harbor an intricate web of chemical reactions that sculpt the materials essential for planet formation. Among the diverse array of chemical species within these disks, the methyl cation (CH3+) stands out as a key molecular fragment. Recent research has shed light on the intriguing formation of the methyl cation through photochem...

Elementary Euclidean space | GENERAL RELATIVITY INT.

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Minkowski space is closely associated with  Einstein's  theory of  special relativity  and is the most common mathematical structure on which special relativity is formulated. While the individual components in Euclidean space and time may differ due to  length contraction  and  time dilation , in Minkowski spacetime, all frames of reference will agree on the total distance in spacetime between events. Because it treats time differently than it treats the 3 spatial dimensions, Minkowski space differs from  four-dimensional Euclidean space . In 3-dimensional Euclidean space (e.g. simply  space  in  Galilean relativity ), the  isometry group  (the maps preserving the regular  Euclidean distance ) is the  Euclidean group . It is generated by  rotations ,  reflections  and  translations . When time is amended as a fourth dimension, the further transformations of translations in time and Galilean b...