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(最多只允许输入30个字)It is not often that an article on the topic of illusion and deception makes it into a chemical journal. Such is addressed (DOI: ) in no less an eminent journal than Angew Chemie. The illusion (or deception if you will) actually goes to the heart of how we represent three-dimensional molecules in two dimensions, and the meanings that may be subverted by doing so. A it happens, it is also a recurring theme of this particular blog, which is the need to present chemistry with data for all three dimensions fully intact (hence the Click for 3D captions which often appear profusely here).
Molecular Penrose stair. Click for
3D.The molecule above
has been synthesized and a crystal structure obtained (if you click above, you will get the
3D the above is pruned of some sidechains which are irrelevant here). The authors assert it as an example of a Penrose stair, or perhaps the better known lithograph by M. C. Escher known as . This is a visual paradox, the point of which is to show how the eye can be easily deceived if the brain is asked to fill in a third dimension given only two. The molecule above has been drawn with the illusion of depth, using (or mis-using) the embolded bonds akin to those proposed by
(who meant something quite different as it happens). It should be worrying to any chemist who cares about stereochemistry to think that use of these time honoured conventions could actually result in a paradox! So perhaps this accounts for why an article on this very topic has made it onto the pages of such an eminent journal.
What might be of (chemical) interest about this molecule, other than its illusory aspects? Well, could you for example work out, given ONLY the representation above, that the molecule has D2 symmetry, and is therefore chiral? I wondered if it might also be M?bius (with perhaps two half twists), although in fact the π-system in this case has a linking number Lk of zero (not
2). It also has some interesting rather close H…H contacts in the middle, and the inner periphery appears to be a 14-annulene and the outer 26, both conforming to the Huckel 4n+2 rule. Despite this the central C-C bond is actually quite long, and the conjugation is hence significantly interrupted. There is more chemistry in the original article.
But I want to close here on the point that to overcome the deception and illusion, you need to get the three dimensional data in chemistry. You can do this by clicking above. Or, by going to the original article and striving to do so there. I think you will find the latter route the greater challenge! Then, ask yourself why an eminent journal, in publishing an article on the topic of deception and illusion, makes it so relatively difficult to overcome that illusion. Certainly more difficult than I hope it proves to be on this blog!
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Sorry, your blog cannot share posts by email.Future radio observatories for pulsar studies
Title:Future radio observatories for pulsar studies
Affiliation:AA(University of Manchester, Jodrell Bank Observatory, Jodrell Bank, United Kingdom)
Publication:On the Present and Future of Pulsar Astronomy, 26th meeting of the IAU, Joint Discussion 2, 16-17 August, 2006, Prague, Czech Republic, JD02, id.#44
Publication Date:08/2006
Origin:IAU
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Over the next decade, radio astronomers will have new, exciting
instruments available to answer fundamental questions in physics and
astrophysics. Without doubts, new discoveries will be made, revealing
new objects and phenomena. We can expect pulsar astronomers to receive
their fair share. In many respects, the field of pulsar astrophysics
will change, as the science will not simply be a continuation of what
has been done so successfully over the past 40 years. Instead, the huge
number of pulsars to be discovered and studied with an unprecedented
sensitivity will provide a step forward into exciting times. Instruments
like the Low Frequency Array (LOFAR), the Square Kilometre Array (SKA)
and their powerful pathfinder telescopes will enable a complete census
of Galactic pulsars, ultimate tests of gravitational physics, unique
studies of the emission process and much more. This talk will
demonstrate the potential of the future instruments by presenting
highlights of the science to be conducted.
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arXiv e-printsTowards an algebraic theory of Boolean circuits - ScienceDirect
Download PDFDownloadExport JavaScript is disabled on your browser. Please enable JavaScript to use all the features on this page., 1 November 2003, Pages 257-310Author links open overlay panelShow moreopen archiveAbstractBoolean circuits are used to represent programs on finite data. Reversible Boolean circuits and quantum Boolean circuits have been introduced to modelize some physical aspects of computation. Those notions are essential in complexity theory, but we claim that a deep mathematical theory is needed to make progress in this area. For that purpose, the recent developments of knot theory is a major source of inspiration.Following the ideas of Burroni, we consider logical gates as generators for some algebraic structure with two compositions, and we are interested in the relations satisfied by those generators. For that purpose, we introduce canonical forms and rewriting systems. Up to now, we have mainly studied the basic case and the linear case, but we hope that our methods can be used to get presentations by generators and relations for the (reversible) classical case and for the (unitary) quantum case.MSC15-XXRecommended articlesCiting articles (0)}