scholarly journals Deviation probabilities for arithmetic progressions and other regular discrete structures

Author(s):  
Gonzalo Fiz Pontiveros ◽  
Simon Griffiths ◽  
Matheus Secco ◽  
Oriol Serra
Author(s):  
Glen B. Haydon

High resolution electron microscopic study of negatively stained macromolecules and thin sections of tissue embedded in a variety of media are difficult to interpret because of the superimposed phase image granularity. Although all of the information concerning the biological structure of interest may be present in a defocused electron micrograph, the high contrast of large phase image granules produced by the substrate makes it impossible to distinguish the phase ‘points’ from discrete structures of the same dimensions. Theory predicts the findings; however, it does not allow an appreciation of the actual appearance of the image under various conditions. Therefore, though perhaps trivial, training of the cheapest computer produced by mass labor has been undertaken in order to learn to appreciate the factors which affect the appearance of the background in high resolution electron micrographs.


2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Yingfeng Yang ◽  
Hanze Ying ◽  
Zhixia Li ◽  
Jiang Wang ◽  
Yingying Chen ◽  
...  

AbstractMacrocycles are unique molecular structures extensively used in the design of catalysts, therapeutics and supramolecular assemblies. Among all reactions reported to date, systems that can produce macrocycles in high yield under high reaction concentrations are rare. Here we report the use of dynamic hindered urea bond (HUB) for the construction of urea macrocycles with very high efficiency. Mixing of equal molar diisocyanate and hindered diamine leads to formation of macrocycles with discrete structures in nearly quantitative yields under high concentration of reactants. The bulky N-tert-butyl plays key roles to facilitate the formation of macrocycles, providing not only the kinetic control due to the formation of the cyclization-promoting cis C = O/tert-butyl conformation, but also possibly the thermodynamic stabilization of macrocycles with weak association interactions. The bulky N-tert-butyl can be readily removed by acid to eliminate the dynamicity of HUB and stabilize the macrocycle structures.


2020 ◽  
Vol 161 (2) ◽  
pp. 507-515
Author(s):  
J. Pach ◽  
I. Tomon

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