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

2021 ◽  
Author(s):  
Gonzalo Fiz Pontiveros ◽  
Simon Griffiths ◽  
Matheus Secco ◽  
Oriol Serra
Keyword(s):  
Arithmetic Progressions ◽  
Discrete Structures

The High Resolution Appearance of Biological Substrates

1969 ◽  
Vol 27 ◽  
pp. 416-417
Author(s):  
Glen B. Haydon
Keyword(s):  
High Resolution ◽  
Phase Image ◽  
Biological Structure ◽  
Electron Microscopic ◽  
Thin Sections ◽  
Resolution Electron ◽  
Discrete Structures ◽  
Large Phase ◽  
Biological Substrates ◽  
High Resolution Electron Micrographs

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.

Eigensolution sensitivity of discrete structures

1992 ◽  
Author(s):  
BO WANG
Keyword(s):  
Discrete Structures

scholarly journals Near quantitative synthesis of urea macrocycles enabled by bulky N-substituent

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Yingfeng Yang ◽  
Hanze Ying ◽  
Zhixia Li ◽  
Jiang Wang ◽  
Yingying Chen ◽  
...  
Keyword(s):  
High Efficiency ◽  
Molecular Structures ◽  
High Yield ◽  
Kinetic Control ◽  
High Concentration ◽  
Weak Association ◽  
Quantitative Synthesis ◽  
Thermodynamic Stabilization ◽  
Discrete Structures ◽  
Very High

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.

scholarly journals On t-core and self-conjugate (2t − 1)-core partitions in arithmetic progressions

2021 ◽  
Vol 183 ◽  
pp. 105479
Author(s):  
Kathrin Bringmann ◽  
Ben Kane ◽  
Joshua Males
Keyword(s):  
Arithmetic Progressions

scholarly journals Colorings with only rainbow arithmetic progressions

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

scholarly journals On some questions of V.I. Arnold on the stochasticity of geometric and arithmetic progressions

Nonlinearity ◽  
2015 ◽  
Vol 28 (10) ◽  
pp. 3663-3675
Author(s):  
Christoph Aistleitner
Keyword(s):  
Arithmetic Progressions

Two combinatorial theorems on arithmetic progressions

1962 ◽  
Vol 29 (1) ◽  
pp. 129-140 ◽  
Author(s):  
Wolfgang M. Schmidt
Keyword(s):  
Arithmetic Progressions

scholarly journals Product sets cannot contain long arithmetic progressions

2013 ◽  
Vol 43 ◽  
pp. 169-170
Author(s):  
Dmitry Zhelezov
Keyword(s):  
Arithmetic Progressions ◽  
Product Sets

scholarly journals The Riemann Zeta Function on Vertical Arithmetic Progressions

2013 ◽  
Vol 2015 (2) ◽  
pp. 325-354 ◽  
Author(s):  
Xiannan Li ◽  
Maksym Radziwiłł
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Arithmetic Progressions ◽  
The Riemann Zeta Function ◽  
Riemann Zeta
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