scholarly journals The Walsh model for $M_2^*$ Carleson

2008 ◽  
pp. 721-744
Author(s):  
Ciprian Demeter ◽  
Michael Lacey ◽  
Terence Tao ◽  
Christoph Thiele
Keyword(s):  
Walsh Model

scholarly journals Hardy spaces and a Walsh model for bilinear cone operators

1999 ◽  
Vol 351 (8) ◽  
pp. 3267-3300 ◽  
Author(s):  
John E. Gilbert ◽  
Andrea R. Nahmod
Keyword(s):  
Hardy Spaces ◽  
Walsh Model

A comparative study of bent-bond vs. Walsh model in strained systems. Bicyclo(1.1.0)butane

1984 ◽  
Vol 66 (3-4) ◽  
pp. 193-205 ◽  
Author(s):  
Mirjana Eckert-Maksić ◽  
Zvonimir B. Maksić ◽  
Rolf Gleiter
Keyword(s):  
Comparative Study ◽  
Walsh Model

The Bonding and Reactivity of α-Carbonyl Cyclopropanes

Synthesis ◽  
2019 ◽  
Vol 52 (01) ◽  
pp. 27-39 ◽  
Author(s):  
Alexander J. Craig ◽  
Bill C. Hawkins
Keyword(s):  
Total Synthesis ◽  
Materials Science ◽  
Synthetic Methods ◽  
Specific Nature ◽  
Donor Acceptor ◽  
History Of ◽  
Walsh Model ◽  
The Relationship ◽  
Strain Model

The cyclopropane functionality has been exploited in a myriad of settings that range from total synthesis and methodological chemistry, to medical and materials science. While it has been seen in such a breadth of settings, the typical view of the cyclopropane moiety is that its reactivity is derived primarily from the release of ring strain. While this simplified view is a useful shorthand, it ignores the specific nature of cyclopropyl molecular orbitals. This review aims to present the different facets of cyclopropane bonding by examining the main models that have been used to explain the reactivity of the functionality over the years. However, even with advanced theory, being able to precisely predict the reactivity of an exact system is nigh impossible. Specifically chosen, carbonyl-bearing cyclopropyl species act as so-called acceptor cyclopropanes and, if correctly derivatised, donor–acceptor cyclopropanes. By undertaking a case study of the history of carbonyl cyclopropanes in organic synthesis, this review highlights the relationship between the understanding of theory and pattern recognition in developing new synthetic methods and showcases those successful in balancing this critical junction.1 Cyclopropanes2 The Strain Model3 The Forster–Coulsin–Moffit Model4 The Walsh Model5 Acceptor, Donor, and Donor–Acceptor Cyclopropanes6 Reactions of Carbonyl Cyclopropanes

Vibration Frequencies and Normal Coordinates of 3Radialene

2001 ◽  
Vol 56 (6-7) ◽  
pp. 505-508
Author(s):  
Rehab M. Kubba
Keyword(s):  
Normal Coordinate Analysis ◽  
Ir Absorption ◽  
Vibration Frequencies ◽  
Mo Calculations ◽  
Normal Coordinate ◽  
Normal Coordinates ◽  
Central Carbon ◽  
Walsh Model

Abstract SCF-MO calculations of the vibration frequencies and IR absorption intensities of 3radialene are re­ ported. Complete normal coordinate analysis for the molecule was done. The C=C str. frequencies of 3radialene are found to be intermediate between the values for ethylene and acetylene. The results are explained in terms of a modified Förster-Walsh model for the 3ring in which the central carbon atoms show sp hybridization.

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