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47.1.3.1 Diels–Alder Reactions

DOI: 10.1055/sos-SD-047-00252

Fringuelli, F.; Piermatti, O.; Pizzo, F.; Vaccaro, L.Science of Synthesis, (201047561.

General Introduction

The DielsAlder reaction has a preeminent position in organic synthesis for the construction of six-membered rings, containing up to four stereogenic centers, in a regio- and stereocontrolled way.[‌1‌‌3‌] The reaction involves a cycloaddition[‌4‌] between a conjugated diene and a second component called a dienophile, which has at least one π-bond. Examples of common types of such reactions are shown in Schemes 17. Diene and dienophile can be distinct molecules (intermolecular DielsAlder reactions) (Scheme 1),[‌5‌,‌6‌] or can be part of the same molecule (intramolecular DielsAlder reactions) (Scheme 2).[‌7‌] Since its discovery, more than 50000 papers have been published concerning the synthetic, mechanistic, and theoretical aspects of this procedure. Indeed, the potential of this type of cycloaddition is enormous: carboncarbon, carbonheteroatom, and heteroatomheteroatom bonds can all be formed allowing the syntheses of carbocycles and also heterocycles (hetero-DielsAlder reactions) (Scheme 3).[‌8‌] In addition, as many as three rings can be formed in a single operation (with or without isolating the intermediates) by sequential DielsAlder reactions (multiple DielsAlder reactions).[‌9‌‌15‌] Multiple DielsAlder procedures can be of the domino type (Scheme 4),[‌10‌] where the second and third cycloadditions are the consequence of the functionality generated in the preceding reaction, or cascade, tandem, or timed reactions, where there are two or more cycloadditions in sequence (Scheme 5).[‌11‌‌13‌] Consecutive or transmissive reactions are also possible in which, after the first addition, new reagents and new experimental conditions are used to promote successive cycloadditions (Scheme 6).[‌14‌,‌15‌] Moreover, a sequence of a DielsAlder cycloaddition with other types of reactions allow the syntheses of both simple and complex molecules. A representative example of this type is illustrated in Scheme 7; it utilizes a domino Knoevenagel reaction and a hetero-DielsAlder cycloaddition combination.[‌16‌,‌17‌]

Meeeee 8 Meeeeeeeeeeeee Meeeeeeeeeeeee MeeeeMeeee Meeeeeeee[‌8‌,‌8‌]

Meeeee 8 M Meeeeeeeeeeeee Meeeeeeeeeeeee MeeeeMeeee Meeeeeee[‌8‌]

Meeeee 8 M Meeeeeeeeeeeee Meeeee-MeeeeMeeee Meeeeeee[‌8‌]

Meeeee 8 M Meeeeeeeeeeeee Meeeee MeeeeMeeee Meeeeeee[‌88‌]

Meeeee 8 M Meeeeeeeeeeeee Meeeeee (Meeeee, Meeee) MeeeeMeeee Meeeeeee[‌88‌,‌88‌]

Meeeee 8 M Meeeeeeeeeeeee Meeeeeeeeee ee Meeeeeeeeeee MeeeeMeeee Meeeeeee[‌88‌,‌88‌]

Meeeee 8 M Meeeee Meeeeeeeeee eee Meeeee-MeeeeMeeee Meeeeeee Meeeeeeeeee[‌88‌,‌88‌]

Mee eeeeeeeeeeeee eeeeeeeee eee ee eeeeeee eee eeeee e eeeeeee ee eeeeeeeeeeee eeeeeeeeee, eeee eeeeeee eee eeeee eeee eeeeeeee, eee eeeeeeee ee Meeee eeeee, Meøeeeee eeeee, eeeeeeeee eeeeeeeee, eeeeeeeee eeeee eeeeeeee, eeeeeeeeee, eeeeeeeeee, eeeeeeeeeeeeeeee, eeeeeeee, ee eeeeeeeeeeee. Mee eeeeeeeee eee eeee eeeeeeeee ee eeeeeee eeeeeee, eeeeeee eeeeeeeeeee/eeeeeee eeeee, eeeeeee eeeeeeeeeee/eeeeeeeeeeee, eeeee eeeeeee, eeeeeeeeeeeeee, eeeeeeeeeeeee eeeeee, eeeeeeeee eeeeeeee, eeeee, ee eeeee eeeeeee-eeee eeeeeeeeee.[‌8‌]

Mee MeeeeMeeee eeeeeeee eee eeee eeeee e eeeee eeeeeee ee eeeeeeeeeee eeeeeee eee eee eeeeeeeeeee ee eee eeeeeeeeee ee eee MeeeeeeeMeeeeee eeeee[‌88‌] eeee eeeeee eeeeeee eee eeeeeeeeeeeee eeeeeeeeee eeeeeeeee. Meeeeeee ee eeeeeeeee eeeeeee ee eeee ee eeeeeeee eeeeee eee MeeeeMeeee eeeeeeee eeee eeeee eeeeeeee ee eee eeeeeeeeee ee eee 88ee eeeeeee ee Meeeee eee eeeeeeeeeeee eee eeeeeeeeeeee ee eeeeeeeeeeeeeeeeeeeeeeeeeeee ee ee eeeeeeeeeeee ee eee eeeeeeeee ee eeeeeeeeee-8-eeeeeeeeeeeeeeee-8-eee-8-eeeeeeeeee eeee.[‌88‌‌88‌] Me 8888 Meeee,[‌88‌] eeee eeeeeeee eee eeeeeeeeee ee eeeeeee eeeeeeeee eeee eeeeeeeee eeeeeee eeeeeee eeeeeeeeeeeeeeee eee eeeeee eeeeeeeeeeeeeee ee eeeeeeee, eeeeeeeeee eeee eeeee eeeeeeeee eeee eeeeeee ee eeee ee eeeee eeeee-8,8-eeeeeee eeeeeeee eeee eeeeeeee. Meee eeee eeeeeeee eee eeee eeeeeeeeee eeeeeeeee ee 8888 ee Meeee eee Meeeeeeee;[‌88‌] eeeeeee, eee eeeeeeee eeeeee eeee eeeee eeeeeeeeeee eee eeeeeee eeeeeeeee eeeeee eeeee, eee eeeeeee, eeeeeeeeee eeee eeeeeeeee ee Meeee eee Meeee ee 88888888,[‌88‌,‌88‌] eeeee eeee eee eeeee eeeeeeee eeeee eeeeeeeeeee.[‌88‌] Meee eeeeeee eeeeee eee eeeeeee eeee eeeeeeeee ee eee eeeeeeeee eeeee.[‌88‌] Me eee eeeeeeeee, eeeeeeeee eeeeeeeeeeeee eee eeeeeeeeeeeee eeee eeee;[‌88‌] eee eeeeeee, eee eeeeeeee eee eeeee eeeeee eee MeeeeMeeee eeeee eeeeeeeee, eee eee eeeeeeeeee eee eeeeeeee ee ee eee eeeeeeeeee; eee eeeeeeee eeeeeeeeee eeee eeeee eeeeee eeeeeeeeee eee eee eeeeeeee eeeeee eee eeeeee eee eeeeee. Me 8888, Meee Meeee eee Meee Meeee eeeeee eee Meeee eeeee ee eeeeeeeee eee eee eeeeeeeee ee eeee eeeeeeee.

Mee eeeeee eee eeeeeee ee eeeeeeeeee eeeeee eeeeeeee ee eee MeeeeMeeee eeeeeeeeeeeee ee eeeee.[‌8‌] Meeeeeeeeeeeee eeeeeeee ee eeee-eeeee, eeeeeeeee, eeee-/eeeeeeeee, eee eeee-/eeeeeeeeee eeeeee, eeeeee eeeeee eee eeeee, eee eeeee eeeeeeeeeee eee eeeeeeeeeee ee Meeeeee 888.

Meeeee 8 Meeeeeeeeeeeee Meeeeeee ee Meee-Meeee Meeeee eee Meeee Meeeeeeeeee

Meeeee 8 Meeeeeeeeeeeee Meeeeeee ee Meeeeeeee Meeeee eee Meeee Meeeeeeeeee

Meeeee 88 Meeeeeeeeeeeee Meeeeeee ee Meee-/Meeeeeeee Meeeee eee Meeee Meeeeeeeeee

Meeeee 88 Meeeeeeeeeeeee Meeeeeee ee Meeeee eee Meeee Meeeeeeeeee Meeeee Mee Meeee

Meeeee 88 Meeeeeeeeeeeee Meeeeeee ee Meee-/Meeeeeeeee Meeeee eee Meeee Meeeeeeeeee

Me eee eeeeee, eeee eeeeeeeeeee eeee eeee eeee ee MeeeeMeeee eeeeeeeeeeeeee;[‌8‌] eeeeeee, ee ee eeeeeeeee ee eeeeeeee eeee eee ee eeeee eeeeeeeeeee. Meee eeeeeeeeeeeeee eeeeeeeeeee eee eeeeeeeeeee ee Meeee 8.

Meeee 8 Meeeeeeeeeeeee Meeeeeeeeee

Meeeeeeee Meee
eeeeeeee (eeeeeeee)
eeeeee eeeeeeee
eeeeee eeeee eeeeee
eeeeeeeeeeeee
eeeeee eeeeeeeeee
eeeeeeee eeeeeeeeeeeeeeeeeeeeee
eeeeeeeeeeeeeeee
eeeeeeee eeeeeee
eeeeeeee eeeeeeee
M-eeeeeeeeeeeeeee
eeeeee eeeeeeeee
8-eeeeee-8M-8,8,8-eeeeeeee-8,8(8M)-eeeee (M-eeeeee-8,8,8-eeeeeeeeee-8,8-eeeee)
eeeeeeee-8-eeeee
eeeee-8,8-eeeeeee
eeeeeee (eeeeeeeeeeeeee)
M88 eeeeeee eeeeee
M88 eeeeeee eeeeee
eeeeeeeeeee
eeeeeeeeeeeeee

Meee-eeeee eeeeee eeeee ee ee e-eee/e-eeeee (eeeeee/eeeeeeee) eeeeeeeeeee. Meee eee e-eee- (eeeeee) eeeeeeeee eeeeeeeee eeeeeeeeeeeee[‌88‌,‌88‌] ee eeeeeeee eee e-eeeee- (eeeeeeee) eeeeeeeee eee eee eeeeee eeeeee ee eee ee eeeeeeeeeee eeeeeeee eee, eeeee eeeeeeeeeeeee, eeeee eeee ee ee eeeeeeeeeeeee eeeeeeeee eeeeeeeeee eee-eeeeeeee eeee eeee eee eeeeee eeee ee eee eeeee eeeeeeeeeeeee. Meee eeeeeeeee ee eeeeeeeeeee ee Meeeee 88 eeeee eeeee-8,8-eeeee (8; eeeeeeeeee) (ee eeeeeeee) eee eeeeeeeeeeeeeee (8) eee eeeeeeeeeeeeeee ee eeeeeeee eeeeee, eeeeeee e-eeeee-8,8-eeeeeeeeeeee-8,8-eeeee (8), 8-eeeeeeeeeeeeeeeeeeee (8), eee 8,8,8,8,8,8e-eeeeeeeeeeeeeeeeeeee (8) eee eeeeeeeeee.

Meeeee 88 Meeeeeee eee Meeeeeeeee Meeeee

Meeeeeee-eeee eeeeee eeeee eeeeeeeeeeeeee eeee eeeeeeee-eeeeeeeee eeeeeeeeeee eee, ee eeee eeeee, eee eeeeeeee eeee ee eeeeeeeee ee eeeeeeee-eeeeeeee eeeeeeeeeeee ee eee eeeeee eee ee eeeeeeee-eeeeeeeeeee eeeeeeeeeeee ee eee eeeeeeeeeee. Me eee eeeeeeeeee eeee eeeeee ee eeeee ee eee Meeee eeee.[‌88‌] Meeeeeee[‌88‌] eeeeee eeee eeee ee eeeeeeee e eeeeee eeeeeeee-eeeeee MeeeeMeeee eeeeeeee, eeeee ee eeeee ee e eeeeeeeee eeeeeeeeeee ee eee eeeee MMMM eee eee eeeeeeeeee MMMM. M eeeeeee eeeeeee ee eeeeeeee ee eee eeeeeeeeeeeee eeee eeeee ee eee eeeeeeeeeee 8 (Meeeee 88).[‌8‌] Meeeeeee-eeeeeeeee eeeeee eeeee eeeeeeeeeeeeee eeee eeeeeeee-eeee eeeeeeeeeee, eee eeeeeeee-eeeeeeeeeee eeeeeeeeeeee eeeeeee ee eee eeeee ee eeee ee eeeeeeee-eeeeeeee eeeeeeeeeeee ee eee eeeeeeeeeee eeeeeee eeeeeeeeee eee eeeeeeee (ee eeeeeee-eeeeeeee-eeeeee MeeeeMeeee eeeeeeee).[‌88‌] Mee eeeee eeeeeee ee eeee eeee ee eeeeeeee eee eeeeeeee ee Meeeeeee eee Meee,[‌88‌] eee ee ee eee eeee eeeeeeeeeee eee eee eeeeeeeee ee eeeeeeeeeeee eeee eeeeeee eeee eee eeeeeeee eeeeeee ee eeee eeeeeeeee eeeeeeeee eeeeeeeee.[‌88‌‌88‌] Mee eeee eeeeeeeeeeeee eeeeee eeee eee eeeeeeeee 8 eeeeee eeee eeeeeee ee eeeeee eee eeeeeeee eeeeee 8 (Meeeee 88).[‌8‌] Me eee eeee eeeeeeee ee eee MeeeeMeeee eeeeeeeeeeeee ee eeeeee eeeeeeeeeee ee eee eeeeee ee eeeeeeeeeeee eeeeeee ee eee eeeee eee ee eee eeeeeeeeee, eee eeeeeeee ee eeeeeeeeee ee e eeeeeee-eeeeeeee-eeeeee MeeeeMeeee eeeeeeee. Mee eeeee eeeeeee ee eeee eeee ee eeeeeeeeeeeee ee eeeee ee Meeeee 88; ee eee eeeeeeee ee Meeeeeeee eee Meeeeeeee ee 8888.[‌88‌]

Meeeee 88 M Meeeee-Meeeeeee-Meeeee MeeeeMeeee Meeeeeee[‌8‌]

Meeeee 88 Me Meeeeee-Meeeeeee-Meeeee MeeeeMeeee Meeeeeee[‌8‌]

Meeeee 88 M Meeeeee-Meeeeeee-Meeeee MeeeeMeeee Meeeeeee[‌88‌]

Meee eeeeee eee eee ee e eeeee ee eeee ee e eeeeeeeeee. Meeeeee eeeeeeee eee eee eeeeeeeeeeeee ee eeeeeeeeeeeeeee[‌88‌] eee eeeeeeeeeeeeeeeeee,[‌88‌,‌88‌] eee eee eeeeeeee ee 8,8-eeeeeeeeeeeeeeeee 8,8-eeeeeee (8) eeee eeeeeeeeeeeeeee[‌88‌] (Meeeee 88). Meeeeeeeeeeeeee ee eeeeeeeeeeee eeeeeeeee eeee ee e eeeee ee eeee eeeeeeeeeee, eee eee eeeeeee ee eeeeeeee ee 888°M ee e eeeee-MeeeeMeeee eeeeeeee ee eee eeeee.

Meeeee 88 Meeeee Meee Meee Mee ee Meeeeeeeeee[‌88‌‌88‌]

Mee eeeeeeeeee ee eee eeeeeeee eeeeeeeeeee, eeeeee eee eeeeeeeee, ee eeee eee eeee eeeeee eeeeeeee-eeee eeeeee, eee eeeeeeeee eeee eeeee eeeeeeeee eeeeeee eeeeeee ee ee eeeeeeeee ee eeee eeeeeeeeeee.[‌8‌,‌88‌,‌88‌,‌88‌] Meeeee eeee eeeee eeeeeeeeee eeeeee eeeeeeee-eeeeeeeee eeeeee.[‌88‌,‌88‌] Meee eeeeee ee eeeeeeeeeee eeee ee eeeeeeeee ee eeee eeeeeee ee eeeee eeee eeeeeeeeee eee/ee eeeeeeeeeee. Meeeeeee eee 8,8-eeeeeeeeeee-8,8-eeeeeeeeeeeeeeee (88),[‌88‌] eeeeeee (eeeeeeeeeeeeee) (88),[‌88‌] eee eeeeee 8-(eeeeeeeeeeeeeeeeeee)eeee-8-eeeeee (88) (Meeeee 88).[‌88‌] Meeeeee ee e MeeeeMeeee eeeeeeee ee eeeee ee eeeeeeeee eee ee eeeeeeeeeee eeeeeee eee eeeeeeeeeeeee eeeeeeee eee eeeeee eeeeeeeeeeeeee ee eeeeeeeeeeeeeeee eeeeeeeee ee eee eeeee eee eeeeeeeeee eeee eee eeeeeee ee eee eeeeeeee ee eeeeee eeeeeeeee.[‌88‌]

Meeeee 88 Meeeee eee Meeeeeeeeee Meeeeeeee Me Meee[‌88‌‌88‌]

Mee MeeeeMeeee eeeeeeee ee e eeeeeeeeeeeee ee eeeee eee eeeee eee eee π-eeeeeeeee eee eeeeeeee ee eeee eee eee σ-eeeee eee eee π-eeee. Meeee eeee eeeeeeeeee eeeeeeee eeee eeeee eeeeeeeeeeeee, eee eeeeeeee ee eeeee eeeeeeeee ee e [π8e + π8e] eeeeeeeeeeeee.[‌88‌,‌88‌] Meeeeee, eeee eeeeeeeeeee ee eee eeeeeeeeeee, eeeeeee ee eeee eeeeeeee eeeee eeeeeeeeeeeeee eeeeeeeee eee eeee eeeeee ee eeeeeeeee (e.e., 8,8-eeeeeee eeeeeeeeeeeeee) eee ee ee ee eeee eee eeee MeeeeMeeee eeee eeeeeeee eeeeeeeee eee eeee ee eeeeeeee. Mee eeeeeeeee ee eee MeeeeMeeee eeeeeeee eee eeee eeeeeeeeeee eeeeeeeeeeee, eeee eeee eeeeeeeeeee eee eeeeeeeeeeee eeeeee ee eeee.[‌88‌‌88‌] Mee eeee eeeeee ee eeee eeeeeeeee eeeee eeee eee eee MeeeeMeeee eeeeeeeee eee ee eeeeeeeee ee eeee eee eeeeeeeee. Meee-eeeeeee eee eeee-eeeeeeee eeeeeee eee eeeeeeeeee eee eeeee eeeeeee eee eeee eeeeeeee eeeeeeee: (e) e eee-eeee eeeeeeeee eeeeeeee eeee e eee-eeeeeeee eeee eeeeeeeeee eeeee, ee eeeee eee eeeeeeeee eee eee eeeeeeee ee σ- eee π-eeeee eeeee eeeeeeeeeeeeee (eeeeeeeee eee eeeeeeeeeee eeeeeeee)[‌88‌,‌88‌] ee eee σ-eeee ee eeeeee ee eeeeeee ee eee eeeee (eeeeeeeee eeeeeeeeeeee eeeeeeee),[‌88‌,‌88‌,‌88‌] ee (ee) e eee-eeee eeeeeeeee ee eeeee eee eee σ-eeeee eee eeeeee eee eee eeeeeeeeee eeeeeeeeee eeeeee eeeeeeeee e eeeeeeeeeeee ee e eeeeeeeee eeeeeeeeeeee (Meeeee 88).[‌88‌,‌88‌‌88‌] Meee eee eeeeeeeeeeee ee e eeeeeeeee, eee eeeeeeeeeeeee ee e eeeeeee eee e eeeeeee eeeeeee eeee ee eeeeeeeeee, ee eeeee ee eeeeeeeee.

Meeeee 88 Meeeeeeeee ee eee MeeeeMeeee Meeeeeee[‌88‌,‌88‌‌88‌]

Meeeeeeeee eeeeeeeee eee eeeeeeeeeeeeee eeee eeeeee eeeeeee e eeeeeeeeee eeeee ee eeeee eee eeee-eeeeeee eee eeee-eeeeeeee eeeeee eeeeeeeeeeeeee eeeeeee eee eeeeeeeee ee ee eeeeeeeeeeee;[‌88‌] eeeee, eeee MeeeeMeeee eeeeeeeee eeee eeeeeee ee e eee-eeee eeeeeeeee eee ee eee eeeeeeeeee eeee. M eee-eeee, eeeeeeeee eeeeeeeee ee eeeeee eeeeeeeee ee eee eeeeeeeeeee eeee eee eeeeeeeeeeee eeeeee ee eeeee 8 eee 8 ee eee eeeee eeeeee eeeeee ee eee eeeeee. Meee, eee eeeeeeeeeeee ee e 8,8-eeeee,eeeee-eeeeeeeeeeeee eeeee eeeeee eeee ee e eee-eeeeeeeeeeee ee eee eeeeee, eeeee eee eeeeeeeeeeee ee e 8,8-eeeee,eee-eeeeeeeeeeeee eeeee eeee ee ee eeeee-eeeeeeee eeee eeeeeee ee eeee eeeee ee eee eeeeee. Mee eee- ee eeeee-eeeeeeeeeee ee eeeeeeeeeeee ee eee eeeeee eeee ee eee eeeeeeeeee ee eeeeeeee ee eee eeeeee [eee MeeeeMeeee eee eeeeeeeee (eee eeeee)].

Meee eeeeeee MeeeeMeeee eeeeeeeee, eeeeeeeeeeee eeeee eeeeeeeee eeeeee eeeeee eee eeeeeeeeeee, eee eeeeeeeee ee e eee-eeee, eeeeeeeee eeeeeeeee.[‌88‌] Me eeeee-eeeeeeeee MeeeeMeeee eeeeeeeee eee eeeeeeeeee eeeee eee ee eeeeeee ee e eeeeeeeee, eeeeeeeeeeee eeeeee.[‌88‌] Meeee[‌88‌‌88‌] eee eeeeeee[‌88‌‌88‌] MeeeeMeeee eeeeeeeee eee eeeeeeeee eee eeeeeeeeee ee eeeeee eee eeeeeee ee e eeeeeeee eeeeeeeee; eee eeeeee eeeeeeeeeeeeee eee-eeeeeeee eeee ee eeeeeeeee eeeeeeee eee eeee eeeeeeeeeeee eeee eee eeeeeeeeee eeee eee eeee eeeeeee eeeeeee ee eee eeeeee ee eeeeee eeee eee eeeeeeee eeeeee e eeeeee eeee.

Mee MeeeeMeeee eeeeeeee ee e eeeeeeeeee eeeeeeeeeeeee, eee eee eeeeeeeee eeeee ee eeeeeeeeee ee eeeeeeeeeeeeee; eeee, eee eeeeeeeee ee e eee-eeeeeeee eeee ee eeeeeee eeeeeee eeeeeee eee π-eeeee eee eeeeeeee ee eee σ-eeeee. Mee eeeeeeeeeeeeee (eeeee-MeeeeMeeee eeeeeeee) eeeeee eeeeee eeee e eeeeee eeeeeeee eee ee eeeeeee eeee eee eeeeeeee eeeeee. Meeeeeee eee eeeee-MeeeeMeeee eeeeeeee eeeeeeeee eeeeeeee eeee eeeeeeeeeeee, ee eee ee eeeeeeeeeee ee eeeeeeeeeeeee ee eeeee eeeee eeeeeeeeeee ee eee eeeeeeee eeeeee ee eee eeeeeeee eeeee ee ee eee ee8 eeeeee ee eee eeeeeeeeee.[‌88‌,‌88‌] Mee eeeeeeeeeee ee MeeeeMeeee eeeeeeeeeeeee eee eeeee-MeeeeMeeee eeeeeeeee eee ee eeee ee eeeeeee eeeeeeeee ee eeee e eeeee eeeeeeee,[‌88‌] ee eeeeeee e eeeeee eeee,[‌88‌‌88‌] eee ee eeeeeee eeeeee eeeeeeeee[‌88‌] (Meeeee 88).

Meeeee 88 Meeeeeeeeeeeee Meeee-MeeeeMeeee Meeeeeeee[‌88‌,‌88‌,‌88‌]

Meee eeeeeeee eee eee eeee eeee-MeeeeMeeee eeeeeeee ee eeeeeeee eee [8π+8π+8π] eeeeeeeeeeeee eeeeeee e eeeeeeeeee eee e eeeee ee eeeee ee ee8-eeeeeeeeee eeeeee eeee eeeeeeeee eee eeeeee eeeee (eeeeeeeee). Meeeeeee ee eee [π8e + π8e] MeeeeMeeee eeeeeeee, ee eeeee eee σ-eeeee eee eeeeee, ee e eeee-MeeeeMeeee eeeeeeeeeeeee e eeeee σ-eeee ee eeeeeee eeeeeee ee e π-eeee (eee Meeeee 88),[‌88‌] eee e eeeeeee eeeeee ee eeeeeeee.[‌88‌‌88‌] Mee eeeeeeeeeeeee ee eeeeeeeeeeeee eeee eeeeee eeeeeeeee eee eee eeeee eeeeeee ee e eeee-MeeeeMeeee eeeeeeee ee ee eeeeeeeee.[‌88‌]

Meeeee 88 Meeeeeee ee Meee-MeeeeMeeee Meeeeeeee[‌88‌]

Me ee eeeeeeeee ee eeee eeee eeee eeeeeeee eee eee eeee eeee-MeeeeMeeee eeeeeeee ee eeee e [8π+8π] eeeeeeeeeeeee ee eeeee eee eeeee eeeeeeee ee eee eeeeeeeeeeee ee e eee-eeeeeeee eeee eee eee eeeeeee.[‌88‌]

Mee eeeeeeeeeeeee eeeeeee eee ee eeeeee ee eee eeeeeeeeeeeee ee eeeeeeeeeeeee eeeeeeeeee eee eeee eee eeeee eeeee eee eeeeeee eeeeeeeeeeee ee eeeeeeeeeeeee eeeeeeee; eeee eeeeeeeeeeeeee eeeeeeee eee eeeee ee Meeeee 88.[‌88‌‌88‌] M eee eeeeee ee eeeeeeeeeeee eee eeee eeee eeeeeeee ee eeeeeeee eeeeeeeeeeee eeeeeeeeeee eeee eeeee-eeeeeeeeeee eeeeeee.[‌88‌] Mee eeeeeeeeeeeeeeee ee eee eeeeeeee ee eeeeeeeeee ee eee eeee ee eeeeeeeeeeee, eee eeeeeeee, eee eee eeeeeeee eeeeeeeeee.[‌88‌,‌88‌,‌88‌] Mee eeeee- eee eeee-eeeeeee, eeeeeeeeeeee, eee eee eeee eeeeeeeeeeee eeee eee eeeeeeeee ee 8- eee 8-eeeeeeeeeee eeeeeeeeee eeee eeeeeeeeeeeeeee eeeeeeeeeee.[‌88‌] Meee eeeeeeeee eeeeeeeeeeee eee eeeeeee ee eee eeeee, eee eeeeeeeeeeeeeeee ee eee eeeeeeee ee eeeeeeeeee ee eee ee eeee.[‌8‌] Meee, ee eee eeeeeeee ee 8-eeeeeee-8-(eeeeeeeeeeeeee)eeee-8,8-eeeee (88) eeee eeeeee eeeee eeeeee, ee ee eee eeeeeeeeeeeeee eeeee eeee eeeee ee eee eeeeeeeeeeeee.[‌88‌,‌88‌] Mee eeeeeeee eeeeeeeeeeeeee eee ee eeeeeeeee ee eeeeeeeeeee eee eeeeeeeeee eeeeee ee eee eeeeeeeeeeee (eee eeee eeeeeeee eee eeeeeeeeee eeeeee ee eee eeeeeeeeeee eee eeee eeeeeeeeeeeeee eee eeeeeeee) ee ee eeeee eee eeeeeeee eeeeeeeee eeeeeee (MMM) eeeeee.[‌88‌,‌88‌,‌88‌]

Meeeee 88 Meeeeeeeeeeee ee Meeeeeeeeeeee Meeeeeeeeee ee MeeeeMeeee Meeeeeeee[‌88‌‌88‌]

Me eeeeeeeee MeeeeMeeee eeeeeeeeeeeeee, eee eee eee eeeee eee eeeeee ee eee eeee eeee ee eeeeee eee eeeee ee eee eeeeeeeeee, eeeeeee ee eeeeeeeee ee eeeee eeee eeeeeeeeee eee eeeeeee eeeeeeeeeeeee (eeeeeeeeee eeeeeeee).[‌88‌,‌88‌] Meee eeeeee ee eeee eeeeeee eeeeeeeee eee eeeeee eeeeeeeeeee ee eee eeeeeeeeeeee eeeeeee ee eee eeeee eee eee eeeeeeeeee. Meeee eee Meeee eeeeeeeeee eeee eeeeeeeeeee ee eee eee eeeeeeeee (Meeeee 88).[‌88‌]

Meeeee 88 MeeeeMeeee eee Meeeeeeee[‌88‌]

Meee ee, eee eeeeeeeeeeeee ee eee eeeeee eeeeee eeeeeee ee eee eeeeeeee eeeeeeeeeee ee eee eeeeeeeeee eee, eeeeee eeeeeeee, eeeee eeeeeeeeeeee eee ee eeee ee eee eee eee ee eeee. Me eeee eeeeeeee eeeeee eeee eee eeeeeee eeee ee eee eeeee eee ee eee eeeeeeeeee eee eee eeeee eee eeeee (eeeeeeee-eeee eeeeeeeeeee), eeeee ee ee eee-eeeeeeee eee eeeeeee eeee ee eee eeeeeeeee ee eeeee eee eeeeeee eeee ee eee eeeee. Mee eee-eeeeee ee eeeeeee eee eeeeeeeeeeeeeeeee eeee eeeeee, eee ee eee eeee-eeeeee ee eeeeeeeeeee eeeeeee, eee ee eeeeeeeee eeeeeee eeeeeeeeeeee eeee eeeeeeeee eee eeeeeeeeee eeeeeeeeee eeeee, eee eeee-eeeeee ee eeeeeeee eee eeeee eeeeeeee eeeeeee. Mee eeee eeeeeeeeee ee eeee eeeee ee eee Meeee eeee eeee.[‌88‌] Me eeeeeee ee eeeee eee eee eeeeeeee ee eeeeeeeeeeeeeee eeee eeeee-8,8-eeeeeee (Meeeee 88).[‌88‌]

Meeeee 88 Me Meeeeee ee eeee eeeeee eee Meeeeeeeeee[‌88‌,‌88‌]

M eee,eeee eeeeeeeeeee eeeeee eeee eee eeeee ee eee ee eeee eeeeeeeeee eee eeeeeeeeeeeeee eee eee eeeeeeeeeeee eeeeeeee ee eee eeeeeeeee ee eeee eeeeeeeee eeeeeeeeee ee eeeeee eeeeeeeeeee (eee Meeeee 88).[‌88‌]

Meeeee 88 Meeeeeee ee eeee/eee eee eee/eeee Meeeeeeeeeee[‌88‌]

Meeeeeeeeeeeee eee eeeeeeeeeeeee eeeeeee eee eeee e eeee ee eee eeee eeee; ee eeeeeeeeeeee ee eeeeeeee ee eee eeeeee ee eee eeeeeeeeeeee eeeeeeee eeee eee eeeeeeeeeee ee eeeeee eeeeeeee eee (8M)-8-eeeeeeeeee-8,8-eeeee (Meeeee 88).[‌88‌]

Meeeee 88 Meeeeeee ee eeee/eee eee eeeee/eeee Meeeeeeeeeee[‌88‌]

Mee eeeeeeee eeee, eeeeeeeeeeeeeeee, eee eeeeeeeeeeeeeee ee eee MeeeeMeeee eeeeeeee eee eeeeee eeeeeeeee ee eeeeeeee eeeeeeeee eeeeeee (MMM) eeeeee, eeeee eeeeee eeee eeee eeeeeeee ee eeeeeeeeee ee eee eeeeeeeeeee ee-eeeee eeeeeeeeeee ee eee eeeeeee eeeeeeee eeeeeeeee eeeeeee (MMMM) ee eee eeeeeeeee eee eee eeeeee eeeeeeeeee eeeeeeeee eeeeeee (MMMM) ee eee eeeee.[‌88‌,‌88‌‌88‌] Mee eeeeeeee eeee eeeeeee ee eee eeeeee MMMMMMMM eeeeee eeeeeeeeee ee eee eeeeeeeeee. Mee eeeeeeee eeeeeee eeeeeeeeeee ee eee eeeeee eeeeeeee-eeeeee MeeeeMeeee eeeeeeee ee MMMM eeeee/MMMM eeeeeeeeee (MMMM-eeeee eeeeeeeeee), eee ee eee eeeeeee-eeeeeeee-eeeeee MeeeeMeeee eeeeeeee ee ee MMMM eeeee/MMMM eeeeeeeeee (MMMM-eeeee eeeeeeeeee). Mee MMMM eee MMMM eeeeeeee ee eee eeeeeeeeee eee eeeeeeee ee eee eeeeeeeeeeee: eeeeeeeee eeeeeeee, ee eeeeeeee-eeeeeeee eeeeeeeeeee (MMM; e.e., Me, MMe, MMe8) eeeeee ee eeee eeeeee eeeeeeeeeee 88 eee eeeeee 88 eee 88 eeeeee eee eeeeee ee eeee eee MMMM eee MMMM ee eee eeeee eee eee eeeeeeeeee, eee eeeeeeee-eeeeeeeeeee eeeeeeeeeeee (MMM; e.e., Me, MM, MM8) eeeee eeee eee MMMM eee MMMM ee eee eee eeeeeeeeee (Meeee 8). Meeeeeeee eeeee eeeeeeeeeeee eeeee eeee eeeeeee ee eeeeee eee eee MMMMe eee MMMMe ee eeeeeeeeeeeeeee eeeeeee eee 8-eeeee- eee 8-eeeeeeeeeee eeee-8,8-eeeeee eeeeeeee ee eee eeeeeeeeeeeee eeeeeeeee eeeeeeee ee eeeeee eee eeee-8,8-eeeee, eeeeeeeeeeee, eeeeeeee eeee e eeeeee eeeeeeeeeee ee eeeeeee ee eee eeeeeeeeeee eeeeeeeee ee eee eee eeeeee ee eeeeeeee eee MMMM eee eeeeeee eee MMMM eeeeeeee ee eee eeeeee eeeeee eee eeeee (Meeee 8).[‌88‌]

Meeee 8 Meeeee Meeeeeeeeeeeeee Meee eee Meeeee Meeeeeeeee Meeeeeeeee ee MMMM eee MMMM Meeeeeee Meeeeeee ee eee Meeeeeeeeeeee Meeeeeeee Meeeeeeee ee eee Meeeee Meeeeeeee[‌88‌]

M8 MMMMe MMMMe Mee
Me + [‌88‌]
MMe + + [‌88‌]
MMe8 + + [‌88‌]
Me + + [‌88‌]
MMM [‌88‌]
MM [‌88‌]
MM8 [‌88‌]

e Meeeeeeee ee eeeeee (+=eeeeeee; =eeeeeeee) ee MMMM eee MMMM.

Meeeeeee-eeeeeeee eeeeeeeeeeee ee eee eeeee eee eeeeeeee-eeeeeeeeeee eeeeeeeeeeee ee eee eeeeeeeeee eeeeeeeeee eee eeeeee-eeeeeeee-eeeeee MeeeeMeeee eeeeeeee (Meeeee 8), eeeee eee eeeeeeee ee eeeeeeee-eeeeeeeeeee eeeeeeeeeeee ee eee eeeee eee eeeeeeee-eeeeeeee eeeeee ee eee eeeeeeeeee eeeeeeeeee eee eeeeeee-eeeeeeee-eeeeee MeeeeMeeee eeeeeeeee (Meeeee 8). Me eeee ee eeeee eeeeeee eee eeeeeeee eeeee eee eeeeeee eee eeee eeee ee eeeee eee eeeeeeeeee.

Meeeee 8 MMM Meeeeeeeeeee eee Meeeee-Meeeeeee-Meeeee MeeeeMeeee Meeeeeeee[‌88‌]

Meeeee 8 MMM Meeeeeeeeeee eee Meeeeee-Meeeeeee-Meeeee MeeeeMeeee Meeeeeeee[‌88‌]

Mee eeeeeeeeeeeeeeee ee eee MeeeeMeeee eeeeeeee ee eeeeeeeee ee eeeeeeee eeeeeeeee eeeeeee eeeeee ee eee eeeee ee eeeeeee eeeeeeeeeeee ee eeeee ee eeeeeeeeee eeee eeee eee eee σ-eeeee. Me eeeeeee eee eeeeeeeeeeeeeeee, ee ee eeeeeeeee (e) ee eeeeeeee eee MMMMMMMM eeeeee eeee eeeeeeee eee eeeeeeee eeee, (ee) ee eeeeeeee eee eeeeeeee eeee ee eee eeeeee eeeeeee eeeeeeeeeeee ee eeeee eeeee eeee eeee eee σ-eeeee, eee (eee) ee eeeee eee eeeeee eeeeeeeeeeee eeee eeee eeeee (Meeeeee 88 eee 88). Mee eeeeeeeeeee ee ee eeeeee eeeeeee ee eeeeeeeeeee ee e eeeeee, eee eeeeeeee ee eeeee ee eeeeeee eeeeeeeeeeee ee eee eeee (eee eeeeeeee eee Meeeeee 8 eee 8); eee eeeeeee eee eeeeeeeeee eeeeeee eee eeeeeee eeeeeeeeeeee ee eee eeeeeeeeee, eee eeee eeeeeeeeeeeeee eee eeeeeeee.

Meeeee 88 Meeeeeeeeeee ee Meeeeeeee Meeeeeee eee Meeeeeeeeeeeeeee ee Meeeee-Meeeeeee-Meeeee MeeeeMeeee Meeeeeee

Meeeee 88 Meeeeeeeeeee ee Meeeeeeee Meeeeeee eee Meeeeeeeeeeeeeee ee Meeeeee-Meeeeeee-Meeeee MeeeeMeeee Meeeeeee

Meeee eee Meeee eeeee eeeeeeeee eee eeee eeeeeeee eeeeeeeeee ee eee eeeee ee eeeeeee eeeeeeeeeeeee ee eeeeee eeeee ee eee eeeeeeeeeeeeee eeeeee ee eeeeeeee.[‌88‌] Mee eeeeeeee eeeeeeeee eeeeeee eeeeee eeeeeeee eeee eeeeeee eeeeeeee ee eee eeeee ee eeeeeeeee eeeeeee eeeeeeeeeeee (eeeeeeeeee eee-eeeeeee eeeeeeeeeeee) eeee eeeee eee eeeeee ee eee eeee-eeeeeeeeee eeeee eeee eeeeeee ee eeee ee eee eee-eeeeeeeeee eeeee (eee Meeeee 88).

Meeeee 88 Meeeeeeee Meeeeee Meeeeeeeeeee ee eee eeee Meeeeeee ee Meeeee- eee Meeeeee-Meeeeeee-Meeeee MeeeeMeeee Meeeeeeee

Meeeeeeee MeeeeMeeee eeeeeeeee eeee eeeeeeee eeeeeeeee eeeee 8888, eeee ee eee eeeee eeee eee eeeeeeee ee eeeeeeee-eeeeeeeee eeeeeeeeeee eeee eeeeeeeeee ee eeeeeee eeeeeeeeeee ee eee eeeeeeee ee eeeeeeee eeeeeeeeeee.[‌88‌] Meeeeeee, ee ee eeee eeeee eeee e eeeeeeee eeeeeeee (eeeeee e Meeee eeee) eeeeee eee eeeeeeeeeeeee (e) ee ee eeeeeee eee eeeee eeeeee eeeeeeeeee eeee eeee ee eeeeeeee ee eeeee, (ee) ee eeeee ee e eeeeee eeee, eee (eee) ee ee eeee eeeee- eee eeeeeeeeeeeeeeeeee. Mee eeeeeeee eeeeeeeee eeeeeee eeeeee eeee eeeeeeee eee eeeeeeee eeeeeeeee ee Meeee eeeee; eee eeeeeee, eee eeeeeeee eeeeeeeeeee eeeeeeeee MeeeeMeeee eeeeeeeee ee eeeeeeeeeeeeee eeee eeee-8,8-eeeeee[‌88‌] eee eeeeeeee eeeeeeeeeee ee eeeeeeeeeeee eeeeeee eee eeeeeeee eeeee eee eee Meeee eeee, eeeeeee eeeeeeeeee eee eeeeeeeeeee eeeeee ee eee eee eeeee ee eee M=M eeee. Me eeee eeee eeeeeee eee eeeeee ee eee MMMM ee eee eeeeeeeeee eee eeeeee eee eeeeee eeeeeeeeee eeeeeee eee MMMM ee eee eeeee eee eee MMMM ee eee eeeeeeeeee. Mee eeeeeeeee eee eeee eeee eeeee- eee eeeeeeeeeeeeeee eeeeeee eee eeeeee eeeeeeeeeeee eeeeeeeee eee MMMM eeeeeeeeeee ee eee eeeeeeee eeeee eee eeeeeeeeeeee, eeee eeeeeeeee eee eeeeeeeeee ee eeeeee eeeeeee eeeeeeeeeeee ee eee eeeeeeeeee, eee eee eeeeeeeeeee eeeeee ee eee eeeeeeeee eeeeeee eeeeeeeeeeee. M eeeeeee ee eeeeee eee Meeee eeee eeeeeeeee MeeeeMeeee eeeeeeeee ee eeeeeeeeeeeeee ee eee eeeee.[‌88‌] Me eeeeeeee eeee eeeeeeeeee, eeeeeeeeeee eeeeeeeeee[‌88‌] eee eee eee ee eeeeeee eeeeeeeee eeee eeee eeeeeeeee.[‌8‌‌8‌,‌88‌]

References