Action variables for Toda Lattices

This Letter contains constructions of complex action variables for both the full Kostant-Toda Lattice in sl(n, ) and the generalized nonperiodic tridiagonal Toda lattice associated to an arbitrary complex semisimple Lie algebra g. The main tool is the explicit factorization solution for certain Hamiltonian flows. The Letter also contains a generalization of the standard factorization solution theorem necessary for the analysis of the full Kostant-Toda lattice.     

Generation of Ethyl Metathiophosphate by Thermal Fragmentation of O-Ethyl N-Substituted Phosphoramidothioates

O-Ethyl N-1-adamantylphosphoramidothioate was synthesized and found to fragment on heating in inert solvents to form the pyrophosphate AdNHP(S)(OEt)OP(S)(OEt)OH. The proposed mechanism involves an elimination of the amine portion with release of ethyl metathiophosphate (EtOP(S)O), as was confirmed in previous work for the comparable structure with oxygen. This transient compound then phosphorylates the starting phosphoramidothioate. O-Ethyl N,N-diethylphosphoramidothioate was also synthesized, and while it gave a similar pyro compound on heating, the reaction mixture was more complex. Both phosphoramidothioates, however, served effectively as thiophosphorylating agents toward alcohols, a silanol, and the silanol groups on the surface of silica gel. Exploratory experiments showed that these phosphoramidothioates also could thiophosphorylate the OH group of a monoester of phosphoric acid, as well as that of phosphinic acids, forming anhydrides with the partial structure     

The Landau-Lifshitz equation,elliptic curves and the ward transform

The Landau-Lifshitz (LL) equation is studied from a point of view that is close to that of Segal and Wilson's work on KdV. The LL hierarchy is defined and shown to exist using a dressing transformation that involves parameters ₁, ₂, ₃ that live on an elliptic curve . The crucial role of the groupK ₂ × ₂ of translations by the half-periods of and its non-trivial central extension is brought out and an analogue of Birkhoff factorisation for -equivariant loops in is given. This factorisation theorem is given two treatments, one in terms of the geometry of an infinite-dimensional Grassmannian, and the other in terms of the algebraic geometry of bundles over . Further, a Ward-like transform between a class of holomorphic vector bundles on the total spaceZ of a line-bundle over and solutions of LL is constructed. An appendix is devoted to a careful definition of the Grassmannian of the Frechet spaceC (S ¹).     

Catalyzed Addition of Aldehydes to Activated Double Bonds—A New Synthetic Approach

In the presence of cyanide ions as catalyst, aromatic and heterocyclic aldehydes can be smoothly added to α,β-unsaturated ketones, esters, and nitriles in aprotic solvents to form γ-diketones, 4-oxo carboxylic esters, and 4-oxo nitriles. Thiazolium salts in the presence of bases are also suitable catalysts; they permit not only addition of aromatic and heterocyclic aldehydes but also the addition of aliphatic aldehydes.     

Bestimmung des Gleichgewichts der salpetrigen Säure mit Nitritacidium-Ion auf chemischem Wege

Zusammenfassung Die Struktur des Nitritacidium-Ions¹ kann nach einer Interpretation vonSeel mit der Mesomerie zwischen zwei Grenzzuständen A und B (s. S. 428) erklärt werden. Es ist anzunehmen, daß sich bei einer Verminderung der Aktivität des Wassers der Resonanzzustand des Ions in Richtung von A nach B verschiebt. In sehr schwach perchlorsaurer, wäßriger Lösung läßt sich die Gleichgewichtskonstante der Bildung des Nitritacidium-Ions aus salpetriger Säure und Wasserstoffion aus kinetischen Daten vonHermann Schmid näherungsweise berechnen. In sehr stark perchlorsaurer, wäßriger Lösung läßt sich diese Gleichgewichtskonstante unter Verwendung der SäurefunktionJ ₀ aus Gleichgewichtsmessungen des Salpetrigsäurezerfalles ermitteln. (Der gefundene Wert stimmt mit den vonSeel und vonDeno, Berkheimer, Evans undPeterson aus optischen Untersuchungen erhaltenen Werten und mit dem kürzlich vonGerhard Schmid undU. Neumann mit Hilfe der NO/NO⁺-Elektrode gemessenen Wert größenordnungsmäßig überein.) Der vonChallis undRidd gefundene Mediumeffekt bei der Diazotierung aromatischer Amine in perchlorsaurer, wäßriger Lösung kann durch die oben erwähnte Verschiebung in der Resonanzstruktur des Nitritacidium-Ions erklärt werden.     

Untersuchungen zurFriesschen Verschiebung von Estern derortho- undpara-Methoxybenzoesäure

TheFries rearrangement of different methoxy benzoates has been investigated. Frompara-methoxy benzoates the corresponding hydroxy-4-methoxy benzophenones could be obtained in good yields by treatment withLewis acids (especially TiCl₄) in nitromethane at 20°C (4-hydroxy derivatives) or without solvent at 120°C (2-hydroxy derivatives). Under the same conditions only demethylation occurs withortho-methoxy benzoates leading to the corresponding salicylates. Small amounts of hydroxy-2-methoxy benzophenones were obtained by treatment with polyphosphoric acid.