Die durch Silberionen katalysierte Umlagerung von Propargyl-phenyläther

It is known that propargyl-phenylethers rearrange at about 200° to 2 H-chromenes [1–4]. It is shown that this rearrangement occurs in benzene or chloroform at lower temperatures (20–80°) in the presence of silver-tetrafluoroborate (or-trifluoracetate). The ethers examined are presented in Scheme 1. Thus in chloroform at 61° in the presence of AgBF₄, phenyl-propargylether ( 3 ) yields 2 H-chromene ( 13 ). With 0.78 molar equivalents AgBF₄ in benzene at 80° the same ether 3 yields a 3:1 mixture of 2-methyl-cumaron ( 14 ) and 2 H-chromene ( 13 ). From 1′-methylpropargyl-phenylether ( 4 ) and 2′-butinyl-3,5-dimethylphenylether ( 5 ) under similar conditions the corresponding chromenes 16 and 17 resp. are obtained. Rearrangement of propargyl- and 2′-butinyl-1-methyl-2-naphthylether ( 6 and 7 resp.) in benzene at 80° in the presence of AgBF₄ gives the corresponding allenyl-naphthalenones 18 and 19 resp. Treatment of propargyl- and 2′-butinyl-mesityl-ether ( 8 and 9 resp.), and propargyl- and l′-methylpropargyl- 2 , 6 -dimethyl-phenylether ( 10 and 11 resp.) in benzene at 80° with AgRF, yields as the only product the corresponding 3 -allenyl-phenols 21 , 22 , 24 and 25 (Scheme 3). It is shown that in the presence of μ-dichlor-dirhodiuni (1)-tetracarbonyl in benzene a t 80° the ether 4 rearranges to 2-methyl-2H-chromene (16). However with this catalyst the predominant reaction is a cleavage to phenol. No reaction was observed when ethers 3 and 12 , (Scheme 7 ) were treated with the tris-(trimethylsily1)-ester of vanadic acid in benzene a t 80° (see also [8]). By analogy with the known mechanism for thc silver catalysis of the reversible propargylesterl/allenylester rearrangement [S], the silver (1)ion is assumed to form a pre-equilibrium π-complex with the C, C-triplebond of the substrate. This complex then undergoes a [3s, 3s]-sigmatropic rearrangement (Scheme 2). In the case of the others 6 , 7 and 12 the resulting allenyldienones were isolated. The 2,G-dimethyl substituted ethers 8 , 9 , 10 and 11 resp. first give the usual allenyl- dienones (Scheme 3). These then undergo a novel silver catalysed dienon-phenol-rearrangement (Sclzenzu4) to give the 3-allenylphenols 21 , 22 , 24 and 25 . Thc others 3 , 4 and 5 with free ortho positions presumably rearrange first to the non-isolated 2-allenyl-phenols 15 , 42 and 43 resp.(Scheme 7). These then rearrange, either thermally or by silver (1)ion catalysis to the 2H-chromenes 13 , 16 and 17 resp. The rate of the rearrangement of 2-allenylphenol ( 15 ) to 13 at room temperature in benzene or chloroform is approximately doubled when silver ions are present as catalyst.     

Banach convolution algebras of functions II

LetG be a noncompact, locally compact group. By means of generalized dyadic decompositions ofG, translation invariant Banach spacesF(B, B, X) of (classes of) measurable functions onG are constructed, e. g. certain weighted amalgams ofL ^p -spaces. Basic properties of these spaces are derived and connections with spaces considered in the literature are indicated. As a main result, sufficient conditions are given which imply that a space of this type is a Banach algebra with respect to convolution.With 1 Figure     

Rasterbare Texturen

Zusammenfassung Es wird eine KlasseR von beschränkten Punktmengen des s-dimensionalen Raumes eingeführt, die rasterbar genannt wird. Die KlasseR dürfte jene Punktmengen umfassen, die den theoretischen Bedürfnissen der Stereologie angepasst und in anschaulichem Sinne als normal zu bezeichnen sind.Der Ausdruck rasterbar bezeichnet die Eigenschaft dieser Punktmengen, dass sie durch das Raster jener Punkte einess-dimensionalen regulären Punktgitters repräsentierbar sind, die der Punktmenge angehören. Die Repräsentierbarkeit bezieht sich auf die Minkowskischen Quermasse und ist stochastisch zu interpretieren. Durch Auszählungen im Punktraster lassen sich die Minkowskischen Quermasse im Sinne der Statistik schätzen.Es wird weiter gezeigt, dass die Minkowskischen Quermasse der Punktmengen vonR als Entwicklungskoeffizienten einer ihnen zugeordneten Autokorrelationsfunktion interpretiert werden können. Insbesondere folgt hieraus, dass das Wienerspektrum einer zweidimensionalen, rasterbaren Textur die topologischen Eigenschaften der Textur nicht abbildet, weil das Wienerspektrum mit der Fouriertransformierten der reduzierten Autokorrelationsfunktion übereinstimmt.

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Summary In Euclidian space, (dimensionn=1, 2, 3), a general class of pointsets is introduced which is named rasterable.The term rasterable designates the important property of these pointsets that they can be represented by the raster of those points of a lattice which belong to the pointset.The representability of a pointset by a pointpicture concerns the directional Minkowski measures, which for rasterable pointsets can be interpreted as coefficients of the expansion of the corresponding auto-correlation function and therefore may be defined as derivatives.

     

über die Striktionslinien von einparametrigen Scharen linearer Räume

A generalisation of a ruled surface in n-dimensional euclidean space may be generated by euclidean motion of a s-plane A_s. For this one-parametric family {A_s} the curve of striction is defined and the following theorems are proved:

1. The generators A_s are parallel along the curve of striction, i.e. the multivectors representing A_s form a parallel vector field along the curve of striction.
2. If the curve of striction is geodesic on {A_s}, it is also an isogonal trajectory of the family of generators {A_s}.

     

Quantum Chaos,Random Matrices,and Irreversibility in Interacting Many-Body Quantum Systems

The Pauli master equation describes the statistical equilibration of a closed quantum system. Simplifying and generalizing an approach developed in two previous papers, we present a derivation of that equation using concepts developed in quantum chaos and random-matrix theory. We assume that the system consists of subsystems with strong internal mixing. We can then model the system as an ensemble of random matrices. Equilibration results from averaging over the ensemble. The direction of the arrow of time is determined by an (ever-so-small) coupling to the outside world. The master equation holds for sufficiently large times if the average level densities in all subsystems are sufficiently smooth. These conditions are quantified in the text, and leading-order correction terms are given.     

Synthesis of Carbohydrate Derived α-Methylene-γ-lactones by Diasterecseldctive,Low Temperature Reformatsky-Type Reactions

Hexopyranoside- and hexofuranose uloses with either ethyl 2-(branamethyl)acrylate in the presence of laminar Zn/Ag-graphite or ethyl 2-(trimethylsilylinethyl)acrylate/tetra-n-butylanrnonium fluoride undergo stereoselective branching, mainly with formation of spiro α-methylene-γ-lactones.