Naphthaceno[5,6-cd]-1,2-dithiole,C18H10S2

C₁₈H₁₀S₂,M=290.34, monoclinic,P2₁,a=20.556(5),b=15.843(3),c=3.963(1) Å,β=92.79(2)° at 18°C,Z=4,D _x =1.496 g cm^?3,μ(Cu Kα)=3.53 mm^?1. Full-matrix least-squares refinement resulted in a final conventionalR value of 0.036 for 2030 observed reflections. The average C-S bond distance is 1.747(16) Å, the S-S bond length is 2.074(1) Å. The torsion angles at the disulfide group are close to zero, at 3.5 and 0.8°. The carbon frameworks are nearly planar, and closely approximate symmetrymmm. Bond distances are comparable with those in related molecules.     

Remarks on Banach spaces of compact operators

Let E and F be Banach spaces. We generalize several known results concerning the nature of the compact operators K(E, F) as a subspace of the bounded linear operators L(E, F). The main results are: (1) If E is a c₀ or l_p (1 < p < ∞) direct sum of a family of finite dimensional Banach spaces, then each bounded linear functional on K(E) admits a unique norm preserving extension to L(E). (2) If F has the bounded approximation property there is an isomorphism of $\text{L(E, F)}\text{into}\text{K(E, F)}{}^7$ such that its restriction to K(E, F) is the canonical injection. (3) If E is infinite dimensional and if F contains a complemented copy of c₀, K(E, F) is not complemented in L(E, F).     

An isoperimetric problem with a nonlinear side condition for sloshing in a symmetric shallow canal

Summary The eigenfrequencies of the oscillations of an ideal liquid in a symmetric, shallow canal are investigated. The shape of the cross section is determined, for which thenth eigenfrequency becomes as large as possible, when the width and the wetted are length of the canal cross section are prescribed. This variational problem leads to a nonlinear eigenvalue problem for two functions. The problem is solved numerically, and, in addition, upper and lower bounds for the maximal eigenvalues are reported.

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Zusammenfassung Die Eigenfrequenzen der Schwingungen einer idealen Flüssigkeit in einem symmetrischen, untiefen Kanal werden untersucht. Es wird die Form desjenigen Querschnittes bestimmt, für den dien-te Eigenfrequenz möglichst gross wird, wenn die Breite und die benetzte Bogenlänge des Kanalquerschnittes vorgeschrieben werden. Dieses Variationsproblem führt auf ein nichtlineares Eigenwertproblem für zwei Funktionen. Das Problem wird numerisch gelöst, und ausserdem werden obere und untere Schranken für die maximalen Eigenwerte angegeben.

     

Alumina-accelerated methanolysis and hydrolysis of acyl and phosphoryl fluorides

We have discovered that Woelm chromatographic γ-alumina substantially accelerates hydrolysis (and methanolysis) of acyl and phosphoryl fluorides. Compared to the corresponding $\text{homogeneous}$ reactions, these $\text{heterogeneous}$ alumina-promoted reactions occur about 250–350 times faster for acyl fluorides and about 1800–3000 times faster for phosphoryl fluorides.     

Organoboranes : XIV. Reaction of organoboranes with mercuric acetate. A convenient preparation of dialkylmercurials via hydroboration-mercuration

Organoboranes derived from terminal olefins react with mercuric acetate in tetrahydrofuran (THF) giving rise to dialkylmercury compounds. The first two alkyl groups react rapidly at room temperature while the third is more sluggish. Organoboranes derived from internal olefins are unreactive to various mercury(II) salts under these conditions. Dicyclohexylalkylboranes give rise to quantitative yields of dialkylmercurials when reacted with mercuric acetate. Alkylmercuric acetates are converted in high yields to dialkylmercury compounds when treated with zinc dust at room temperature in the presence of Lewis acid catalysts.