New bounds for dilepton production from heavy neutral leptons

Bounds on 〈E_?ⁿ〉/〈E₊ⁿ〈, 〉E₊E_?〈/〉E₂²〈 and 〈E₊E_?〉/〈E₊〉〈E_?〉 are direved for the processes ν_μN → μ^?μ⁺(e⁺) + X and μN → μ^?μ⁺ + X if dileptons are mediated by a $\text{spin}\text{-}\text{1}\text{2}$ heavy neutral lepton L₀. The bounds are shown to be independent of the production mechanism and mass of L₀. Useful conditional bounds are obtained relating the bounded quantities, which give information about the structure of the weak current responsible for L₀ decay.     

Unexpected Hydroxyspirolactone Formation upon Baeyer-Villiger Oxidation of a trans-α-decalone (trans-octahydronaphthalen-1(2H)-one) and X-ray structure of the product

trans-4,4,10-Trimethyl-9-decalone ( = trans-5,5,8a-trimethyl-octahydronaphthalen-1(2H)-one; 1 ), when treated with trifluoroperacetic acid, gave the unexpected hydroxyspirolactone 7-hydroxy-7,11,11-trimethyl-1-oxaspiro[5.5]undecan-2-one ( 6 ), in which the two new O-atoms were introduced in a 1,2-trans relationship. The structure of this compound was conclusively proven by X-ray crystallography. The process involves the intermediacy of 7-membered lactone 2 , the expected Baeyer-Villiger product, which could also be successfully prepared under controlled conditions at 0° in a buffered medium containing Na₂HPO₄.     

Azametalla-closo-dodecaboranes

The azaborate K₂[nido-NB₁₀H₁₁] is gained from nido-NB₁₀H₁₃ and K[BHEt₃] in a 1:2 ratio. The anion [NB₁₀H₁₁]^2?, which is isoelectronic with [C₂B₉H₁₁]^2?, reacts with [{η⁶-(C₆R₆) · RuCl₂}₂] (R = H, Me), [{η⁵-(C₅Me₅)RhCl₂}₂], or [Ni(PPh₃)₂Cl₂] to give the azametalla-closo-dodecaboranes MNB₁₀H₁₁ with M = (C₆Me₆)Ru ( 2 ), (C₆H₆)Ru ( 3 ), (C₅Me₅)Rh ( 4 ), and (Ph₃P)₂Ni ( 5 ), respectively. The azametallaborane K[Co(NB₁₀H₁₁)₂] ( 6 ), which contains a sandwich-type coordinated Co atom, is formed from K₂[NB₁₀H₁₁] and CoCl₂. The structure of 2 · CH₂Cl₂ was determined by X-ray diffraction. The products 2 – 6 can be derived from the icosahedral anion [B₁₂H₁₂]^2? on replacing a BH^2? moiety by the isoelectronic nitrene NH and a BH moiety by the isolobal metal-complex fragment M. The N atom is six-coordinated in the cluster skeletons 2 – 6 .     

Connected 4-dimensional stable planes with many central collineations

This paper gives a complete classification of all connected 4-dimensional stable planes with the property that every point is the centre of a non-trivial central collineation. It is shown that under these assumptions the automorphism group has an open orbit on the point space. This implies the existence of an open subplane that carries the additional structure of a generalized symmetric space in the sense of differential geometry. Now the classification of all 4-dimensional generalized symmetric planes yields the desired classification.Dedicated to Professor H. Salzmann on his 60th birthday