Metallacycloalkanes: I. Preparation and characterisation of α,α′-bipyridyl-5-nickela-3,3,7,7-tetramethyl-trans-tricyclo[4.1.0.02,4]heptane

Oxidative addition of 2 molecules of 3,3-dimethylcyclopropene (I) to α,α′-bipyridyl(1,5-cyclooctadiene)nickel(0) (III) gave the title compound (IV) in over 90% yield. Complex IV was characterized by mass, ¹H NMR and ¹³C NMR spectroscopy. Its structure was determined by X-ray diffraction (a 13.7081(2), b 14.638(2), c 9.5139(1) Å, β 110.82(1)°, C2/c, R = 0.05 for 1614 reflections).     

Bound state methods for elastic scattering phase shifts

Three methods are investigated for obtaining elastic phase shifts in the scattering of electrons from atoms and ions that use a bound-state representation of the scattering wavefunction. Results for singlet p-wave scattering by H and by He⁺ are compared with previous calculations.     

Three polymorphs of 4‐4′‐diiodobenzalazine,and 4‐chloro‐4′‐iodobenzalazine

Three polymorphs of 4,4′‐diiodobenzalazine (systematic name: 4‐iodobenzaldehyde azine), C₁₄H₁₀I₂N₂, have crystallographically imposed inversion symmetry. 4‐Chloro‐4′‐iodobenzalazine [systematic name: 1‐(4‐chlorobenzylidene)‐2‐(4‐iodobenzylidene)diazane], C₁₄H₁₀ClIN₂, has a partially disordered pseudocentrosymmetric packing and is not isostructural with any of the polymorphs of 4,4′‐diiodobenzalazine. All structures pack utilizing halogen–halogen interactions; some also have weak π (benzene ring) interactions. A comparison with previously published methylphenylketalazines (which differ by substitution of methyl for H at the azine C atoms) shows a fundamentally different geometry for these two classes, namely planar for the alazines and twisted for the ketalazines. Density functional theory calculations confirm that the difference is fundamental and not an artifact of packing forces.     

Enantiomer differentiation in intramolecular carbon—hydrogen insertion reactions of racemic secondary alkyl diazoacetates catalyzed by chiral dirhodium(ii) carboxamidates

Highly efficient kinetic resolution of racemic secondary alkyl diazoacetates in intramolecular carbon-hydrogen insertion reactions has been achieved using chiral dirhodium(ii) carboxamidates. Products formed from catalytic diazo decomposition of racemic 2-octyl diazoacetate and, separately, its (2R)- and (2S)-enantiomeric forms, as well as bothcis- andtrans-2-methylcyclohexyl diazoacetates, have been systematically evaluated. Enantioselectivities up to 99 %ee have been obtained for -lactone formation. -Lactone production has been observed and, although minor with cyclohexyl diazoacetates, is the major insertion pathway for diazo decomposition of 2-octyl diazoacetate.Dedicated to Academician of the RAS N. S. Zefirov (on his 60th birthday).Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1798–1803, September, 1995.Financial support for this research from the National Institutes of Health (GM 46503) and the National Science Foundation of the United States is gratefully acknowledged. We thank D. A. Pierson for her preparation of 2-methylcyclohexyl diazoacetates and preliminary studies of their diazo decomposition and A. Melekhov from the Higher College of Chemistry for his preparation and catalytic studies of rac-2-octyl diazoacetate.     

A public-key cryptosystem utilizing cyclotomic fields

While it is well-known that the RSA public-key cryptosystem can be broken if its modulusN can be factored, it is not known whether there are other ways of breaking RSA. This paper presents a public-key scheme which necessarily requires knowledge of the factorization of its modulus in order to be broken. Rabin introduced the first system whose security is equivalent to the difficulty of factoring the modulus. His scheme is based on squaring (cubing) for encryption and extracting square (cube) roots for decryption. This introduces a 14 (19) ambiguity in the decryption. Various schemes which overcome this problem have been introduced for both the quadratic and cubic case. We generalize the ideas of Williams' cubic system to larger prime exponents. The cases of higher prime order introduce a number of problems not encountered in the quadratic and cubic cases, namely the existence of fundamental units in the underlying cyclotomic field, the evaluation of higher power residue symbols, and the increased difficulty of Euclidean division in the field.     

Clumping Data in 2-Way Tables: A User-Orientated Perspective

Following a critique of existing algorithms, an algorithm is presented which will re-organize a 2-way data table to bring like rows together, and like columns together. Extensions of the method are described, and justified, to accommodate distances measured in modular arithmetic, and with bipolar columns/rows, as in repertory grid analysis. One value of the algorithms is that the user can see relationships in the tables without the data in the cells themselves ever having been transformed. Thus, users will continue to feel they own their data.