2,6-dicyano-1,5-dimethylsemibullvalene as a probe for homoaromatic molecules of the Dewar-Hoffman type

The 2,6-dicyano-1,5-dimethylsemibullvalene (2d) synthesized via the bicyclo[3.3.0]octanedione 7 exists as a classical ground state which is lower in energy by less than 5 kcal/mole than the homoaromatic transition of the Cope rearrangement of 2d.     

Oxidation of alcohols by electrochemically regenerated nickel oxide hydroxide. Selective oxidation of hydroxysteroids

Primary alcohols, α,ω-diols and secondary alcohols are easily transformed into carboxylic acids, dicarboxylic acids or ketones, respectively, by heterogeneous oxidation with nickel oxide hydroxide electrochemically regenerated at a nickel hydroxyde electrode. The results are discussed in comparison to those of the nickel peroxide and chromic acid oxidation. The oxidation rate decreases with increasing steric hindrance of the alcohol, thus allowing the selective oxidation of the 3-position in hydroxysteroids.     

Force field and 13C-NMR investigations of substituted cyclopentanes. A concept for the adaption of 13C NMR shifts to varying torsional arrangements in flexible conformers

MM2 Exploration of the conformational space for methylcyclopentane, in contrast to cyclopentanone yields more and flatter minima than known previously. Calculations of cyclopentanes with substituents X = F, Cl, CHMe₂, and CMe₃ with two stable conformations indicate <2° torsional angle changes with the different substituents. Cyclopentanes bearing not more than 2 substituents can accommodate all groups in pseudoequatorial positions without changing the basic envelope and twist chair geometries significantly. A model for ¹³C-shift calculation is proposed in which shift increments for the different torsional arrangements are obtained by linear interpolation between corresponding cyclohexane values. After correction for the nonequivalent carbon shifts in the hydrocarbon itself, again using the linear interpolation, a significant improvement of the shift correlations is observed. For disubstituted cyclopentanes these predict the shifts within ± 1.7 ppm with Me, CHMe₂, CMe₃, Cl, Br and OH as substituents. Configurational assignments are difficult with 1,3-di-substituted cyclopentanes, but straightforward with 1,2-di- and trisubstituted compounds. Thus, due to the presence of smaller torsional angles between, e.g. diequatorial vicinal substituents in the 1,2- cis series as compared to the trans compounds, the latter show deshielding, particularly at C2, by 1–4 ppm. Several epimers are stereo-selectively prepared by suitable ketone reduction and displacement methods.     

Intermediate optimal gevrey exponents occur

Hypoellipticity in Gevrey classes G^s is characterized for a simple family of sums of suares of verctor fields satisfying the bracket hypothesis, with analytic coefficients. It is shown that hypoellipticity holds if and only if s is greater than or equal to an optimal exponent that may take on any rational value.     

Spreading Code Design Using a Global Optimization Method

The performance of a code division multiple access system depends on the correlation properties of the employed spreading code. Low cross-correlation values between spreading sequences are desired to suppress multiple access interference and to improve bit error performance. An auto-correlation function with a distinct peak enables proper synchronization and suppresses intersymbol interference. However, these requirements contradict each other and a trade-off needs to be established. In this paper, a global two dimensional optimization method is proposed to minimize the out-of-phase average mean-square aperiodic auto-correlation with average mean-square aperiodic cross-correlation being allowed to lie within a fixed region. This approach is applied to design sets of complex spreading sequences. A design example is presented to illustrate the relation between various correlation characteristics. The correlations of the obtained sets are compared with correlations of other known sequences.     

Lexicographic generation of projective spaces

Lexicographic or first choice constructions of geometric objects sometimes lead to amazingly good results. Usually it is difficult to determine the precise identity of the resulting geometries. Here we find infinitely many cases where the identification actually can be accomplished.     

Multidimensional van der Corput and sublevel set estimates

Van der Corput's lemma gives an upper bound for one-dimensional oscillatory integrals that depends only on a lower bound for some derivative of the phase, not on any upper bound of any sort. We establish generalizations to higher dimensions, in which the only hypothesis is that a partial derivative of the phase is assumed bounded below by a positive constant. Analogous upper bounds for measures of sublevel sets are also obtained. The analysis, particularly for the sublevel set estimates, has a more combinatorial flavour than in the one-dimensional case.