Stereocontrolled synthesis of Z-dienes via an unexpected pericyclic cascade rearrangement of 5-amino-2,4-pentadienals

Donor-acceptor dienes known as Zincke aldehydes, which derive readily from the ring-opening reactions of pyridinium salts with secondary amines, undergo a fascinating thermal rearrangement reaction to afford Z-alpha,beta,gamma,delta-unsaturated amides with excellent stereoselectivity. Efficient, stereocontrolled access to Z-trisubstituted alkenes with two different substitution patterns is possible in three steps beginning with the appropriately substituted pyridine derivative. Preliminary studies have shown that both the amide and the monosubstituted alkene termini can be selectively functionalized. Ease of access, generality of scope, and facile product manipulation render this process attractive for the synthesis of complex polyenes.     

Calorimetric and computational thermochemical study of 3,3-tetramethyleneglutaric acid, 3,3-tetramethyleneglutaric anhydride, and 3,3-tetramethyleneglutarimide

The standard (p(o) = 0.1 MPa) molar energies of combustion in oxygen, at T = 298.15 K, of solid 3,3-tetramethyleneglutaric acid and the related 3,3-tetramethyleneglutaric anhydride and 3,3-tetramethyleneglutarimide were measured by static bomb combustion calorimetry. The values of the standard molar enthalpies of sublimation, at T = 298.15 K, were obtained by Calvet microcalorimetry, allowing the calculation of the standard molar enthalpies of formation of the compounds, in the gaseous state, at T = 298.15 K. The geometries of the experimentally studied compounds were fully optimized using density functional theory with the B3LYP functional and extended basis sets. More accurate energies were also obtained from single-point calculations at the most stable B3LYP/6-311G** geometries, using the cc-pVTZ basis set. From these calculations the standard molar enthalpies of formation of 3,3-tetramethyleneglutaric acid, 3,3-tetramethyleneglutaric anhydride, and 3,3-tetramethyleneglutarimide were estimated using isodesmic reactions involving glutaric acid, glutaric anhydride, and glutarimide, respectively. Experimental and computational results were used in the discussion of the interrelation of energetics and structure in these compounds and compared with other structurally related compounds.     

The restricted isometry property for time–frequency structured random matrices

This paper establishes the restricted isometry property for a Gabor system generated by n ² time–frequency shifts of a random window function in n dimensions. The sth order restricted isometry constant of the associated n × n ² Gabor synthesis matrix is small provided that s ≤ c n ^2/3 / log² n. This bound provides a qualitative improvement over previous estimates, which achieve only quadratic scaling of the sparsity s with respect to n. The proof depends on an estimate for the expected supremum of a second-order chaos.     

Robust cutpoints in the logical analysis of numerical data

Techniques for the logical analysis of binary data have successfully been applied to non-binary data which has been ‘binarized’ by means of cutpoints; see Boros et al. (1997, 2000) [7], [8]. In this paper, we analyze the predictive performance of such techniques and, in particular, we derive generalization error bounds that depend on how ‘robust’ the cutpoints are.     

Stock options as barrier contingent claims

A comprehensive model is suggested that values securities as options and consequently ordinary stock options as compound options. Extending the basic Black–Scholes model, it can incorporate common contractual features and stylized facts. More specifically, a closed form solution is derived for the price of a call option on a down‐and‐out call. It is then shown how the result obtained can be generalized in order to price options on complex corporate securities, allowing among other things for corporate taxation, costly financial distress and deviations from the absolute priority rule. The characteristics of the model are illustrated with numerical examples.     

Paradigms and paradoxes: revisiting the relation of oxidation state and acidity of polyhydride cations

Structural Chemistry - Nearly four decades ago, we published a simple chemical regularity: the proton affinity of MHa is higher than that of MHb when “a” is greater than...