A theoretical NMR study of the structure of benzynes and some of their carbocyclic and heterocyclic analogs

This work reports the theoretical study of the aromaticity of a series of carbocycles (benzene, cyclohexane, bent and planar cyclooctatetraene) and heterocycles (pyridine, furan, thiophene, pyrrole) and their didehydro forms (arynes and hetarynes). As aromaticity probe Schleyer's NICS were used and represented in two 3D isosurfaces of the electron density. The spatial 3D representation of the NICS is shown to be a powerful tool to visualize the aromaticity (or its absence) of different molecules.     

Fourier Inversion Formulas in Option Pricing and Insurance

Several authors have used Fourier inversion to compute prices of puts and calls, some using Parseval’s theorem. The expected value of max (S – K, 0) also arises in excess-of-loss or stop-loss insurance, and we show that Fourier methods may be used to compute them. In this paper, we take the idea of using Parseval’s theorem further: (1) formulas requiring weaker assumptions; (2) relationship with classical inversion theorems for probability distributions; (3) formulas for payoffs which occur in insurance. Numerical examples are provided.      

Optimal Control of an Evolution Problem Involving Time-Dependent Maximal Monotone Operators

Journal of Optimization Theory and Applications - We consider a control problem in a finite-dimensional setting, which consists in finding a minimizer for a standard functional defined by way of...     

Experimental and Computational Studies of Anti‐Bredt Amidinium Salts

Experimental and computational investigations of anti‐Bredt amidinium salts are presented. Calculations show that the pyramidalization of an amino group can significantly destabilize the formal carbocation center of amidiniums, due to the decreased π donation. In some cases, the unfavorable ‐I effect of nitrogen surpasses its beneficial +M effect, and amidiniums become less stable than iminiums. It is shown that although 1‐aza‐3‐azonia[3.3.1]bicyclo‐non‐2‐enes can be isolated, they feature a nonclassical reactivity, which is more typical for iminium than amidinium salts, such as pronounced electrophilicity and azomethineylide instead of carbene formation.     

The Structure of the Elusive Simplest Dipeptide Gly-Gly

Among the hundreds of peptide compounds for which conformations have been determined by using different spectroscopic techniques, the structure of the simplest dipeptide glycylglycine (Gly-Gly) is conspicuously absent. Herein, for the first time, solid samples of Gly-Gly have been vaporized by laser ablation and three different structures have been revealed in a supersonic expansion by Fourier transform microwave spectroscopy. The intramolecular hydrogen bonding interactions that stabilize the observed forms have been established based on the ¹⁴N nuclear quadrupole hyperfine structure. We have illustrated how conformer interconversion distorts the equilibrium conformational distribution, giving rise to missing conformers in the conformational landscape.