Increasing Selections from Increasing Multifunctions

We study when the existence of an increasing selection can be derived from the monotonicity of a multifunction w.r.t. an extension of the basic order from points to subsets. The most interesting results emerge when the target is a lattice and monotonicity is interpreted in one of the ways suggested by A.F. Veinott, Jr. An increasing selection exists if (1) the multifunction is weakly ascending while every value satisfies a completeness condition, e.g., is chain-complete, or (2) the multifunction is ascending while the target is a sublattice of the Cartesian product of a finite number of chains.     

Competition of Different Addition and Cycloaddition Processes During Reaction of Phosphorus(II) and (III) Halides with Alkynes

Abstract

Addition of P-halogenophosphaalkenes to I-alkoxyalkynes provides either 2-phosphabutadienes 2 or P(II1)-substituted allenes 3. The reaction o f P-halogenophosphaalkenes I with I-aminoalkynes leads to the phosphetines 4 wa 5 - the product of 1,2-addition reaction.     

Heterocyclization of electrophilic alkenes with tetranitromethane revisited: regiochemistry and the mechanism of nitroisoxazole formation

Revised regiochemistry for the heterocyclization of electrophilic alkenes with tetranitromethane (TNM) in the presence of triethylamine, providing rapid access to nitroisoxazoles, is reported. The formation of 5-nitroisoxazoles previously incorrectly assigned as 3-nitro regioisomers, has now been established unambiguously by X-ray crystallography. Empirical computations with ACD/CNMR Predictor, based both on hierarchical ordering of spherical environments (HOSE) and an algorithm of artificial neural networks (ANN), and also Density Functional Theory computations of the ¹³C NMR chemical shifts for the 3- versus 5-nitroisoxazoles are shown to consistently match the spectra of the experimentally observed 5-regioisomers.     

Phosphorylation of Conjugated Enamines

Abstract

Introduction of benzylidene group at α-position of enamines derived from cyclic ketones substantially increases strength of C-P bond thus permitting further syntheses without splitting of the C-P bond. A wide set of phosphorylated derivatives of type (I) were prepared and their properties were studied. Combination of an enamine moiety with other nucleophilic centers such as C or N in a molecule allows to carry out cyclisation giving five- and six-membered phosphorus-containing heterocycles of types (II, III).     

Direct Evidence of Significantly Different Chemical Behavior and Excited‐State Dynamics of 1,7‐ and 1,6‐Regioisomers of Pyrrolidinyl‐Substituted Perylene Diimide

Novel bay‐functionalized perylene diimides with additional substitution sites close to the perylene core have been prepared by the reaction between 1,7(6)‐dibromoperylene diimide 6 (dibromo‐PDI) and 2‐(benzyloxymethyl)pyrrolidine 5 . Distinct differences in the chemical behaviors of the 1,7‐ and 1,6‐regioisomers have been discerned. While the 1,6‐dibromo‐PDI produced the corresponding 1,6‐bis‐substituted derivative more efficiently, the 1,7‐dibromo‐PDI underwent predominant mono‐debromination, yielding a mono‐substituted PDI along with a small amount of the corresponding 1,7‐bis‐substituted compound. By varying the reaction conditions, a controlled stepwise bis‐substitution of the bromo substituents was also achieved, allowing the direct synthesis of asymmetrical 1,6‐ and 1,7‐PDIs. The compounds were isolated as individual regioisomers. Fullerene (C₆₀) was then covalently linked at the bay region of the newly prepared PDIs. In this way, two separate sets of perylene diimide–fullerene dyads, namely single‐bridged (SB‐1,7‐PDI‐C₆₀ and SB‐1,6‐PDI‐C₆₀) and double‐bridged (DB‐1,7‐PDI‐C₆₀ and DB‐1,6‐PDI‐C₆₀), were synthesized. The fullerene was intentionally attached at the bay region of the PDI to achieve close proximity of the two chromophores and to ensure an efficient photoinduced electron transfer. A detailed study of the photodynamics has revealed that photoinduced electron transfer from the perylene diimide chromophore to the fullerene occurs in all four dyads in polar benzonitrile, and also occurs in the single‐bridged dyads in nonpolar toluene. The process was found to be substantially faster and more efficient in the dyads containing the 1,7‐regioisomer, both for the singly‐ and double‐bridged molecules. In the case of the single‐bridged dyads, SB‐1,7‐PDI‐C₆₀ and SB‐1,6‐PDI‐C₆₀, different relaxation pathways of their charge‐separated states have been discovered. To the best of our knowledge, this is the first observation of photoinduced electron transfer in PDI‐C₆₀ dyads in a nonpolar medium.     

Translations and rotations are correlated in granular gases

In a granular gas of rough particles the axis of rotation is shown to be correlated with the translational velocity of the particles. The average relative orientation of angular and linear velocities depends on the parameters which characterize the dissipative nature of the collision. We derive a simple theory for these correlations and validate it with numerical simulations for a wide range of coefficients of normal and tangential restitution. The limit of smooth spheres is shown to be singular: even an arbitrarily small roughness of the particles gives rise to orientational correlations.