Straightforward carbamoylation of nucleophilic compounds employing organic azides, phosphines, and aqueous trialkylammonium hydrogen carbonate

In the presence of aqueous trialkylammonium hydrogen carbonate, the Staudinger reaction leads to the intermediate formation of the corresponding isocyanate, which, in turn, reacts further with a nucleophilic reagent also present in the mixture and results in carbamoylation with good yield. On the basis of this reaction a practical carbamoylation procedure was devised and a comparative study on suitability of different solvents and phosphorus (III) derivatives for carbamoylation reaction was conducted. The versatility of the method was demonstrated by examples with different classes of nucleophilic compounds that included the aminomethyl resin and natural compounds that display poor solubility in organic solvents.     

No-Forcing and No-Matching Theorems for Classical Probability Applied to Quantum Mechanics

Correlations of spins in a system of entangled particles are inconsistent with Kolmogorov’s probability theory (KPT), provided the system is assumed to be non-contextual. In the Alice–Bob EPR paradigm, non-contextuality means that the identity of Alice’s spin (i.e., the probability space on which it is defined as a random variable) is determined only by the axis $\alpha _{i}$ chosen by Alice, irrespective of Bob’s axis $\beta _{j}$ (and vice versa). Here, we study contextual KPT models, with two properties: (1) Alice’s and Bob’s spins are identified as $A_{ij}$ and $B_{ij}$ , even though their distributions are determined by, respectively, $\alpha _{i}$ alone and $\beta _{j}$ alone, in accordance with the no-signaling requirement; and (2) the joint distributions of the spins $A_{ij},B_{ij}$ across all values of $\alpha _{i},\beta _{j}$ are constrained by fixing distributions of some subsets thereof. Of special interest among these subsets is the set of probabilistic connections, defined as the pairs $\left( A_{ij},A_{ij'}\right) $ and $\left( B_{ij},B_{i'j}\right) $ with $\alpha _{i}\not =\alpha _{i'}$ and $\beta _{j}\not =\beta _{j'}$ (the non-contextuality assumption is obtained as a special case of connections, with zero probabilities of $A_{ij}\not =A_{ij'}$ and $B_{ij}\not =B_{i'j}$ ). Thus, one can achieve a complete KPT characterization of the Bell-type inequalities, or Tsirelson’s inequalities, by specifying the distributions of probabilistic connections compatible with those and only those spin pairs $\left( A_{ij},B_{ij}\right) $ that are subject to these inequalities. We show, however, that quantum-mechanical (QM) constraints are special. No-forcing theorem says that if a set of probabilistic connections is not compatible with correlations violating QM, then it is compatible only with the classical–mechanical correlations. No-matching theorem says that there are no subsets of the spin variables $A_{ij},B_{ij}$ whose distributions can be fixed to be compatible with and only with QM-compliant correlations.