Electrochemical Vicinal Difluorination of Alkenes: Scalable and Amenable to Electron‐Rich Substrates

Fluorinated alkyl groups are important motifs in bioactive compounds, positively influencing pharmacokinetics, potency and conformation. The oxidative difluorination of alkenes represents an important strategy for their preparation, yet current methods are limited in their alkene‐types and tolerance of electron‐rich, readily oxidized functionalities, as well as in their safety and scalability. Herein, we report a method for the difluorination of a number of unactivated alkene‐types that is tolerant of electron‐rich functionality, giving products that are otherwise unattainable. Key to success is the electrochemical generation of a hypervalent iodine mediator using an “ex‐cell” approach, which avoids oxidative substrate decomposition. The more sustainable conditions give good to excellent yields in up to decagram scales.     

Collision-induced dissociation mass spectrometry of nonionic surfactants following direct supercritical fluid injection

Direct injection from a capillary supercritical fluid chromatography system was used as an inlet technique for chemical ionization (CI) and low energy collision-induced dissociation (CID) mass spectrometry of a series of low volatility nonionic surfactant mixtures. Characteristic fragment ions produced by CID for various classes of nonionic surfactant molecules were found to depend greatly on the structure of the surfactant hydrophobe. This was the case even when the charge on the molecule appeared localized away from the hydrophobe. Numerous decomposition pathways are suggested by the fragment ions produced. The use of direct supercritical fluid injection as an inlet technique does not appear to influence adversely the ability to produce cm mass spectra. Direct supercritical fluid introduction allows CI to be compared with other ionization mechanisms more commonly used for multifunctional, low volatility samples.     

Score vectors of tournaments

A tournament T on any set X is a dyadic relation such that for any x, y ∈ X (a) (x, x) ? T and (b) if x ≠ y then (x, y) ∈ T iff (y, x) ? T. The score vector of T is the cardinal valued function defined by R(x) = |{y ∈ X : (x, y) ∈ T}|. We present theorems for infinite tournaments analogous to Landau's necessary and sufficient conditions that a vector be the score vector for some finite tournament. Included also is a new proof of Landau's theorem based on a simple application of the “marriage” theorem.     

Theory of reality

Bell's theorem is used to guide the formulation of a unified theory of reality that incorporates the basic principles of relativistic quantum theory.Work supported by U. S. Energy Research and Development Administration.     

A new look at Bergström’s theorem on convergence in distribution for sums of dependent random variables

In his 1972Periodica Mathematica Hungarica paper, H. Bergström stated a theorem on convergence in distribution for triangular arrays of dependent random variables satisfying, a ?-mixing condition. A gap in his proof of this theorem is explained and a more general version is proved under weakened hypotheses. The method used consists of comparisons between the given array and associated arrays which are parameterized by a truncation variable. In addition to the main theorem, this method yields a proof of equality of limiting finite-dimensional distributions for processes generated by the given associated arrays as well as the result that if a limit distribution for the centered row sums does exist, it must be infinitely divisible. Several corollaries to the main theorem specialize this result for convergence to distributions within certain subclasses of the infinitely divisible laws.     

Comments on “quantum theory does not require action at a distance”

Kraus claims that the argument for action at a distance depends upon the classical prejudice that a measurement always measures something that already exists. It is shown that in the example considered by Kraus no assumption about pre-existing results is needed. A criterion proposed by Kraus for a theory to be compatible with locality is shown to be untenable.