Facile and Convenient Synthesis of Functionalized Aryl-Containing Isoindigo Derivatives via Substituted Indolin-2-one Carbene Dimerization

The reaction of substituted benzyl-, aroylmethyl-, or 1-phenetylisatins with hexaethyltriaminophosphine has been shown to lead to the formation of a library of 3,3′-biindolinylidene-2,2′-diones with functionalized benzyl-, aroylmethyl-, and 1-phenetyl fragments at the nitrogen atom.     

Surface tension of liquid marbles

Effective surface tension of liquid marbles was measured by three independent experimental techniques: vibration, shape analysis, and maximal marble height. Marbles obtained with various powders: polyvinylidene fluoride, polytetrafluoroethylene, polyethylene, and lycopodium, were studied. The effective surface tension depends strongly on the kind of powder coating the marble. The capillary interaction between particles coating the marble was involved for qualitative interpretation of the reported data.     

KKM type theorems with boundary conditions

We consider generalizations of Gale’s colored KKM lemma and Shapley’s KKMS theorem. It is shown that spaces and covers can be much more general and the boundary KKM rules can be substituted by more weaker boundary assumptions.     

Supersymmetric electron in a Coulomb field

We analyze the motion of an electron in a Coulomb field using the Di Vecchia-Ravndal model for a supersymmetric Dirac particle. We find an exact analytic solution of the spatial part of the pseudoclassical Bargmann-Michel-Telegdi equations. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 1, pp. 75–80, April, 2000.     

Bounds for codes by semidefinite programming

Delsarte’s method and its extensions allow one to consider the upper bound problem for codes in two-point homogeneous spaces as a linear programming problem with perhaps infinitely many variables, which are the distance distribution. We show that using as variables power sums of distances, this problem can be considered as a finite semidefinite programming problem. This method allows one to improve some linear programming upper bounds. In particular, we obtain new bounds of one-sided kissing numbers.