Some remarks on the boundary regularity for minima of variational problems with obstacles

We minimize the Dirichlet-integral in a class of vector-valued functions u:^N defined by Dirichlet-boundary conditions and a side-condition of the form u()M with M bounded and open in ^N having smooth boundary M. If the boundary values are sufficiently regular we show that the minimizer can only have interior singularities, i.e. the solution is smooth in a neighborhood of .     

The Photochemical and Thermal Interconversion of Some Cyclopentadienone Dimers

In continuation of previous work on cyclopentadienone dimers [3], thermal and photochemical interconversions of the isomeric diketones 1, 3 , and 5 by skeletal rearrangements have been established to the extent summarized in schemes 2 and 3, and the intramolecular [2+2] cycloaddition 1 → 2 was found to be reversible photochemically.     

β relaxation theory for simple systems: some addenda

The evolution of the tagged particle probability density for a hard sphere system is evaluated within the -relaxation window. Relaxation curves obtained by molecular dynamics studies by Barrat, Hansen and Roux for a binary mixture are analyzed quantitatively with -relaxation scaling formulae. The dynamical light scattering data obtained by Pusey and van Megen for colloidal suspensions are described by the combined - and -relaxation scaling results. The range of validity of asymptotic expressions near a glass transition singularity is discussed for the Debye-Waller factor as a function of packing fraction. The applied theoretical formulae are those of the mode coupling theory for the liquid to glass transition.