Rational approximation and universality for a quasilinear parabolic equation

Approximation theorems, analogous to results known for linear elliptic equations, are obtained for solutions of the heat equation. Via the Cole-Hopf transformation, this gives rise to approximation theorems for one of the simplest examples of a nonlinear partial differential equation, Burgers’ equation.     

Der erste sechsgliedrige Zinn(II)-Übergangsmetallzyklus – [Mn(CO)4SnCl(DMF)]3

First Compound with a Six-Membered Tin(II) Transition Metal Ring – [Mn(CO)₄SnCl(DMF)]₃ Tin(II) chloride and dimanganese decacarbonyl were reacted in dimethyl-(DMF) at 150°C or monomethylformamide (MMF) at 120°C to yellow product solvates of the type [Mn(CO)₄SnCl(D)]₃ (D = DMF and MMF). Their identification in the case of the compound [Mn(CO)₄SnCl(DMF)]₃ was undertaken by a single crystal X-ray analysis. As result of this determination, its central molecular fragment contained a non-planar (SnMn)₃ ring with the following average bond parameters: Sn? Mn bond lengths of 258.8(5) pm, endocyclic bond angle at Mn Atom of 90.5(2)° and the corresponding angle at Sn atom of 141.6(2)°. After the result of ¹¹⁹Sn Mößbauer spectroscopic measurements of the title substance a tin(II) oxidation state was present. The ν(CO) i.r. absorption bands and ¹H n.m.r. data of both obtained products were measured for a further characterization. With view to the mechanistic pathway of the product formation, it was ascertained by separate experiments that the postulated intermediate Cl₃SnMn(CO)₅ and tin(II) chloride in DMF solution produced the title compound.     

On the definition of the resonance with examples two-channel models

In an exactly solvable model of separable potentials a two channel scattering problem is solved in l = 0 state. The location and the width of a resonance are then defined in three different ways and the resonance parameters so extracted are then compared. This problem is of interest vis-a-vis the Δ(3, 3) resonance parameters.     

Approximation by harmonic functions on closed subsets of Riemann surfaces

Given continuous functionsu and ∈ on a closed subsetF of a Riemann surface, we seek a harmonic functionv on the surface (possibly with logarithmic singularities) such that |u−v|<∈ onF. Research supported in part by NSERC—Canada and FCAR—Quebec.