Partial sums of hypergeometric series of unit argument

The asymptotic behaviour of partial sums of generalized hypergeometric series of unit argument is investigated.

     

Synthesis,characterization and properties of methylaminocellulose

Homogeneously prepared tosylcelluloses (TC) with degrees of substitution (DS) of DS_Tos 0.1–1.8 were used as intermediates for the synthesis of methylaminocelluloses (MAC) by nucleophilic substitution with methylamine. TC with DS_Tos up to 1.1 were shown to be valuable intermediates for selective synthesis of MAC with DS_MA varying from 0.1 to approximately 1. No nucleophilic substitution was observed at higher DS_Tos. At the chosen reaction conditions (60 °C, 48 h) residual tosyl moieties remained unchanged and little hydrolysis took place. The samples obtained were characterized by means of elemental analysis, FTIR and ¹³C CP/MAS NMR spectroscopy. ¹³C CP/MAS NMR spectroscopy was found to be an efficient tool for quantification of DS_MA. Furthermore, the swelling behaviour in water was investigated and preliminary tests concerning the bilirubin adsorption capacity of MAC were carried out.     

Circle actions on 4-manifolds I

Using cohomological methods it is proved that the intersection form of a closed (cohomology-) 4-manifoldM withH ₁(M)=0 which admits a non-trivial circle action is the sum of one- and two-dimensional forms provided every fixed point has a neighbourhood containing at most 4 orbit types.     

The change of the superstructure of semicrystalline polymers during deformation: results from small-angle scattering with synchrotron radiation

The change of the superstructure of different polyethylenes during uniaxial deformation is investigated. The method used is small-angle scattering with synchrotron radiation. For branched polyethylene (Lupolen 1840D) the whole deformation range is analyzed. Beginning with superstructure of the lamellar cluster type, the superstructure partly disappears on a time scale of a few minutes and the fibrillar structure is built up. The degree of destruction and rebuilding depends on the drawing temperature. For very high molecular weight polyethylene (GUR) a reversible change of the superstructure at higher deformation ratios and at different temperatures is observed. The superstructure of (ethylene—hexene) copolymers (TIPELIN) at high draw ratios depends on the drawing temperature and is almost independent of the side group content. Interfibrillar microcracks parallel to the draw direction are produced in samples with a low side group content for draw ratios λ ≥ 1.5.     

Some Characterizations of Ergodic Probability Measures

Let P be a Markov kernel defined on a measurable space (X, ??). A P-ergodic probability is an extreme point of the family of all P-invariant probability measures on ??. Several characterizations of P-ergodic probabilities are given. In particular, for the special case of a topological space X both P-ergodic Baire probabilities and P-ergodic Borel probabilities with additional regularity properties are characterized.