Die Glastemperatur von Copolymeren

Ohne ZusammenfassungAuszugsweise vorgetragen auf dem Makromolekularen Kolloquium, Freiburg, März 1963.Meinen Kollegen Herrn Dr.Kastning, Dr.Gerrens und Dr.Löchner sei für die Herstellung und überlassung der Copolymeren aus Styrol und Acrylsäure, Vinylidenchlorid und Methacrylat, sowie der äthylencopolymeren auch an dieser Stelle herzlich gedankt. Ebenso danke ich Herrn Dr.Kanig für zahlreiche Diskussionen.     

Das Spektrum der stetigen Endomorphismen von ψ

Ohne Zusammenfassung     

Asymptotic Behavior of Solutions to the Cahn-Hilliard Equation in Spherically Symmetric Domains

The Cahn-Hilliard equation is a fourth-order parabolic partial differential equation that is one of the leading models for the study of phase separation in isothermal, isotropic, binary mixtures, such as molten alloys. The asymptotic behavior of solutions to the Cahn-Hilliard equation with Dirichlet boundary conditions and the associated stationary problem have been studied. In particular, it is proved that the only possible stable equilibrium solutions in spherically symmetric domains are spherically symmetric and monotone in the radial direction.     

Ordinary and symbolic powers are Golod

Let S$S$ be a positively graded polynomial ring over a field of characteristic 0$0$, and I⊂S$I\subset S$ a proper graded ideal. In this note it is shown that S/I$S/I$ is Golod if ∂(I)²⊂I$\partial {\left(I\right)}^2\subset I$. Here ∂(I)$\partial \left(I\right)$ denotes the ideal generated by all the partial derivatives of elements of I$I$. We apply this result to find large classes of Golod ideals, including powers, symbolic powers, and saturations of ideals.     

Bounds on the regularity and projective dimension of ideals associated to graphs

In this paper, we give new upper bounds on the regularity of edge ideals whose resolutions are k-step linear; surprisingly, the bounds are logarithmic in the number of variables. We also give various bounds for the projective dimension of such ideals, generalizing other recent results. By Alexander duality, our results also apply to unmixed square-free monomial ideals of codimension two. We also discuss and connect these results to more classical topics in commutative algebra.     

The Dedekind-Mertens lemma and the contents of polynomials

We prove a sharpening of the Dedekind-Mertens Lemma relating the contents of two polynomials to the content of their product. We show that for a polynomial the integer in the Dedekind-Mertens Lemma may be replaced by the number of local generators of the content of . We also raise a question concerning the converse.

     

omega-(Bis(trifluoromethyl)amino)alkane-1-sulfonates: synthesis and mass spectrometric study of the biotransformation products

In search of fluorinated functional groups which could undergo defluorination, and therefore be included in novel non-polluting fluorinated surfactants, omega-(bis(trifluoromethyl)amino)alkane-1-sulfonates (BTFMA-AS) with a homologue distribution from seven to thirteen methylene groups were synthesized and investigated for aerobic biodegradation applying both a standardized test and a fixed-bed bioreactor (FBBR). These compounds were prepared as part of a screening study for potentially mineralizable fluorinated endgroups.Application of hybrid triple quadrupole-linear ion trap mass spectrometry (QqQ(LIT)-MS) coupled to high-performance liquid chromatography (HPLC) allowed the tracking of primary degradation as well as the detection and structural elucidation of biotransformation intermediates. An understanding of the fragmentation pathway of the test compounds allowed selective precursor ion scans to reveal the presence of stable fluorinated metabolites. Structures were confirmed by enhanced product ion scans and MS(3) scans in the linear ion trap mode.The primary biodegradation rate and the extent of biodegradation were found to be chain-length dependent, with higher homologues being completely primarily degraded within 10 days. For the first time, two simultaneous metabolic pathways for substituted linear alkane-1-sulfonates were discovered: Desulfonation, oxidation to a carboxylic acid and subsequent chain-length shortening by beta-oxidation dominated the metabolism. This pathway resulted in the formation of 3-(bis(trifluoromethyl)amino)propionic acid and bis(trifluoromethyl)aminoacetic acid, which showed recalcitrance in this experiment. Oxidation of the alkyl chain to the respective carbonyl derivative represents the minor pathway. Only the long-chain homologues of these oxidized species were partially degraded; the short-chain homologues were not attacked.