On the Description of the Content-Equality by a Relation

In the geometry of polyhedra we understand by an elementary content-functional a real valued, non-negative, finite additive measure on the set of polyhedra which is invariant under isometries. There are close relations between the content-measurement and the relation of equidecomposability. Two polyhedra are called equidecomposable if they are decomposed into pairwise congruent pieces. For an example we consider the set of all polygons in the euclidean plane. It is well known that planar polygons have the same area if and only if they are equidecomposable. In the three-dimensional euclidean space one also can describe the content-equality of polyhedra by a relation. Two polyhedra have the same volume if they are equidecomposable with respect to equiaffine mappings (see [3]). In [4] the concept of an invariant content of polyhedra in a topological Klein space is introduced. Each regular closed quasicompact set ot the space is called polyhedron. Under this supposition two polyhedra have equal contents if they are equivalent by decomposition. The relation “equivalent by decomposition” is closely related to the relation “equidecomposable”.     

Everywhere H?lder continuity of the spatial gradient of weak solutions to nonlinear parabolic systems

We consider weak solutions to the parabolic system ∂u ⁱ∂t−D _α A _i ^α (∇u)=B _i(∇u) in (i=1,...,) (Q=Ω×(0,T), R ⁿ a domain), where the functionsB _i may have a quadratic growth. Under the assumptionsn≤2 and ∇u ɛL _loc ^4+δ (Q; R ^nN ) (δ>0) we prove that ∇u is locally H?lder continuous inQ.     

Biotechnological Production of 20-alpha-Dihydrodydrogesterone at Pilot Scale

The human sex hormone progesterone plays an essential and complex role in a number of physiological processes. Progesterone deficiency is associated with menstrual disorders and infertility as well as premature birth and abortion. For progesterone replacement therapy, the synthetic progestogen dydrogesterone is commonly used. In the body, this drug is metabolized to 20α-dihydrodydrogesterone (20α-DHD), which also shows extensive pharmacological effects and hence could act as a therapeutic agent itself. In this study, we describe an efficient biotechnological production procedure for 20α-DHD that employs the stereo- and regioselective reduction of dydrogesterone in a whole-cell biotransformation process based on recombinant fission yeast cells expressing the human enzyme AKR1C1 (20α-hydroxysteroid dehydrogenase, 20α-HSD). In a fed-batch fermentation at pilot scale (70 L) with a genetically improved production strain and under optimized reaction conditions, an average 20α-DHD production rate of 190 μM day⁻¹ was determined for a total biotransformation time of 136 h. Combined with an effective and reliable downstream processing, a continuous production rate of 12.3 ± 1.4 g 20α-DHD per week and fermenter was achieved. We thus established an AKR-dependent whole-cell biotransformation process that can also be used for the production of other AKR1C1 substrates (as exemplarily shown by the production of 20α-dihydroprogesterone in gram scale) and is in principle suited for the production of further human AKR metabolites at industrial scale.     

Evaluation of tip-enhanced Raman spectroscopy for characterizing different virus strains

Tip-enhanced Raman spectroscopy (TERS) is a highly sensitive spectroscopic technique which combines the advantages of optical spectroscopy with the requirements needed for the characterization of biological nano-structures. In this study, TERS was used to investigate the applicability of this spectroscopic technique for the detection of different virus strains like avipoxvirus and adeno-associated virus. TERS spectra obtained from different particles of the same virus strain show variations in relative peak intensities and positions of most spectral features observed. These spectral variations were higher for the larger avipoxvirus particles (?≈350 nm) than for the smaller adeno-associated virus particles (?≈26 nm).     

Synthesis of fully substituted polyhydroxylated pyrrolizidines via Cope-House cyclization

Total synthesis of the proposed structure of (-)-hyacinthacine C(5) and its epimers at C6 and C7 is described. A key step of the synthesis was the construction of the bicyclic pyrrolizidine system by means of a nucleophilic addition of a dithiane to a cyclic nitrone followed by a Cope-House cyclization.     

Detection of viral nucleoprotein binding to anti-influenza aptamers via SERS

A highly sensitive surface-enhanced Raman (SERS)-based method for detection of influenza viral nucleoproteins is described. The intrinsic SERS spectrum of the aptamer-nucleoprotein complex provides direct evidence of binding between a polyvalent anti-influenza aptamer and the nucleoproteins of three influenza strains.     

Strukturen von neuen Bis(pentafluorophenyl)halogenomercuraten [{Hg(C6F5)2}3(μ‐X)]— (X = Cl,Br, I)

Structures of New Bis(pentafluorophenyl)halogeno Mercurates [{Hg(C₆F₅)₂}₃(μ‐X)]^— (X = Cl, Br, I) From the reactions of [PNP]Cl or [PPh₄]Y (Y = Br, I) with Hg(C₆F₅)₂ crystals of the composition [Cat][{Hg(C₆F₅)₂}₃X] (Cat = PNP, X = Cl ( 1 ); Cat = PPh₄, X = Br ( 2 ), I ( 3 )) are formed. 1 crystallizes in the triclinic space group P1¯, 2 and 3 crystallize isotypically in the monoclinic space group C2/c. In the crystals the halide anions are surrounded by three Hg(C₆F₅)₂ molecules. The reaction of [PPh₄]Br with Hg(C₆F₅)₂ under slightly changed conditions gives the compound [PPh₄]₂[{Hg(C₆F₅)₂}₃(μ‐Br)][{Hg(C₆F₅)₂}₂(μ‐Br)] ( 4 ).