Über die Klasse der Summenmengen

Ohne Zusammenfassung     

Continuous bordering of matrices and continuous matrix decompositions

Summary. Let be the set of all real -matrices of rank . We prove that for there are no continuous vector fields such that the bordered matrix is regular for all . This result has some relevance for the numerical analysis of steady state bifurcation. As a by-product we show that there is no nonvanishing continuous vector field with for all , where is the set of all matrices of rank deficiency one. This implies that there is no singular value decomposition of depending continuously on in any matrix set which contains . As another application we prove that in general there is no global analytic singular value decomposition for analytic matrix valued functions of more than one real variable. Received October 6, 1993 / Revised version received July 18, 1994     

Physicochemical investigation of a lipid with a new core structure for gene transfection: 2-amino-3-hexadecyloxy-2-(hexadecyloxymethyl)propan-1-ol

Cationic liposomes/DNA complexes can be used as nonviral vectors for direct delivery of DNA-based biopharmaceuticals to damaged cells and tissues. In order to obtain more effective and safer liposome-based gene transfection systems, the new cationic lipid 2-amino-3-hexadecyloxy-2-(hexadecyloxymethyl)propan-1-ol (AHHP) was synthesized. In this paper we report on the synthesis of AHHP and investigations of its physical-chemical properties. Langmuir monolayers of AHHP were studied at the air/buffer interface by film balance measurements, grazing incidence X-ray diffraction (GIXD), and infrared reflection absorption spectroscopy (IRRAS). Structure and thermotropic phase behavior of AHHP in aqueous dispersion were examined by small-angle and wide-angle X-ray scattering (SAXS/WAXS) and differential scanning calorimetry (DSC). The results show clear differences in structure and phase behavior of AHHP, both in the monolayer system and in aqueous dispersions, in dependence on the subphase pH due to protonation or deprotonation of the primary amine in the lipid head group. Thermodynamic data derived from pi-A isotherms provide information about the critical temperature (Tc), which is in rough agreement with the temperature of the lipid phase transition from gel to fluid state (Tm) found by X-ray and calorimetry studies of AHHP aqueous dispersions. The packing properties of the molecules in mono- and bilayer systems are very similar. DNA couples to the monolayer of the new lipid at low as well as at high pH but in different amounts. The DNA coupling leads to an alignment of adsorbed DNA strands indicated by the appearance of a Bragg peak. The distance between aligned DNA strands does not change much with increasing monolayer pressure.     

Functionalization of bolalipid nanofibers by silicification and subsequent one-dimensional fixation of gold nanoparticles

In the present work, we describe the successful stabilization of bolalipid nanofibers by sol-gel condensation (silicification) of tetraethoxysilane (TEOS) or 3-mercaptopropyltriethoxysilane (MP-TEOS), respectively, onto the nanofibers. The conditions for an effective and reproducible silicification reaction were determined, and the silicification process was pursued by transmission electron microscopy (TEM). The resulting bolalipid-silica composite nanofibers were characterized by means of differential scanning calorimetry (DSC), TEM, (13)C, and (31)P NMR spectroscopy. Finally, the novel silicified bolalipid nanofibers were used as templates for the fixation of 5 and 2 nm AuNPs, respectively, resulting in one of the rare examples of one-dimensional AuNP arrangements in aqueous suspension.     

Temperature-dependent behavior of a symmetric long-chain bolaamphiphile with phosphocholine headgroups in water: from hydrogel to nanoparticles

The temperature-dependent self-assembly of the single-chain bolaamphiphile dotriacontan-1,1'-diyl-bis[2-(trimethylammonio)ethyl phosphate] (PC-C32-PC) was investigated by transmission electron microscopy (TEM), differential scanning calorimetry (DSC), Fourier transform infrared spectroscopy (FT-IR), X-ray scattering, rheological measurements, and dynamic light scattering (DLS). At room temperature this compound, in which two phosphocholine headgroups are connected by a C(32) alkyl chain, proved to be capable of gelling water very efficiently by forming a dense network of nanofibers (Kohler et al. Angew. Chem., Int. Ed. 2004, 43, 245). A specific feature of this self-assembly process is that it is not driven by hydrogen bonds but solely by hydrophobic interactions of the long alkyl chains. The nanofibers have a thickness of roughly the molecular length and show a helical superstructure. A model for the molecular structure of the fibrils which considers the extreme constitution of the bolaamphiphile is proposed. Upon heating the suspensions three different phase transitions can be detected. Above 49 degrees C, the temperature of the main transition where the alkyl chains become "fluid", a clear low-viscosity solution is obtained due to a breakdown of the fibrils into smaller aggregates. Through mechanical stress the gel structure can be destroyed as well, indicating a low stability of these fibers. The gel formation is reversible, but as a drastic rearrangement of the molecules takes place, metastable states occur.     

Structural flexibility and role of vicinal 2-thienyl rings in 2,3-dicyano-5,6-di(2-thienyl)-1,4-pyrazine, [(CN)2Th2Pyz], its palladium(II) complex [(CN)2Th2Pyz(PdCl2)2], and the related pentametallic pyrazinoporphyrazines [(PdCl2)4Th8TPyzPzM] (M = Mg(II)(H2O), Zn(II))

The solid state and solution structure of 2,3-dicyano-5,6-di(2-thienyl)-1,4-pyrazine, [(CN)(2)Th(2)Pyz], and its Pd(II) derivative, [(CN)(2)Th(2)Pyz(PdCl(2))(2)]·H(2)O, formed by reaction of [(CN)(2)Th(2)Pyz] with [(C(6)H(5)CN)(2)PdCl(2)] were characterized by X-ray, UV-visible, (1)H and (13)C NMR, and extended X-ray absorption fine structure (EXAFS) spectral measurements. The X-ray crystal structure of [(CN)(2)Th(2)Pyz] shows the presence of one thienyl ring positioned orthogonal to the rest of the molecule, with the two vicinal thienyl rings lying orthogonal to each other in a rare arrangement. NMR studies of [(CN)(2)Th(2)Pyz] in the solid state and in solutions of dimethylformamide or dimethyl sulfoxide confirm a nonequivalence of the thienyl rings in the solid state and also in solution. EXAFS results indicate that two distinct Pd(II) coordination sites are formed at the di(2-thienyl)pyrazino moiety of [(CN)(2)Th(2)Pyz(PdCl(2))(2)]·H(2)O, with identical Pd-N(pyz) (2.03(3) ?) and Pd-Cl (2.36(3) ?) bond lengths but with different Pd-S1 (2.25(4) ?) and Pd-S2 (3.21(5) ?) bond distances in an overall asymmetric molecular framework. Density functional theory (DFT) and time-dependent DFT (TDDFT) theoretical studies also provide information about the structure and spectral behavior of the precursor and its metalated Pd(II) derivative. (1)H/(13)C NMR and UV-visible spectral measurements were also carried out on two heteropentametallic porphyrazine macrocycles which were prepared by a reaction of PdCl(2) with [Th(8)TPyzPzM] where Th(8)TPyzPz = tetrakis-2,3-[5,6-di-(2-thienyl)-pyrazino]porphyrazinato dianion and M = Mg(II)(H(2)O) or Zn(II). Spectroscopic data on the newly synthesized [(PdCl(2))(4)Th(8)TPyzPzM] compounds suggest that the binding of PdCl(2) involves coordination sites of the type S(2(th))PdCl(2) with the two thienyl rings of each di(2-thienyl)pyrazino fragment bound to Pd(II) in an equivalent manner ("th-th" coordination). This is similar to what was found for the corresponding octapyridinated analogues ("py-py" coordination).     

Systematic studies on the determination of Hg-labelled proteins using laser ablation-ICPMS and isotope dilution analysis

A method was developed for the precise and accurate determination of ovalbumin labelled with p-hydroxy-mercuribenzoic acid (pHMB) using polyacrylamide gel electrophoresis with ns-laser ablation–inductively coupled plasma mass spectrometry. Following systematic optimisation of the ablation process in terms of detection sensitivity, two different quantification strategies were applied: external calibration using standards of the derivatized protein after ¹³C⁺ normalization and, as a proof of concept, label-specific isotope dilution analysis (IDA) using pHMB enriched in the isotope ¹⁹⁹Hg. Due to the inhomogeneous distribution of the protein within the gel bands, it could be demonstrated that the IDA approach was superior in terms of precision and accuracy. Furthermore, it permits a reliable quantification, if more complex separation protocols are applied, as typically occurring analyte loss and degradation can be compensated for as soon as complete mixture of spike and sample is achieved. The estimated limit of detection was 160 fmol in the case of ovalbumin. In contrast to earlier studies using metals naturally present in proteins, no loss of mercury was observed during separation under denaturing conditions and other sample preparation steps. Using label-specific IDA, the measured isotope ratios in the gel corresponded to recoveries between 95% and 103%.     

Correlation of current quenching and occurrence of metal vapor in apseudospark discharge

The quenching phenomenon, i.e., a sudden interrupt of the discharge current, was investigated in a pseudospark discharge with charging voltage of 2.5 kV, maximum current of 2 kA and discharge duration of 3 μs. The working gas was hydrogen at a pressure of 40 Pa. Concerning electrode material and geometric parameters, molybdenun electrodes were chosen with hole diameters of 5 mm; the electrode distance was 3 mm. In this parameter range, a temporal correlation of current quenching and the occurrence of metal vapor could be detected by means of time-resolved optical spectroscopy. With each current interruption a sudden increase of emission from neutral molybdenum atoms as well as an increase of cathode spot emission, which is spatially localized on the cathode, occurs. Also oxygen ions were observed which show a similar time-dependence, however with a significant delay of the order of 200 ns. The results are discussed in the scope of the mechanism proposed for quenching, i.e., ion depletion in the plasma boundary layer, and the mechanisms occurring in the high current phase of a pseudospark discharge