Nicolaus Cusanus und implizite Funktionen

Mathematische Semesterberichte - Nicolaus Cusanus’ Beiträge zur Mathematik des 15. Jahrhunderts betreffen hauptsächlich Kreisquadraturen. Wir besprechen seinen...     

Improved oxygen delivery in a continuous-roller-bottle reactor

Variations to the original aeration system in a continuous roller bottle reactor of novel design have been tested and compared for optimal oxygen (O) delivery. Reactor operating parameters that affect O transfer are rotation rate, liquid-volume level, fresh-feed rate, and supplementary-aeration rate. Design modifications to enhance gas-liquid O transfer include the addition of wall baffles and center baffles. The number and location of each of these baffles are compared for their effect on k_La values in the reaction chamber. The liquid feed into the system has been modified to improve the axial liquid mixing and O transfer.     

The Four-Connected Net in the CeCu(2) Structure and Its Ternary Derivatives. Its Electronic and Structural Properties

The crystallochemistry of and the bonding in the orthorhombic four-connected nets of BaIn(2) (CeCu(2) structure) and of CaPtSn (TiNiSi structure, a derivative of the CeCu(2) structure) are analyzed with approximate molecular orbital calculations. Following the Zintl concept, in BaIn(2) the In(-) ions are isoelectronic with group IV tin and should adopt a four-connected structure. In contrast to alpha-tin, which has a cubic diamond structure, the indium ions in BaIn(2) build up an orthorhombic three-dimensional four-connected net containing distorted tetrahedra and ladder polymers of four-membered rings. In the CeCu(2) structure (space group Imma) two bond angles in these distorted tetrahedra are fixed at 90 degrees. The four-connected net in the CeCu(2) structure is topologically related to the layers in black phosphorus (space group Cmca). In CaPtSn (TiNiSi structure) the orthorhombic four-connected net is formed by (PtSn)(2)(-) ions in an ordered arrangement. Calculations on BaIn(2) and CaPtSn show that the four-connected nets are increasingly stabilized as the valence electron count is increased from 16 to 30 valence electrons per 4 formula units. For more than 30e, the nets are destabilized due to filling of M-E antibonding states. Structural data obtained by precise single crystal investigations for the TiNiSi series CaPdIn (20e), CaPdSn (24e), CaPdSb (28e), and CaAgSb (32e), confirm the results of the extended Hückel calculations. We find an interesting and understandable angular asymmetry of the tetrahedral sites in these ternary compounds.     

Semi-preparative liquid-chromatographic separation of all four stereoisomers of α-bisabolol on tribenzoylcellulose

Summary A semi-preparative low-pressure liquid-chromatographic procedure using tribenzoylcellulose has been developed for the separation and isolation of the four -bisabolol stereoisomers. Stereochemical assignments were made by HPLC-polarimeter coupling and by using the authentical isomers. This method can be applied to the quality control of chamomile preparations, as it allows the detection of adulterations resulting from admixtures of synthetic -bisabolol. In addition, the isolation of all four -bisabolol stereoisomers from commercially available synthetic -bisabolol has been made possible.     

Identification of formylglycine in sulfatases by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

C(alpha)-Formylglycine, the catalytic amino acid residue in the active site of sulfatases, is generated by post-translational modification of a cysteine or serine residue. We describe a highly sensitive procedure for the detection of C(alpha)-formylglycine-containing peptides in tryptic digests of sulfatase proteins. The protocol is based on the formation of hydrazone derivatives of C(alpha)-formylglycine-containing peptides when using dinitrophenylhydrazine as a matrix for matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS). The hydrazone derivatives desorb and ionize with high efficiency and can be detected in the sub-femtomole range. The presence of C(alpha)-formylglycine is indicated by a mass increment of 180.13 u, corresponding to the hydrazone moiety, and also by a unique C-terminal fragment ion, characteristic of sulfatases, that becomes prominent in MALDI post-source decay mass spectra of the hydrazone derivatives.     

Homopolar- and Heteropolar Bond Dissociation Energies and Heats of Formation of Radicals and Ions in the Gas Phase. I. Data on organic molecules

The literature data on heteropolar and homopolar 2-center bond dissociation energies in organic molecules in the gas phase and the corresponding heats of formation of radicals and ions have been critically evaluated. Data for more than 500 bonds are represented in tabular form together with the pertinent literature references. Selected electron affinities and π-bond dissociation energies have also been incorporated. The follow-up paper will discuss some empirical general aspects of these data particularly regarding the effect of structure on the bond dissociation energies.     

Internal rotation and pyramidal inversion in triacylphosphines

MO calculations predict a P-C rotation barrier in triformylphosphine of less than 6 kcal/mol, and an inversion barrier of ca 14 kcal/mol.     

Fluorodiazadiphosphetidine, 12. Mitt.: Reaktionen von Oktafluoro-1,3,2λ6,4λ6-diazoniadiphosphatetidinen

Reaction of (CH₃NHPF₄)₂ with selected organometallic reagents yields (CH₃NPF₃)₂, while reaction with non-nucleophilic bases such as 1,4-diazabicyclo[2.2.2]octane (DABCO) or 1,8-Bis(dimethylamino)naphthalin and with alkali fluorides yields ionic compounds with the diazoniadiphosphatetidine ring as a dianion.     

1,3-Oxazolidin-4-ones. Synthesis and configuration of cis and trans isomers

Mixtures of cis and trans 1,3-oxazolidin-4-ones were obtained by cyclodehydration, in the presence of p-toluenesulfonic acid or boron trifluoride etherate, of lactamide and N-methyl-lactamide with aromatic and aliphatic aldehydes. The products were separated by column (silica) chromatography and their configurations were determined.     

Structure and diffusion in amorphous aluminum silicate: a molecular dynamics computer simulation

The amorphous aluminum silicate (Al2O3)2(SiO2) [AS2] is investigated by means of large scale molecular dynamics computer simulations. We consider fully equilibrated melts in the temperature range 6100 K> or =T> or =2300 K as well as glass configurations that were obtained from cooling runs from T=2300 to 300 K with a cooling rate of about 10(12) K/s. Already at temperatures as high as 4000 K, most of the Al and Si atoms are fourfold coordinated by oxygen atoms. Thus, the structure of AS2 is that of a disordered tetrahedral network. The packing of AlO4 tetrahedra is very different from that of SiO4 tetrahedra in that Al is involved with a relatively high probability in small-membered rings and in triclusters in which an O atom is surrounded by four cations. We find as typical configurations two-membered rings with two Al atoms in which the shared O atoms form a tricluster. On larger length scales, the system shows a microphase separation in which the Al-rich network structure percolates through the SiO2 network. The latter structure gives rise to a prepeak in the static structure factor at a wave number q=0.5 A(-1). A comparison of experimental x-ray data with the results from the simulation shows good agreement for the structure function. The diffusion dynamics in AS2 is found to be much faster than in SiO2. We show that the self-diffusion constants for O and Al are very similar and that they are by a factor of 2-3 larger than the one for Si.