The converse of a theorem of W. Gaschütz on Frattini subgroups

Dedicated to W. Gaschütz on the occasion of his 75th birthday Received 26 January 1995; in final form 2 May 1995     

Direct fluorometric analysis of a newly synthesised fluorescein-labelled marker for glomerular filtration rate

There is an obvious and growing medical need for an accurate determination of kidney function in the diagnosis and management of renal diseases. The glomerular filtration rate (GFR) is the accepted gold standard measurement of kidney function. Several approaches to estimate the GFR are available, but most of them are inconvenient and, therefore, of limited acceptance. A new method of quantification with fluorescein-isothiocyanate (FITC) sinistrin (FS), a novel GFR marker, has been evaluated. The method is based on the fluorescence label of FS and can be performed with a standard fluorometer. To control the interference of protein with the fluorescence signal, a calibration function was developed. The accuracy of the fluorometric method established is comparable to the so-called gold standard of enzymatic determination of polyfructosan. Moreover, FS is easy to handle and requires low-cost instruments. Our results demonstrate the potential of the direct fluorometric analysis of the new FITC-labelled marker of being a precise, simple, rapid and cost-effective method for diagnosing disturbed kidney function and monitoring its treatment efficacy. The dramatic decrease in analytical effort will result in a significantly higher acceptability of GFR determination.     

Mesoporous TiO<Subscript>2</Subscript> thin films prepared from hydrothermally treated precursor powder sols

Two series of TiO₂ thin films were prepared based on soluble precursor powders: The first run originated directly from an alcohol-based coating solution whereas for the second batch the aqueous precursor powder sol had previously undergone a hydrothermal treatment. The respective microstructures were characterized by electron microscopy, the phase evolution was monitored by X-ray diffraction. Ellipsometric porosimetry (EP) was employed to reveal changes of porosity and pore size induced by thermal treatment of the films.

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Soluble TiO₂ precursor powders were hydrothermally treated to yield coating solutions. Films from these sols were compared with those directly obtained by dissolving the precursor powders. Results indicate that crystallization to anatase is induced under hydrothermal conditions and the resulting films mostly maintain their porosity throughout thermal treatment. In contrast to that coatings processed from as-dissolved precursor powders undergo more extensive densification

     

Fast Sodium‐Ion Conductivity in Supertetrahedral Phosphidosilicates

Fast sodium‐ion conductors are key components of Na‐based all‐solid‐state batteries which hold promise for large‐scale storage of electrical power. We report the synthesis, crystal‐structure determination, and Na⁺‐ion conductivities of six new Na‐ion conductors, the phosphidosilicates Na₁₉Si₁₃P₂₅, Na₂₃Si₁₉P₃₃, Na₂₃Si₂₈P₄₅, Na₂₃Si₃₇P₅₇, LT‐NaSi₂P₃ and HT‐NaSi₂P₃, based entirely on earth‐abundant elements. They have SiP₄ tetrahedra assembled interpenetrating networks of T3 to T5 supertetrahedral clusters and can be hierarchically assigned to sphalerite‐ or diamond‐type structures. ²³Na solid‐state NMR spectra and geometrical pathway analysis show Na⁺‐ion mobility between the supertetrahedral cluster networks. Electrochemical impedance spectroscopy shows Na⁺‐ion conductivities up to σ (Na⁺)=4×10^?4 S cm^?1. The conductivities increase with the size of the supertetrahedral clusters through dilution of Na⁺‐ions as the charge density of the anionic networks decreases.     

Polymers of carbonic acid. XIV. High molecular weight poly(trimethylene carbonate) by ring-opening polymerization with butyltin chlorides as initiators

Numerous BuSnCl, Bu₂SnCl, and Bu₃SnCl-initiated polymerizations of cyclo(tri-methylene carbonate) (TMC) were conducted in bulk. In addition to the initiator, reaction time, temperature, and monomer/initiator (M/I) ratio were varied. Yields above 90% were obtained with all three initiators, but their reactivities decrease in the order BuSnCl₃ > Bu₂SnCl₂ > Bu₃SnCl. The maximum molecular weights decrease in the same order. With BuSnCl₃ M_ws up to 250,000 were obtained. These molecular weights were determined by GPC on the basis of the universal calibration method. In this connection Mark-Houwink equations for two solvents, tetrahydrofuran (THF) and CH₂Cl₂ were determined and compared with literature data. Furthermore, mechanistic aspects were studied. ¹H- and ¹³C- NMR spectra revealed that BuSnCl₃ forms complexes with the CO-group of TMC, whereas Bu₂SnCl₃ do not cause NMR spectroscopic effects. Kinetic studies in chloroform and nitrobenzene and a comparison with Bu₃SnOMe suggest that at least BuSnCl₃ initiates a cationic mechanism. However, in contrast to SnCl₄ (or SnBr₄), BuSnCl₃ does not cause decarboxylation. Regardless of the initiator ¹H-NMR spectroscopy revealed CH₂OH and CH₂CI endgroups in all cases. © 1995 John Wiley & Sons, Inc.     

NMR probing of protein-protein interactions using reporter ligands and affinity tags

A novel method is proposed for the detection and quantification of protein-protein interactions in solution. In this approach, one protein binding partner is tagged with a ligand binding domain, and protein-protein interaction is monitored via changes in the NMR relaxation of a reporter ligand which reversibly binds to the ligand binding domain. The particular benefit of the method is that only minute amounts of protein material and no isotope labeling are required. Its ease of implementation and the high-throughput capabilities make the method an attractive complement to existing proteomic methodology.     

Epimeric 2-norbornyl cations in the solvolysis of 6-exo- and 6-endo-substituted 2-exo-norbornyl p-toluenesulfonates

Solvolysis of 6-exo- and 6-endo-substituted 2-exo-norbornyl tosylates $\text{1}$ and $\text{3}$, respectively, yields identical or different product mixtures depending on the inductive effect of the substituent, indicating that induction involves graded σ-participation.     

Phase behavior of colloidal hard tetragonal parallelepipeds (cuboids): a Monte Carlo simulation study

The impact of particle geometry on the phase behavior of hard colloidal tetragonal parallelepipeds (TPs) was studied by using Monte Carlo simulations in continuum space. TPs or "cuboids" of aspect ratios varying from 0.25 to 8 were simulated by approximating their shapes with multisite objects, i.e., via rigid clusters of hard spheres. Using equation of state curves, order parameters, radial distribution functions, particle distribution functions along three directions, and visual analysis of configurations, an approximate phase diagram for the TPs was mapped out as a function of aspect ratio (r) and volume fraction. For r > 3 and intermediate concentrations, the behavior of the TPs was similar to that of spherocylinders, exhibiting similar liquid crystalline mesophases (e.g., nematic and smectic phases). For r = 1, a cubatic phase occurs with orientational order along the three axes but with little translational order. For 1 < r < 4, the TPs exhibit a cubatic-like mesophase with a high degree of order along three axes where the major axes of the particles are not all aligned in the same direction. For r < 1, the TPs exhibit a smectic-like phase where the particles have rotational freedom in each layer but form stacks with tetratic order. The equation of state for perfect hard cubes (r = 1) was also simulated and found to be consistent with that of the rounded-edge r = 1 TPs, except for its lack of discontinuity at the cubatic-solid transition.     

Facile synthesis of @-tide beta-strand peptidomimetics: improved assembly in solution and on solid phase

The synthesis of @-tide beta-strand peptidomimetics has been improved such that oligomers now can be obtained from solution- and solid-phase synthesis protocols approaching the efficiency and flexibility of peptide chemistry. These methods enable the synthesis of @-tide oligomers with a variety of amino acids and with lengths up to 13 units. [reaction: see text]     

The quickest flow problem

Consider a network =(G, c, ) whereG=(N, A) is a directed graph andc _ij and _ij , respectively, denote the capacity and the transmission time of arc (i, j) A. The quickest flow problem is then to determine for a given value the minimum numberT() of time units that are necessary to transmit (send) units of flow in from a given sources to a given sinks.In this paper we show that the quickest flow problem is closely related to the maximum dynamic flow problem and to linear fractional programming problems. Based on these relationships we develop several polynomial algorithms and a strongly polynomial algorithm for the quickest flow problem.Finally we report computational results on the practical behaviour of our metholds. It turns out that some of them are practically very efficient and well-suited for solving large problem instances.Partial financial support by the Air Force Office of Scientific Research under grants AFOSR-89-0512 and AFOSR-90-0008 is gratefully acknowledged by the first author.