On a conjecture of R. E. Miles about the convex hull of random points

Denoty byp _d+i (B _d ,d+m) the probability that the convex hull ofd+m points chosen independently and uniformly from ad-dimensional ballB _d possessesd+i(i=1,...,m) vertices. We prove Mile's conjecture that, given any integerm, p _d+m (B _d ,d+m)»1 asd». This is obvious form=1 and was shown by Kingman form=2 and by Miles form=3. Further, a related result by Miles is generalized, and several consequences are deduced.Dedicated to Professor E. Halwaka on the occasion of his seventieth     

Dynamic Fourier transform infrared spectroscopy in polymer research

The rapid-scanning capability of FTIR instrumentation has revitalized the field of vibrational spectroscopy in polymer research and will be discussed with reference to the study of polyurethane kinetics, the temperature dependence of hydrogen bonding in polyamide 6 and strain-induced crystallization in a polydimethylsiloxane elastomer.     

X-ray structure and variable temperature NMR spectra of [meso-triarylcorrolato]copper(III)

The diamagnetic square planar d(8) complexes [meso-arylcorrolato]copper(III) become paramagnetic upon warming, indicative of the equilibrium between the [corrolato]copper(III) and the [corrolato](+)* copper(II) forms of the complex. [meso-Triphenylcorrolato]copper(III) was structurally characterized and found to be saddled.     

Solubility of gases in liquids. 18. High-precision determination of Henry fugacities for argon in liquid water at 2 to 40°C

The solubility of argon in pure liquid water was measured at ca. 100 kPa and from 2 to 40°C using an analytical method characterized by an imprecision of about ±0.05%. From the experimental results, Henry fugacities H _2,1 (T,P _s,1 ) (also known as Henry's Law constants or Henry coefficients) at the vapor pressure P _s,1 of water as well as Ostwald coefficients L _2,1 at infinite dilution were obtained. Measurements were made at roughly 0.5°C and/or 1° intervals between 2 and 8°C (region I), and at 5°C intervals above 10°C (region II). A difference plot lnH _2,1 /T suggests an unusual temperature dependence in region I, i.e., between 2 and 8°C. Because of this, the data were treated separately in two parts corresponding to these two regions. Our results are compared with the recent high-precision data of Krause and Benson (Henry fugacities), and with calorimetrically determined quantities (enthalpies and heat capacities of solution). Finally, experimental results are compared with values calculated via scaled particle theory.Communicated in part at the 2^nd International Symposium on Solubility Phenomena in Newark, New Jersey, August 12–15, 1986, and at the 4^th ISSP in Troy, New York, July 20–August 3, 1990.     

Use of solid-phase microextraction-capillary-gas chromatography (SPME-CGC) for the varietal characterization of wines by means of chemometrical methods

The extraction of wine aroma compounds was studied by direct-SPME (DI/SPME), headspace-SPME (HS/SPME) and multiple-headspace-extraction-SPME (MHE/SPME). The aromagrams obtained by HS/SPME-CGC were evaluated with chemometrical methods for the varietal classification of wines. Received: 25 July 1997 / Revised: 24 September 1997 / Accepted: 7 October 1997     

Protein-Loop Mimetics: A Diketopiperazine-Based Template to Stabilize Loop Conformations in Cyclic Peptides Containing the NPNA and RGD Motifs

We explore here an approach to mimic the structures and biological functions of protein loops in small synthetic molecules, by grafting the loop of interest onto an organic template comprising a bicyclic diketopiperazine, prepared by the formal coupling of (2S,4S)-4-aminoproline (Pro(NH₂)) and aspartic acid (Asp). The Fmoc-protected template 4 is used to prepare cyclo(-Ala¹-Asn²-Pro³-Asn⁴-Ala⁵- Ala⁶-Temp-) ( 5 ) and cyclo(-Ala¹-Arg²-Gly³-Asp⁴-Temp-) ( 6 ) (where Temp = template derived from 4 ), containing the Asn-Pro-Asn-Ala (NPNA) and Arg-Gly-Asp (RGD) motifs. The conformational properties of these molecules are studied in aqueous solution by NMR and simulated-annealing methods. The NPNA motif, an immunodominant epitope on the circumsporozoite surface protein of the malaria parasite Plasmodium falciparum, is shown to adopt a stable type-I β-turn in 5 . The template in 5 adopts a preferred conformation with Pro(NH₂)χ₁ ≈? ?35° and the Asp moiety χ₁ ≈? 70°. A different template conformation is inferred for 6 , with Pro(NH₂)χ₁ ≈? 0°, but the ARGD loop appears by NMR to undergo rapid conformational averaging. Solid-phase binding assays reveal that 6 displays modest antagonist activity towards both the integrin α_IIbβ₃ and α_vβ₃ receptors.     

Ab initio study of the binding of Trichostatin A (TSA) in the active site of histone deacetylase like protein (HDLP)

Histone deacetylase (HDAC) inhibitors have recently attracted considerable interest because of their therapeutic potential for the treatment of cell proliferative diseases. An X-ray structure of a very potent inhibitor, Trichostatin A (TSA), bound to HDLP (an HDAC analogue isolated from Aquifex aeolicus), is available. From this structure, an active site model (322 atoms), relevant for the binding of TSA and structural analogues, has been derived, and TSA has been minimized in this active site at HF 3-21G* level. The resulting conformation is in excellent accordance with the X-ray structure, and indicates a deprotonation of the hydroxamic acid in TSA by His 131. Also, a water molecule was minimized in the active site. In addition to a similar deprotonation, in accordance with a possible catalytic mechanism of HDAC as proposed by Finnin et al. (M. S. Finnin, J. R. Donigian, A. Cohen, V. M. Richon, R. A. Rifkind and P. A. Marks, Nature, 1999, 401, 188-193), a displacement of the resulting OH- ion in the active site was observed. Based on these results, the difference in energy of binding between TSA and water was calculated. The resulting value is realistic in respect to experimental binding affinities. Furthermore, the mechanism of action of the His 131-Asp 166 charge relay system was investigated. Although the Asp residue in this motif is known to substantially increase the basicity of the His residue, no proton transfer from His 131 to Asp 166 was observed on binding of TSA or water. However, in the empty protonated active site, this proton transfer does occur.     

L'acide hydroxylamine-O-sulfonique,réactif de choix pour la conversion d'aldéhydes en nitriles

Hydroxylamine-O-sulfonic acid: a convenient reagent for the conversion of aldehydes into nitriles . Hydroxylamine-O-sulfonic acid (HAS) proved to be an excellent reagent for the conversion of aliphatic, aromatic and heteroatomic aldehydes into nitriles. There, aldehydes in the form of suspension in HAS water solution, react rapidely to give the corresponding nitriles in high yield. Only with formylpyridines could the intermediate oxime-O-sulfonic acids be isolated.     

Enhancing chemical analysis with signal derivatization using simple available software packages

Derivative techniques for analytical signal processing are useful for solving some noise and signal resolution problems in various fields of study such as titrimetry, spectrophotometry, chromatography and electrochemistry. The broad use of these techniques, however, is often limited by costly inflexible built-in software packages in commercial analytical instruments. We propose here the application of commercial simple software packages such as Microsoft® Excel and Microcal Origin for signal smoothing and fitting, and for obtaining derivative analytical signals in batch and flow-based analyses, including potentiometric titration, spectrophotometry, chromatography, voltammetry and sequential injection analysis (SIA). The worldwide (especially Excel) software packages are easy-to-use for less experienced users and have also capabilities for advanced users, and therefore employing such packages can result in expansion of useful derivative techniques. We demonstrate application of the available package-aided derivative capabilities for enhancing some chemical analyses, including potentiometric acid–base titration, Bradford assay of protein, chromatographic separation of ajmaline and reserpine and anodic stripping voltammetry of copper. The derivative signals from smoothed and fitted curves offer better accuracy and precision, even for non-resolving peaks and tailing peaks. In some cases, the optimization of experimental conditions is not further required, which can lead to fast method development.     

Strukturen und Molekül-Eigenschaften ladungsgestörter Moleküle. 52. Mitteilung. 2, 3-Diphenylchinoxalin-Radikalanionen in Lösung und im Kristall

Structures and Molecular Properties of Charge-Pertubed Molecules. 2, 3-Diphenylquinoxaline Radical Anions in Solution and in Crystals The Na⊕ and K⊕ radical-ion salts of 2, 3-diphenylquinoxaline seem to be (according to a structural database search) among the first ones of N-heterocyclic radical anions in crystals. The one-electron reduction in aprotic 1, 2-dimethoxyethan (DME) solution at metal mirrors and the crystallization under Ar have been preceded by cyclovoltammetric (CV) and ESR/ENDOR measurement. The first electron insertion at ?1.63 V proves to be reversible, whereas the irreversible second step, which is accompanied by an overcrossing of the CV line, can be rationalized by an ‘ECE-DISP’ mechanism via a dianion redox disproportionation. The ENDOR spectrum resolves four ¹H couplings and allows to simulate the ESR spectrum including the ¹⁴N hyperfine splittings. Both dark-blue single crystals of the radical ion salts $[2,3{\rm - diphenylquinoxaline}^{{.} \ominus} {\rm Met}^ \oplus ({\rm DME})]^.$ show unexpected similarities for Met⊕ = Na⊕, K⊕ despite the 36-pm difference in their ionic radii. The largest structural changes inflicted by the one-electron reduction of the N-heterocyclic molecule are observed in the vicinity of the N-centers bearing the highest effective nuclear charge. The DME-chelated metal cations coordinate at the N electron pairs and form Met⊕(DME)-bridged polymer chains of the radical anion, which are differently ondulated in the Na⊕ and K⊕ radical anion salts. The take-home lesson suggests that many more N-heterocyclic molecules might be analogously reduced under optimized conditions and isolated as single crystals.