Factorial regular representation of groups in complete graphs

A necessary and sufficient condition for the group of isomorphisms involved in a factorization of a complete graph into isomorphic factors is established.     

Retaining and recovering enzyme activity during degradation of TCE by methanotrophs

To determine if compounds added during trichloroethylene (TCE) degradation could reduce the loss of enzyme activity or increase enzyme recovery, different compounds serving as energy and carbon sources, pH buffers, or free radical scavengers were tested. Formate and formic acid (reducing power and a carbon source), as well as ascorbic acid and citric acid (free radical scavengers) were added during TCE degradation at a concentration of 2 mM. A saturated solution of calcium carbonate was also tested to address pH concerns. In the presence of formate and methane, only calcium carbonate and formic acid had a beneficial effect on enzyme recovery. The calcium carbonate and formic acid both reduced the loss of enzyme activity and resulted in the highest levels of enzyme activity after recovery.     

Conditional solubility versus pO2− of cerium(III) oxide in molten equimolar NaCl+KCl at 727°C

Reactions between cerium trichloride and oxide ions were studied in NaCl+KCl (1/1) at 1000°K, by potentiometry with a calcia-stabilized zirconia membrane electrode. Titration curves clearly demonstrated the existence of soluble cerium oxychloride (CeO⁺) and precipitated cerium oxide (Ce₂O₃), with respective dissociation constants 10^?11 and 10^?30 (molality scale). The corresponding conditional solubility diagram {log S (Ce^III)=f(pO^2?)} is presented and discussed.     

Alkylidinphosphane und -arsane. I [P ≡ C?S]−[Li(dme)3]+ – Synthese und Struktur

Alkylidynephosphanes and -arsanes. I [P ≡ C? S]^?[Li(dme)₃]⁺ – Synthesis and Structure O,O′-Diethyl thiocarbonate and bis(tetrahydrofuran)-lithium bis(trimethylsilyl)phosphanide dissolved in 1,2-dimethoxyethane, react below 0°C to give ethoxy trimethylsilane and tris(1,2-dimethoxyethane-O,O′)lithium 2λ³-phosphaethynylsulfanide – [P≡C? S]^? [Li(dme)₃]⁺ – ( 1a ). Apart from bis(trimethylsilyl)sulfane or carbon oxide sulfide, dark red concentrated solutions of λ³-phosphaalkyne 1 are also obtained from reactions of carbon disulfide with bis(tetrahydrofuran)-lithium bis(trimethylsilyl)phosphanide or with the homologous lithoxy-methylidynephosphane ( 2 ) [1]. The ir spectrum shows two absorptions at 1762 and 747 cm^?1 characteristic for the P≡C and C? S stretching vibrations. The nmr parameters {δ(³¹P) ? 121.3; δ(¹³C) 190.8 ppm; ¹J_CP 18.2 Hz} resemble much more values of diorganylamino-2λ³-phosphaalkynes than those of bis(1,2-dimethoxyethane-O,O′)lithoxy-methylidyne-phosphane ( 2a ). As found by an X-ray structure analysis (P2₁/c; a = 1192.6(16); b = 1239.1(19); c = 1414.8(26) pm; β = 105.91(13)° at ?100 ± 3°C; Z = 4 formula units; wR = 0.064) of pale yellow crystals (mp. + 16°C) isolated from the reaction with O,O′-diethyl thiocarbonate, the solid is built up of separate [P≡C? S]^? and [Li(dme)₃]⁺ ions. Typical bond lengths and angles are: P≡C 155.5(11); C? S 162.0(11); Li? O 206.4(17) to 220.3(20) pm; P≡C? S 178.9(7)°.     

On bounds for the range of ordered variates II

Letx ₁, ,x _n be real numbers with ₁ ⁿ x _j =0, |x ₁ ||x ₂ ||x _n |, and ₁ ⁿ f(|x _i |)=A>0, wheref is a continuous, strictly increasing function on [0, ) withf(0)=0. Using a generalized Chebycheff inequality (or directly) it is easy to see that an upper bound for |x _m | isf ^–1 (A/(n–m+1)). If (n–m+1) is even, this bound is best possible, but not otherwise. Best upper bounds are obtained in case (n–m+1) is odd provided either (i)f is strictly convex on [0, ), or (ii)f is strictly concave on [0, ). Explicit best bounds are given as examples of (i) and (ii), namely the casesf(x)=x ^p forp>1 and 0<p<1 respectively.     

Synthesis and Systematic Study on the Effect of Different PEG Units on Stability of PEGylated,Integrin-αvβ6-Specific A20FMDV2 Analogues in Rat Serum and Human Plasma

A20FMDV2 is a 20-mer peptide that exhibits high selectivity and affinity for the tumour-related αvβ6 integrin that can compete with extracellular ligands for the crucial RGD binding site, playing a role as a promising αvβ6-specific inhibitor for anti-cancer therapies. Unfortunately, the clinical value of A20FMDV2 is limited by its poor half-life in blood caused by rapid renal excretion and its reported high susceptibility to serum proteases. The incorporation of poly (ethylene glycol) chains, coined PEGylation, is a well-established approach to improve the pharmacokinetic properties of drug molecules. Here, we report a systematic study on the incorporation of a varying number of ethylene glycol units (1–20) into the A20FMDV2 peptide to establish the effects of PEGylation size on the peptide stability in both rat serum and human plasma. In addition, the effect of acetyl and propionyl PEGylation handles on peptide stability is also described. Selected peptide analogues were assessed for integrin-αvβ6-targeted binding, showing good specificity and activity in vitro. Stability studies in rat serum established that all of the PEGylated peptides displayed good stability, and an A20FMDV2 peptide containing twenty ethylene glycol units (PEG₂₀) was the most stable. Surprisingly, the stability testing in human plasma identified shorter PEGs (PEG₂ and PEG₅) as more resistant to degradation than longer PEGs, a trend which was also observed with affinity binding to integrin αvβ6.     

Unusual Reactivities of ortho-Hydroxy-β-nitrostyrene

Nitrostyrene derivatives are widely used in organic syntheses as a substrate for Michael addition, photoisomerization and cycloaddition. In contrast, ortho-hydroxy derivatives exhibit unusual behaviors in these reactions. Conjugate addition proceeded upon treatment of the ortho-hydroxy-β-nitrostyrene with an amine; however, subsequent C–C bond cleavage readily occurred to afford the corresponding imine. Moreover, conversion of the trans-isomer to a cis-isomer did not occur efficiently, even when UV light was irradiated. We studied these unusual behaviors of β-nitrostyrene, focusing on the role of the ortho-hydroxy group.     

Chemical composition and phase identification of sodium titanate nanostructures grown from titania by hydrothermal processing

Fine titanium dioxide particles were hydrothermally treated in a sodium hydroxide aqueous solution. The treatment extended from 1 to 6 days leading to belt-like and wire-like structures of a metastable phase of sodium titanate, with typical widths and diameters between 8 and 40 nm, and lengths from 100 nm to several micrometers. These conclusions are supported by X-ray photoelectron spectroscopy, X-ray diffraction, Raman spectroscopy and high resolution transmission electron microscopy. The latter method revealed two set of space fringes with characteristic distances of 0.29 and 0.34 nm. These distances could correspond to the lattice spacing of and planes in Na₂Ti₆O₁₃ compounds. The nanomaterial was found to be stable up to temperatures as high as 200 or depending on the reaction time and the concentration.     

Spectroscopy of light nuclei with skyrme-type interactions

Deformed Hartree-Fock calculations are performed for some light nuclei in a large configuration space consisting of first four major shells. The interaction employed is the modified Skyrme interaction in which the deformed density is replaced by the band averaged scalar density that makes the Hamiltonian rotationally invariant rendering the spectroscopic calculations feasible. It is shown that the introduction of density dependence spreads out the energy spectra and that the Skyrme variant SIV which has a weak density dependence gives best overall agreement for energy spectra and the available data for the electromagnetic properties of the nuclei studied. It is found that the maximum contribution to the energy of any state in the low lying spectrum comes from thes-state attractive ands-state repulsive parts of the Skyrme interaction. It is also shown that when two-body density dependent version of Skyrme interaction is used, the Koopmans theorem no longer holds.     

Fortschritte in der Auswertung von Markierungsversuchen an dynamischen Systemen

In einem dynamischen System vollziehen sich kontinuierlich ablaufende Stoffwandlungen, deren Ausgangsstoffe dem System ständig zufließen und deren Folgeprodukte das System kontinuierlich verlassen. Es wird das Verhalten eines solchen Systems mit drei Pools bei Markierungsexperimenten untersucht. Die Ergebnisse dieser mathematischen Untersuchungen werden auf die Erforschung des Stickstoffstoffwechsels laktierender Rinder mit Hilfe des stabilen Isotops ¹⁵N angewandt. In diesem Fall enthält das dynamische System zwei kleine stoffwechselaktive Pools und einen großen, niclit intensiv am Stoffwechsel beteiligten Körpereiweiβ-Pool.