A tight Hermite–Hadamard inequality and a generic method for comparison between residuals of inequalities with convex functions

Periodica Mathematica Hungarica - We present a tight parametrical Hermite–Hadamard type inequality with probability measure, which yields a considerably closer upper bound for the mean value...     

Harnack inequality for some classes of Markov processes

In this paper we establish a Harnack inequality for nonnegative harmonic functions of some classes of Markov processes with jumps. Mathematics Subject Classification (2000): Primary 60J45, 60J75, Secondary 60J25.This work was completed while the authors were in the Research in Pairs program at the Mathematisches Forschungsinstitut Oberwolfach. We thank the Institute for the hospitality.The research of this author is supported in part by NSF Grant DMS-9803240.The research of this author is supported in part by MZT grant 0037107 of the Republic of Croatia.     

Reagent concentration effects in the REM resin solid phase synthesis of tertiary amines

The use of reagent concentration has resulted in increased rates for all stages of the REM resin synthesis of tertiary amines. These increases in rate translate into faster reaction times, higher yields and lower reagent consumption. Of the methods examined, the most successful was the use of perfluorous solvents, either alone or with a small amount of organic co-solvent.     

Modelling of composting of food waste in a column reactor

The composting of organic solid waste, the mixture of fruit and vegetable leftovers enriched with night soil, was investigated in a closed thermally insulated reactor. It was found that 80.9 % of the original substrate biodegraded after 14 days. A mathematical model of the column reactor was proposed where the biodegradation rate of the organic solid waste was described using simple n-thorder kinetics. A good prediction of process performance was obtained using the proposed kinetics and experimentally obtained reaction heat. Presented at the 33rd International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 22–26 May 2006.     

Contributions of restructuring and oxidation to the aging of the surface of plasma polymers containing heteroatoms

The properties and composition of plasma polymer surfaces stored in air can change considerably over time, especially as a result of oxidative reactions. When plasma polymers contain an element other than O, it is possible to probe for mechanisms in addition to oxidation that contribute to the aging of the surface. Plasma polymers containing N were fabricated from either 1,3-diaminopropane (DAP),n-heptylamine (nHA), or allylamine (AA), and studied by X-ray photo-electron spectroscopy (XPS) and air/water contact angles (CA). For each of the plasma polymers, a multiexponential increase in the O/C ratio was observed over time using XPS. The N/C ratios remained constant (AA) or decreased somewhat (nHA and DAP). In contrast, the trends in CA values differed, declining for the nHA surfaces, rising for the AA, and changing little for the DAP. Surface roughness, assessed by scanning tunnelling or atomic force microscopy, did not change over time. The diverse adjustments in the polarity of each surface and the similar compositional changes between them are reconcilable if the aging of the plasma polymer surface is a manifestation of the superposition of concurrent oxidative reactions and partial surface reorientation; the former introduce polar groups and the latter transports then from the surface to deeper regions beyond the CA probe depth but within the XPS analysis depth. These processes vary between different plasma polymers. Data for the alkylamine plasma polymers is also compared with that for two plasma polymers fabricated from methanol. The change in composition, but not polarity, of the DAP surface after 4 days of storage demonstrates the importance of using multiple techniques to characterize the aging of plasma polymer surfaces.     

Silver(I) undecafluorodiantimonate(V)

The reaction between AgBF4 and excess of SbF5 in anhydrous hydrogen fluoride (aHF) yields the white solid AgSb2F11 after the solvent and the excess of SbF5 have been pumped off. Reaction between equimolar amounts of AgSb2F11 and AgBF4 yields AgSbF6. Meanwhile, oxidation of solvolyzed AgSb2F11 in aHF by elemental fluorine yields a clear blue solution of solvated Ag(II) cations and SbF6- anions. AgSb2F11 is orthorhombic, at 250 K, Pbca, with a=1091.80(7) pm, b=1246.28(8) pm, c=3880.2(3) pm, V=5.2797(6) nm3, and Z=24. The crystal structure of AgSb2F11 is related to the already known crystal structure of H3OSb2F11. Vibrational spectra of AgSb2F11 entirely match the literature-reported vibrational spectra of beta-Ag(SbF6)2, for which a formulation of a mixed-valence AgI/AgIII compound was suggested (AgIAgIII(SbF6)4). On the basis of obtained results it can be concluded that previously reported beta-Ag(SbF6)2 is in fact Ag(I) compound with composition AgSb2F11.     

Copper(I) hexafluoroantimonate - an example of a compound with Cu in a solely fluorine environment

Yellow-orange single crystals of CuSbF₆, were prepared by reacting Cu wire (∼10 mmol) with SbF₅ (∼3 mmol) in liquid anhydrous hydrogen fluoride (aHF) and by reduction of Cu(SbF₆)₂ with Cu metal in aHF. CuSbF₆ crystallizes rhombohedral at 296 K with the LiSbF₆ structure type, with a = 530.4(4) pm, c = 1453(1) pm and Z = 3, space group R (no. 148). The structure is dominated by isolated layers of regular [SbF₆]⁻ octahedra and Cu⁺ cations.An attempt to prepare CuF by reaction between CuSbF₆ and CsF in aHF at ∼190 K failed. Instead of CuF, a mixture of Cu and CuF₂ was obtained.     

Rapid quantitative capillary zone electrophoresis method for monitoring the micro-heterogeneity of an intact recombinant glycoprotein

A simple high-resolution capillary zone electrophoresis (CZE) method capable of rapidly assessing the micro-heterogeneity of a 24 kDa molecular weight glycoprotein, has been developed. Separation is carried out using a bare silica capillary at a pH of 2.5 in a commercially available electrophoresis buffer system composed of triethanolamine and phosphoric acid. Over 30 peaks were detected within a run time of 15 min using a 27 cm capillary and approximately 60 peaks were detected using a 77 cm capillary. Although most of the peaks arise from differences in the oligosaccharide structures present on the one glycosylation site on this molecule, other forms of micro-heterogeneity due to the presence of the nonglycosylated form of this glycoprotein and various types of chemical degradation, e.g., deamidation, are also responsible for the multitude of peaks observed. Although the exact chemical identity of each peak in the resulting electropherogram of this glycoprotein is not known, useful information can be obtained for assessing comparability, stability, and batch consistency. Factors impacting the resolution, precision, accuracy, and robustness of the assay are also discussed along with inherent advantages and limitations associated with measuring the micro-heterogeneity of intact glycoproteins.     

Surface structure and electrochemical characteristics of natural graphite fluorinated by ClF3

Natural graphite samples with average particle sizes of 5, 10 and 15 μm (NG5 μm, NG10 μm and NG15 μm, respectively) were fluorinated by ClF₃ (3 × 10⁴ Pa) at 200 and 300 °C for 2 min. X-ray photoelectron spectra of surface-fluorinated samples showed that surface fluorine concentration increased with increase in the particle size of graphite and reaction temperature. Small amounts of chlorine were also detected in all the fluorinated samples. Raman spectra of original and surface-fluorinated samples indicated that the surface disordering was increased for NG10 μm and NG15 μm. Surface areas were decreased by the fluorination for NG5 μm and NG10 μm but unchanged for NG15 μm. The mesopores with diameter of 1.5-2 nm increased while those of 2-3 nm decreased for all the samples. First coulombic efficiencies for NG10 μm and NG15 μm were highly increased by surface fluorination in 1 mol/dm³ LiClO₄-EC/DEC/PC (EC: ethylene carbonate, DEC: diethyl carbonate, PC: propylene carbonate) solution.