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.     

Parameter determination of a thermal desorption model

A new method for the analysis of thermal desorption spectra is presented, based on the experimental peak maximum functions for temperatureT _m(β) and pressureP _m(β) and a rigorous mathematical treatment. The resonant heating rate β_r is determined, satisfyingT _m(β_r)=T _r, whereT _r is the resonant temperature defined byA exp(−E _d/(RT _r))=1. Desorption energyE _d and frequency factorA can be determined simultaneously with relatively high robustness towards statistical experimental errors as demonstrated by computer-simulated thermal desorption spectra.     

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.     

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.     

Early reactions of light-induced protochlorophyllide and chlorophyllide transformations analyzed in vivo at room temperature with a diode array spectrofluorometer

The steps of protochlorophyllide (Pchlide) photoreduction and subsequent chlorophyllide (Chlide) transformations which occur in the seconds to minutes time-scale were studied using a diode array spectrofluorometer in dark-grown barley leaves. The intensity of the excitation light was varied between 3 and 2,500 micromol m(-2) s(-1) and a series of fluorescence spectra were recorded at room temperature in the seconds and minutes time scales. In certain experiments, 77-K emission spectra were measured with the same equipment. The high quality of the spectra allowed us to run spectral resolution studies which proved the occurrence, at room temperature, of multiple Pchlide and Chlide forms found previously in 77-K spectra. The comparison of the 77-K and room-temperature spectra showed that the fluorescence yields of the nonphotoactive 633-nm Pchlide form and of the Chlide product emitting at 678 nm were temperature independent. The fluorescence intensity of aggregated NADPH-pigment-POR complexes (photoactive 656-nm Pchlide and 693-nm Chlide forms) were strongly increased at 77 K, while that of the NADP(+)-Chlide-POR (684-686-nm Chlide form) was much less affected by temperature. Information was obtained also about the dynamics of the transformation of pigment forms in the light at different photon densities. At low light intensities, the phototransformation of the 642-644-nm Pchlide form was faster than that of the 654-656-nm form. The relative amplitudes of Gaussian components related to different Chlide forms found after exposure to a constant amount of photons strongly depended on the light intensity used. Strong quenching of all Chlide components occurred upon prolonged exposure to high intensity light. These effects are discussed by considering the interconversion processes between different forms of the pigment-protein complexes, their relative fluorescence yields and energy migration processes.     

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.