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.     

Homomorphic images of finite subdirectly irreducible unary algebras

We prove that a finite unary algebra with at least two operation symbols is a homomorphic image of a (finite) subdirectly irreducible algebra if and only if the intersection of all its subalgebras which have at least two elements is nonempty. While working on this paper the first and the third authors were partially supported by the Grant Agency of the Czech Republic, grant #201/02/0594, and by the institutional grant MSM0021620839; the second author was supported by the Ministry of Science, Technologies and Development of Republic of Serbia, grant no. 1227.     

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.     

Small angle neutron scattering studies on nonaqueous dispersions of calcium carbonate Part 2. Determination of the form factor for concentric spheres

Colloidal dispersions of calcium carbonate, stabilised primarily by a surface active agent, in both toluene and dodecane have been examined by small angle neutron scattering. A model has been developed to simulate the scattering behaviour of the particles and is based on the idea of a concentric sphere with a homogeneous layer of adsorbed material surrounding a core particle. Computations based on the model show a wide variation of scattering behaviour with variation of the coherent scattering length of the dispersion medium. These predictions were confirmed by experiment. A method is described for analysis of the experimental data which leads to a determination of the thickness of the adsorbed layer, the radius of the core particle and the standard deviation of core particle radius.     

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.     

Carbon-bromine cleavage by dimethyl sulfoxide: the key step of C(5) functionalization of push-pull 2-alkylidene-4-oxothiazolidine vinyl bromides

Push-pull 2-alkylidene-4-oxothiazolidine vinyl bromides undergo efficient C(5) functionalization through DMSO-assisted carbon-bromine cleavage, followed by a bromine transfer-substitution (or elimination) sequence. A mechanism for this novel transformation is proposed.     

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.