Integration on then th power of a hyperbolic space in terms of invariants under diagonal action of isometries (Lorentz transformations)

The integral of a function over then'th power of hyperbolicd-dimensional spaceH is decomposed into integration along each orbit under diagonal action onH ⁿ of the isometry groupG onH, followed by integration over the orbit space, parametrized in terms of a complete set of invariants. The Jacobian entering in this last integral is expressed explicitly in terms of certain determinants. When viewingH as a half-hyperboloid in _d+1 ,G is induced by the homogeneous Lorentz groupO (1,d) acting on _d+1 .     

Dirichlet forms,quasiregular functions and Brownian motion

Summary Given a quasiregular function on an open setU in ⁿ it is shown that there exists a diffusionX _t inU such that mapsX _t inton-dimensional Brownian motion. The process is constructed from a Dirichlet form which can be described explicitly. This enables us to apply stochastic methods in the investigation of quasiregular mappings. Some examples of applications are given, including boundary behaviour and value distribution.     

Sequential cycloaddition approach to the tricyclic core of vibsanin E. Total synthesis of (+/-)-5-epi-10-epi-vibsanin E

[chemical reaction: see text]. A direct access to (+/-)-5-epi-10-epi-vibsanin E is described, based on three key cycloaddition steps, a rhodium-catalyzed [4 + 3] cycloaddition, a heteronuclear [4 + 2] cycloaddition, and a photochemically induced [4 + 2] cycloaddition.     

Evaluations of solid electrodes for use in voltammetric monitoring of heavy metals in samples from metallurgical nickel industry

Evaluation of different solid electrode systems for detection of zinc, lead, cobalt, and nickel in process water from metallurgical nickel industry with use of differential pulse stripping voltammetry has been performed. Zinc was detected by differential pulse anodic stripping voltammetry (DPASV) on a dental amalgam electrode as intermetallic Ni–Zn compound after dilution in ammonium buffer solution. The intermetallic compound was observed at –375 mV, and a linear response was found in the range 0.2–1.2 mg L^–1 (r²=0.98) for 60 s deposition time. Simultaneous detection of nickel and cobalt in the low g L^–1 range was successfully performed by use of adsorptive cathodic stripping voltammetry (AdCSV) of dimethylglyoxime complexes on a silver–bismuth alloy electrode, and a good correlation was found with corresponding AAS results (r²=0.999 for nickel and 0.965 for cobalt). Analyses of lead in the g L^–1 range in nickel-plating solution were performed with good sensitivity and stability by DPASV, using a working electrode of silver together with a glassy carbon counter electrode in samples diluted 1:3 with distilled water and acidified with H₂SO₄ to pH 2. A new commercial automatic at-line system was tested, and the results were found to be in agreement with an older mercury drop system. The stability of the solid electrode systems was found to be from one to several days without any maintenance needed.     

Effectiveness of antioxidants: Suppression of evolution of gaseous degradation products from low-density polyethylene during thermo-oxidation

The present investigation is part of a project concerning improvements of the working environment for polymer manufacturing processes at high temperatures; for example, welding and extrusion coating.The evolution of gaseous degradation products from unstabilized and antioxidant stabilized low-density polyethylene during thermo-oxidation in air at 210°C has been studied by a simple technique using a modified gas chromatograph. Of the thirteen antioxidants investigated (phenols, phosphites, phosphonites, sulphides and metal dithiocarbamates), only phenols (radical scavengers) effectively suppress the formation of gaseous degradation products from the polymer during an induction period.The gaseous degradation products were analysed with combined gas chromatography-mass spectrometry (GC-MS), using direct trapping on the GC column (Porapak® QS). Apart from water and carbon dioxide, the major products are formaldehyde, acetaldehyde, formic and acetic acids. The addition of effective antioxidants strongly reduces the absolute amounts of the degradation products during the induction period, but does not change their relative quantities.     

Electrolysis in calorimetry

The procedure used by many electrochemists in calculating enthalpy in calorimetric measurements of electrolysis reactions is compared to a purely thermodynamic approach, using the data published by Fleischmannet al. [J. Electroanal. Chem., 287 (1990) 293.] as a case study.The set of excess values dH _ex/dt=dH _obs/dt -dH_calo/dt obtained with the former procedure was neither correlated to any of the experimental parameters nor to the set of values found using thermodynamics. The latter, smaller by factors of up to two orders of magnitude, are shown to follow an expression of the form dH _ex/dt=–kI exp (–E _a/RT) with an activation enthalpy of about 85 kJ·mol^–1. It is suggested that recombination of electrolysis gases may account for this.

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Zusammenfassung Das von vielen Elektrochemikern verwendete Verfahren zur Berechnung der Enthalpie in kalorimetrischen Messungen an Elektrolysereaktionen wurde unter Anwendung der von Fleischmann et.al. in einer Fallstudie [J. Electroanal. Chem., 287 (1990) 293.] veröffentlichten Angaben mit einer rein thermodynamischen Näherung verglichen.Eine Reihe von mit der ersten Methode erhaltenen überschu\werten dH _ex/dt=dH _obs/dt-dH _calc/dt korrelierte weder mit den experimentellen Parametern noch mit den entsprechenden, thermodynamisch gefundenen Werten. Letztere, um etwa zwei Grö\enordnungen kleinere Werte konnten durch die Gleichung dH _ex/dt= -kI exp (-E _a/RT) mit einer Aktivierungsenthalpie von etwa 85 kJ·mol^–1 beschrieben werden. Es wird deshalb nahegelegt, da\ dies einer Rekombinierung der Elektrolysegase zugeschrieben werden kann.

     

Competition and selectivity of organic reactions on semiconductor surfaces: reaction of unsaturated ketones on Si(100)-2 x 1 and Ge(100)-2 x 1

A combined experimental and theoretical study of a model system of multifunctional unsaturated ketones, including ethyl vinyl ketone (EVK), 2-cyclohexen-1-one, and 5-hexen-2-one, on the Si(100)-2 x 1 and Ge(100)-2 x 1 surfaces was performed in order to probe the factors controlling the competition and selectivity of organic reactions on clean semiconductor surfaces. Multiple internal reflection infrared spectroscopy data and density functional theory calculations indicate that EVK and 2-cyclohexen-1-one undergo selective [4 + 2] hetero-Diels-Alder and [4 + 2] trans cycloaddition reactions on the Ge(100)-2 x 1 surface at room temperature. In contrast, on the Si(100)-2 x 1 surface, evidence is seen for significant ene and possibly [2 + 2] C=O cycloaddition side products. The greater selectivity of these compounds on Ge(100) versus Si(100) is explained by differences between the two surfaces in both thermodynamic factors and kinetic factors. With 5-hexen-2-one, for which [4 + 2] cycloaddition is not possible, a small [2 + 2] C=C cycloaddition product is observed on Ge(100) and possibly Si(100), even though the [2 + 2] C=C transition state is calculated to be the highest barrier reaction by several kilocalories per mole. The results suggest that, due to the high reactivity of clean semiconductor surfaces, thermodynamic selectivity and control will play important roles in their selective functionalization, favoring the use of Ge for selective attachment of multifunctional organics.     

Simultaneous extraction of tetracycline, macrolide and sulfonamide antibiotics from agricultural soils using pressurised liquid extraction, followed by solid-phase extraction and liquid chromatography-tandem mass spectrometry

The veterinary antibacterial agents chlortetracycline (CTC), oxytetracycline (OTC), sulfadiazine (SDZ), erythromycin (ERY) and tylosin (TYL A, B, C and D) were extracted from soil using pressurized liquid extraction (PLE). Citric acid (pH 4.7) and methanol was used as extraction buffer, followed by tandem-solid-phase extraction (SPE) clean-up (SAX + HLB) for all compounds. For quantification two slightly different methods were employed using LC-MS-MS with MRM detection. The soil extraction method was validated using a loamy sand soil and a sandy soil, representing two typical Danish agricultural soils. Recoveries were 50-80% for the tetracyclines (CTC and OTC) and sulfadiazine (SDZ) and 60-100% for the macrolides (TYL and ERY). Limits of detection for the soil extraction method (LOD(soil)) were 0.6-5.6 microg kg(-1) soil for CTC and OTC, 0.9-2.9 microg kg(-1) soil for SDZ and 2.4-5.5 microg kg(-1) soil for TYL A and ERY. Furthermore, the method was applied to field samples taken from two agricultural fields fertilised with liquid manure containing CTC and TYL A. These results showed a decline in the content of antibacterial agents throughout the sampling period of 155 days from 10 to 15 microg CTC kg(-1) soil and 20-55 microg TYL A kg(-1) soil to below or near the LOD(soil) listed above. Finally, the method was applied to barley grains harvested from the fields. None of the antibacterial agents were measured in grain samples, but recoveries for spiked grain samples were similar to soil recoveries.     

Some properties of the riesz charge associated with a δ-subharmonic function

The first property is a refinement of earlier results of Ch. de la Vallée Poussin, M. Brelot, and A. F. Grishin. Let w=u–v with u, v superharmonic on a suitable harmonic space (for example an open subset of R ⁿ ), and let [w]=[u]–[v] denote the associated Riesz charge. If w0, and if E denotes the set of those points of at which the lim inf of w in thefine topology is 0, then the restriction of [w] to E is 0. Another property states that, if e denotes a polar subset of such that the fine lim inf of |w| at each point of e is finite, then the restriction of [w] to e is 0.     

Molecular structure and conformation of 2,3-dichloro-1-propene as determined by gas-phase electron diffraction

The molecular structure and conformation of 2,3-dichloro-1-propene have been determined by gas-phase electron diffraction at nozzle temperatures of 24, 90 and 273°C. The molecules exist as a mixture of two conformers with the chlorine atoms anti (torsion angle ∠φ = 0°) or gauche (∠φ = 109°) to each other and with the anti form the more stable. The composition (mole fraction) of the vapor with uncertainties estimated at 2σ was found to be 0.55 (0.08), 0.49 (0.08) and 0.41 (0.10) at 24, 90 and 273°, respectively. These values correspond to an energy difference with estimated standard deviation ΔE° = E°_g-E°_a = 0.7 ± 0.3 kcal mol^?1 and an entropy difference ΔS° = S°_g-S°_a = 0.6 ± 0.9 cal mol^?1 K^?1. Some of the diffraction results, together with spectroscopic observations, permit the evaluation of an approximate torsional potential function of the form 2V = V₁ (1 - cos φ) + V₂ (1 - cos 2φ) + V₃ (1 - cos 3φ); the results are V₁ = 4.4 ± 0.5, V₂ = ?2.9 ± 0.5 and V₃ = 4.8 ± 0.2, all in kcal mol^?1. The results at 24°C for the distance (r_a) and angle (∠_α) parameters, with estimated uncertainties of 2σ, are: r(C_sp²-H) = 1.098(0.020)Å, r(C_sp³-H) = 1.103(0.020)Å, r(CC) = 1.334(0.009)Å, r(C-C) = 1.504(0.013)Å, r(C_sp²-Cl) = 1.752(0.021)Å, r(C_sp³-Cl) = 1.776(0.020)Å, ∠C-CC = 127.6(1.1)°, ∠C_sp³-C_sp²-Cl = 110.2(1.0), ∠C_sp²-C_sp³-Cl = 113.1(1.2)°, ∠H-C_sp³-H = 109.5° (assumed), ∠CC-H = 120.0° (assumed) and ∠φ = 108.9(3.4)°.