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.

     

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)°.     

Pseudochelin A,a siderophore of Pseudoalteromonas piscicida S2040

A new siderophore containing a 4,5-dihydroimidazole moiety was isolated from Pseudoalteromonas piscicida S2040 together with myxochelins A and B, alteramide A and its cycloaddition product, and bromo- and dibromoalterochromides. The structure of pseudochelin A was established by spectroscopic techniques including 2D NMR and MS/MS fragmentation data. In bioassays selected fractions of the crude extract of S2040 inhibited the opportunistic pathogen Pseudomonas aeruginosa. Pseudochelin A displayed siderophore activity in the chrome azurol S assay at concentrations higher than 50 μM, and showed weak activity against the fungus Aspergillus fumigatus, but did not display antibacterial, anti-inflammatory or anticonvulsant activity.     

Singular value decomposition of energy matrices in theoretical atomic structure calculations

The singular value decomposition, SVD, is applied to the linear eigenvalue problem in atomic structure calculations. By comparing with recent calculations of energy levels in neutral Ca, it is shown that the SVD can give quite accurate results and much faster than normal diagonalization techniques, even of the Davidson type. However, the energy levels calculated in this approach are more strongly bound than the real eigenvalues, and this is ascribed to an artefact of the SVD, caused by the use of a discretized continuum in the calculations. This effect can lead to fairly large errors if there is strong CI present. The property of the linear eigenvalue problem that the spectrum is unchanged when a constant is added to the diagonal does not apply to the SVD. This means that it is impossible to solve the problems connected with a discretized continuum simply by shifting the spectrum.     

The ABC of Insulin: The Organic Chemistry of a Small Protein

Insulin is a small protein crucial for regulating the blood glucose level in all animals. Since 1922 it has been used for the treatment of patients with diabetes. Despite consisting of just 51 amino acids, insulin contains 17 of the proteinogenic amino acids, A- and B-chains, three disulfide bridges, and it folds with 3 α-helices and a short β-sheet segment. Insulin associates into dimers and further into hexamers with stabilization by Zn²⁺ and phenolic ligands. Selective chemical modification of proteins is at the forefront of developments in chemical biology and biopharmaceuticals. Insulin's structure has made it amenable to organic and inorganic chemical reactions. This Review provides a synthetic organic chemistry perspective on this small protein. It gives an overview of key chemical and physico-chemical aspects of the insulin molecule, with a focus on chemoselective reactions. This includes N-acylations at the N-termini or at Lys^B29 by pH control, introduction of protecting groups on insulin, binding of metal ions, ligands to control the nano-scale assembly of insulin, and more.     

Rheological Properties of Particle-Stabilized Emulsions

We have studied the rheological properties of fumed silica particle-stabilized emulsions. Two particles of different polarity were considered, the first more hydrophilic “Aerosil R7200,” the second more hydrophobic “Aerosil R972.” These particles flocculate and probably form a network at the investigated concentration. The flow curves of emulsions stabilized by a single type of particles exhibit yield stress, shear-thinning behavior and thixotropy. Moreover they display rheological features typical of gels. These features are attributed to strengthening of the particle network by droplets. Moreover the rheological properties of w/o emulsions stabilized by hydrophobic are similar to the ones of o/w emulsions stabilized by hydrophilic particles. The rheological properties of o/w emulsions stabilized by mixtures of hydrophilic and hydrophobic particles have then been studied by keeping the total particle concentration constant and varying the mass ratio between particles. The results show that when the hydrophobic particle concentration increases, the viscosity and stability of emulsions decrease establishing evidence that the network is weakened due to preferential orientation of hydrophobic particles towards the oil phase.