Twist points of planar domains

We establish a potential theoretic approach to the study of twist points in the boundary of simply connected planar domains.

     

R-Matrices for Leibniz Algebras

Leibniz agebras are a generalization of Lie algebras, where no symmetry properties of the bracket are required. In this Letter we introduce a notion of R-matrices for this structure and the related Yang–Baxter equations, and discuss some of their basic properties.     

A three-phase single sheet tester with digital control of flux loci based on the contraction mapping principle

Tight control of flux loci in 2D testing of soft magnetic laminations is realized by a method based on the principle of contraction mapping. It is implemented through digital control of the currents supplying a three-phase yoke magnetizer and the use of circular samples. Faithful realization of the prescribed loci and good measuring accuracy are demonstrated in grain-oriented and non-oriented Fe–Si laminations.     

Aromatic hydrocarbons, carbocyclic ligands spanning several oxidation states in both Main Group and transition elements. Recent advances with early transition d elements

In this paper some synthetic procedures to obtain (η⁶-arene)metal derivatives are reviewed. The metal-atom-arene-vapor co-condensation technique is the most appropriate to generate complexes of polycyclic aromatic hydrocarbons or heterocycles. As far as the aluminium halide-mediated synthesis is concerned, two classes of reaction are observed. When AlX₃ is used with a metal halide in the presence of an aromatic hydrocarbon in the absence of any reducing agent, AlX₃ can function as a dehalogenating agent, to give ionic compounds of general formula [M(η⁶-arene)n](AlX₄)_m, or it can add across the M---X bond with formation of M(μ-X)_nAlX_4−n systems. In both cases the metal displays its typical oxidation state. However, the use of AlX₃ in combination with aluminium (the Fischer-Hafner reducing system) affords ionic or covalent low-oxidation-state metal(η⁶-arene) complexes. Attention is focused on our most recent results concerning the synthesis, properties and reactivity of η⁶-arene derivatives of Group 4 and 5 elements, showing, inter alia, the first example of a tetraarylborate anion behaving as a 12-electron donor to one metal atom and low-valent η⁶-arene compounds as useful reagents in the inorganic and coordination chemistry of the corresponding metal in nonaqueous systems.     

Potassium-selective optrode based on an immobilized fluorogenic crown ether

A new optical sensor phase for potassium ions has been developed based on the immobilization of the pH-dependent fluorogenic crown ether 4-acryloylamidobenzo-18-crown-6 on the non-ionic polymeric resin Amberlite XAD-2.Two different optical designs, a flow-through sensor and a fibre optic probetype sensor (optrode), have been constructed and their analytical performance characteristics have been evaluated. The resulting fluorimetric sensors for K⁺ ions exhibited detection limits of 0.4 or 0.8 M of K⁺ (16 g/l or 31 g/l), depending on the design, while the linear response occurred from 1 to 25 M of the metal concentrations. The precision, evaluated as the relative standard deviation of measurements of K⁺ levels at around ten times the detection limit (e.g. 5 M), turned out to be around ±2%.Advantageous features of this fluorimetric sensing phase and optrode include ease of construction, simplicity of use, reversibility, short response times (ca. 1 min full scale deflection) selectivity and operational stability, suitable for sensing potassium at low levels in complex matrices such as biological fluids.The fluorimetric optical sensor has been successfully applied to the direct determination of potassium in clinically important samples (serum and urine) and in natural waters. Very good accuracy has been obtained just using adequate synthetic aqueous potassium standards for calibration.     

Amine catalysis in phosphoryl transfer from 2,4-dinitrophenyl phosphate in aprotic and protic solvents

Reactions of tetra-n-butylammonium 2,4-dinitrophenyl hydrogen phosphate, (ArPH)^?(R₄N)⁺, in aprotic and protic solvents, in the absence and in the presence of alcohols or water, ROH, are compared with analogous reactions of the salt in the presence of hindered and unhindered amines, e.g. diisopropylethyl amine and quinuclidine. Similar studies are performed with the acid, ArPH₂, in the presence of variable amounts of amines. The release of phenol and the fate of the phosphorus compounds are followed by ¹H and ³¹P NMR spectrometry. In the absence of free unhindered amine, reactions of the monoanion are relatively slow, sensitive to steric hindrance in the alcohol, and incapable of producing t-butyl phosphate from t-butanol; reactions of the dianion are relatively fast, insensitive to steric hindrance in the alcohol, and produce t-butyl phosphate. In the presence of free unhindered amine, reactions of the monoanion are relatively fast but still sensitive to steric hindrance in the alcohol, and hence do not produce t-butyl phosphate. The intermediate CH(CH₂CH₂)₃⁺NP(O)(OH)O^? is detected in the presence of quinuclidine. Reactions of the dianion in the presence of unhindered amines are analogous to those observed in the presence of hindered amines. The uncatalyzed and the nucleophilic amine-catalyzed reactions of the monoanion are assumed to proceed via oxyphosphorane, P(5), intermediates. The dianion reactions, which are not susceptible to nucleophilic catalysis, are assumed to proceed via the monomeric metaphosphate ion intermediate, PO₃^?. Significant effects related to solvent properties are observed in these reactions.     

Effects of temperature on the triplet behavior of the styrylphenanthrene isomers

The properties of the triplet state of five styrylphenanthrene (StPh) trans isomers were studied in 2-methyltetrahydrofuran (MTHF) as a function of temperature. At room temperature the T-T absorption was observed only for 4- and 9-StPh, while under these conditions 1-, 2-, and 3-StPh have too low a quantum yield of triplet formation (Φ_T <0.02); their T-T absorption spectra were obtained at low temperature. Φ_T of 1- and 2-StPh increases more than tenfold on going from 293 to 77 K, and the triplet lifetime (τ_T) increases by four orders of magnitude and approaches values of 5–40 ms at 77 K. The change in τ_T is explained in terms of an equilibrium between trans and perpendicular (perp) conformations of the lowest triplet state in fluid solution and temperature and viscosity effects on the trans → perp rotation. Evidence is presented for the existence of two conformeric trans triplet states of 3-StPh at 77 K. Semi-empirical calculations were performed to obtain the energy of the triplet state, the wavelengths of several T-T absorption maxima (λ_T), and the oscillator strength. The calculated λ_T values coincide with those measured in n-hexane.     

A regularity result for a class of non-uniformly elliptic operators

Archiv der Mathematik - We obtain an explicit Hölder regularity result for viscosity solutions of a class of second order fully nonlinear equations led by operators that are neither...     

Matrix-isolation FT-IR spectra and theoretical study of dimethyl sulfate

The preferred conformations of dimethyl sulfate and their vibrational spectra were studied by matrix-isolation FT-IR spectroscopy and theoretical methods (DFT and MP2, with basis sets of different sizes, including the quadruple-zeta, aug-cc-pVQZ basis). Conformer GG (of C2 symmetry and exhibiting OSOC dihedral angles of 74.3 degrees ) was found to be the most stable conformer in both the gaseous phase and isolated in argon. Upon annealing of the matrix, the less stable observed conformer (GT; with C1 symmetry) quickly converts to the GG conformer, with the resulting species being embedded in a matrix-cage which corresponds to the most stable matrix-site for GG form. The highest energy TT conformer, which was assumed to be the most stable conformer in previous studies, is predicted by the calculations to have a relative energy of ca. 10 kJ mol-1 and was not observed in the spectra of the matrix-isolated compound.