Anionic Indole N-carbamoyl N --> C translocation. A directed remote metalation route to 2-Aryl- and 2-heteroarylindoles. synthesis of benz[a]carbazoles and Indeno[1,2-b]indoles

A new LDA-induced anionic N-C carbamoyl migration of 2-arylindoles (7) is reported. Treatment of N-carbamoylindoles 10 and 13, readily available by direct and ipso-borodesilylative Suzuki-Miyaura cross-coupling routes from 8 and 12, respectively, provides a general route to functionalized 2-arylindoles 11 and 14, respectively (Tables 1 and 2). The reaction has been applied to the synthesis of benzo[ a]carbazoles 16 and indeno[1,2- b]indoles 18, and its intramolecularity has been established by a crossover experiment (Scheme 4).     

Contractive Automorphisms of Locally Compact Groups and the Concentration Function Problem

Let G be a noncompact locally compact group. We show that a necessary and sufficient condition in order that G support an adapted probability measure whose concentration functions fail converge to zero is that G be the semidirect product , where is an automorphism of N contractive modulo a compact subgroup. Any adapted a probability measure whose concentration functions fail to converge to zero has the form =v×₁ where v is a probability measure on N. If G is unimodular then the concentration functions of an adapted probability measure fail to converge to zero if and only if is supported on a coset of a compact normal subgroup.     

Liquid-solid equilibrium for the NaCl-NaHCO3-Na2CO3-H2O system at 45°C. Validation of mixed solvent electrolyte model

The main objective of this work was to verify the mixed solvent electrolyte (MSE) thermodynamic model for the prediction of the liquid-solid equilibrium in the soda system. The full quaternary system NaCl-NaHCO₃-Na₂CO₃-H₂O and its three subsystems were considered. Validation of the thermodynamic model was based on experimental data from literature. Phase diagrams for the soda system are plotted for isotherms of 45°C. Good agreement of the MSE results with those from experiments was found at 45°C. Similar phase diagrams for other temperature levels can be constructed based on the validated MSE model.     

Temperature Compensation by Embedded Temperature Variation Method for an AC Voltammeric Analyzer of Electroplating Baths

An in‐situ sensor utilizing a variety of DC‐ and AC‐voltammetric techniques is an integral component of the on‐line monitoring system that provides a complete chemical analysis of different plating solutions by predicting concentration values of all deliberately‐added bath constituents with a single device despite differences in the constituents’ chemical properties. Such sensors are employed routinely for electroplating process control in semiconductor manufacturing. This voltammetric approach exploits quantitatively the physicochemical processes (like adsorption) which are temperature dependent. Therefore the accuracy of analyte concentration predictions can be affected adversely by temperature fluctuations. This paper introduces a novel comprehensive method which allows the mitigation of temperature variation effects on voltammetric scans allowing accurate concentration prediction. Specifically, this study introduces a multi‐step rigorous routine for the development and subsequent validation of the analytical method utilizing a chemometric model with temperature variation embedded in regression for exemplary determination of leveler additive concentration. This approach analyses the effect on AC voltammograms resulting from two qualitatively indistinguishable sources of variation: leveler concentration and temperature. A critical step of this routine of fundamental novelty, which aims to select the variables (index points of voltammogram) to be utilized for building of the analytical model in the presence of two concurrent sources of variation, is introduced to incorporate temperature variation.     

Molecular probe FET: Long-wavelength fluorescence excitation effect and proton transfer reaction

We studied the steady-state fluorescence spectra of solutions of FET (4′-(diethylamino)-3-hydroxyflavone) in acetonitrile that were excited at different temperatures by quanta with different energies located in the range of the main absorption band and in its long-wavelength wing. We found that, at room temperature, the emission intensity ratio of the bands of the normal and tautomeric forms, which are located at 505 and 570 nm, respectively, depends on the excitation wavelength. In the range of the main absorption band 300–360 nm, this ratio remains nearly the same, i.e., 1.45, while, upon excitation in the range of the long-wavelength wing 360–380 nm of the main band, it decreases to 1.33 at a wavelength of 460 nm. In this same range, a long-wavelength excitation effect that is unusual for liquid inviscid solvents at room temperature, i.e., a bathochromic shift of the entire short-wavelength emission band by 11 nm, manifests itself. We propose to explain these dependences using energy diagrams, which take into account the dependence of free energy on the orientational polarization of the polar solvent. The observed effect of the long-wavelength shift of the fluorescence spectrum with increasing excitation wavelength is explained in terms of the inhomogeneous broadening of electronic spectra of polar solutions, and it should be described using the scheme of energy states that takes into account sublevels of orientational broadening due to orientational dipole-dipole interactions of the fluorophore with nearest molecules of the polar solvent, as well as the relation between the fluorophore lifetime in the excited state and the dielectric relaxation time of solvent molecules in the field of the fluorophore dipole.     

Mathematics teaching development as a human practice: identifying and drawing the threads

The didactic triangle links mathematics, teachers and students in a consideration of teaching?Clearning interactions in mathematics classrooms. This paper focuses on teachers and teaching in the development of fruitful learning experiences for students with mathematics. It recognises primarily that teachers are humans with personal characteristics, subject to a range of influences through the communities of which they are a part, and considers aspects of teachers?? personhood, identity and agency in designing teaching for the benefit of their students. Teaching is seen as a developmental process in which inquiry plays a central role, both in doing mathematics in the classroom and in exploring teaching practice. The teacher-as-inquirer in collaboration with outsider researchers leads to growth of knowledge in teaching through development of identity and agency for both groups. The inclusion of the outsider researcher brings an additional node into the didactic triangle.