Using Goffman's concepts to explore collaborative interaction processes in elementary school mathematics

The present paper describes the combined implementation of two approaches which are based on the work of Erving Goffman and focus on the analysis of the interactional participation structures. Our aim is to examine the ways that differing interpretations of the ongoing interactions may lead the students to adopt differing roles, which in turn affects the process of negotiating and establishing shared meanings. For this purpose we analyse the interaction processes in one ‘expert’ group within the ‘Jigsaw’ form of cooperation (Aronson, 1978 Aronson, E. 1978. The jigsaw classroom, Beverly Hills, CA: Sage.  [Google Scholar]), decomposing the participants’ roles according to their interactional status and their interpersonal effect. Our analysis points out the different roles that emerge in the process of collaborative interaction, and the influence of these roles on group achievement and individual learning possibilities.     

Modeling of polarization effects on n-GaN/i-InGaN/p-Gan solar cells with ultrathin GaN interlayers

We report the numerical study of n-GaN/i-InGaN/p-GaN solar cells on Ga-face substrates with thin GaN interlayers present in the intrinsic InGaN region. These interlayers have recently been shown to significantly increase the crystal quality of thick InGaN layers $(>\!\!\!120\,\text{ nm})$ . We find that tunneling is efficient in n-i-p structures having interlayers $\le \! 1.5\,\text{ nm}$ thick if polarization charges are sufficiently screened. If left unscreened, the large polarization charges naturally formed at the heterointerfaces degrades n-i-p performance, at a given interlayer thickness, because polarization charges increase the distance that carriers must tunnel. Simulations identify favorable parameter ranges.     

One‐pot Synthesis of Fused Dipyranocoumarins from Dihydroxycoumarins and Propargyl Chlorides under Microwave Irradiation

Dipetalolactone and 4‐methyldipetalolactone are prepared in excellent yield by a one‐pot tandem propargylation/Claisen rearrangement/cyclization reaction of the corresponding 5,7‐dihydroxycoumarins with 3‐chloro‐3‐methylbut‐1‐yne in the presence of Cs₂CO₃ under microwave irradiation. The analogous reactions of propargyl chloride with esculetins or 5,7‐dihydroxycoumarins led to dipropargyloxy derivatives. The later by treatment with gold nanoparticles supported on TiO₂ or BF₃.Et₂O in N,N‐dimethylformamide (DMF) under microwave irradiation resulted in very good to excellent yield to the corresponding fused dipyranocoumarins. The reactions of esculetins with 3‐chloro‐3‐methylbut‐1‐yne gave mainly exomethylene fused dioxino[g]coumarins.     

Spontaneous Resolution by Crystallization of an Octanuclear Iron(III) Complex Using Only Racemic Reagents

The P and M enantiomers of the octanuclear [Fe₈(μ₄‐O)₄(μ‐4‐Cl‐pz)₁₂Cl₄] complex, having T symmetry, were resolved by temporary substitution of chloride ligands by racemic 4‐^sBu‐phenolates and subsequent crystallization, where the (S)‐ and (R)‐phenolates coordinate selectively to the M and P complexes, respectively. The complexes were characterized by circular dichroism analysis and X‐ray structure determination. This work constitutes a rare example of enantiomeric recognition resulting in spontaneous resolution upon crystallization.     

Unprecedented Five‐Coordinate Iron(IV) Imides Generate Divergent Spin States Based on the Imide R‐Groups

Three five‐coordinate iron(IV) imide complexes have been synthesized and characterized. These novel structures have disparate spin states on the iron as a function of the R‐group attached to the imide, with alkyl groups leading to low‐spin diamagnetic (S=0) complexes and an aryl group leading to an intermediate‐spin (S=1) complex. The different spin states lead to significant differences in the bonding about the iron center as well as the spectroscopic properties of these complexes. Mössbauer spectroscopy confirmed that all three imide complexes are in the iron(IV) oxidation state. The combination of diamagnetism and ¹⁵N labeling allowed for the first ¹⁵N NMR resonance recorded on an iron imide. Multi‐reference calculations corroborate the experimental structural findings and suggest how the bonding is distinctly different on the imide ligand between the two spin states.     

Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature

We present the first Monte Carlo results for supersymmetric matrix quantum mechanics with 16 supercharges at finite temperature. The recently proposed nonlattice simulation enables us to include the effects of fermionic matrices in a transparent and reliable manner. The internal energy nicely interpolates the weak coupling behavior obtained by the high temperature expansion, and the strong coupling behavior predicted from the dual black-hole geometry. The Polyakov line asymptotes at low temperature to a characteristic behavior for a deconfined theory, suggesting the absence of a phase transition. These results provide highly nontrivial evidence for the gauge-gravity duality.     

Global approximation to arbitrary cost functions: A Bayesian approach with application to US banking

This paper proposes and estimates a globally flexible functional form for the cost function, which we call Neural Cost Function (NCF). The proposed specification imposes a priori and satisfies globally all the properties that economic theory dictates. The functional form can be estimated easily using Markov Chain Monte Carlo (MCMC) techniques or standard iterative SURE. We use a large panel of U.S. banks to illustrate our approach. The results are consistent with previous knowledge about the sector and in accordance with mathematical production theory.     

Electrocatalytic Hydrogen Evolution Using A Molecular Antimony Complex under Aqueous Conditions: An Experimental and Computational Study on Main-Group Element Catalysis

Electrocatalytic hydrogen gas production is considered a potential pathway towards carbon-neutral energy sources. However, the development of this technology is hindered by the lack of efficient, cost-effective, and environmentally benign catalysts. In this study, a main-group-element-based electrocatalyst, SbSalen , is reported to catalyze the hydrogen evolution reaction (HER) in an aqueous medium. The heterogenized molecular system achieved a Faradaic efficiency of 100 % at −1.4 V vs. NHE with a maximum current density of −30.7 mA/cm². X-ray photoelectron spectroscopy of the catalyst-bound working electrode before and after electrolysis confirmed the molecular stability during catalysis. The turnover frequency was calculated as 43.4 s⁻¹ using redox-peak integration. The kinetic and mechanistic aspects of the electrocatalytic reaction were further examined by computational methods. This study provides mechanistic insights into main-group-element electrocatalysts for heterogeneous small-molecule conversion.     

Euler Characteristics on virtually free products

We define Euler characteristics on classes of residually finite and virtually torsion free groups and we show that they satisfy certain formulas in the case of amalgamated free products and HNN extensions over finite subgroups. These formulas are obtained from a general result which applies to the rank gradient and the first L²?Betti number of a finitely generated group.