Silicon heterojunction solar cell with amorphous silicon oxide buffer and microcrystalline silicon oxide contact layers

This Letter reports on the fabrication and characterization of silicon heterojunction solar cells with silicon oxide based buffer (intrinsic amorphous silicon oxide) and contact layers (doped microcrystalline silicon oxide) on flat p‐type wafers. The critical dependency of the cell performance on the front and rear buffer layer thickness reveals a trade‐off between the open circuit voltage V_oc and the fill factor FF. At the optimum, the highest efficiency of 18.5% (active area = 0.67 cm²) was achieved with V_oc = 664 mV, short circuit current J_sc = 35.7 mA/cm² and FF = 78.0%. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hydrogen bonding in cyclic imides and amide carboxylic acid derivatives from the facile reaction of cis‐cyclohexane‐1,2‐carboxylic anhydride with o‐ and p‐anisidine and m‐ and p‐aminobenzoic acids

The structures of the open‐chain amide carboxylic acid rac‐cis‐2‐[(2‐methoxyphenyl)carbamoyl]cyclohexane‐1‐carboxylic acid, C₁₅H₁₉NO₄, (I), and the cyclic imides rac‐cis‐2‐(4‐methoxyphenyl)‐3a,4,5,6,7,7a‐hexahydroisoindole‐1,3‐dione, C₁₅H₁₇NO₃, (II), chiral cis‐3‐(1,3‐dioxo‐3a,4,5,6,7,7a‐hexahydroisoindol‐2‐yl)benzoic acid, C₁₅H₁₅NO₄, (III), and rac‐cis‐4‐(1,3‐dioxo‐3a,4,5,6,7,7a‐hexahydroisoindol‐2‐yl)benzoic acid monohydrate, C₁₅H₁₅NO₄·H₂O, (IV), are reported. In the amide acid (I), the phenylcarbamoyl group is essentially planar [maximum deviation from the least‐squares plane = 0.060 (1) Å for the amide O atom] and the molecules form discrete centrosymmetric dimers through intermolecular cyclic carboxy–carboxy O—H...O hydrogen‐bonding interactions [graph‐set notation R₂²(8)]. The cyclic imides (II)–(IV) are conformationally similar, with comparable benzene ring rotations about the imide N—C_ar bond [dihedral angles between the benzene and isoindole rings = 51.55 (7)° in (II), 59.22 (12)° in (III) and 51.99 (14)° in (IV)]. Unlike (II), in which only weak intermolecular C—H...O_imide hydrogen bonding is present, the crystal packing of imides (III) and (IV) shows strong intermolecular carboxylic acid O—H...O hydrogen‐bonding associations. With (III), these involve imide O‐atom acceptors, giving one‐dimensional zigzag chains [graph‐set C(9)], while with the monohydrate (IV), the hydrogen bond involves the partially disordered water molecule which also bridges molecules through both imide and carboxy O‐atom acceptors in a cyclic R₄⁴(12) association, giving a two‐dimensional sheet structure. The structures reported here expand the structural database for compounds of this series formed from the facile reaction of cis‐cyclohexane‐1,2‐dicarboxylic anhydride with substituted anilines, in which there is a much larger incidence of cyclic imides compared to amide carboxylic acids.     

The space of linear anti-symplectic involutions is a homogenous space

In this note we prove that the space of linear anti-symplectic involutions is the homogenous space ${{{\rm Gl}(n, \mathbb{R})\backslash{\rm Sp}(n)}}$ . This result is motivated by the study of symmetric periodic orbits in the restricted 3-body problem.     

On a theorem by Ekeland-Hofer

In [EH89, Theorem 1] Ekeland-Hofer prove that for a centrally symmetric, restricted contact type hypersurface in ℝ²ⁿ and for any global, centrally symmetric Hamiltonian perturbation there exists a leaf-wise intersection point. In this note we show that if we replace restricted contact type by star-shaped, there exist infinitely many leaf-wise intersection points or a leaf-wise intersection point on a closed characteristic.     

Infinitely many leaf-wise intersections on cotangent bundles

If the homology of the free loop space of a closed manifold B$B$ is infinite dimensional then generically there exist infinitely many leaf-wise intersection points for fiberwise star-shaped hypersurfaces in T^∗B$T^{\ast }B$. We illustrate this in the case of the restricted three body problem.     

Die eindeutige Primfaktorzerlegung

Zusammenfassung  Die Frage der Primfaktorzerlegung in Unterringen der komplexen Zahlen und der unmittelbar damit zusammenh?ngenden S?tze wird in der heutigen Algebra ohne grossen Aufwand und fast nebenbei behandelt: Studierende haben damit auch kaum Schwierigkeiten. In der Geschichte allerdings verlief die Entwicklung alles andere als gradlinig. Ein genauerer Blick auf die historischen Einzelheiten erlaubt interessante und in vielerlei Hinsicht überraschende Einsichten in die vertrackte Art und Weise, wie sich Mathematik manchmal entwickelt. Hier soll diese Geschichte erz?hlt werden, wie sie sich aus den neueren mathematikhistorischen Forschungen von H.M. Edwards, R. B?lling, O. Neumann und F. Lemmermeyer ergibt, und zwar auf einem Niveau, das einem Mathematikstudierenden nach einer Algebra-Vorlesung zug?nglich ist.     

One-Dimensional Hydrogen-Bonded Structures in the 1:1 Proton-Transfer Salts of 4,5-Dichlorophthalic Acid with the Aliphatic Lewis Bases Diisopropylamine and Hexamethylenetetramine

Abstract  

The crystal structures of the 1:1 proton-transfer compounds of 4,5-dichlorophthalic acid with the aliphatic Lewis bases diisopropylamine and hexamethylenetetramine, viz. diisopropylaminium 2-carboxy-4,5-dichlorobenzoate (1) and hexamethylenetetraminium 2-carboxy-4,5-dichlorobenzoate hemihydrate (2), have been determined. Crystals of both 1 and 2 are triclinic, space group P − 1, with Z = 2 in cells with a = 7.0299(5), b = 9.4712(7), c = 12.790(1) ?, α = 99.476(6), β = 100.843(6), γ = 97.578(6)° (1) and a = 7.5624(8), b = 9.8918(8), c = 11.5881(16) ?, α = 65.660(6), β = 86.583(4), γ = 86.987(8)° (2). In each, one-dimensional hydrogen-bonded chain structures are found: in 1 formed through aminium N⁺–H…O_carboxyl cation–anion interactions. In 2, the chains are formed through anion carboxyl O···H–O_{bridging water} interactions with the cations peripherally bound. In both structures, the hydrogen phthalate anions are essentially planar with short intra-species carboxylic acid O–H…O_carboxyl hydrogen bonds [O…O, 2.381(3) ? (1) and 2.381(8) ? (2)].