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In this paper, we give a detailed introduction to the theory of (curved) L ∞ -algebras and L ∞ -morphisms, avoiding the concept of operads and providing explicit formulas. In particular, we recall the notion of (curved) Maurer–Cartan elements, their equivalence classes and the twisting procedure. The main focus is then the study of the homotopy theory of L ∞ -algebras and L ∞ -modules. In particular, one can interpret L ∞ -morphisms and morphisms of L ∞ -modules as Maurer–Cartan elements in certain L ∞ -algebras, and we show that twisting the morphisms with equivalent Maurer–Cartan elements yields homotopic morphisms. We hope that these notes provide an accessible entry point to the theory of L ∞ -algebras. [ABSTRACT FROM AUTHOR]

The global formality of Dolgushev depends on the choice of a torsion-free covariant derivative. We prove that the globalized formalities with respect to two different covariant derivatives are homotopic. More explicitly, we derive the statement by proving a more general homotopy equivalence between L∞-morphisms that are twisted with gauge equivalent Maurer-Cartan elements. [ABSTRACT FROM AUTHOR]

Abstract. In this paper, we propose a reduction scheme for multivector fields phrased in terms of L∞-morphisms. Using well-known geometric properties of the reduced manifolds, we perform a Taylor expansion of multivector fields, which allows us to build up a suitable deformation retract of differential graded Lie algebras (DGLAs). We first obtained an explicit formula for the L∞- projection and -inclusion of generic DGLA retracts.We then applied this formula to the deformation retract that we constructed in the case of multivector fields on reduced manifolds. This allows us to obtain the desired reduction L∞-morphism. Finally, we perform a comparison with other reduction procedures. [ABSTRACT FROM AUTHOR]

Four different three-dimensional metal-fullerene frameworks were synthesized through polymerization of two C60-derived dodecaacids with varying alkyl spacers in the presence of Ca2+, Cu2+ or Cd2+ ions. Structural analysis of the frameworks was performed by single-crystal X-ray diffraction and porosity of the materials was investigated by sorption measurements. [ABSTRACT FROM AUTHOR]

We describe a method for recording the Rabi nutation of nuclear spin polarized He by optically pumped cesium magnetometers. The measurement is performed by detecting the time-dependent magnetic field produced by the He magnetization. The observed signals are compared to theoretical models and the results are used to precisely trace the evolution of the magnetization. This procedure represents a convenient way to control and measure the Rabi flip angle and the degree of spin polarization in experiments using He magnetometers. The method requires only very coarse knowledge of the applied magnetic field's magnitude. Graphical abstract: [ABSTRACT FROM AUTHOR]

Verwaltungsschalen bilden zusammen mit den Assets der digitalen Fabrik I4.0-Komponenten. Interaktionen zwischen den Verwaltungsschalen sind wichtige Bestandteile der Wertschöpfungsketten in den I4.0-Systemen. Dafür benötigen die Verwaltungsschalen eine gemeinsame Sprache. Auf der Basis der Festlegungen der DIN SPEC 91345, d. h. des RAMIs und der Struktur der Verwaltungsschale, wird hier das Interaktionskonzept beschrieben. Asset Administration Shells (AAS) and assets form I4.0 components in a digital factory. Interactions between Asset Administration Shells are important elements of process chains. The Asset Administration Shells need a common language to understand each other. This paper proposes an interaction model based on DIN SPEC 91345 (RAMI4.0). [ABSTRACT FROM AUTHOR]

Hexakis-substituted [60]fullerene adducts with icosahedral symmetry provide an unprecedented scaffold for the spatial arrangement of twelve functional groups with high geometric precision. This unique molecular symmetry identifies such polyfunctional organic building blocks as potential highly connective linkers for coordination polymer and metal-organic framework synthesis. Hereby, the linker exhibits a higher connectivity than the metal ions and with the main connectivity based on the ligand, this can create a new type of inversely cross-linked framework. Two hexakis adducts bearing either twelve glycolic acid or 3-hydroxypropionic acid side chains attached to its malonate units were incorporated as organic connectivity centers in the first fullerene-containing three-dimensional frameworks by coordination with Zn2+. [ABSTRACT FROM AUTHOR]

Multivalent organic molecules possessing spherically well-arranged functionalities are promising building blocks for extended molecular networks. [60]Fullerene hexakisadducts are intriguing candidates allowing the organization of up to 12 functional groups within one molecule with high geometric precision. We have synthesized a hexakisadduct bearing 12 glycolic acid side-chains in good yield and with high regioisomeric purity and elucidated its solid-state structure from single crystals grown by the slow diffusion of dichloromethane into a methanol solution. Individual fullerene moieties are arranged in cubic close-packing mode and form an extended network by means of multiple supramolecular interactions. Each molecule forms 24 hydrogen bonds and is connected to six neighbouring fullerene derivatives. The crystal structure showcases the first example of a 3D arrangement of fullerene derivatives by directed hydrogen bonding in the solid state. These findings indicate the high potential of six-fold substituted fullerene derivatives as building blocks for crystalline frameworks. [ABSTRACT FROM AUTHOR]

The article presents a discussion on German literature from after 1945, with a focus on the ways in which the so-called German "generation literature" can be taken to reflect German post-war society. Particular attention is paid to the relations between generations described in this literature. It is noted that literature from the late 1960s deals with children's perspectives on Nazi fathers. Further themes to be found in this period of German literature are discussed, including the authority of fathers, fathers' involvement in war crimes, and emotional trauma associated with war experiences.

Bridging the gap between fullerenes and MOFs: Against the background of the Golden Gate Bridge, various metal‐organic coordination motifs illustrate the great potential of highly functionalized [60]fullerene derivatives as organic connectivity centers in metal‐organic frameworks. In their Communication on page 15864 ff., Beuerle et al. report on the synthesis and crystallographic analysis of four new metal‐fullerene frameworks cross‐linked by Cu2+, Ca2+, or Cd2+ clusters that feature chiral pores or extended hydrogen‐bonding networks throughout the crystals. [ABSTRACT FROM AUTHOR]

Review: 71 refs. [ABSTRACT FROM AUTHOR]