Fused vs. spiro: Kinetic,not thermodynamic preference may direct the reaction of α-carbonyl oxonium ylides

Rh(II)-catalyzed decomposition of certain cyclic α-diazocarbonyl compounds in the presence of cyclic ethers has been shown to give bicyclic ring expansion products. These are thought to arise from a [1,4]-alkyl shift toward the carbonyl oxygen atom and are in contrast with the recently observed spirocyclic products of a Stevens-type [1,2]-alkyl shift within the postulated oxonium ylide intermediate. Quantum chemical calculations performed at the B3LYP/6-31G* level of theory showed that the former reaction pathway (toward fused bicycles) is kinetically preferred.     

Complementarity between micro-micro and micro-macro entanglement in a Bose–Einstein condensate with two Rydberg impurities

We theoretically study complementarity between micro-micro and micro-macro entanglement in a Bose–Einstein condensate with two Rydberg impurities. We investigate quantum dynamics of micro-micro and micro-macro entanglement in the micro-macro system. It is found that strong micro-macro entanglement between Rydberg impurities and the BEC can be generated by the use of initial micro-micro entanglement between two Rydberg impurities, which acts as the seed entanglement to create micro-macro entanglement. We demonstrate a curious complementarity relation between micro-micro and micro-macro entanglement, and find that the complementarity property can be sustained to some extent even though in the presence of the BEC decoherence.     

Approximation of quantum assemblages

In this paper, we derive a set of projectors on a large Hilbert space which can universally work for approximating quantum assemblages with binary inputs and outputs. The dimension of the Hilbert space depends on the accuracy of the approximation.     

Organic–Inorganic Hybrid Gold Halide Perovskites: Structural Diversity through Cation Size

Crystal structures of a series of organic–inorganic hybrid gold iodide perovskites, formulated as A₂[Au^II₂][Au^IIII₄] [A=methylammonium (MA) ( 1 ) and formamidinium (FA) ( 2 )], A′₂[I₃]_1−x[Au^II₂]_x[Au^IIII₄] [A′=imidazolium (IMD) ( 3 ), guanidinium (GUA) ( 4 ), dimethylammonium (DMA) ( 5 ), pyridinium (PY) ( 6 ), and piperizinium (PIP) ( 7 )], systematically changed depending on the cation size. In addition, triiodide (I₃⁻) ions were partly incorporated into the AuI₂⁻ sites of 3 – 7 , whereas they were not incorporated into those of 1 and 2 . Such a difference comes from the size of the organic cation. Optical absorption spectra showed characteristic intervalence charge-transfer bands from Au^I to Au^III species, and the optical band gap increased as the size of the cation became larger.     

Direct Intermediate Regulation Enabled by Sulfur Containers in Working Lithium–Sulfur Batteries

Polysulfide intermediates (PSs), the liquid-phase species of active materials in lithium–sulfur (Li-S) batteries, connect the electrochemical reactions between insulative solid sulfur and lithium sulfide and are key to full exertion of the high-energy-density Li-S system. Herein, the concept of sulfur container additives is proposed for the direct modification on the PSs species. By reversible storage and release of the sulfur species, the container molecule converts small PSs into large organosulfur species. The prototype di(tri)sulfide-polyethylene glycol sulfur container is highly efficient in the reversible PS transformation to multiply affect electrochemical behaviors of sulfur cathodes in terms of liquid-species clustering, reaction kinetics, and solid deposition. The stability and capacity of Li-S cells was thereby enhanced. The sulfur container is a strategy to directly modify PSs, enlightening the precise regulation on Li-S batteries and multi-phase electrochemical systems.     

Congruence criteria for finite subsets of complex projective and complex hyperbolic spaces

We investigate congruence classes and direct congruence classes of m-tuples in the complex projective space ℂP ⁿ . For direct congruence one allows only isometries which are induced by linear (instead of semilinear) mappings. We establish a canonical bijection between the set of direct congruence classes of m-tuples of points in ℂP ⁿ and the set of equivalence classes of positive semidefinite Hermitean m×m-matrices of rank at most n+1 with 1's on the diagonal. As a corollary we get that the direct congruence class of an m-tuple is uniquely determined by the direct congruence classes of all of its triangles, provided that no pair of points of the m-tuple has distance π/2. Examples show that the situation changes drastically if one replaces direct congruence classes by congruence classes or if distances π/2 are allowed. Finally we do the same kind of investigation also for the complex hyperbolic space ℂH ⁿ . Most of the results are completely analogous, however, there are also some interesting differences. Received: 15 January 1996     

A dual graph-norm refinement indicator for finite volume approximations of the Euler equations

Summary. We generalise and apply a refinement indicator of the type originally designed by Mackenzie, Süli and Warnecke in [15] and [16] for linear Friedrichs systems to the Euler equations of inviscid, compressible fluid flow. The Euler equations are symmetrized by means of entropy variables and locally linearized about a constant state to obtain a symmetric hyperbolic system to which an a posteriori error analysis of the type introduced in [15] can be applied. We discuss the details of the implementation of the refinement indicator into the DLR--Code which is based on a finite volume method of box type on an unstructured grid and present numerical results. Received May 15, 1995 / Revised version received April 17, 1996