Quantum K-theory. II. Homotopy invariance of the Chern character

We prove that the Chern character of quantum algebras is invariant under a class of deformations of the Dirac operator. We also extend the definition of the Chern character to include certain unbounded operators.     

Indestructibility and level by level equivalence and inequivalence

If κ < λ are such that κ is indestructibly supercompact and λ is 2^λ supercompact, it is known from [4] that

• {δ < κ | δ is a measurable cardinal which is not a limit of measurable cardinals and δ violates level by level equivalence between strong compactness and supercompactness}

must be unbounded in κ. On the other hand, using a variant of the argument used to establish this fact, it is possible to prove that if κ < λ are such that κ is indestructibly supercompact and λ is measurable, then

• {δ < κ | δ is a measurable cardinal which is not a limit of measurable cardinals and δ satisfies level by level equivalence between strong compactness and supercompactness}

must be unbounded in κ. The two aforementioned phenomena, however, need not occur in a universe with an indestructibly supercompact cardinal and sufficiently few large cardinals. In particular, we show how to construct a model with an indestructibly supercompact cardinal κ in which if δ < κ is a measurable cardinal which is not a limit of measurable cardinals, then δ must satisfy level by level equivalence between strong compactness and supercompactness. We also, however, show how to construct a model with an indestructibly supercompact cardinal κ in which if δ < κ is a measurable cardinal which is not a limit of measurable cardinals, then δ must violate level by level equivalence between strong compactness and supercompactness. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Enhanced second-harmonic generation in AlGaAs microring resonators

Highly efficient second-harmonic generation can be achieved by harnessing resonance effects in microring resonator structures. We propose an angular quasi-phase-matching scheme based on the position dependence of polarization inside the ring resonator.     

Balance equations and structural models for phase interfaces

The general balance equations are developed for an interface represented by a dividing surface and for a moving common line represented as an intersection of dividing surfaces. The surface excess variables associated with a dividing surface are expressed both in terms of those variables describing the three-dimensional interfacial region of finite thickness and in terms of those variables describing bulk phases that extend up to the dividing surface.A structural model for the interface is suggested in which a suspension of solid bodies representing surfactant molecules is distributed about a singular surface separating two adjacent bulk solvent phases. The suspension is required to have the same average behavior as the interfacial region. This is interpreted as meaning that the general jump balance for a continuum dividing surface represented by an interfacial suspension is a local area average. Specific results are derived for two structural models, each in the same simple shear field. One consists of a dilute suspension of neutrally buoyant spheres floating with their centers restricted to the dividing surface. The other is a dilute suspension of chains of neutrally buoyant spheres with the sphere at one end of the chain floating in the dividing surface.     

An Efficient Halogen‐Free Electrolyte for Use in Rechargeable Magnesium Batteries

Unlocking the full potential of rechargeable magnesium batteries has been partially hindered by the reliance on chloride‐based complex systems. Despite the high anodic stability of these electrolytes, they are corrosive toward metallic battery components, which reduce their practical electrochemical window. Following on our new design concept involving boron cluster anions, monocarborane CB₁₁H₁₂^? produced the first halogen‐free, simple‐type Mg salt that is compatible with Mg metal and displays an oxidative stability surpassing that of ether solvents. Owing to its inertness and non‐corrosive nature, the Mg(CB₁₁H₁₂)₂/tetraglyme (MMC/G4) electrolyte system permits standardized methods of high‐voltage cathode testing that uses a typical coin cell. This achievement is a turning point in the research and development of Mg electrolytes that has deep implications on realizing practical rechargeable Mg batteries.     

Hybridization Gap and Dresselhaus Spin Splitting in EuIr4In2Ge4

EuIr₄In₂Ge₄ is a new intermetallic semiconductor that adopts a non‐centrosymmetric structure in the tetragonal ${I\bar 42m}$ space group with unit cell parameters a=6.9016(5) Å and c=8.7153(9) Å. The compound features an indirect optical band gap E_g=0.26(2) eV, and electronic‐structure calculations show that the energy gap originates primarily from hybridization of the Ir 5d orbitals, with small contributions from the Ge 4p and In 5p orbitals. The strong spin–orbit coupling arising from the Ir atoms, and the lack of inversion symmetry leads to significant spin splitting, which is described by the Dresselhaus term, at both the conduction‐ and valence‐band edges. The magnetic Eu²⁺ ions present in the structure, which do not play a role in gap formation, order antiferromagnetically at 2.5 K.     

Unstrained C–C bond activation and directed fluorination through photocatalytically-generated radical cations

Expanding the repertoire of controlled radical fluorination techniques, we present a photosensitized unstrained C–C bond activation/directed monofluorination method using Selectfluor and 9-fluorenone. The reaction is amenable to the opening of multiple 1-acetal-2-aryl substituted rings to yield ω-fluoro carboxylic acids, esters, alcohols, and ketones with relative ease. Initial mechanistic insight suggests radical ion intermediates.