23,427 research outputs found
Truncation of Unitary Operads
We introduce truncation ideals of a -linear unitary symmetric operad
and use them to study ideal structure, growth property and to classify operads
of low Gelfand-Kirillov dimension
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Boron carboxylate catalysis of homoallylboration.
Boron tris(trifluoroacetate) is identified as the first effective catalyst for the homoallyl- and homocrotylboration of aldehydes by cyclopropylcarbinylboronates. NMR spectroscopic studies and theoretical calculations of key intermediates and transition states both suggest that a ligand-exchange mechanism, akin to our previously reported PhBCl2-promoted homoallylations, is operative. Our experimental and theoretical results also suggest that the catalytic activity of boron tris(trifluoroacetate) might originate from more facile catalytic turnover of the trifluoroacetate ligands (in agreement with DFT calculations) or from a lower propensity for formation of off-pathway reservoir intermediates (as observed by (1)H NMR). This work shows that carboxylates are viable catalytic ligands for homoallyl- and homocrotylations of carbonyl compounds and opens the door to the development of catalytic asymmetric versions of this transformation
Spectral Representation Theory for Dielectric Behavior of Nonspherical Cell Suspensions
Recent experiments revealed that the dielectric dispersion spectrum of
fission yeast cells in a suspension was mainly composed of two sub-dispersions.
The low-frequency sub-dispersion depended on the cell length, while the
high-frequency one was independent of it. The cell shape effect was simulated
by an ellipsoidal cell model but the comparison between theory and experiment
was far from being satisfactory. Prompted by the discrepancy, we proposed the
use of spectral representation to analyze more realistic cell models. We
adopted a shell-spheroidal model to analyze the effects of the cell membrane.
It is found that the dielectric property of the cell membrane has only a minor
effect on the dispersion magnitude ratio and the characteristic frequency
ratio. We further included the effect of rotation of dipole induced by an
external electric field, and solved the dipole-rotation spheroidal model in the
spectral representation. Good agreement between theory and experiment has been
obtained.Comment: 19 pages, 5 eps figure
Many-body Green's function theory of ferromagnetic Heisenberg systems with single-ion anisotropies in more than one direction
The behaviour of ferromagnetic systems with single-ion anisotropies in more
than one direction is investigated with many-body Green's function theory
generalizing earlier work with uniaxial anisotropies only. It turns out to be
of advantage to construct Green's functions in terms of the spin operators S^x,
S^y and S^z, instead of the commonly used S^+,S^- and S^z operators. The
exchange energy terms are decoupled by RPA and the single-ion anisotropy terms
by a generalization of the Anderson-Callen decoupling. We stress that in the
derivation of the formalism none of the three spatial axes is special, so that
one is always able to select a reference direction along which a magnetization
component is not zero. Analytical expressions are obtained for all three
components of the magnetization and the expectation values ,
and for any spin quantum number S. The formalism considers both
in-plane and out-of-plane anisotropies. Numerical calculations illustrate the
behaviour of the magnetization for 3-dimensional and 2-dimensional systems for
various parameters. In the 2-dimensional case, the magnetic dipole-dipole
coupling is included, and a comparison is made between in-plane and
out-of-plane anisotropies.Comment: 16 pages, 8 figures, missing figures adde
Ballistic spin field-effect transistors: Multichannel effects
We study a ballistic spin field-effect transistor (SFET) with special
attention to the issue of multi-channel effects. The conductance modulation of
the SFET as a function of the Rashba spin-orbit coupling strength is
numerically examined for the number of channels ranging from a few to close to
100. Even with the ideal spin injector and collector, the conductance
modulation ratio, defined as the ratio between the maximum and minimum
conductances, decays rapidly and approaches one with the increase of the
channel number. It turns out that the decay is considerably faster when the
Rashba spin-orbit coupling is larger. Effects of the electronic coherence are
also examined in the multi-channel regime and it is found that the coherent
Fabry-Perot-like interference in the multi-channel regime gives rise to a
nested peak structure. For a nonideal spin injector/collector structure, which
consists of a conventional metallic ferromagnet-thin insulator-2DEG
heterostructure, the Rashba-coupling-induced conductance modulation is strongly
affected by large resonance peaks that arise from the electron confinement
effect of the insulators. Finally scattering effects are briefly addressed and
it is found that in the weakly diffusive regime, the positions of the resonance
peaks fluctuate, making the conductance modulation signal sample-dependent.Comment: 18 pages, 15 figure
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