4,636 research outputs found
Naive Noncommutative Blowing Up
Let B(X,L,s) be the twisted homogeneous coordinate ring of an irreducible
variety X over an algebraically closed field k with dim X > 1. Assume that c in
X and s in Aut(X) are in sufficiently general position. We show that if one
follows the commutative prescription for blowing up X at c, but in this
noncommutative setting, one obtains a noncommutative ring R=R(X,c,L,s) with
surprising properties. In particular:
(1) R is always noetherian but never strongly noetherian.
(2) If R is generated in degree one then the images of the R-point modules in
qgr(R) are naturally in (1-1) correspondence with the closed points of X.
However, both in qgr(R) and in gr(R), the R-point modules are not parametrized
by a projective scheme.
(3) qgr R has finite cohomological dimension yet H^1(R) is infinite
dimensional.
This gives a more geometric approach to results of the second author who
proved similar results for X=P^n by algebraic methods.Comment: Latex, 42 page
-NMR of Isolated Li Implanted into a Thin Copper Film
Depth-controlled -NMR was used to study highly spin-polarized Li
in a Cu film of thickness 100 nm deposited onto a MgO substrate. The positive
Knight Shifts and spin relaxation data show that Li occupies two sites at
low temperatures, assigned to be the substitutional () and octahedral ()
interstitial sites. Between 50 to 100 K, there is a site change from to
. The temperature dependence of the Knight shifts and spin-lattice
relaxation rates at high temperatures, i.e. when all the Li are in the
site, is consistent with the Korringa Law for a simple metal.Comment: Accepted for publication in Phys. Rev.
Isolation, purification, and full NMR assignments of cyclopamine from Veratrum californicum
The Hedgehog signaling pathway is essential for embryogenesis and for tissue homeostasis in the adult. However, it may induce malignancies in a number of tissues when constitutively activated, and it may also have a role in other forms of normal and maladaptive growth. Cyclopamine, a naturally occurring steroidal alkaloid, specifically inhibits the Hedgehog pathway by binding directly to Smoothened, an important Hedgehog response element. To use cyclopamine as a tool to explore and/or inhibit the Hedgehog pathway in vivo, a substantial quantity is required, and as a practical matter cyclopamine has been effectively unavailable for usage in animals larger than mice
Epoxidation of Alkenes by Peracids:From Textbook Mechanisms to a Quantum Mechanically Derived Curly-Arrow Depiction
Using the intrinsic bond orbital (IBO) analysis based on accurate quantum mechanical calculations of the reaction path for the epoxidation of propene using peroxyacetic acid, we find that the four commonly used curly arrows for representing this reaction mechanism are insufficient and that seven curly arrows are required as a result of changes to sigma and pi bonding interactions, which are usually neglected in all textbook curly arrow representations. The IBO method provides a convenient quantitative method for deriving curly arrows in a rational manner rather than the normal ad hoc representations used ubiquitously in teaching organic chemistry
Hyperfine Fields in an Ag/Fe Multilayer Film Investigated with 8Li beta-Detected Nuclear Magnetic Resonance
Low energy -detected nuclear magnetic resonance (-NMR) was used
to investigate the spatial dependence of the hyperfine magnetic fields induced
by Fe in the nonmagnetic Ag of an Au(40 \AA)/Ag(200 \AA)/Fe(140 \AA) (001)
magnetic multilayer (MML) grown on GaAs. The resonance lineshape in the Ag
layer shows dramatic broadening compared to intrinsic Ag. This broadening is
attributed to large induced magnetic fields in this layer by the magnetic Fe
layer. We find that the induced hyperfine field in the Ag follows a power law
decay away from the Ag/Fe interface with power , and a field
extrapolated to T at the interface.Comment: 5 pages, 4 figure. To be published in Phys. Rev.
Deconstructing holographic liquids
We argue that there exist simple effective field theories describing the
long-distance dynamics of holographic liquids. The degrees of freedom
responsible for the transport of charge and energy-momentum are Goldstone
modes. These modes are coupled to a strongly coupled infrared sector through
emergent gauge and gravitational fields. The IR degrees of freedom are
described holographically by the near-horizon part of the metric, while the
Goldstone bosons are described by a field-theoretical Lagrangian. In the cases
where the holographic dual involves a black hole, this picture allows for a
direct connection between the holographic prescription where currents live on
the boundary, and the membrane paradigm where currents live on the horizon. The
zero-temperature sound mode in the D3-D7 system is also re-analyzed and
re-interpreted within this formalism.Comment: 21 pages, 2 figure
Explicitly solvable cases of one-dimensional quantum chaos
We identify a set of quantum graphs with unique and precisely defined
spectral properties called {\it regular quantum graphs}. Although chaotic in
their classical limit with positive topological entropy, regular quantum graphs
are explicitly solvable. The proof is constructive: we present exact periodic
orbit expansions for individual energy levels, thus obtaining an analytical
solution for the spectrum of regular quantum graphs that is complete, explicit
and exact
Putting the micro into the macro: A molecularly augmented hydrodynamic model of dynamic wetting applied to flow instabilities during forced dewetting
Putting the micro into the macro : a molecularly augmented hydrodynamic model of dynamic wetting applied to flow instabilities during forced dewetting
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