188,408 research outputs found
A direct proof of Kim's identities
As a by-product of a finite-size Bethe Ansatz calculation in statistical
mechanics, Doochul Kim has established, by an indirect route, three
mathematical identities rather similar to the conjugate modulus relations
satisfied by the elliptic theta constants. However, they contain factors like
and , instead of . We show here that
there is a fourth relation that naturally completes the set, in much the same
way that there are four relations for the four elliptic theta functions. We
derive all of them directly by proving and using a specialization of
Weierstrass' factorization theorem in complex variable theory.Comment: Latex, 6 pages, accepted by J. Physics
Cramer-Rao Lower Bound for Point Based Image Registration with Heteroscedastic Error Model for Application in Single Molecule Microscopy
The Cramer-Rao lower bound for the estimation of the affine transformation
parameters in a multivariate heteroscedastic errors-in-variables model is
derived. The model is suitable for feature-based image registration in which
both sets of control points are localized with errors whose covariance matrices
vary from point to point. With focus given to the registration of fluorescence
microscopy images, the Cramer-Rao lower bound for the estimation of a feature's
position (e.g. of a single molecule) in a registered image is also derived. In
the particular case where all covariance matrices for the localization errors
are scalar multiples of a common positive definite matrix (e.g. the identity
matrix), as can be assumed in fluorescence microscopy, then simplified
expressions for the Cramer-Rao lower bound are given. Under certain simplifying
assumptions these expressions are shown to match asymptotic distributions for a
previously presented set of estimators. Theoretical results are verified with
simulations and experimental data
A Schematic Model For Density-Dependent Vector Meson Masses
A schematic two-level model consisting of a "collective" bosonic state and an
"elementary" meson is constructed that provides interpolation from a hadronic
description (a la Rapp/Wambach) to B/R scaling for the description of
properties of vector mesons in dense medium. The development is based on a
close analogy to the degenerate schematic model of Brown for giant resonances
in nuclei.Comment: 20 pages, latex with 8 figures: Talk given by GEB at AIP Klaus
Kinder-Geiger Memorial Meeting, 3 October 199
Graphyne: Hexagonal network of carbon with versatile Dirac cones
We study alpha, beta, and gamma graphyne, a class of graphene allotropes with
carbon triple bonds, using a first-principles density-functional method and
tight-binding calculation. We find that graphyne has versatile Dirac cones and
it is due to remarkable roles of the carbon triple bonds in electronic and
atomic structures. The carbon triple bonds modulate effective hopping matrix
elements and reverse their signs, resulting in Dirac cones with reversed
chirality in alpha graphyne, momentum shift of the Dirac point in beta
graphyne, and switch of the energy gap in gamma graphyne. Furthermore, the
triple bonds provide chemisorption sites of adatoms which can break sublattice
symmetry while preserving planar sp2-bonding networks. These features of
graphyne open new possibilities for electronic applications of carbon-based
two-dimensional materials and derived nanostructures.Comment: 5 pages, 5 figures, 1 tabl
Solid state image sensor research Final technical report
Fifty-element linear arrays of InAs photodiode
Traversable wormhole in the deformed Ho\v{r}ava-Lifshitz gravity
Asymptotically flat wormhole solutions are found in the deformed
Ho\v{r}ava-Lifshitz gravity. It turns out that higher curvature terms can not
play the role of exotic matters which are crucial to form a traversable
wormhole, and external exotic sources are still needed. In particular, the
exotic matter behaves like phantom energy if Kehagias-Sfetsos vacuum is
considered outside the wormhole. Interestingly, the spherically symmetric
setting makes the matter and the higher curvature contribution satisfy
four-dimensional conservation of energy in the covariant form.Comment: 13 pages, 2 figures, version published in Phys. Rev.
- …