2,398 research outputs found
Uniform interpolation and coherence
A variety V is said to be coherent if any finitely generated subalgebra of a
finitely presented member of V is finitely presented. It is shown here that V
is coherent if and only if it satisfies a restricted form of uniform deductive
interpolation: that is, any compact congruence on a finitely generated free
algebra of V restricted to a free algebra over a subset of the generators is
again compact. A general criterion is obtained for establishing failures of
coherence, and hence also of uniform deductive interpolation. This criterion is
then used in conjunction with properties of canonical extensions to prove that
coherence and uniform deductive interpolation fail for certain varieties of
Boolean algebras with operators (in particular, algebras of modal logic K and
its standard non-transitive extensions), double-Heyting algebras, residuated
lattices, and lattices
AdS boundary conditions and the Topologically Massive Gravity/CFT correspondence
The AdS/CFT correspondence provides a new perspective on recurrent questions
in General Relativity such as the allowed boundary conditions at infinity and
the definition of gravitational conserved charges. Here we review the main
insights obtained in this direction over the last decade and apply the new
techniques to Topologically Massive Gravity. We show that this theory is dual
to a non-unitary CFT for any value of its parameter mu and becomes a
Logarithmic CFT at mu = 1.Comment: 10 pages, proceedings for XXV Max Born Symposium, talks given at
Johns Hopkins workshop and Holographic Cosmology workshop at Perimeter
Institute; v2: added reference
Towards an 'average' version of the Birch and Swinnerton-Dyer Conjecture
The Birch and Swinnerton-Dyer conjecture states that the rank of the
Mordell-Weil group of an elliptic curve E equals the order of vanishing at the
central point of the associated L-function L(s,E). Previous investigations have
focused on bounding how far we must go above the central point to be assured of
finding a zero, bounding the rank of a fixed curve or on bounding the average
rank in a family. Mestre showed the first zero occurs by O(1/loglog(N_E)),
where N_E is the conductor of E, though we expect the correct scale to study
the zeros near the central point is the significantly smaller 1/log(N_E). We
significantly improve on Mestre's result by averaging over a one-parameter
family of elliptic curves, obtaining non-trivial upper and lower bounds for the
average number of normalized zeros in intervals on the order of 1/log(N_E)
(which is the expected scale). Our results may be interpreted as providing
further evidence in support of the Birch and Swinnerton-Dyer conjecture, as
well as the Katz-Sarnak density conjecture from random matrix theory (as the
number of zeros predicted by random matrix theory lies between our upper and
lower bounds). These methods may be applied to additional families of
L-functions.Comment: 20 pages, 2 figures, revised first draft (fixed some typos
Supermembrane on the PP-wave Background
We study the closed and open supermembranes on the maximally supersymmetric
pp-wave background. In the framework of the membrane theory, the superalgebra
is calculated by using the Dirac bracket and we obtain its central extension by
surface terms. The result supports the existence of the extended objects in the
membrane theory in the pp-wave limit. When the central terms are discarded, the
associated algebra completely agrees with that of Berenstein-Maldacena-Nastase
matrix model. We also discuss the open supermembranes on the pp-wave and
elaborate the possible boundary conditions.Comment: 17 pages, no figures, LaTeX;(v2) typos correcte
Passage of Time in a Planck Scale Rooted Local Inertial Structure
It is argued that the `problem of time' in quantum gravity necessitates a
refinement of the local inertial structure of the world, demanding a
replacement of the usual Minkowski line element by a 4+2n dimensional
pseudo-Euclidean line element, with the extra 2n being the number of internal
phase space dimensions of the observed system. In the refined structure, the
inverse of the Planck time takes over the role of observer-independent
conversion factor usually played by the speed of light, which now emerges as an
invariant but derivative quantity. In the relativistic theory based on the
refined structure, energies and momenta turn out to be invariantly bounded from
above, and lengths and durations similarly bounded from below, by their
respective Planck scale values. Along the external timelike world-lines, the
theory naturally captures the `flow of time' as a genuinely structural
attribute of the world. The theory also predicts expected
deviations--suppressed quadratically by the Planck energy--from the dispersion
relations for free fields in the vacuum. The deviations from the special
relativistic Doppler shifts predicted by the theory are also suppressed
quadratically by the Planck energy. Nonetheless, in order to estimate the
precision required to distinguish the theory from special relativity, an
experiment with a binary pulsar emitting TeV range gamma-rays is considered in
the context of the predicted deviations from the second-order shifts.Comment: 17 pages; Diagram depicting "the objective flow of time" is replaced
with a much-improved diagra
Supergravity, Supermembrane and M(atrix) model on PP-Waves
In the first part of this paper, we study the back-reaction of large-N light
cone momentum on the maximally supersymmetric anti-pp-wave background. This
gives the type IIA geometry of large-N D0-branes on curved space with fluxes.
By taking an appropriate decoupling limit, we conjecture a new duality between
string theory on that background and dual field theory on D0-branes which we
derive by calculating linear coupling terms. Agreement of decoupling
quantities, SO(3) \times SO(6) isometry and Higgs branch on both theories are
shown. Also we find whenever dual field theory is weakly coupled, the curvature
of the geometry is large. In the second part of this paper, we derive the
supermembrane action on a general pp-wave background only through the
properties of null Killing vector and through this, derive the Matrix model.Comment: 19 pages, LaTeX. v2: corrected interpretation of supergravity
solutio
Anatomical review of internal jugular vein cannulation
The internal jugular veins (IJV) are the primary venous outflow channels of the head and neck. The IJV is of clinical interest since it is often used for central venous access. This literature aims at presenting an overview of the anatomical variations, morphometrics based on various imaging modalities, cadaveric and surgical findings, and the clinical anatomy of IJV cannulation. Additionally, the anatomical basis of complications, techniques to avoid complications, and cannulation in special instances are also included in the review.
The review was performed by a detailed literature search and review of relevant articles. A total of 141 articles were included and organized into anatomical variations, morphometrics, and clinical anatomy of IJV cannulation.
The IJV is next to important structures such as the arteries, nerve plexus, and pleura, which puts them at risk of injury during cannulation. Anatomical variations such as duplications, fenestrations, agenesis, tributaries, and valves, may lead to an increased failure rate and complications during the procedure, if unnoticed. The morphometrics of IJV, such as the cross-sectional area (CSA), diameter, and distance from the skin-to-cavo-atrial junction may assist in choosing the appropriate cannulation techniques and hence reduce the incidence of complications. Age, gender, and side-related differences explained variations in the IJV-common carotid artery relationship, CSA, and diameter. Accurate knowledge of anatomical variations in special considerations such as pediatrics and obesity may help prevent complications and facilitate successful cannulation
Measurement of the Transverse Beam Spin Asymmetry in Elastic Electron Proton Scattering and the Inelastic Contribution to the Imaginary Part of the Two-Photon Exchange Amplitude
We report on a measurement of the asymmetry in the scattering of transversely
polarized electrons off unpolarized protons, A, at two Q values of
\qsquaredaveragedlow (GeV/c) and \qsquaredaveragedhighII (GeV/c) and a
scattering angle of . The measured transverse
asymmetries are A(Q = \qsquaredaveragedlow (GeV/c)) =
(\experimentalasymmetry alulowcorr \statisticalerrorlow
\combinedsyspolerrorlowalucor) 10 and
A(Q = \qsquaredaveragedhighII (GeV/c)) = (\experimentalasymme
tryaluhighcorr \statisticalerrorhigh
\combinedsyspolerrorhighalucor) 10. The first
errors denotes the statistical error and the second the systematic
uncertainties. A arises from the imaginary part of the two-photon
exchange amplitude and is zero in the one-photon exchange approximation. From
comparison with theoretical estimates of A we conclude that
N-intermediate states give a substantial contribution to the imaginary
part of the two-photon amplitude. The contribution from the ground state proton
to the imaginary part of the two-photon exchange can be neglected. There is no
obvious reason why this should be different for the real part of the two-photon
amplitude, which enters into the radiative corrections for the Rosenbluth
separation measurements of the electric form factor of the proton.Comment: 4 figures, submitted to PRL on Oct.
- …