552 research outputs found
Continuous approximation of binomial lattices
A systematic analysis of a continuous version of a binomial lattice,
containing a real parameter and covering the Toda field equation as
, is carried out in the framework of group theory. The
symmetry algebra of the equation is derived. Reductions by one-dimensional and
two-dimensional subalgebras of the symmetry algebra and their corresponding
subgroups, yield notable field equations in lower dimensions whose solutions
allow to find exact solutions to the original equation. Some reduced equations
turn out to be related to potentials of physical interest, such as the
Fermi-Pasta-Ulam and the Killingbeck potentials, and others. An instanton-like
approximate solution is also obtained which reproduces the Eguchi-Hanson
instanton configuration for . Furthermore, the equation under
consideration is extended to --dimensions. A spherically symmetric form
of this equation, studied by means of the symmetry approach, provides
conformally invariant classes of field equations comprising remarkable special
cases. One of these enables us to establish a connection with the
Euclidean Yang-Mills equations, another appears in the context of Differential
Geometry in relation to the socalled Yamabe problem. All the properties of the
reduced equations are shared by the spherically symmetric generalized field
equation.Comment: 30 pages, LaTeX, no figures. Submitted to Annals of Physic
Functional Integration Over Geometries
The geometric construction of the functional integral over coset spaces
is reviewed. The inner product on the cotangent space of
infinitesimal deformations of defines an invariant distance and volume
form, or functional integration measure on the full configuration space. Then,
by a simple change of coordinates parameterizing the gauge fiber , the
functional measure on the coset space is deduced. This
change of integration variables leads to a Jacobian which is entirely
equivalent to the Faddeev-Popov determinant of the more traditional gauge fixed
approach in non-abelian gauge theory. If the general construction is applied to
the case where is the group of coordinate reparametrizations of
spacetime, the continuum functional integral over geometries, {\it i.e.}
metrics modulo coordinate reparameterizations may be defined. The invariant
functional integration measure is used to derive the trace anomaly and
effective action for the conformal part of the metric in two and four
dimensional spacetime. In two dimensions this approach generates the
Polyakov-Liouville action of closed bosonic non-critical string theory. In four
dimensions the corresponding effective action leads to novel conclusions on the
importance of quantum effects in gravity in the far infrared, and in
particular, a dramatic modification of the classical Einstein theory at
cosmological distance scales, signaled first by the quantum instability of
classical de Sitter spacetime. Finite volume scaling relations for the
functional integral of quantum gravity in two and four dimensions are derived,
and comparison with the discretized dynamical triangulation approach to the
integration over geometries are discussed.Comment: 68 pages, Latex document using Revtex Macro package, Contribution to
the special issue of the Journal of Mathematical Physics on Functional
Integration, to be published July, 1995
Arithmeticity vs. non-linearity for irreducible lattices
We establish an arithmeticity vs. non-linearity alternative for irreducible
lattices in suitable product groups, such as for instance products of
topologically simple groups. This applies notably to a (large class of)
Kac-Moody groups. The alternative relies on a CAT(0) superrigidity theorem, as
we follow Margulis' reduction of arithmeticity to superrigidity.Comment: 11 page
The constraint equations for the Einstein-scalar field system on compact manifolds
We study the constraint equations for the Einstein-scalar field system on
compact manifolds. Using the conformal method we reformulate these equations as
a determined system of nonlinear partial differential equations. By introducing
a new conformal invariant, which is sensitive to the presence of the initial
data for the scalar field, we are able to divide the set of free conformal data
into subclasses depending on the possible signs for the coefficients of terms
in the resulting Einstein-scalar field Lichnerowicz equation. For many of these
subclasses we determine whether or not a solution exists. In contrast to other
well studied field theories, there are certain cases, depending on the mean
curvature and the potential of the scalar field, for which we are unable to
resolve the question of existence of a solution. We consider this system in
such generality so as to include the vacuum constraint equations with an
arbitrary cosmological constant, the Yamabe equation and even (all cases of)
the prescribed scalar curvature problem as special cases.Comment: Minor changes, final version. To appear: Classical and Quantum
Gravit
Structural Instability in Polyacene : A Projector Quantum Monte Carlo Study
We have studied polyacene within the Hubbard model to explore the effect of
electron correlations on the Peierls' instability in a system marginally away
from one-dimension. We employ the projector quantum Monte Carlo method to
obtain ground state estimates of the energy and various correlation functions.
We find strong similarities between polyacene and polyacetylene which can be
rationalized from the real-space valence-bond arguments of Mazumdar and Dixit.
Electron correlations tend to enhance the Peierls' instability in polyacene.
This enhancement appears to attain a maximum at and the maximum
shifts to larger values when the alternation parameter is increased. The system
shows no tendency to destroy the imposed bond-alternation pattern, as evidenced
by the bond-bond correlations. The cis- distortion is seen to be favoured over
the trans- distortion. The spin-spin correlations show that undistorted
polyacene is susceptible to a SDW distortion for large interaction strength.
The charge-charge correlations indicate the absence of a CDW distortion for the
parameters studied.Comment: 13 pages, 10 figures available on reques
A compactness theorem for scalar-flat metrics on manifolds with boundary
Let (M,g) be a compact Riemannian manifold with boundary. This paper is
concerned with the set of scalar-flat metrics which are in the conformal class
of g and have the boundary as a constant mean curvature hypersurface. We prove
that this set is compact for dimensions greater than or equal to 7 under the
generic condition that the trace-free 2nd fundamental form of the boundary is
nonzero everywhere.Comment: 49 pages. Final version, to appear in Calc. Var. Partial Differential
Equation
Daclatasvir/asunaprevir based direct-acting antiviral therapy ameliorate hepatitis C virus-associated cryoglobulinemic membranoproliferative glomerulonephritis: a case report
About curvature, conformal metrics and warped products
We consider the curvature of a family of warped products of two
pseduo-Riemannian manifolds and furnished with metrics of
the form and, in particular, of the type , where are smooth
functions and is a real parameter. We obtain suitable expressions for the
Ricci tensor and scalar curvature of such products that allow us to establish
results about the existence of Einstein or constant scalar curvature structures
in these categories. If is Riemannian, the latter question involves
nonlinear elliptic partial differential equations with concave-convex
nonlinearities and singular partial differential equations of the
Lichnerowicz-York type among others.Comment: 32 pages, 3 figure
Nonlinear quantum gravity on the constant mean curvature foliation
A new approach to quantum gravity is presented based on a nonlinear
quantization scheme for canonical field theories with an implicitly defined
Hamiltonian. The constant mean curvature foliation is employed to eliminate the
momentum constraints in canonical general relativity. It is, however, argued
that the Hamiltonian constraint may be advantageously retained in the reduced
classical system to be quantized. This permits the Hamiltonian constraint
equation to be consistently turned into an expectation value equation on
quantization that describes the scale factor on each spatial hypersurface
characterized by a constant mean exterior curvature. This expectation value
equation augments the dynamical quantum evolution of the unconstrained
conformal three-geometry with a transverse traceless momentum tensor density.
The resulting quantum theory is inherently nonlinear. Nonetheless, it is
unitary and free from a nonlocal and implicit description of the Hamiltonian
operator. Finally, by imposing additional homogeneity symmetries, a broad class
of Bianchi cosmological models are analyzed as nonlinear quantum
minisuperspaces in the context of the proposed theory.Comment: 14 pages. Classical and Quantum Gravity (To appear
Subcutaneous tanezumab for osteoarthritis of the hip or knee: efficacy and safety results from a 24-week randomised phase III study with a 24-week follow-up period
Trial registration number NCT02709486[Abstract] Objective. Tanezumab, a nerve growth factor inhibitor, was investigated for osteoarthritis (OA) of the hip or knee in a study with 24-week treatment and 24-week safety follow-up.
Methods. This double-blind, randomised, phase III study enrolled adults in Europe and Japan with moderate-to-severe OA who had not responded to or could not tolerate standard-of-care analgesics. Patients were randomised to tanezumab 2.5 mg or 5 mg subcutaneously or matching placebo every 8 weeks (three doses). Co-primary end points were change from baseline to week 24 in Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC) Pain and Physical Function, and Patient’s Global Assessment of OA (PGA-OA). Joint safety and neurological assessments continued throughout the 48-week study.
Results. From March 2016 to December 2017, 849 patients were randomised and evaluated (placebo n=282, tanezumab 2.5 mg n=283, tanezumab 5 mg n=284). At week 24, there was a statistically significant improvement from baseline for tanezumab 5 mg compared with placebo for WOMAC Pain (least squares mean difference±SE –0.62±0.18, p=0.0006), WOMAC Physical Function (–0.71±0.17, p<0.0001) and PGA-OA (–0.19±0.07, p=0.0051). For tanezumab 2.5 mg, there was a statistically significant improvement in WOMAC Pain and Physical Function, but not PGA-OA. Rapidly progressive osteoarthritis (RPOA) was observed in 1.4% (4/283) and 2.8% (8/284) of patients in the tanezumab 2.5 mg and tanezumab 5 mg groups, respectively and none receiving placebo. Total joint replacements (TJRs) were similarly distributed across all three treatment groups (6.7%–7.8%). Tanezumab-treated patients experienced more paraesthesia (5 mg) and hypoaesthesia (both doses) than placebo.
Conclusion. Tanezumab 5 mg statistically significantly improved pain, physical function and PGA-OA, but tanezumab 2.5 mg only achieved two co-primary end points. RPOA occurred more frequently with tanezumab 5 mg than tanezumab 2.5 mg. TJRs were similarly distributed across all three groups
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