4,184 research outputs found
Blow-up solutions for linear perturbations of the Yamabe equation
For a smooth, compact Riemannian manifold (M,g) of dimension N \geg 3, we
are interested in the critical equation where \Delta_g is the Laplace--Beltrami
operator, S_g is the Scalar curvature of (M,g), , and
is a small parameter
On determining spectral parameters, tracking jitter, and GPS positioning improvement by scintillation mitigation
A method of determining spectral parameters p (slope of the phase PSD) and T (phase PSD at 1 Hz) and hence tracking error variance in a GPS receiver PLL from just amplitude and phase scintillation indices and an estimated value of the Fresnel frequency has been previously presented. Here this method is validated using 50 Hz GPS phase and amplitude data from high latitude receivers in northern Norway and Svalbard. This has been done both using (1) a Fresnel frequency estimated using the amplitude PSD (in order to check the accuracy of the method) and (2) a constant assumed value of Fresnel frequency for the data set, convenient for the situation when contemporaneous phase PSDs are not available. Both of the spectral parameters ( p, T ) calculated using this method are in quite good agreement with those obtained by direct measurements of the phase spectrum as are tracking jitter variances determined for GPS receiver PLLs using these values. For the Svalbard data set, a significant difference in the scintillation level observed on the paths from different satellites received simultaneously was noted. Then, it is shown that the accuracy of relative GPS positioning can be improved by use of the tracking jitter variance in weighting the measurements from each satellite used in the positioning estimation. This has significant advantages for scintillation mitigation, particularly since the method can be accomplished utilizing only time domain measurements thus obviating the need for the phase PSDs in order to extract the spectral parameters required for tracking jitter determination
Quaternion-Octonion SU(3) Flavor Symmetry
Starting with the quaternionic formulation of isospin SU(2) group, we have
derived the relations for different components of isospin with quark states.
Extending this formalism to the case of SU(3) group we have considered the
theory of octonion variables. Accordingly, the octonion splitting of SU(3)
group have been reconsidered and various commutation relations for SU(3) group
and its shift operators are also derived and verified for different iso-spin
multiplets i.e. I, U and V- spins.
Keywords: SU(3), Quaternions, Octonions and Gell Mann matrices
PACS NO: 11.30.Hv: Flavor symmetries; 12.10-Dm: Unified field theories and
models of strong and electroweak interaction
Nuclear structure and reaction studies at SPIRAL
The SPIRAL facility at GANIL, operational since 2001, is described briefly.
The diverse physics program using the re-accelerated (1.2 to 25 MeV/u) beams
ranging from He to Kr and the instrumentation specially developed for their
exploitation are presented. Results of these studies, using both direct and
compound processes, addressing various questions related to the existence of
exotic states of nuclear matter, evolution of new "magic numbers", tunnelling
of exotic nuclei, neutron correlations, exotic pathways in astrophysical sites
and characterization of the continuum are discussed. The future prospects for
the facility and the path towards SPIRAL2, a next generation ISOL facility, are
also briefly presented.Comment: 48 pages, 27 figures. Accepted for publication in Journal of Physics
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
- …