1,371 research outputs found
General moments of the inverse real Wishart distribution and orthogonal Weingarten functions
Let be a random positive definite symmetric matrix distributed according
to a real Wishart distribution and let be its inverse
matrix. We compute general moments explicitly. To do so, we employ the orthogonal Weingarten
function, which was recently introduced in the study for Haar-distributed
orthogonal matrices. As applications, we give formulas for moments of traces of
a Wishart matrix and its inverse.Comment: 29 pages. The last version differs from the published version, but it
includes Appendi
Einstein energy associated with the Friedmann -Robertson -Walker metric
Following Einstein's definition of Lagrangian density and gravitational field
energy density (Einstein, A., Ann. Phys. Lpz., 49, 806 (1916); Einstein, A.,
Phys. Z., 19, 115 (1918); Pauli, W., {\it Theory of Relativity}, B.I.
Publications, Mumbai, 1963, Trans. by G. Field), Tolman derived a general
formula for the total matter plus gravitational field energy () of an
arbitrary system (Tolman, R.C., Phys. Rev., 35(8), 875 (1930); Tolman, R.C.,
{\it Relativity, Thermodynamics & Cosmology}, Clarendon Press, Oxford, 1962));
Xulu, S.S., arXiv:hep-th/0308070 (2003)). For a static isolated system, in
quasi-Cartesian coordinates, this formula leads to the well known result , where is the
determinant of the metric tensor and is the energy momentum tensor of
the {\em matter}. Though in the literature, this is known as "Tolman Mass", it
must be realized that this is essentially "Einstein Mass" because the
underlying pseudo-tensor here is due to Einstein. In fact, Landau -Lifshitz
obtained the same expression for the "inertial mass" of a static isolated
system without using any pseudo-tensor at all and which points to physical
significance and correctness of Einstein Mass (Landau, L.D., and Lifshitz,
E.M., {\it The Classical Theory of Fields}, Pergamon Press, Oxford, 2th ed.,
1962)! For the first time we apply this general formula to find an expression
for for the Friedmann- Robertson -Walker (FRW) metric by using the same
quasi-Cartesian basis. As we analyze this new result, physically, a spatially
flat model having no cosmological constant is suggested. Eventually, it is seen
that conservation of is honoured only in the a static limit.Comment: By mistake a marginally different earlier version was loaded, now the
journal version is uploade
Pain outcomes in patients with bone metastases from advanced cancer: assessment and management with bone-targeting agents
Bone metastases in advanced cancer frequently cause painful complications that impair patient physical activity and negatively affect quality of life. Pain is often underreported and poorly managed in these patients. The most commonly used pain assessment instruments are visual analogue scales, a single-item measure, and the Brief Pain Inventory Questionnaire-Short Form. The World Health Organization analgesic ladder and the Analgesic Quantification Algorithm are used to evaluate analgesic use. Bone-targeting agents, such as denosumab or bisphosphonates, prevent skeletal complications (i.e., radiation to bone, pathologic fractures, surgery to bone, and spinal cord compression) and can also improve pain outcomes in patients with metastatic bone disease. We have reviewed pain outcomes and analgesic use and reported pain data from an integrated analysis of randomized controlled studies of denosumab versus the bisphosphonate zoledronic acid (ZA) in patients with bone metastases from advanced solid tumors. Intravenous bisphosphonates improved pain outcomes in patients with bone metastases from solid tumors. Compared with ZA, denosumab further prevented pain worsening and delayed the need for treatment with strong opioids. In patients with no or mild pain at baseline, denosumab reduced the risk of increasing pain severity and delayed pain worsening along with the time to increased pain interference compared with ZA, suggesting that use of denosumab (with appropriate calcium and vitamin D supplementation) before patients develop bone pain may improve outcomes. These data also support the use of validated pain assessments to optimize treatment and reduce the burden of pain associated with metastatic bone disease
Solar Mikheyev-Smirnov-Wolfenstein Effect with Three Generations of Neutrinos
Under the assumption that the density variation of the electrons can be
approximated by an exponential function, the solar Mikheyev-Smirnov-Wolfenstein
effect is treated for three generations of neutrinos. The generalized
hypergeometric functions that result from the exact solution of this problem
are studied in detail, and a method for their numerical evaluation is
presented. This analysis plays a central role in the determination of neutrino
masses, not only the differences of their squares, under the assumption of
universal quark-lepton mixing.Comment: 22 pages, LaTeX, including 2 figure
Cosmological Solutions in Bimetric Gravity and their Observational Tests
We obtain the general cosmological evolution equations for a classically
consistent theory of bimetric gravity. Their analytic solutions are
demonstrated to generically allow for a cosmic evolution starting out from a
matter dominated FLRW universe while relaxing towards a de Sitter (anti-de
Sitter) phase at late cosmic time. In particular, we examine a subclass of
models which contain solutions that are able to reproduce the expansion history
of the cosmic concordance model inspite of the nonlinear couplings of the two
metrics. This is demonstrated explicitly by fitting these models to
observational data from Type Ia supernovae, Cosmic Microwave Background and
Baryon Acoustic Oscillations.Comment: Latex, 26 pages. References added and minor revision of introduction
and appendix
Pulsational Mapping of Calcium Across the Surface of a White Dwarf
We constrain the distribution of calcium across the surface of the white
dwarf star G29-38 by combining time series spectroscopy from Gemini-North with
global time series photometry from the Whole Earth Telescope. G29-38 is
actively accreting metals from a known debris disk. Since the metals sink
significantly faster than they mix across the surface, any inhomogeneity in the
accretion process will appear as an inhomogeneity of the metals on the surface
of the star. We measure the flux amplitudes and the calcium equivalent width
amplitudes for two large pulsations excited on G29-38 in 2008. The ratio of
these amplitudes best fits a model for polar accretion of calcium and rules out
equatorial accretion.Comment: Accepted to the Astrophysical Journal. 16 pages, 10 figures
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