In the presence of nuisance parameters, we derive an explicit higher order asymptotic formula to compare the expected lengths of conndence intervals given by likelihood ratio statistics arising from the usual proole likelihood and various adjustments thereof. Highest posterior density regions, with approximate frequentist validity, are also included in the study.

The existing thermodynamics of the cosmological horizon in de Sitter spacetime is established in the micro-canonical ensemble, while thermodynamics of black hole horizons are established in the canonical ensemble. Generally in the ordinary thermodynamics and statistical mechanics, both of the micro-canonical and canonical ensembles yield the same equation of state for any thermodynamic system. ...

The four equations of stellar structure are reformulated as two alternate pairs of variational principles. Different thermodynamic representations lead to the same hydromechanical equations, but the thermal equations require, not the entropy, but the temperature as the thermal field variable. Our treatment emphasizes the hydrostatic energy and the entropy production rate of luminosity produced ...

We review the remarkable relationship between the laws of black hole mechanics and the ordinary laws of thermodynamics. It is emphasized that – in analogy with the laws of thermodynamics – the validity the laws of black hole mechanics does not appear to depend upon the details of the underlying dynamical theory (i.e., upon the particular field equations of general relativity). It also is emphas...

Cuprous oxide (Cu2O) nanocubes were synthesized by reducing Cu(OH)2 in the presence of sodium citrate at room temperature. The samples were characterized in detail by field-emission scanning electron microscopy, transmission electron microscopy, high-resolution transmission electron microscopy, X-ray powder diffraction, and N2 absorption (BET specific surface area). The equations for acquiring ...

Thermodynamics of 22 oligonucleotides with internal single G.A mismatches dissolved in 1 M NaCl were determined from absorbance versus temperature melting curves. These data, combined with five literature sequences, were used to derive nearest-neighbor thermodynamic parameters for seven linearly independent trimer sequences with internal G.A mismatches and Watson-Crick flanking base pairs. The ...

The existing thermodynamics of the cosmological horizon in de Sitter spacetime is established in the micro-canonical ensemble, while the thermodynamics of black hole horizons is established in the canonical ensemble. Generally in the ordinary thermodynamics and statistical mechanics, both of the micro-canonical and canonical ensembles yield the same equation of state for any thermodynamic syste...

We discuss the quantum mechanics and thermodynamics of the (2+1)dimensional black hole, using both minisuperspace methods and exact results from Chern-Simons theory. In particular, we evaluate the first quantum correction to the black hole entropy. We show that the dynamical variables of the black hole arise from the possibility of a deficit angle at the (Euclidean) horizon, and briefly specula...

For hypotheses of the type H0 : θ = θ0 vs H1 : θ 6= θ0 we demonstrate the equivalence of a Bayesian hypothesis test using a Bayes factor and the corresponding classical test, for a large class of models, which are detailed in the paper. In particular, we show that the role of the prior and critical region for the Bayes factor test is only to specify the type I error. This is their only role sin...