Do we know the mass of a black hole? Mass of some cosmological black hole models

Using a cosmological black hole model proposed recently, we have calculated the quasi-local mass of a collapsing structure within a cosmological setting due to different definitions put forward in the last decades to see how similar or different they are. It has been shown that the mass within the horizon follows the familiar Brown–York behavior. It increases, however, outside the horizon again after a short decrease, in contrast to the Schwarzschild case. Further away, near the void, outside the collapsed region, and where the density reaches the background minimum, all the mass definitions roughly coincide. They differ, however, substantially far from it. Generically, we are faced with three different Brown–York mass maxima: near the horizon, around the void between the overdensity region and the background, and another at cosmological distances corresponding to the cosmological horizon. While the latter two maxima are always present, the horizon mass maxima is absent before the onset of the central singularity.     

The dynamics of multidimensional cosmological models in the presence of quantum effects. I. The case FRW ×T D at high temperatures

The dynamical system approach is applied to the study of dynamics of multidimensional cosmological models with topology FRW ×T ^D (D-dimensional torus) in the presence of high-temperature quantum effects. The stability methods developed in the paper of Szydowski (Gen. Rel. Grav.,20, 221, 1988) are used in the analysis of typical states of the metric in the neighborhood of singularities and for large time values. The problems of dynamical dimensional reduction, structure of singularities, isotropization, etc., are discussed in this context.     

What is the recall rate of breast MRI when used for screening asymptomatic women at high risk?

Breast screening acceptability is dependent on sensitivity and recall rate. We aimed to establish the recall rate for MRI and mammography, separately and together, when screening a cohort of women at high genetic risk. Women aged 35-49 years in the MARIBS study form the cohort. We analysed the recall rate, the number of extra tests and their effectiveness. Wilcoxon Rank test was used to estimate the effect of age and logistic regression with robust variance the effect of mammographic density on recall rates. The first 726 screening studies took place in 415 women. Following 86 of these recall occurred, comprising 140 additional investigations. 28 of the cases were resolved without further MRI, and 18 women had more than 2 additional tests. Neither age nor mammographic density was associated with recall. MRI had a recall of rate of 10.19%, and mammography 4.00%. The two techniques largely recalled different cases and 10 cases only (11.62% of those recalled) were abnormal by both tests. The two together had a recall rate of 11.85%. Recall rates varied widely between centres of the study. Breast MRI in asymptomatic high-risk women age 35-49 years largely recalls different women from mammography. The combined figure of approximately 12% may be acceptable for screening and will be useful for planning similar studies.     

Multiple-quantum MAS NMR of quadrupolar nuclei. Do five-, seven- and nine-quantum experiments yield higher resolution than the three-quantum experiment?

The question of whether or not higher-order (five-, seven- and nine-quantum) multiple-quantum magic angle spinning (MQMAS) experiments yield isotropic NMR spectra of half-integer quadrupolar nuclei with higher resolution than the basic three-quantum MAS experiment is examined. The frequency dispersion is shown theoretically to be greatly increased in higher-order MQMAS spectra, but it is argued that whether or not this translates into an increase in resolution depends upon the ratio of the homogeneous to inhomogeneous contributions to the isotropic linewidth. Experimentally, it is demonstrated using three-, five- and seven-quantum 45Sc MAS NMR and three- and five-quantum 27Al MAS NMR of crystalline samples that higher-order MQMAS experiments can yield a real and useful increase in resolution but that, owing to the presence of inhomogeneous broadening in the isotropic spectra, this increase is less than the theoretically predicted value. A number of practical issues relating to resolution in MQMAS NMR are also pointed out.