The Thermonuclear Explosion Of Chandrasekhar Mass White Dwarfs

The flame born in the deep interior of a white dwarf that becomes a Type Ia supernova is subject to several instabilities. We briefly review these instabilities and the corresponding flame acceleration. We discuss the conditions necessary for each of the currently proposed explosion mechanisms and the attendant uncertainties. A grid of critical masses for detonation in the range $10^7$ - $2 \times 10^9$ g cm$^{-3}$ is calculated and its sensitivity to composition explored. Prompt detonations are physically improbable and appear unlikely on observational grounds. Simple deflagrations require some means of boosting the flame speed beyond what currently exists in the literature. ``Active turbulent combustion'' and multi-point ignition are presented as two plausible ways of doing this. A deflagration that moves at the ``Sharp-Wheeler'' speed, $0.1 g_{\rm eff} t$, is calculated in one dimension and shows that a healthy explosion is possible in a simple deflagration if the front moves with the speed of the fastest floating bubbles. The relevance of the transition to the ``distributed burning regime'' is discussed for delayed detonations. No model emerges without difficulties, but detonation in the distributed regime is plausible, will produce intermediate mass elements, and warrants further study.Comment: 28 pages, 4 figures included, uses aaspp4.sty. Submitted to Ap

Value-at-risk портфелю цінних паперів (Portfolio value-at-risk)

У статті досліджено формули для Value-at-Risk портфеля цінних паперів із застосуванням ваги активів у ньому. Зважаючи на недоліки класичного підходу, де Value-at-Risk розглядається подібно стандартному відхиленню дохідності, розроблено більш досконалі формули. Проведений бектестинг Value-at-Risk для індексного портфелю Dow Jones показав, що похибка оцінки ризику є меншою за розробленими формулами порівняно із класичною. Крім того, аналіз отриманих результатів показав, що ця похибка у багатьох випадках частково компенсує похибку оцінки математичного сподівання та стандартного відхилення через вибіркові статистики. (In this paper the portfolio Value-at-Risk formulas are investigated using the portfolio assets weights. Considering drawbacks of the classic approach, where Value-at-Risk is treated like the standard deviation of return, more sophisticated formulas are derived. The Value-at-Risk back-testing of the Dow Jones index portfolio shows that the estimation error for the derived formulas is lower than for the classic approach. Moreover, analysis of the results shows that in many cases this error partially offsets the estimation error for the expected returns and their standard deviations through sample statistics.