Critical value

In differential topology, a critical value of a differentiable function ƒ : M → N between differentiable manifolds is the image (value) ƒ(x) in N of a critical point x in M^[1].

The basic result on critical values is Sard's lemma. The set of critical values can be quite irregular; but in Morse theory it becomes important to consider real-valued functions on a manifold M, such that the set of critical values is in fact finite. The theory of Morse functions shows that there are many such functions; and that they are even typical, or generic in the sense of Baire category.

Statistics

In statistics, a critical value is the value corresponding to a given significance level. This cutoff value determines the boundary between those samples resulting in a test statistic that leads to rejecting the null hypothesis and those that lead to a decision not to reject the null hypothesis. If the calculated value from the statistical test is greater than the critical value, then the null hypothesis is rejected in favour of the alternative hypothesis, and vice versa.

Examples

• critical value of complex quadratic map

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This topology-related article is a stub. You can help Wikipedia by expanding it.v · edit] References ^ Carmo, Manfredo Perdigão do.. Differential geometry of curves and surfaces . Upper Saddle River, N.J.: Prentice-Hall, 1976. Print. Wikimedia Foundation. 2010. Игры ⚽ Поможем написать курсовую List of state leaders in 1330 List of state leaders in 1329 Look at other dictionaries: critical value — kritinė reikšmė statusas T sritis automatika atitikmenys: angl. critical value vok. kritischer Wert, m rus. критическое значение, n pranc. valeur critique, f …   Automatikos terminų žodynas critical value — kritinė vertė statusas T sritis Standartizacija ir metrologija apibrėžtis Kritinę medžiagos būseną atitinkančio dydžio vertė. atitikmenys: angl. critical value vok. kritischer Wert, m rus. критическое значение, n pranc. valeur critique, f …   Penkiakalbis aiškinamasis metrologijos terminų žodynas critical value — kritinė vertė statusas T sritis fizika atitikmenys: angl. critical value vok. kritischer Wert, m rus. критическое значение, n pranc. valeur critique, f …   Fizikos terminų žodynas critical value — noun mathematics : the value of the argument or independent variable corresponding to a critical point of a function * * * Statistics. the value of the random variable at the boundary between the acceptance region and the rejection region in the… …   Useful english dictionary critical value — noun Date: circa 1909 the value of an independent variable corresponding to a critical point of a function …   New Collegiate Dictionary critical value — Statistics. the value of the random variable at the boundary between the acceptance region and the rejection region in the testing of a hypothesis. [1905 10] * * * …   Universalium critical value — maximum or minimal range for …   English contemporary dictionary Critical Chain Project Management — (CCPM) is a method of planning and managing projects that puts more emphasis on the resources required to execute project tasks developed by Eliyahu M. Goldratt. This is in contrast to the more traditional Critical Path and PERT methods, which… …   Wikipedia Critical chain project management — Critical Chain redirects here. For the novel, see Critical Chain (novel). Critical chain project management (CCPM) is a method of planning and managing projects that puts the main emphasis on the resources required to execute project tasks. It… …   Wikipedia Critical point (mathematics) — See also: Critical point (set theory) The abcissae of the red circles are stationary points; the blue squares are inflection points. It s important to note that the stationary points are critical points, but the inflection points are not nor are… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”