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In mathematics, spaces of non-positive curvature occur in many contexts and form a generalization of hyperbolic geometry.In the category of Riemannian manifolds, one can consider the sectional curvature of the manifold and require that this curvature be everywhere less than or equal to zero.
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The English suffix-mania denotes an obsession with something; a mania. The suffix is used in some medical terms denoting mental disorders . It has also entered standard English and is affixed to many different words to denote enthusiasm or obsession with that subject.
In mathematics, the signature (v, p, r) [clarification needed] of a metric tensor g (or equivalently, a real quadratic form thought of as a real symmetric bilinear form on a finite-dimensional vector space) is the number (counted with multiplicity) of positive, negative and zero eigenvalues of the real symmetric matrix g ab of the metric tensor with respect to a basis.
In mathematics and theoretical physics, the induced metric is the metric tensor defined on a submanifold that is induced from the metric tensor on a manifold into which the submanifold is embedded, through the pullback. [1]
The ASRM scale has been shown to be an effective self-reported questionnaire for screening patients with acute mania as well as measuring anti-manic treatment effects. [ 2 ] [ 3 ] Though only a 5-question instrument, the scale's compatibility with the clinician administered Young Mania Rating Scale and the DSM-IV criteria give substantial ...
The Young Mania Rating Scale (YMRS), developed and popularised by Robert Young and Vincent E Ziegler, is an eleven-item multiple choice diagnostic questionnaire which psychiatrists use to measure the presence and severity of mania and associated symptoms. [1]
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