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Orientation is a function of the mind involving awareness of three dimensions: time, place and person. [1] Problems with orientation lead to disorientation, and can be due to various conditions.
The 3-sphere is naturally a smooth manifold, in fact, a closed embedded submanifold of R 4. The Euclidean metric on R 4 induces a metric on the 3-sphere giving it the structure of a Riemannian manifold. As with all spheres, the 3-sphere has constant positive sectional curvature equal to 1 / r 2 where r is the radius.
A torus is an orientable surface The Möbius strip is a non-orientable surface. Note how the disk flips with every loop. The Roman surface is non-orientable.. In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "anticlockwise". [1]
The mental status examination (MSE) is an important part of the clinical assessment process in neurological and psychiatric practice. It is a structured way of observing and describing a patient's psychological functioning at a given point in time, under the domains of appearance, attitude, behavior, mood and affect, speech, thought process, thought content, perception, cognition, insight, and ...
Three spheres, triple spheres, and related terms may refer to any of the following: Architecture.
Rotation formalisms are focused on proper (orientation-preserving) motions of the Euclidean space with one fixed point, that a rotation refers to.Although physical motions with a fixed point are an important case (such as ones described in the center-of-mass frame, or motions of a joint), this approach creates a knowledge about all motions.
S 3: a 3-sphere is a sphere in 4-dimensional Euclidean space. Spheres for n > 2 are sometimes called hyperspheres. The n-sphere of unit radius centered at the origin is denoted S n and is often referred to as "the" n-sphere. The ordinary sphere is a 2-sphere, because it is a 2-dimensional surface which is embedded in 3-dimensional space.
A Casson-Walker invariant is a surjective map λ CW from oriented rational homology 3-spheres to Q satisfying the following properties: 1. λ(S 3) = 0. 2. For every 1-component Dehn surgery presentation (K, μ) of an oriented rational homology sphere M′ in an oriented rational homology sphere M: