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The prime decomposition theorem for 3-manifolds states that every compact, orientable 3-manifold is the connected sum of a unique (up to homeomorphism) collection of prime 3-manifolds. A manifold is prime if it cannot be presented as a connected sum of more than one manifold, none of which is the sphere of the same dimension.
In particular if the surgery coefficient is of the form /, then the surgered 3-manifold is still the 3-sphere. If M {\displaystyle M} is the 3-sphere, L {\displaystyle L} is the right-handed trefoil knot , and the surgery coefficient is + 1 {\displaystyle +1} , then the surgered 3-manifold is the Poincaré dodecahedral space .
A clinical pathway is a multidisciplinary management tool based on evidence-based practice for a specific group of patients with a predictable clinical course, in which the different tasks (interventions) by the professionals involved in the patient care are defined, optimized and sequenced either by hour (ED), day (acute care) or visit (homecare).
The standard treatment, also known as the standard of care, is the medical treatment that is normally provided to people with a given condition. In many scientific studies, the control group receives the standard treatment rather than a placebo while a treatment group receives the experimental treatment. [ 1 ]
There are 3 such curvatures (positive, zero, and negative). This is a classical result, and as stated, easy (the full uniformization theorem is subtler). The study of surfaces is deeply connected with complex analysis and algebraic geometry, as every orientable surface can be considered a Riemann surface or complex algebraic curve. While the ...
The protocol was originally developed as a memory aid for rescuers performing cardiopulmonary resuscitation, and the most widely known use of the initialism is in the care of the unconscious or unresponsive patient, although it is also used as a reminder of the priorities for assessment and treatment of patients in many acute medical and trauma ...
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A closed 3-manifold has a geometric structure of at most one of the 8 types above, but finite volume non-compact 3-manifolds can occasionally have more than one type of geometric structure. (Nevertheless, a manifold can have many different geometric structures of the same type; for example, a surface of genus at least 2 has a continuum of ...