Round Function
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online.In topology and in calculus, a round function is a scalar function Mto{mathbb{R}}, over a manifold M, whose critical points form one or several connected components, each homeomorphic to the circle S1, also called critical loops. They are special cases of Morse-Bott functions. Scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are often used in physics, for instance to ...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online.In topology and in calculus, a round function is a scalar function Mto{mathbb{R}}, over a manifold M, whose critical points form one or several connected components, each homeomorphic to the circle S1, also called critical loops. They are special cases of Morse-Bott functions. Scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are often used in physics, for instance to indicate the temperature distribution throughout space, or the air pressure. Mathematically, a scalar field on a region U is a real or complex-valued function on U. The region U may be a set in some Euclidean space, or more generally a subset of a manifold, and it is typical to impose further conditions on the field, such that it be continuous or often continuously differentiable to some order. In a mathematical context, the term "scalar field" may be used to distinguish a function of this kind with a more general tensor field, density, or differential form.
