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C: curl, G: gradient, L: Laplacian, CC: curl of curl. Each arrow is labeled with the result of an identity, specifically, the result of applying the operator at the arrow's tail to the operator at its head. The blue circle in the middle means curl of curl exists, whereas the other two red circles (dashed) mean that DD and GG do not exist.
The curl of a vector field F, denoted by curl F, or , or rot F, is an operator that maps C k functions in R 3 to C k−1 functions in R 3, and in particular, it maps continuously differentiable functions R 3 → R 3 to continuous functions R 3 → R 3. It can be defined in several ways, to be mentioned below:
An options chain provides a range of summary information about a specific option expiration in a table, allowing the trader to quickly glance at vital data about these options. The data shown in a ...
Moreover, it is also possible to define parametrizations of k-dimensional subsets for k < n, and this makes it possible to define integrals of k-forms. To make this precise, it is convenient to fix a standard domain D in R k, usually a cube or a simplex. A k-chain is a formal sum of smooth embeddings D → M. That is, it is a collection of ...
This article uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and φ): . The polar angle is denoted by [,]: it is the angle between the z-axis and the radial vector connecting the origin to the point in question.
Options Clearing Corporation's (OCC) Options Symbology Initiative (OSI) mandated an industry-wide change to a new option symbol structure, resulting in option symbols 21 characters in length. March 2010 - May 2010 was the symbol consolidation period in which all outgoing option roots will be replaced with the underlying stock symbol.
The curl of an order-n > 1 tensor field () is also defined using the recursive relation = ; = where c is an arbitrary constant vector and v is a vector field. Curl of a first-order tensor (vector) field
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