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The gradient of F is then normal to the hypersurface. Similarly, an affine algebraic hypersurface may be defined by an equation F(x 1, ..., x n) = 0, where F is a polynomial. The gradient of F is zero at a singular point of the hypersurface (this is the definition of a singular point). At a non-singular point, it is a nonzero normal vector.
In other words, there exists a real number M such that | | for all x in X. A function that is not bounded is said to be unbounded. Sometimes, if f(x) ≤ A for all x in X, then the function is said to be bounded above by A. On the other hand, if f(x) ≥ B for all x in X, then the function is said to be bounded below by B.
This following list features abbreviated names of mathematical functions, function-like operators and other mathematical terminology. This list is limited to abbreviations of two or more letters (excluding number sets). The capitalization of some of these abbreviations is not standardized – different authors might use different capitalizations.
Gradient sro, a Czech aircraft manufacturer; Image gradient, a gradual change or blending of color Color gradient, a range of position-dependent colors, usually used to fill a region; Texture gradient, the distortion in size which closer objects have compared to objects further away; Spatial gradient, a gradient whose components are spatial ...
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Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
The following list includes the continued fractions of some constants and is sorted by their representations. Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one.
In optimization, a gradient method is an algorithm to solve problems of the form min x ∈ R n f ( x ) {\displaystyle \min _{x\in \mathbb {R} ^{n}}\;f(x)} with the search directions defined by the gradient of the function at the current point.