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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.
The Alveolar–arterial gradient (A-aO 2, [1] or A–a gradient), is a measure of the difference between the alveolar concentration (A) of oxygen and the arterial (a) concentration of oxygen. It is a useful parameter for narrowing the differential diagnosis of hypoxemia. [2] The A–a gradient helps to assess the integrity of the alveolar ...
The grade (US) or gradient (UK) (also called stepth, slope, incline, mainfall, pitch or rise) of a physical feature, landform or constructed line is either the elevation angle of that surface to the horizontal or its tangent. It is a special case of the slope, where zero indicates horizontality. A larger number indicates higher or steeper ...
The curl of the gradient of any continuously twice-differentiable scalar field (i.e., differentiability class) is always the zero vector: =. It can be easily proved by expressing ∇ × ( ∇ φ ) {\displaystyle \nabla \times (\nabla \varphi )} in a Cartesian coordinate system with Schwarz's theorem (also called Clairaut's theorem on equality ...
The gradient theorem states that if the vector field F is the gradient of some scalar-valued function (i.e., if F is conservative), then F is a path-independent vector field (i.e., the integral of F over some piecewise-differentiable curve is dependent only on end points). This theorem has a powerful converse:
Slope: = = In mathematics, the slope or gradient of a line is a number that describes the direction of the line on a plane. [1] Often denoted by the letter m, slope is calculated as the ratio of the vertical change to the horizontal change ("rise over run") between two distinct points on the line, giving the same number for any choice of points.
After months of speculating that right-hand man James Bender or even ex-husband Ant Anstead would join, The Flip Off premiere revealed that Haack has a team rallying behind her. Here's what we know.
A linear, or axial, color gradient. In color science, a color gradient (also known as a color ramp or a color progression) specifies a range of position-dependent colors, usually used to fill a region. In assigning colors to a set of values, a gradient is a continuous colormap, a type of color scheme.