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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 the French flag model, the French flag is used to represent the effect of a morphogen on cell differentiation: a morphogen affects cell states based on concentration, these states are represented by the different colors of the French flag: high concentrations activate a "blue" gene, lower concentrations activate a "white" gene, with "red" serving as the default state in cells below the ...
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.
Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, . [1] The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration.
The concept of paired metamorphic belts was originally theorized by the Japanese geologist, Akiho Miyashiro in 1961. The parallel arrangement between the metamorphic belts and the similar ages of each belt, led Miyashiro to the idea that metamorphic belts formed together as pairs.
M. C. Escher's lithograph print Ascending and Descending illustrates a non-conservative vector field, impossibly made to appear to be the gradient of the varying height above ground (gravitational potential) as one moves along the staircase. The force field experienced by the one moving on the staircase is non-conservative in that one can ...
At each point in the image, the result of the Prewitt operator is either the corresponding gradient vector or the norm of this vector. The Prewitt operator is based on convolving the image with a small, separable, and integer valued filter in horizontal and vertical directions and is therefore relatively inexpensive in terms of computations ...
Isocratic elution is typically effective in the separation of simple mixtures. Gradient elution is required for complex mixtures, with varying interactions with the stationary and mobile phases. This is the reason why in gradient elution the composition of the mobile phase is varied typically from low to high eluting strength.