Search Results for ""

Given a knot diagram, it is possible to construct a collection of variables and equations, and given such a collection, a group naturally arises that is known as the group of ...

On a measure space X, the set of square integrable L2-functions is an L^2-space. Taken together with the L2-inner product with respect to a measure mu, <f,g>=int_Xfgdmu (1) ...

The Lambert azimuthal equal-area projection is a map projection having transformation equations x = k^'cosphisin(lambda-lambda_0) (1) y = ...

In practice, the vertical offsets from a line (polynomial, surface, hyperplane, etc.) are almost always minimized instead of the perpendicular offsets. This provides a ...

A surface of revolution defined by Kepler. It consists of less than half of a circular arc rotated about an axis passing through the endpoints of the arc. The equations of ...

Levenberg-Marquardt is a popular alternative to the Gauss-Newton method of finding the minimum of a function F(x) that is a sum of squares of nonlinear functions, ...

A minimal surface that contains lemniscates as geodesics which is given by the parametric equations x = R[sqrt(2)cos(1/3zeta)sqrt(cos(2/3zeta))] (1) y = ...

The distance between two skew lines with equations x = x_1+(x_2-x_1)s (1) x = x_3+(x_4-x_3)t (2) is given by D=(|(x_3-x_1)·[(x_2-x_1)x(x_4-x_3)]|)/(|(x_2-x_1)x(x_4-x_3)|) (3) ...

Consider the general system of two first-order ordinary differential equations x^. = f(x,y) (1) y^. = g(x,y). (2) Let x_0 and y_0 denote fixed points with x^.=y^.=0, so ...

For a logarithmic spiral given parametrically as x = ae^(bt)cost (1) y = ae^(bt)sint, (2) evolute is given by x_e = -abe^(bt)sint (3) y_e = abe^(bt)cost. (4) As first shown ...