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A projection is the transformation of points and lines in one plane onto another plane by connecting corresponding points on the two planes with parallel lines. This can be ...

A stochastic approximation method that functions by placing conditions on iterative step sizes and whose convergence is guaranteed under mild conditions. However, the method ...

The third Brocard point has triangle center function alpha=a^(-3) and is Kimberling center X_(76) (Kimberling 1998, p. 78). The point may have received its name since its ...

The Thomson cubic Z(X_2) of a triangle DeltaABC is the locus the centers of circumconics whose normals at the vertices are concurrent. It is a self-isogonal cubic with pivot ...

Nonhomogeneous matrix equations of the form Ax=b (1) can be solved by taking the matrix inverse to obtain x=A^(-1)b. (2) This equation will have a nontrivial solution iff the ...

If at least one solution can be determined for a given problem, a solution to that problem is said to exist. Frequently, mathematicians seek to prove the existence of ...

In cylindrical coordinates, the scale factors are h_r=1, h_theta=r, h_z=1, so the Laplacian is given by del ...

A partial differential diffusion equation of the form (partialU)/(partialt)=kappadel ^2U. (1) Physically, the equation commonly arises in situations where kappa is the ...

A linear congruence equation ax=b (mod m) (1) is solvable iff the congruence b=0 (mod d) (2) with d=GCD(a,m) is the greatest common divisor is solvable. Let one solution to ...

A linear system of equations is a set of n linear equations in k variables (sometimes called "unknowns"). Linear systems can be represented in matrix form as the matrix ...