Search Results for ""

A catastrophe which can occur for four control factors and one behavior axis. The butterfly catastrophe is the universal unfolding of the singularity f(x)=x^6 of codimension ...

Due to nonlinearities in weather processes, a butterfly flapping its wings in Tahiti can, in theory, produce a tornado in Kansas. This strong dependence of outcomes on very ...

If, in two solids of equal altitude, the sections made by planes parallel to and at the same distance from their respective bases are always equal, then the volumes of the ...

A special point which usually has some symmetric placement with respect to points on a curve or in a solid. The center of a circle is equidistant from all points on the ...

A chamfered cube, also inaccurately called a truncated rhombic dodecahedron or more accurately called a tetratruncated rhombic dodecahedron, is a polyhedron obtained by ...

The characteristic equation is the equation which is solved to find a matrix's eigenvalues, also called the characteristic polynomial. For a general k×k matrix A, the ...

The orthogonal polynomials defined by c_n^((mu))(x) = _2F_0(-n,-x;;-mu^(-1)) (1) = ((-1)^n)/(mu^n)(x-n+1)_n_1F_1(-n;x-n+1;mu), (2) where (x)_n is the Pochhammer symbol ...

If two projective pencils of curves of orders n and n^' have no common curve, the locus of the intersections of corresponding curves of the two is a curve of order n+n^' ...

Using a Chebyshev polynomial of the first kind T(x), define c_j = 2/Nsum_(k=1)^(N)f(x_k)T_j(x_k) (1) = 2/Nsum_(k=1)^(N)f[cos{(pi(k-1/2))/N}]cos{(pij(k-1/2))/N}. (2) Then f(x) ...

The constants lambda_(m,n)=inf_(r in R_(m,n))sup_(x>=0)|e^(-x)-r(x)|, where r(x)=(p(x))/(q(x)), p and q are mth and nth order polynomials, and R_(m,n) is the set of all ...