Search Results for ""

The necessary and sufficient condition that an algebraic curve has an algebraic involute is that the arc length is a two-valued algebraic function of the coordinates of the ...

A sequence {a_j} of positive integers is called an iteration sequence if there exists a strictly increasing sequence {s_k} of positive integers such that a_1=s_1>=2 and ...

A framework is called "just rigid" if it is rigid, but ceases to be so when any single bar is removed. Lamb (1928, pp. 93-94) proved that a necessary (but not sufficient) ...

A necessary and sufficient condition for a curve to be a helix is that the ratio of curvature to torsion be constant.

A necessary and sufficient condition for all the eigenvalues of a real n×n matrix A to have negative real parts is that the equation A^(T)V+VA=-I has as a solution where V is ...

A necessary and sufficient condition that [alpha^'] should be comparable with [alpha] for all positive values of the a is that one of (alpha^') and (alpha) should be ...

Let C^omega(I) be the set of real analytic functions on I. Then C^omega(I) is a subalgebra of C^infty(I). A necessary and sufficient condition for a function f in C^infty(I) ...

Let H be a Hilbert space and M a closed subspace of H. Corresponding to any vector x in H, there is a unique vector m_0 in M such that |x-m_0|<=|x-m| for all m in M. ...

Let j, r, and s be distinct integers (mod n), and let W_i be the point of intersection of the side or diagonal V_iV_(i+j) of the n-gon P=[V_1,...,V_n] with the transversal ...

A transformation x^'=Ax is unimodular if the determinant of the matrix A satisfies det(A)=+/-1. A necessary and sufficient condition that a linear transformation transform a ...