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Let the true value of a quantity be x and the measured or inferred value x_0. Then the relative error is defined by deltax=(Deltax)/x=(x_0-x)/x=(x_0)/x-1, where Deltax is the ...

The topology induced by a topological space X on a subset S. The open sets of S are the intersections S intersection U, where U is an open set of X. For example, in the ...

The curve b(u) in the ruled surface parameterization x(u,v)=b(u)+vd(u) is called the directrix (or base curve).

For p(z)=a_nz^n+a_(n-1)z^(n-1)+...+a_0, (1) polynomial of degree n>=1, the Schur transform is defined by the (n-1)-degree polynomial Tp(z) = a^__0p(z)-a_np^*(z) (2) = ...

For any real number r>=0, an irrational number alpha can be approximated by infinitely many rational fractions p/q in such a way that ...

An operator T which commutes with all shift operators E^a, so TE^a=E^aT for all real a in a field. Any two shift-invariant operators commute.

Let K and L be simplicial complexes, and let f:K^((0))->L^((0)) be a map. Suppose that whenever the vertices v_0, ..., v_n of K span a simplex of K, the points f(v_0), ..., ...

P_y(nu)=lim_(T->infty)2/T|int_(-T/2)^(T/2)[y(t)-y^_]e^(-2piinut)dt|^2, (1) so int_0^inftyP_y(nu)dnu = lim_(T->infty)1/Tint_(-T/2)^(T/2)[y(t)-y^_]^2dt (2) = <(y-y^_)^2> (3) = ...

A polynomial which is not necessarily an invariant of a link. It is related to the dichroic polynomial. It is defined by the skein relationship ...

The squeeze theorem, also known as the squeezing theorem, pinching theorem, or sandwich theorem, may be stated as follows. Let there be two functions f_-(x) and f_+(x) such ...