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The knots that make up a knot sum of a composite knot are known as factor knots (Adams 1994, p. 8).

If P(x,y) and P(x^',y^') are two points on an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1, (1) with eccentric angles phi and phi^' such that tanphitanphi^'=b/a (2) and A=P(a,0) and ...

A group action phi:G×X->X is called faithful if there are no group elements g (except the identity element) such that gx=x for all x in X. Equivalently, the map phi induces ...

A representation phi of a group G is faithful if it is one-to-one, i.e., if phi(g)=phi(h) implies g=h for g,h in G. Equivalently, phi is faithful if phi(g)=I_n implies g=e, ...

The third-order ordinary differential equation y^(''')+alphayy^('')+beta(1-y^('2))=0.

The term faltung is variously used to mean convolution and a function of bilinear forms. Let A and B be bilinear forms A = A(x,y)=sumsuma_(ij)x_iy_i (1) B = ...

A phrase used by Tukey to describe data points which are outside the outer fences.

Let A be a matrix and x and b vectors. Then the system Ax=b, x>=0 has no solution iff the system A^(T)y>=0, b^(T)y<0 has a solution, where y is a vector (Fang and Puthenpura ...

Let f(theta) be Lebesgue integrable and let f(r,theta)=1/(2pi)int_(-pi)^pif(t)(1-r^2)/(1-2rcos(t-theta)+r^2)dt (1) be the corresponding Poisson integral. Then almost ...

In a 1631 edition of Academiae Algebrae, J. Faulhaber published the general formula for the power sum of the first n positive integers, sum_(k=1)^(n)k^p = H_(n,-p) (1) = ...