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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 game which is not biased toward any player. A game in which a given player can always win by playing correctly is therefore called an unfair game.

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 = ...

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 ...

A Cantor set with Lebesgue measure greater than 0.

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 ...

The integral 1/(2pi(n+1))int_(-pi)^pif(x){(sin[1/2(n+1)x])/(sin(1/2x))}^2dx which gives the nth Cesàro mean of the Fourier series of f(x).