For any $X$, the product $X\times Y$ has remote points for some $Y$

POINTS ON y = x AT RATIONAL DISTANCE

Nathaniel Dean asks the following: Is it possible to find four nonconcyclic points on the parabola y = x2 such that each of the six distances between pairs of points is rational? We demonstrate that there is a correspondence between all rational points satisfying this condition and orbits under a particular group action of rational points on a fiber product of (three copies of) an elliptic surf...

Connections between C(X) and C(Y), where Y is a subspace of X

In this paper, we introduce a method by which we can find a close connection between the set of prime $z$-ideals of $C(X)$ and the same of $C(Y)$, for some special subset $Y$ of $X$. For instance, if $Y=Coz(f)$ for some $fin C(X)$, then there exists a one-to-one correspondence between the set of prime $z$-ideals of $C(Y)$ and the set of prime $z$-ideals of $C(X)$ not containing $f$. Moreover, c...

Octonion X,Y-Product G2 Variants

The automorphism group G2 of the octonions changes when octonion X,Y-product variants are used. I present here a general solution for how to go from G2 to its X,Y-product variant. * Happy Birthday to Larry Horwitz. If there’s a next time you must come.

Mixed Collocation Methods for Y" = F(x,y)

On the Ratio X/y for The

For a bivariate random vector (X, Y), the distribution of the ratio X/Y is of interest in problems in biological and physical sciences, econometrics, and ranking and selection. Examples include Mendelian inheritance ratios in genetics, mass to energy ratios in nuclear physics, target to control precipitation in meteorology, and inventory ratios in economics. The distribution of X/Y has been stu...