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A partially ordered set P=(X,<=) is an interval order if it is isomorphic to some set of intervals on the real line ordered by left-to-right precedence. Formally, P is an ...

Pick a point O in the interior of a quadrilateral which is not a parallelogram. Join this point to each of the four vertices, then the locus of points O for which the sum of ...

Pairs of points of a line, the product of whose distances from a fixed point is a given constant. This is more concisely defined as a projectivity of period two. If ...

A graph with minimum vertex degree at least 5 is a line graph iff it does not contain any of the above six graphs, known in this work as Metelsky graphs, as an induced ...

Let f(z) be an analytic function of z, regular in the half-strip S defined by a<x<b and y>0. If f(z) is bounded in S and tends to a limit l as y->infty for a certain fixed ...

A topology defined on a totally ordered set X whose open sets are all the finite intersections of subsets of the form {x in X|x>a} or {x in X|x<a}, where a in X. The order ...

The diagonal of a polyhedron is any line segment connecting two nonadjacent vertices of the polyhedron. Any polyhedron having no diagonals must have a skeleton which is a ...

A Euclidean-like space having line element ds^2=(dz^1)^2+...+(dz^p)^2-(dz^(p+1))^2-...-(dz^(p+q))^2, having dimension m=p+q (Rosen 1965). In contrast, the signs would be all ...

A method for fitting a curve (not necessarily a straight line) through a set of points using some goodness-of-fit criterion. The most common type of regression is linear ...

A graph G whose line graph is L(G) is called the root graph R(L(G)) of L(G). In order words, R(L(G))=G. The root graph of a connected graph is unique except for K_3=C_3 (the ...