On quadruples of Griffiths points

Egomotion Estimation Using Quadruples of Collinear Image Points

This paper considers a fundamental problem in visual motion perception, namely the problem of egomotion estimation based on visual input. Many of the existing techniques for solving this problem rely on restrictive assumptions regarding the observer’s motion or even the scene structure. Moreover, they often resort to searching the high dimensional space of possible solutions, a strategy which m...

ON QUADRUPLES OF CONSECUTIVE ¿th POWER RESIDUES

In [2] it was shown that A(&, 4) = co for fe^ 1048909 and it was conjectured that A(&, 4) = =° for all k. In this paper we establish this conjecture with the following Theorem. A(&, 4) = ». Proof. It suffices to prove the theorem for values of k which are prime. The proof makes use of the following proposition which is a special case of a result of Kummer [l] (see also [3]). Proposition. Let k ...

Blume-Emery-Griffiths spin glass and inverted tricritical points.

The Blume-Emery-Griffiths spin glass is studied by renormalization-group theory in d=3 . The boundary between the ferromagnetic and paramagnetic phases has first-order and two types of second-order segments. This topology includes an inverted tricritical point, first-order transitions replacing second-order transitions as temperature is lowered. The phase diagrams show disconnected spin-glass r...

Adjugates of Diophantine Quadruples

Philip Gibbs Diophantine m-tuples with property D(n), for n an integer, are sets of m positive integers such that the product of any two of them plus n is a square. Triples and quadruples with this property can be classed as regular or irregular according to whether they satisfy certain polynomial identities. Given any such m-tuple, a symmetric integer matrix can be formed with the elements of ...

On the covering of pairs by quadruples