Congruence restrictions on axes

Kinematics on oblique axes

We solve a difficult problem involving velocity and acceleration components along oblique axes, and propose two problems of central force motion to be solved using oblique axes.

Representing Homomorphisms of Congruence Lattices as Restrictions of Congruences of Isoform Lattices

Let L1 be a finite lattice with an ideal L2. Then the restriction map is a {0, 1}-homomorphism from ConL1 into ConL2. In 1986, the present authors published the converse. If D1 and D2 are finite distributive lattices, and φ : D1 → D2 is a {0, 1}-homomorphism, then there are finite lattices L1 and L2 with an embedding η of L2 as an ideal of L1, and there are isomorphisms ε1 : ConL1 → D1 and ε2 :...

ON THE CONGRUENCE ax

We give bounds on the number of solutions to the Diophantine equation (X +1/x)(Y +1/y) = n as n tends to infinity. These bounds are related to the number of solutions to congruences of the form ax + by ≡ 1 modulo xy.

Congruence Relations on Multilattices

On triangulation axes of polygons

We propose the triangulation axis as an alternative skeletal structure for a simple polygon P . This axis is a straight-line tree that can be interpreted as an anisotropic medial axis of P , where inscribed disks are line segments or triangles. The underlying triangulation that specifies the anisotropy can be varied, to adapt the axis so as to reflect predominant geometrical and topological fea...