Two examples related to conical energies

Surface Granular Flows: Two Related Examples

Granular surface flows are common in industrial practice and natural systems, however, theoretical description of such flows is at present incomplete. Two prototype systems involving surface flow are compared: heap formation by pouring at a point and rotating cylinders. Continuum models for analysis of these flows are reviewed, and experimental results for quasi-2D systems are presented. Experi...

Some examples related to colorings

We complement the literature by proving that for a fixed-point free map f : X → X the statements (1) f admits a finite functionally closed cover A with f [A]∩A = ∅ for all A ∈ A (i.e., a coloring) and (2) βf is fixed-point free are equivalent. When functionally closed is weakened to closed, we show that normality is sufficient to prove equivalence, and give an example to show it cannot be omitt...

Some Examples Related to Knot Sliceness

It is known that the linking form on the 2-cover of slice knots has a metabolizer. We show that several weaker conditions, or some other conditions related to sliceness, do not imply the existence of a metabolizer. We then show how the Rudolph-Bennequin inequality can be used indirectly to prove that some knots are not slice.

Two Approximations to Learning from Examples

Examples of nonlinear homogenization involving degenerate energies . I . Plane strain

The study of polycrystals of shape-memory alloys and rigid-perfectly plastic materials gives rise to problems of nonlinear homogenization involving degenerate energies. This paper presents a characterization of the stress and strain fields in a class of problems in plane strain, and uses it to study examples including checkerboards and hexagonal microstructures. Consequences for shape-memory al...