A discrete analogue of the holomorphic map z γ is studied. It is given by Schramm's circle pattern with the combinatorics of the square grid. It is shown that the corresponding circle patterns are imbedded and described by special separatrix solutions of discrete Painlevé equations. Global properties of these solutions, as well as of the discrete z γ , are established.

For a given positive integer v with v ≡ 4(mod 6) and v > 4, let CKPD(v) denote a canonical Kirkman packing design of order v. It is proved in this paper that any CKPD(v) can be embedded in a CKPD(u) if u ≡ v ≡ 4 (mod 6), v ≥ 82 and u ≥ 3.5v.

Among the many parameters affecting the design of hydraulic structures on fissured rocks are orientation of principal permeability axes and degree of anisotropy of fissured rocks. Geological explorations rarely provide this type of information. If at all the information is available, methods employed are computationally cumbersome and inefficient. A new concept of simple equations and geometric...

language and culture are now deemed to be co-constitutive; hence english language teaching (elt) textbooks should incorporate cultural aspects and promote intercultural competence. however, careful decisions should be made as regards to the cultural content of materials and the ways in which culture is represented. this study was an attempt to deconstruct the patterns of cultural representation...

Carl Sandburg, in his "The People, Yes," writes of the meeting of an Indian and a white man. The latter, impressed with his own importance, draws a small circle in the sand and says, "This is what the white man knows." The Indian, the much wiser of the two, draws an enormous circle and then correctly points out, "This is where the white man and the red man know nothing." Sandburg's story is an ...

The fact that flat principal circle bundles are characterized by having zero real Euler classes has proved important in recent years in understanding whether total spaces of vector bundles over nonnegatively curved manifolds must support metrics with nonnegative curvature as well (see Theorem 6.3 and the discussion afterwards). Unfortunately, the proofs of this fact of which we are aware use ei...