Jon T. Pitts

Structural isomers of octahedral M6S12 clusters formed from dithiolates. An octahedral hexasilver(I) cluster containing dialkyl dithiophosphate ligands, {Ag[S2P(OC3H7)2]}6, with a different geometrical arrangement from that of {Cu[S2P(OC2H5)2]}6

Abstract The single crystal structure of {Ag[S2P(OC3H7)2}6, Ag6DDP6, 1, is reported. The silver atoms, each of which is trigonally coordinated to three sulfur atoms of the diisopropyl-dithiophosphate ligands, are located at the vertices of a distorted octahedron. The Ag6DDP6 molecular arrangement is different from the structure of Cu6DDP6 which has a molecular S6 symmetry. The displacements of the silver atoms from the plane through the sulfur atoms range from 0.328(1) to 0.392(8) A. The AgS distances range from 2.485(2) to 2.575(2) A. The ligands occupy six of the eight faces of the Ag6 octahedron with bridging μ2-S and terminal μ1-S coordination in an idealized D3d symmetry. The bridging S atoms in 1 occupy the six edges of two triangular faces on opposite sides of the octahedron while in Cu6[S2P(OC2H5)2]6 only terminal S atoms are on these faces. All plausible arrangements for these M6DDP6 complexes have been considered and a catalog of the surprisingly large number of distinct structures with MS3 coordinations with cis and trans uncapped faces is presented.

Computing Least Area Hypersurfaces Spanning Arbitrary Boundaries

The numerical least area problem for oriented hypersurfaces seeks algorithms which approximate area-minimizing hypersurfaces spanning a given boundary in Euclidean n-dimensional space. A mathematical model and numerical implementation are presented for finding the solution to the general least area problem for oriented surfaces in Euclidean three-dimensional space. (The mathematical model is valid for hypersurfaces of arbitrary Euclidean n-dimensional spaces.) There are no a priori restrictions on either the topological complexity of the given boundary or the topological type of the surfaces considered. As an example which illustrates the power of the method, the algorithm is applied to a boundary consisting of a pair of square-shaped linked curves. The resulting numerical surface is compared with an actual physical area-minimizing spanning surface (soap film).

The least-gradient method for computing area minimizing hypersurfaces spanning arbitrary boundaries

In this paper we give a brief presentation of the least-gradient method. The least-gradient method is used to compute an approxination to a globally area minimizing oriented hypersurface having a given boundary, without the necessity of providing any a priori topological information about the area minimizing surface. The method has been successfully implemented. The first results were obtained, and published, for the case in which the boundary curve is required to lie on the surface of a convex body. Subsequent work has dealt with the general problem in which the given boundary curve is essentially unrestricted.

The topology of minimal surfaces in Seifert fiber spaces.

There is provided a laminate of at lest two thermoplastic films which has a plurality of embossed parallel ribs running in at least one direction, said films being blocked together at spaced apart spots along each rib. Such laminate is prepared by passing at least two thermoplastic films in a superimposed and contacting engagement with one another through the nip of a pair of rollers. One roller is provided with a plurality of parallel raised ribs running in one direction and the other roller is provided with a plurality of parallel raised ribs which run in a direction angled to the direction of the ribs on the first roller. At the locations where the ribs on each roller cross at the nip, the films in the laminate are blocked together but otherwise remain unattached. Such laminates have exceptionally high tear strength and added stiffness and are adapted for various uses, including heavy duty bags and grocery sacks.

Energy estimates for area minimizing hypersurfaces with arbitrary boundaries

A notion of constrained least energy is defined for functions mapping a subset of Euclidean space to the circle. Under appropriate hypotheses, existence of such constrained least energy functions is proved. Finally, an integral bound is proved for functions nearly minimizing the constrained energy.