Delaunay Ends of Constant Mean Curvature Surfaces

The generalized Weierstrass representation is used to analyze the asymptotic behavior of a constant mean curvature surface that arises locally from an ordinary differential equation with a regular singularity. We prove that a holomorphic perturbation of an ODE that represents a Delaunay surface generates a constant mean curvature surface which has a properly immersed end that is asymptotically Delaunay. Furthermore, that end is embedded if the Delaunay surface is unduloidal

Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms

We present a theorem on the unitarizability of loop group valued monodromy representations and apply this to show the existence of new families of constant mean curvature surfaces homeomorphic to a thrice-punctured sphere in the simply-connected 3-dimensional space forms $\R^3$, \bbS^3 and \bbH^3. Additionally, we compute the extended frame for any associated family of Delaunay surfaces.Comment: 18 pages, revised versio

Constant mean curvature surfaces of any positive genus

We show the existence of several new families of non-compact constant mean curvature surfaces: (i) singly-punctured surfaces of arbitrary genus $g \geq 1$, (ii) doubly-punctured tori, and (iii) doubly periodic surfaces with Delaunay ends.Comment: 14 pages, 10 figure

Photo sensor array technology development

The development of an improved capability photo sensor array imager for use in a Viking '75 type facsimile camera is presented. This imager consists of silicon photodiodes and lead sulfide detectors to cover a spectral range from 0.4 to 2.7 microns. An optical design specifying filter configurations and convergence angles is described. Three electronics design approaches: AC-chopped light, DC-dual detector, and DC-single detector, are investigated. Experimental and calculated results are compared whenever possible using breadboard testing and tolerance analysis techniques. Results show that any design used must be forgiving of the relative instability of lead sulfide detectors. A final design using lead sulfide detectors and associated electronics is implemented by fabrication of a hybrid prototype device. Test results of this device show a good agreement with calculated values

Discrete Ω\Omega-nets and Guichard nets

We provide a convincing discretisation of Demoulin's $\Omega$-surfaces along with their specialisations to Guichard and isothermic surfaces with no loss of integrable structure.Comment: 39 A4 page

Lunar apatite with terrestrial volatile abundances

The Moon is thought to be depleted relative to the Earth in volatile elements such as H, Cl and the alkalis. Nevertheless, evidence for lunar explosive volcanism has been used to infer that some lunar magmas exsolved a CO-rich and CO_2-rich vapour phase before or during eruption. Although there is also evidence for other volatile species on glass spherules, until recently there had been no unambiguous reports of indigenous H in lunar rocks. Here we report quantitative ion microprobe measurements of late-stage apatite from lunar basalt 14053 that document concentrations of H, Cl and S that are indistinguishable from apatites in common terrestrial igneous rocks. These volatile contents could reflect post-magmatic metamorphic volatile addition or growth from a late-stage, interstitial, sulphide-saturated melt that contained ~1,600 parts per million H_2O and ~3,500 parts per million Cl. Both metamorphic and igneous models of apatite formation suggest a volatile inventory for at least some lunar materials that is similar to comparable terrestrial materials. One possible implication is that portions of the lunar mantle or crust are more volatile-rich than previously thought