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

An Interview with Jayne Barnard

But I think William & Mary Law School has got a huge number of very entrepreneurial students and faculty members who make things happen. And not because somebody told them it had to be done, but because they just decide that they\u27ll do it. -- Jayne Barnard. ------------------------------------ This interview took place in the Reeder Media Center at William & Mary on April 27th, 2023, from 12:00 to 2:00 pm. It begins by discussing Barnard’s career prior to law school, and how there was a movement of women to law schools to find careers where they would be better recognized for their hard work. She discusses joining Jenner and Block, and what it meant for them to have women already working there. She discusses her return to government by working for the mayor of Chicago, Harold Washington, and how she “cleaned up” the law department. From there, she moves to how she came from Illinois to Virginia to join William & Mary faculty in 1985. Barnard then shares her many roles at the law school, from the classes she taught to being a faculty advisor for multiple journals. Through these roles, she highlights her commitment to supporting women, which is further revealed as she talks about her involvement in the ACLU, William & Mary’s Faculty Women’s Cause, and role as Coordinator of the 100th Anniversary of Women at William & Mary. She then discusses her work in corporations, business, and white-collar crime, coming to a head in her article about victim impact statements which helped in passing the Crime Victims’ Rights Act of 2004 and got her a seat in the courtroom during the Bernie Madoff case. The interview finishes with Barnard sharing a few different stories and comments about the general community and entrepreneurship of the students and faculty of William & Mary Law School.https://scholarship.law.wm.edu/oralhist_all/1004/thumbnail.jp

A systematic mixed-integer differential evolution approach for water network operational optimization

The operational management of potable water distribution networks presents a great challenge to water utilities, as reflected by the complex interplay of a wide range of multidimensional and nonlinear factors across the water value chain including the network physical structure and characteristics, operational requirements, water consumption profiles and the structure of energy tariffs. Nevertheless, both continuous and discrete actuation variables can be involved in governing the water network, which makes optimizing such networks a mixed-integer and highly constrained decision-making problem. As such, there is a need to situate the problem holistically, factoring in multidimensional considerations, with a goal of minimizing water operational costs. This paper, therefore, proposes a systematic optimization methodology for (near) real-time operation of water networks, where the operational strategy can be dynamically updated using a model-based predictive control scheme with little human intervention. The hydraulic model of the network of interest is thereby integrated and successively simulated with different trial strategies as part of the optimization process. A novel adapted mixed-integer differential evolution (DE) algorithm is particularly designed to deal with the discrete-continuous actuation variables involved in the network. Simulation results on a pilot water network confirm the effectiveness of the proposed methodology and the superiority of the proposed mixed-integer DE in comparison with genetic algorithms. It also suggests that 23.69% cost savings can be achieved compared with the water utility's current operational strategy, if adaptive pricing is adopted for all the pumping stations

Kyawthuite, Bi^(3+)Sb^(5+)O_4, a new gem mineral from Mogok, Burma (Myanmar)

Kyawthuite, Bi^(3+)Sb^(5+)O_4, is a new gem mineral found as a waterworn crystal in alluvium at Chaung-gyi-ah-le-ywa in the Chaung-gyi valley, near Mogok, Burma (Myanmar). Its description is based upon a single sample, which was faceted into a 1.61-carat gem. The composition suggests that the mineral formed in a pegmatite. Kyawthuite is monoclinic, space group I2/c, with unit cell dimensions a = 5.4624(4), b = 4.88519(17), c = 11.8520(8) Å, β = 101.195(7)°, V = 310.25(3) Å^3 and Z = 4. The colour is reddish orange and the streak is white. It is transparent with adamantine lustre. The Mohs hardness is 5½. Kyawthuite is brittle with a conchoidal fracture and three cleavages: {001} perfect, {110} and {110} good. The measured density is 8.256(5) g cm^(–3) and the calculated density is 8.127 g cm^(–3). The mineral is optically biaxial with 2V = 90(2)°. The predicted indices of refraction are α = 2.194, β = 2.268, γ = 2.350. Pleochroism is imperceptible and the optical orientation is X = b; Y ≈ c; Z ≈ a. Electron microprobe analyses, provided the empirical formula (Bi^(3+)_(0.82)Sb^(3+)_(0.18))_(Σ1.00)( Sb^(5+)_(0.99)Ta^(5+)_(0.01))_(Σ1.00)O_4. The Raman spectrum is similar to that of synthetic Bi^(3+)Sb^(5+)O_4. The infrared spectrum shows a trace amount of OH/H_2O. The eight strongest powder X-ray diffraction lines are [d_(obs) in Å(I)(hkl)]: 3.266(100)(112), 2.900(66)(112), 2.678(24)(200), 2.437(22)(020, 14), 1.8663(21)(024), 1.8026(43)(16,220,204), 1.6264(23)(224,116) and 1.5288(28)(312, 32). In the crystal structure of kyawthuite (R_1 = 0.0269 for 593 reflections with F_o > 4σF), Sb^(5+)O_6 octahedra share corners to form chequerboard-like sheets parallel to {001}. Atoms of Bi^(3+), located above and below the open squares in the sheets, form bonds to the O atoms in the sheets, thereby linking adjacent sheets into a framework. The Bi^(3+) atom is in lopsided 8 coordination, typical of a cation with stereoactive lone electron pairs. Kyawthuite is isostructural with synthetic β-Sb_2O_4 and clinocervantite (natural β-Sb_2O_4)