Umbral Vade Mecum

In recent years the umbral calculus has emerged from the shadows to provide an elegant correspondence framework that automatically gives systematic solutions of ubiquitous difference equations --- discretized versions of the differential cornerstones appearing in most areas of physics and engineering --- as maps of well-known continuous functions. This correspondence deftly sidesteps the use of more traditional methods to solve these difference equations. The umbral framework is discussed and illustrated here, with special attention given to umbral counterparts of the Airy, Kummer, and Whittaker equations, and to umbral maps of solitons for the Sine-Gordon, Korteweg--de Vries, and Toda systems.Comment: arXiv admin note: text overlap with arXiv:0710.230

Deformation Quantization of Nambu Mechanics

Phase Space is the framework best suited for quantizing superintegrable systems--systems with more conserved quantities than degrees of freedom. In this quantization method, the symmetry algebras of the hamiltonian invariants are preserved most naturally, as illustrated on nonlinear $\sigma$-models, specifically for Chiral Models and de Sitter $N$-spheres. Classically, the dynamics of superintegrable models such as these is automatically also described by Nambu Brackets involving the extra symmetry invariants of them. The phase-space quantization worked out then leads to the quantization of the corresponding Nambu Brackets, validating Nambu's original proposal, despite excessive fears of inconsistency which have arisen over the years. This is a pedagogical talk based on hep-th/0205063 and hep-th/0212267, stressing points of interpretation and care needed in appreciating the consistency of Quantum Nambu Brackets in phase space. For a parallel discussion in Hilbert space, see T Curtright's contribution in these Proceedings [hep-th 0303088].Comment: Invited talk by the first author at the Coral Gables Conference (C02/12/11.2), Ft Lauderdale, Dec 2002. 14p, LateX2e, aipproc, amsfont

Multiple litters in the California ground squirrel, Spermophilus beecheyi fisheri, in Tulare County

From the fall of 1977 through late spring of 1979, periodic examination of female ground squirrels in the low oak woodlands of southern Tulare County revealed that as much as 20 percent of the reproductively active females bred a second time within a given breeding season. This began to occur 50 to 80 days after the beginning of the breeding season. Evidence of litter loss from abortion was inapparent in 1979, but grossly obvious uterine inflammation was seen in 2 percent of the females in 1978. Neonatal losses were undetermined. Rebreeding appeared to occur in the older females, 2 years and older, and considering that older females probably constitute 35 percent of the breeding females, 20 percent breed-back would seem to be quite significant

Branched Hamiltonians and Supersymmetry

Some examples of branched Hamiltonians are explored both classically and in the context of quantum mechanics, as recently advocated by Shapere and Wilczek. These are in fact cases of switchback potentials, albeit in momentum space, as previously analyzed for quasi-Hamiltonian chaotic dynamical systems in a classical setting, and as encountered in analogous renormalization group flows for quantum theories which exhibit RG cycles. A basic two-worlds model, with a pair of Hamiltonian branches related by supersymmetry, is considered in detail.Comment: Minor changes to conform to published version. PACS: 03.65.Ca, 03.65.Ta, 45.20.J

Quantum Mechanics in Phase Space

Ever since Werner Heisenberg's 1927 paper on uncertainty, there has been considerable hesitancy in simultaneously considering positions and momenta in quantum contexts, since these are incompatible observables. But this persistent discomfort with addressing positions and momenta jointly in the quantum world is not really warranted, as was first fully appreciated by Hilbrand Groenewold and Jos\'e Moyal in the 1940s. While the formalism for quantum mechanics in phase space was wholly cast at that time, it was not completely understood nor widely known --- much less generally accepted --- until the late 20th century.Comment: A brief history of deformation quantization, ca 1930-1960, with some elementary illustrations of the theor

Elementary results for the fundamental representation of SU(3)

A general group element for the fundamental representation of SU(3) is expressed as a second order polynomial in the hermitian generating matrix H, with coefficients consisting of elementary trigonometric functions dependent on the sole invariant det(H), in addition to the group parameter.Comment: In memoriam Yoichiro Nambu (1921-2015

ECONOMIES OF SCALE IN THE GREENHOUSE FLORICULTURE INDUSTRY

Crop Production/Industries,

Full-size solar dynamic heat receiver thermal-vacuum tests

The testing of a full-size, 120 kW, solar dynamic heat receiver utilizing high-temperature thermal energy storage is described. The purpose of the test program was to quantify receiver thermodynamic performance, operating temperatures, and thermal response to changes in environmental and power module interface boundary conditions. The heat receiver was tested in a vacuum chamber with liquid nitrogen cold shrouds and an aperture cold plate to partly simulate a low-Earth-orbit environment. The cavity of the receiver was heated by an infrared quartz lamp heater with 30 independently controllable zones to allow axially and circumferentially varied flux distributions. A closed-Brayton cycle engine simulator conditioned a helium-xenon gas mixture to specific interface conditions to simulate the various operational modes of the solar dynamic power module on the Space Station Freedom. Inlet gas temperature, pressure, and flow rate were independently varied. A total of 58 simulated orbital cycles, each 94 minutes in duration, was completed during the test conduct period