Binomial-coefficient multiples of irrationals

Denote by $x$ a random infinite path in the graph of Pascal's triangle (left and right turns are selected independently with fixed probabilities) and by $d_n(x)$ the binomial coefficient at the $n$'th level along the path $x$. Then for a dense $G_{\delta}$ set of $\theta$ in the unit interval, $\{d_n(x)\theta \}$ is almost surely dense but not uniformly distributed modulo 1.Comment: 10 pages, to appear in Monatshefte f. Mat

Isospectral Flow and Liouville-Arnold Integration in Loop Algebras

A number of examples of Hamiltonian systems that are integrable by classical means are cast within the framework of isospectral flows in loop algebras. These include: the Neumann oscillator, the cubically nonlinear Schr\"odinger systems and the sine-Gordon equation. Each system has an associated invariant spectral curve and may be integrated via the Liouville-Arnold technique. The linearizing map is the Abel map to the associated Jacobi variety, which is deduced through separation of variables in hyperellipsoidal coordinates. More generally, a family of moment maps is derived, identifying certain finite dimensional symplectic manifolds with rational coadjoint orbits of loop algebras. Integrable Hamiltonians are obtained by restriction of elements of the ring of spectral invariants to the image of these moment maps. The isospectral property follows from the Adler-Kostant-Symes theorem, and gives rise to invariant spectral curves. {\it Spectral Darboux coordinates} are introduced on rational coadjoint orbits, generalizing the hyperellipsoidal coordinates to higher rank cases. Applying the Liouville-Arnold integration technique, the Liouville generating function is expressed in completely separated form as an abelian integral, implying the Abel map linearization in the general case.Comment: 42 pages, 2 Figures, 1 Table. Lectures presented at the VIIIth Scheveningen Conference, held at Wassenaar, the Netherlands, Aug. 16-21, 199

DROUGHT AND CLIMATE CHANGE: IMPLICATIONS FOR THE WEST

Environmental Economics and Policy,

Effects of Climate Change on Water Resources

Environmental Economics and Policy, Resource /Energy Economics and Policy, Q25, Q54,

Stiffness reductions during tensile fatigue testing of graphite/epoxy angle-ply laminates

Tensile fatigue data was generated under carefully controlled test conditions. A computerized data acquisition system was used to permit the measurement of dynamic modulus without interrupting the fatigue cycling. Two different 8-ply laminate configurations, viz, + or - 45 (2s) and + or - 67.5 (2s), of a T300/5208 graphite/epoxy composite were tested. The + or - 45 (2s) laminate did exhibit some modulus decay, although there was no well-defined correlation with applied stress level or number of cycles. The + or - 67.5 (2s) laminate did not exhibit any measurable modulus decay. Secondary effects observed included a small but distinct difference between modulus as measured statically and dynamically, a slight recovery of the modulus decay after a test interruption, and a significant viscoelastic (creep) response of the + or - 45 (2s) laminate during fatigue testing

The persistence of drought impacts across growing seasons: a dynamic stochastic analysis

Agricultural producers throughout much of the United States experienced one of the most severe droughts in the last 100 years during the years 1999-2006. The prolonged nature of this drought highlights a need to better understand the impacts and management of drought across growing seasons, rather than just within a growing season. Producers express specific concern about the tendency of drought impacts to persist even after drought itself has subsided. The persistence of drought impacts has received limited attention in the economics literature. The objectives of this study are two-fold: 1) to determine whether inter-year dynamics, in the form of agronomic constraints and financial flows, can cause persistence of a drought's impact in years subsequent to the drought, and 2) to determine whether the impact of one year of drought can alter the impact of a subsequent year of drought. A multi-year, dynamic and stochastic decision model is developed in a discrete stochastic programming framework and solved to address the objectives. The structure and parameters of the farm-level model are based on irrigated row crop farms in eastern Oregon, USA. Analysis of the model's solution reveals the following results: 1) the impact of a drought can persist long after the drought subsides, and 2) the impact of one year of drought can alter the impact of a subsequent year of drought. Potential implications for the administration of drought-related assistance are discussed briefly.Drought, preparedness, response, uncertainty, dynamics, discrete stochastic programming, agriculture, irrigation, eastern Oregon, row crops, crop rotation, Crop Production/Industries, Risk and Uncertainty,

The Ultimate Halo Mass in a LCDM Universe

In the far future of an accelerating LCDM cosmology, the cosmic web of large-scale structure consists of a set of increasingly isolated halos in dynamical equilibrium. We examine the approach of collisionless dark matter to hydrostatic equilibrium using a large N-body simulation evolved to scale factor a = 100, well beyond the vacuum--matter equality epoch, a_eq ~ 0.75, and 53/h Gyr into the future for a concordance model universe (Omega_m ~ 0.3, Omega_Lambda ~ 0.7). The radial phase-space structure of halos -- characterized at a < a_eq by a pair of zero-velocity surfaces that bracket a dynamically active accretion region -- simplifies at a > 10 a_eq when these surfaces merge to create a single zero-velocity surface, clearly defining the halo outer boundary, rhalo, and its enclosed mass, mhalo. This boundary approaches a fixed physical size encompassing a mean interior density ~ 5 times the critical density, similar to the turnaround value in a classical Einstein-deSitter model. We relate mhalo to other scales currently used to define halo mass (m200, mvir, m180b) and find that m200 is approximately half of the total asymptotic cluster mass, while m180b follows the evolution of the inner zero velocity surface for a < 2 but becomes much larger than the total bound mass for a > 3. The radial density profile of all bound halo material is well fit by a truncated Hernquist profile. An NFW profile provides a somewhat better fit interior to r200 but is much too shallow in the range r200 < r < rhalo.Comment: 5 pages, 3 figures, submitted to MNRAS letter

Tendon proper- and peritenon-derived progenitor cells have unique tenogenic properties.

IntroductionMultipotent progenitor populations exist within the tendon proper and peritenon of the Achilles tendon. Progenitor populations derived from the tendon proper and peritenon are enriched with distinct cell types that are distinguished by expression of markers of tendon and vascular or pericyte origins, respectively. The objective of this study was to discern the unique tenogenic properties of tendon proper- and peritenon-derived progenitors within an in vitro model. We hypothesized that progenitors from each region contribute differently to tendon formation; thus, when incorporated into a regenerative model, progenitors from each region will respond uniquely. Moreover, we hypothesized that cell populations like progenitors were capable of stimulating tenogenic differentiation, so we generated conditioned media from these cell types to analyze their stimulatory potentials.MethodsIsolated progenitors were seeded within fibrinogen/thrombin gel-based constructs with or without supplementation with recombinant growth/differentiation factor-5 (GDF5). Early and late in culture, gene expression of differentiation markers and matrix assembly genes was analyzed. Tendon construct ultrastructure was also compared after 45&nbsp;days. Moreover, conditioned media from tendon proper-derived progenitors, peritenon-derived progenitors, or tenocytes was applied to each of the three cell types to determine paracrine stimulatory effects of the factors secreted from each of the respective cell types.ResultsThe cell orientation, extracellular domain and fibril organization of constructs were comparable to embryonic tendon. The tendon proper-derived progenitors produced a more tendon-like construct than the peritenon-derived progenitors. Seeded tendon proper-derived progenitors expressed greater levels of tenogenic markers and matrix assembly genes, relative to peritenon-derived progenitors. However, GDF5 supplementation improved expression of matrix assembly genes in peritenon progenitors and structurally led to increased mean fibril diameters. It also was found that peritenon-derived progenitors secrete factor(s) stimulatory to tenocytes and tendon proper progenitors.ConclusionsData demonstrate that, relative to peritenon-derived progenitors, tendon proper progenitors have greater potential for forming functional tendon-like tissue. Furthermore, factors secreted by peritenon-derived progenitors suggest a trophic role for this cell type as well. Thus, these findings highlight the synergistic potential of including these progenitor populations in restorative tendon engineering strategies

Measurement of interstage fluid-annulus dynamical properties

The work described in this paper is part of an Electric Power Research Institute sponsored effort to improve rotor vibrational performance on power plant feed water pumps. A major objective of this effort is to reduce vibration levels by devising inter-stage sealing configurations with optimized damping capacity, realizing that the typical multi-stage centrifugal pump has several ore inter-stage fluid annuli than it has journal bearings. Also, the fluid annuli are distributed between the journal bearings where vibration levels are highest and can therefore be 'exercised' more as dampers than can the bearings. Described in this paper is a test apparatus which has been built to experimentally determine fluid-annulus dynamical coefficients for various configurations of inter-stage sealing geometry