Generalizations of Tucker-Fan-Shashkin lemmas

Tucker and Ky Fan's lemma are combinatorial analogs of the Borsuk-Ulam theorem (BUT). In 1996, Yu. A. Shashkin proved a version of Fan's lemma, which is a combinatorial analog of the odd mapping theorem (OMT). We consider generalizations of these lemmas for BUT-manifolds, i.e. for manifolds that satisfy BUT. Proofs rely on a generalization of the OMT and on a lemma about the doubling of manifolds with boundaries that are BUT-manifolds.Comment: 10 pages, 2 figure

EXISTENCE OF UNIQUE LIMITING PROBABILITY VECTORS IN STOCHASTIC PROCESSES WITH MULTIPLE TRANSITION MATRICES

Concepts associated with stochastic process containing multiple transition matricies are discussed. It is proved that under certain conditions, a process with m transition matrices has m unique limiting probability vectors. This result extends the notion of discrete Markov processes to problems with intrayear and interyear dynamics. An example using a large DP model illustrates the usefulness of the concepts developed to applied problems.Research Methods/ Statistical Methods,

PAN AIR: A computer program for predicting subsonic or supersonic linear potential flows about arbitrary configurations using a higher order panel method. Volume 2: User's manual (version 3.0)

A comprehensive description of user problem definition for the PAN AIR (Panel Aerodynamics) system is given. PAN AIR solves the 3-D linear integral equations of subsonic and supersonic flow. Influence coefficient methods are used which employ source and doublet panels as boundary surfaces. Both analysis and design boundary conditions can be used. This User's Manual describes the information needed to use the PAN AIR system. The structure and organization of PAN AIR are described, including the job control and module execution control languages for execution of the program system. The engineering input data are described, including the mathematical and physical modeling requirements. Version 3.0 strictly applies only to PAN AIR version 3.0. The major revisions include: (1) inputs and guidelines for the new FDP module (which calculates streamlines and offbody points); (2) nine new class 1 and class 2 boundary conditions to cover commonly used modeling practices, in particular the vorticity matching Kutta condition; (3) use of the CRAY solid state Storage Device (SSD); and (4) incorporation of errata and typo's together with additional explanation and guidelines

Ecological genetics of an induced plant defense against herbivores: additive genetic variance and costs of phenotypic plasticity

Adaptive phenotypic plasticity in chemical defense is thought to play a major role in plant-herbivore interactions. We investigated genetic variation for inducibility of defensive traits in wild radish plants and asked if the evolution of induction is constrained by costs of phenotypic plasticity. In a greenhouse experiment using paternal half-sibling families, we show additive genetic variation for plasticity in glucosinolate concentration. Genetic variation for glucosinolates was not detected in undamaged plants, but was significant following herbivory by a specialist herbivore, Pieris rapae. On average, damaged plants had 55% higher concentrations of glucosinolates compared to controls. In addition, we found significant narrow-sense heritabilities for leaf size, trichome number, flowering phenology, and lifetime fruit production. In a second experiment, we found evidence of genetic variation in induced plant resistance to P. rapae. Although overall there was little evidence for genetic correlations between the defensive and life-history traits we measured, we show that more plastic families had lower fitness than less plastic families in the absence of herbivory (i.e., evidence for genetic costs of plasticity). Thus, there is genetic variation for induction of defense in wild radish, and the evolution of inducibility may be constrained by costs of plasticity

Barriers to Entry into the Specialty Red Meat Sector: The Role of Food Safety Regulation

Historically, the rules governing red meat food safety in the U.S. were driven as much by global trade and industry rationalization as by food safety. Contemporary and historical documents, statutes, and regulations; a survey of producer and farmers’ market representatives; and key informant interviews show that these rules, and their implementation, have affected the current development of niche marketing opportunities. Three significant issues arise from this research: a) the elimination of the state meat inspections limits producer access to slaughter; b) the Hazard Analysis and Critical Control Points (HACCP) rule limits producer access to processing; and c) uncertainty at the local level limits producer access to direct markets. We conclude that the accumulated rules affect producers’ quality of life; and they raise several issues about the relationship between sustainability and policy including barrier mitigation, balancing competing qualities, and the effects of the broader policy context

Growth and Characterization of Ce- Substituted Nd2Fe14B Single Crystals

Single crystals of (Nd1-xCex)2Fe14B are grown out of Fe-(Nd,Ce) flux. Chemical and structural analysis of the crystals indicates that (Nd1-xCex)2Fe14B forms a solid solution until at least x = 0.38 with a Vegard-like variation of the lattice constants with x. Refinements of single crystal neutron diffraction data indicate that Ce has a slight site preference (7:3) for the 4g rare earth site over the 4f site. Magnetization measurements show that for x = 0.38 the saturation magnetization at 400 K, a temperature important to applications, falls from 29.8 for the parent Nd2Fe14B to 27.6 (mu)B/f.u., the anisotropy field decreases from 5.5 T to 4.7 T, and the Curie temperature decreases from 586 to 543 K. First principles calculations carried out within density functional theory are used to explain the decrease in magnetic properties due to Ce substitution. Though the presence of the lower-cost and more abundant Ce slightly affects these important magnetic characteristics, this decrease is not large enough to affect a multitude of applications. Ce-substituted Nd2Fe14B is therefore a potential high-performance permanent magnet material with substantially reduced Nd content.Comment: 11 Pages, 8 figures, 5 table