Positivity of rational functions and their diagonals

The problem to decide whether a given rational function in several variables is positive, in the sense that all its Taylor coefficients are positive, goes back to Szeg\H{o} as well as Askey and Gasper, who inspired more recent work. It is well known that the diagonal coefficients of rational functions are $D$-finite. This note is motivated by the observation that, for several of the rational functions whose positivity has received special attention, the diagonal terms in fact have arithmetic significance and arise from differential equations that have modular parametrization. In each of these cases, this allows us to conclude that the diagonal is positive. Further inspired by a result of Gillis, Reznick and Zeilberger, we investigate the relation between positivity of a rational function and the positivity of its diagonal.Comment: 16 page

The use of active controls to augment rotor/fuselage stability

The use of active blade pitch control to increase helicopter rotor/body damping is studied. Control is introduced through a conventional nonrotating swashplate. State variable feedback of rotor and body states is used. Feedback parameters include cyclic rotor flap and lead-lag states, and body pitch and roll rotations. The use of position, rate, and acceleration feedback is studied for the various state variables. In particular, the influence of the closed loop feedback gain and phase on system stability is investigated. For the rotor/body configuration analyzed, rotor cyclic inplane motion and body roll-rate and roll-acceleration feedback can considerably augment system damping levels and eliminate ground resonance instabilities. Scheduling of the feedback state, phase, and gain with rotor rotation speed can be used to maximize the damping augmentation. This increase in lead-lag damping can be accomplished without altering any of the system modal frequencies. Investigating various rotor design parameters (effective hinge offset, blade precone, blade flap stiffness) indicates that active control for augmenting rotor/body damping will be particularly powerful for hingeless and bearingless rotor hubs

Degradation of Fe-Mg silicates in hot CO2 atmospheres: Applications to Venus

Experiments demonstrated that oxidation of ferromagnesian silicates and magnetite occurs when these minerals are heated at 800 C in 1 atmosphere of CO2, under which conditions hematite is thermodynamically stable. The 30 ppm oxygen impurity in CO2 presumably facilitates the oxidation of some of the ferrous iron initially present in the crystal structures of the minerals. Mossbauer spectral measurements reveal, however, that only CO2 degraded olivine and pigeonite is hematite formed as a magnetically ordered phase at ambient temperatures. In orthopyroxene, some of the ferric iron produced by oxidation is present as nanophase hematite which, because it remains superparamagnetic until 4.2 K, must exist as particles less than or equal to 4 nm in diameter. In the calcic pyroxenes much of the oxidized ferrous iron may still remain as structural Fe3(+) in the host silicates. Some ferric iron may also be present as unit cell sized Fe2O3 inclusions in the pyroxenes, or be segregated along cleavage planes, or be coating mineral grains. In these states of aggregation, the Fe2O3 is unidentifiable by x ray diffraction and in low temperature Mossbauer spectra. Applications of this research to the surface of Venus are discussed

Mixed-valence iron minerals on Venus: Fe(2+)-Fe(3+) oxides and oxy-silicates formed by surface-atmosphere interactions

Inferences from these investigations are that Fe(3+)-bearing minerals such as hematite magnesioferrite, acmite, and epidote are thermodynamically unstable, and that magnetite is the predominant mixed-valence iron oxide mineral on venus. Recently, the Fe(2+)-Fe(3+) silicate mineral laihunite was proposed to be a reaction product of olivine with the venusian atmosphere. This possibility is discussed further here. We suggest that other mixed-valence Fe(2+)-Fe(3+)-Oz-OH(-) silicates could also result from surface-atmosphere interactions on Venus. Topics discussed include the following: (1) conversion of hematite to magnetite; (2) stability of laihunite; (3) the possible existence of oxy-amphiboles and oxy-micas on Venus; and (4) other mixed-valence Fe(2+)-Fe(3+) silicates likely to exist on Venus

Relationship of Sweet Corn Silking Stage to Oviposition by the Corn Earworm

It is commonly believed that corn earworm (CEW) do not oviposit (i.e., lay eggs) on sweet corn silks after they have dried. If true, insecticide treatments could logically cease at some predetermined time interval after pollination, because silks commence drying within hours of pollination. Problematic however, is that neither conventional wisdom, nor the historical literature, precisely defines the point at which silks are sufficiently dry to become unattractive for oviposition. We hypothesized that CEW cease to oviposit on silks that are 50% dried

The Critical Role of Historiography in Writing IS History

Insightful histories of an academic field can only be written when there is sufficient raw material to serve as “grist for the mill” for historians. This is the first task for those who are monumentally interested in preserving the origins of a field from the ravages of time is to collect artifacts—written, verbal, visual, and physical—that can later be used in historical inquiries. But the critical perspective to know what to collect and how much to collect is served by historiography, the science that elaborates on the variety of methods and procedures that historians use. A simple but incomplete set of these variations include: political history, intellectual history, cultural history, and social history. Each of these viewpoints brings with it a different set of assumptions about what is important and, although there is considerable overlap among them, each brings a different set of requirements for artifactual evidence. Historiography should not be overlooked when the field of information systems begins an all-out effort to collect data about the history of the field

Press Release Regarding Oregon Beach Initiative Measure

Press release from State Treasurer Robert W. Straub about the filing of the beach initiative measure by the Committee to Save the Oregon Beaches. The initiative measure would provide authorization for $30 million bond issue to raise the gasoline tax on passenger vehicles, whose funds would be used to purchase public beach land along the Oregon coast

News Release Regarding Oregon Dunes National Seashore Park

Press release while Straub was Lane County State Senator regarding his opinion of Oregon Dunes National Seashore Park and Governor Mark Hatfield\u27s stance