Some remarks on Levi complements and roots in Lie algebras with cone potential

We study Lie algebras with cone potential which play a prominent role in the Lie theory of semigroups. For these algebras, we obtain a uniqueness theorem for Levi complements and information on the fine structure of the root system.

Cone size and seed yield in young Piceamariana trees

Black spruce (Piceamariana (Mill.) B.S.P.) cones were collected in 1980, l981, and 1982 from young trees in four plantations of different ages. Nine measures of cone size, seed yield per cone, and seed weight were determined by cone analysis, and the variation among plantations and years was assessed by analysis of variance. Relationships among the nine measures were assessed by correlation. Cone length, cone weight, total scales per cone, potential filled seeds per cone, total seeds per cone, total filled seeds per cone, and seed efficiency were all depressed in 1981, the year of poorest cone production. Potential filled-seed yield and actual filled-seed yield were highly correlated with most cone-size measures but poorly correlated with each other. Pollen availability in 1982 was assessed by trapping and by counting pollen cones. The catch of pollen grains was positively correlated with the numbers of pollen cones per tree. Total filled seeds per cone in 1982 was strongly related to pollen availability. Seed efficiencies of less than 35%, which occurred in the younger plantations and in the year of poorest pollen-cone and seed-cone production (1981), indicated excessive loss of potential seed.

Shielding of moving test particles in warm, isotropic plasma

Shielding of test charges in warm, isotropic electron and electron–ion (Te ≫ Ti) plasmas is studied analytically and numerically. For a plasma with hot Maxwellian electrons and cold mobile ions, the potential due to a charge moving faster than the ion acoustic velocity has an ion acoustic Cerenkov cone. Ahead of the particle, the shielding is the usual electron Debye type with a modified longer shielding length. Potential wells with γ−1 dependence exists inside the cone. The potential falls off as along the cone surface. Outside the cone, the potential decays exponentially. A charge moving slower than the ion acoustic velocity also creates a cone, with potential decay as γ−3 outside the cone, potential wells decaying as γ−1 inside the cone, and potential wells falling off as along the cone surface. In both cases a radial logarithmic singularity exists along the trailing axis. Using a mono-energetic ion distribution, the singularity is removed and an ion thermal Cerenkov cone appears. For a monoenergetic electron plasma, assuming immobile ions, a test charge moving faster than the electron thermal velocity excites a thermal Cerenkov cone. Outside the cone, the far-field potential falls off in quadrupole form as γ−3. Inside the cone, potential wells decay as γ−1.