Single spike solutions for strings on S2 and S3

We study solutions for rigidly rotating strings on a two sphere. Among them we find two limiting cases that have a particular interest, one is the already known giant magnon and the other we call the single spike solution. The limiting behavior of this last solution is a string infinitely wrapped around the equator. It differs from that solution by the existence of a single spike of height theta that points toward the north pole. We study its properties and compute its energy E and angular momentum J as a function of theta. We further generalize the solution by adding one angular momentum to obtain a solution on S3. We find a spin chain interpretations of these results in terms of free fermions and the Hubbard model but the exact relation with the same models derived from the field theory is not clear.Comment: LaTeX, 20 pages, 3 figures. v2: Refs adde

Leech Parasitism of the Gulf Coast Box Turtle, Terrapene carolina major (Testudines:Emydidae) in Mississippi, USA

Ten leeches were collected from a Gulf Coast box turtle, Terrapene carolina major, found crossing a road in Gulfport, Harrison County, Mississippi, USA. Eight of the leeches were identified as Placobdella multilineata and 2 were identified as Helobdella europaea. This represents the second vouchered report of leeches from a box turtle. Helobdella europaea is reported for the first time associated with a turtle and for the second time from the New World

On the approach to equilibrium of an Hamiltonian chain of anharmonic oscillators

In this note we study the approach to equilibrium of a chain of anharmonic oscillators. We find indications that a sufficiently large system always relaxes to the usual equilibrium distribution. There is no sign of an ergodicity threshold. The time however to arrive to equilibrium diverges when $g \to 0$, $g$ being the anharmonicity.Comment: 8 pages, 5 figure

Hyperbolic outer billiards : a first example

We present the first example of a hyperbolic outer billiard. More precisely we construct a one parameter family of examples which in some sense correspond to the Bunimovich billiards.Comment: 11 pages, 8 figures, to appear in Nonlinearit

Relation of Root and Shoot Morphology of Grass Seedlings

Grass seedling establishment is dependent on adventitious root development. However, evaluating the establishment status of a seeding by excavating a population of seedlings and determining root morphology is difficult and generally will not be undertaken. Based on both field and greenhouse studies we have found that root and shoot morphological development is closely related within species, for intermediate wheatgrass, [Thinopyrum intermedium (Host) Barkw. and D.R. Dewey], smooth bromegrass (Bromus inermis Leyss.), switchgrass (Panicum virgatum L.), and big bluestem (Andropogon gerardii Vitman) seedling populations. Easily observable developmental stages of seedling shoots were related to adventitious root development. When the average stage of the population of shoots of these grasses reaches three to four collared leaves for intermediate wheatgrass and smooth bromegrass, first secondary tiller for switchgrass and the four to six collared leaf stage for big bluestem, there was an average of two to three adventitious roots which indicates the onset of seedling establishment

Switchgrass Seedling Development as Affected by Seed Size

Seed size has been associated with early seedling vigor (i.e., germination rate, emergence rate, and growth) in grasses. This study was conducted to compare seedling development over a 60-d period in the field as affected by heavy seed (HS) (0.19 to 0.21 g 100 seed-1) and light seed (LS) (0.13 to 0.16 g 100 seed-1) of \u27Blackwell\u27 and \u27Trailblazer\u27 switchgrass (Panicum virgatum L.). The experiment was conducted in 1995 and 1996 at Lincoln, NE, on a Kennebec silt loam (fine-silty, mixed, superactive, mesic Cumnlic Hapludolls). The experimental design was a randomized complete block with four replicates. Seed was separated into two sizes using a South Dakota seed blower. Seed was planted into rows at a rate of 100 pure live seed per meter of row. Plants were excavated and evaluated for shoot weight, leaf area, and root weight. Shoot and root systems were morphologically staged four times during the summer. Seed size differences in switchgrass appeared to produce only slight differences in morphological development of shoot and root systems, leaf area, shoot weight, and adventitious root weight from seedling emergence to 6 wk of growth. Adventitious roots formed more quickly on seedlings from heavier than lighter seed, but the advantage to seedling establishment was minimal even when soil moisture appeared to be lacking. By 8 to 10 wk after emergence, growth and development of LS seedlings were similar to HS seedlings. Once seedlings formed two or more adventitious roots, seed size no longer affected establishment and growth. Seed size in switchgrass appears to have a minimal long-term effect on growth and development of seedlings

Morphological Development of Switchgrass as Affected by Planting Date

Late-spring and early-summer plantings of warm-season grasses often fail, due to dry soil conditions and competition from annual grass and broadleaf weeds. The objective of this study was to compare the morphological development of switchgrass (Panicum virgatum L.) planted in early, mid, and late spring in eastern Nebraska. This study was conducted in 1994 and 1995 at Lincoln, NE, on a Kennebec silt loam (fine-silty, mixed, mesic Cumulic Hapludolls). \u27Blackwell\u27 and \u27Trailblazer\u27 switchgrass were planted in mid-March, late April, and late May using a single-row, precision grass-seed cone planter to a depth of 0.6 to 1.3 cm at 98 pure live seed per linear meter of row in a split-plot design. Twenty seedlings from each plot were excavated to a depth of 20 cm with a spade. Seedling morphological parameters measured were mean stage count root (MSCR) and shoot (MSCS), leaf area, shoot weight, and primary and adventitious root weight. Plots were sampled every 10 d following the first sample date. In 1994, seedlings from the March planting date were more advanced morphologically in MSCR and MSCS, had accumulated 2.5 times more leaf area, and about 3 times more shoot and adventitious root mass than the April planting date when sampled from late May to late June. In 1995, seedlings from the March planting date generally were more advanced morphologically in root and shoot development, had accumulated 2 to 12 times more leaf area, had 2 to 10 times more shoot mass, and had 2 to 33 times more adventitious root mass than the April or May planting dates at the sample periods from early June to mid-July. We suggest that switchgrass should be planted in early spring instead of in late April and May, as suggested by previous research

Enter Yossarian: How to Resolve the Procedural Catch-22 That the Private Securities Litigation Reform Act Creates

Section II of this Article sets forth our understanding of what the Reform Act requires a plaintiff to set forth in a complaint to state a valid claim that a corporation has made false or misleading public statements in violation of section 10(b) and Rule 10(b)(5). Section III describes our case study of GTF. Section IV analyzes the options a court would face in a case similar to the quasi-hypothetical we studied and suggests the option we believe a court should choose