Organisms with external fertilization are often sperm limited, and in echinoids, larger eggs have a higher probability of fertilization than smaller eggs. This difference is thought to be a result of the more frequent sperm-egg collisions experienced by larger targets. Here we report how two components of egg target size, the egg cell and jelly coat, contributed to fertilization success in a se...

A graph G = (V,E) is a threshold tolerance graph if each vertex v ∈ V can be assigned a weight wv and a tolerance tv such that two vertices x, y ∈ V are adjacent if wx +wy ≥ min(tx, ty). Currently, the most efficient recognition algorithm for threshold tolerance graphs is the algorithm of Monma, Reed, and Trotter which has an O(n) runtime. We give an O(n) algorithm for recognizing threshold tol...

The land snail species Drymaeus virgulatus (Férussac, 1821) is recorded in St. Kitts the form of 21 complete or fragmented shells collected on island November 2019. were backshores South Frigate Bay and Majors Bay, while shell fragments come from naturally exposed sections North sand ridge, where they date to pre-Columbian period. This evidence therefore attests past presence this island. absen...

Complex life cycles have evolved independently numerous times in marine animals as well as in disparate algae. Such life histories typically involve a dispersive immature stage followed by settlement and metamorphosis to an adult stage on the sea floor. One commonality among animals exhibiting transitions of this type is that their larvae pass through a 'precompetent' period in which they do no...

Let E/Q be an elliptic curve defined by the equation y 2 = x 3 + ax + b. For a prime p, p ∤ ∆ = −16(4a 3 + 27b 2) = 0, define N p = p + 1 − a p = |E(F p)|. As a precursor to their celebrated conjecture, Birch and Swinnerton-Dyer originally conjectured that for some constant c, p≤x,p∤∆ N p p ∼ c(log x) r , x → ∞. Let α p and β p be the eigenvalues of the Frobenius at p. Define ˜ c n =    α k ...

In the literature of graph recognition algorithms, two of the most extensively covered graphs are interval graphs and permutation graphs [6, 2]. One way of generalizing both interval graphs and permutation graphs is the intersection graph of a collection of trapezoids with corner points lying on two parallel lines. Such a graph is called the trapezoid graph [3, 4]; Ma and Spinrad [8] show that ...

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