Molecular self-assembly is central to many processes in both biology and supramolecular chemistry. The G-quartet, a hydrogen-bonded macrocycle formed by cation-templated assembly of guanosine, was first identified in 1962 as the basis for the aggregation of 5'-guanosine monophosphate. We now know that many nucleosides, oligonucleotides, and synthetic derivatives form a rich array of functional ...

Given a set of n taxa S, exactly one topology for every subset of four taxa, and a positive integer k as the parameter, the parameterized Minimum Quartet Inconsistency (MQI) problem is to decide whether we can find an evolutionary tree inducing a set of quartet topologies that differs from the given set in at most k quartet topologies. The best fixed-parameter algorithm devised so far for the p...

We study ε2ü = f(u, x) = Au (1−u) (φ−u), where A = A(u, x) > 0, φ = φ(x) ∈ (0, 1), and ε > 0 is sufficiently small, on an interval [0, L] with boundary conditions u̇ = 0 at x = 0, L. All solutions with an ε independent number of oscillations are analyzed. Existence of complicated patterns of layers and spikes is proved, and their Morse index is determined. It is observed that the results extend ...

Based on a strict coercivity estimate [8] for a class of nonlinear elliptic operators A : u 7→ ∇·a(·, |∇u|)∇u, it is shown that (with suitable consistency conditions on the data) the problem: u̇+ Au = f, a∇u · ~n = φ, time periodicity has a unique solution depending continuously on f, φ and also on the nonlinear form of the diffusion coefficient a(··). This is then used to obtain existence by a ...

The logic we are going to employ to survey the similarity structure of several kinds of PDEs is the following. The preliminary requirement is that the problem under consideration should be well-posed, or the uniqueness should be guaranteed at least. Let u(x, t) be a solution to such a problem and consider a rescaled function v given by u(x, t) = av(bx, ct), a, b, c > 0. (1.1) The main step is t...

Not long ago, I e-mailed Donald McNeil, Jr. I wanted to know how many HIV/AIDS articles the New York Times reporter had written over the years. “Fiddling with the Times’ website and internal library . . . produces 201 to 495,” McNeil replied. “I think it’s safe to say I’ve written 400 stories about AIDS.” At the end of this piece I’ll share McNeil’s favorite, but for now I’ll state the obvious....

Let A be a simple ring which is not a 4-dimensional algebra over a field of characteristic 2, and let U be a Lie ideal of A. Then Herstein proves in [2] that either U is contained in the center Z of A, or U contains [A, A]; if in addition £/is also assumed to be an associative ring and contains [A, A], then U = A. Herstein and Baxter also prove in [l; 3], and [4] that [A, A] mod [A, A ]C\Z is a...

u’(t)+Au(t)= ‘a(t,s)g(s,u(s))ds+f(t,U(t)), I 120, 0 u(0) = 0. The operator A is the negative infinitesimal generator of an analytic semigroup in a Banach space X. The operator g(t, u) is related to A by a special form g(t, a) = A”*q(t, u), where q(t, u) is an appropriate “lower order” operator. We show the existence and uniqueness of weak solutions and their continuability to infinity under sui...