From the DNA sequences for N taxa, the (generally unknown) phylogenetic tree T that gave rise to them is to be reconstructed. Various methods give rise, for each quartet J consisting of exactly four taxa, to a predicted tree L(J) based only on the sequences in J, and these are then used to reconstruct T. The author defines an "error-correcting map" (Ec), which replaces each L(J) with a new tree...

In this paper we investigate the existence and regularity of the solutions to the complex Ginzburg-Landau equation, @ t u = Au + (a + ii))u ? (b + ii)juj 2 u, on the phase space L r;p (R n) of weighted L p functions in innnite domain R n of arbitrary spatial dimensions. The unique local strong solutions are established for subcritical , i.e., r > n p ? 1. Especially, the classical Lebesgue phas...

which arises in many different areas of applied mathematics and physics. Singular problems of this type that the nonlinearity g may change sign are referred to as singular semipositone problems in the literature. Motivated by BVP (1.1), this paper presents the existence results of the following second-order singular semipositone boundary value problem: { u ′′ + f(t, u) + g(t, u) = 0, 0 < t < 1,...

The dynamic solution behavior during formation of the 2'-deoxyguanosine tetrad (G-quartet) upon addition of alkali metal cations and destruction of the G-quartet upon addition of the guanine-guanine mismatch recognition molecule naphthyridine dimer was observed by cold-spray ionization mass spectrometry.

For a class of two-point boundary value problems we prove exact-ness of an S-shaped bifurcation curve. Our result applies to a problem from combustion theory, which involves nonlinearities like e au=(u+a) for a > 0. 1. Introduction We consider positive solutions of u 00 + f(u) = 0 on (?1; 1); u(?1) = u(1) = 0: (1.1) Here is a positive parameter, and we wish to describe all solutions of (1.1) fo...

The theory of anti-selfdual (ASD) Lagrangians developed in [4] allows a variational resolution for equations of the form Λu+Au+f ∈ −∂φ(u) where φ is a convex lower-semi-continuous function on a reflexive Banach space X , f ∈ X, A : D(A) ⊂ X → X is a skew-adjoint linear operator and where Λ : D(Λ) ⊂ X → X is a non-linear operator that satisfies suitable continuity properties. ASD Lagrangians on ...

Within the framework of the GGA+U implementation of density functional theory, we investigate atomistic and electronic structures of Au adsorbed on the stoichiometric and the defective CeO(2){111} surfaces, in the latter of which either O or Ce vacancies are presented. We show that on the stoichiometric surface, the most stable adsorption site of Au is not on the top of the outermost O atoms, a...

Let and A be the generator of an -times resolvent family 1 α < < 2 α ( ) { } 0 t S t α ≥ on a Banach space X. It is shown that the fractional Cauchy problem , ( ) ( ) ( ) t u t Au t f t α = + D ( ] 0, t r ∈ ; has maximal regularity on ( ) ( 0 , u u′ ) ( ) 0 D A ∈ [ ] ( 0, ; C r ) X if and only if is of bounded semivariation on ( ) ⋅ Sα [ ] 0, r .

Let (M,g(t)), 0 ≤ t ≤ T , be a n-dimensional complete noncompact manifold, n ≥ 2, with bounded curvatures and metric g(t) evolving by the Ricci flow ∂gij ∂t = −2Rij . We will extend the result of L. Ma and Y. Yang and prove a local gradient estimate for positive solutions of the nonlinear parabolic equation ∂u ∂t = ∆u − au log u − qu where a ∈ R is a constant and q is a smooth function on M × [...