The localization transition of the two-dimensional Lorentz model

We investigate the dynamics of a single tracer particle performing Brownian motion in a two-dimensional course of randomly distributed hard obstacles. At a certain critical obstacle density, the motion of the tracer becomes anomalous over many decades in time, which is rationalized in terms of an underlying percolation transition of the void space. In the vicinity of this critical density the dynamics follows the anomalous one up to a crossover time scale where the motion becomes either diffusive or localized. We analyze the scaling behavior of the time-dependent diffusion coefficient D(t) including corrections to scaling. Away from the critical density, D(t) exhibits universal hydrodynamic long-time tails both in the diffusive as well as in the localized phase.     

An elementary proof of Rayleigh's principle

Rayleigh's principle states that the smallest eigenvalue of a regular Sturm-Liouville problem with regular boundary conditions is the minimum value of a certain functional, the so-called Rayleigh quotient, and that this value is attained at the corresponding eigenfunctions only. This can be proved by advanced methods. However, there is an elementary proof, which is presented in this note.     

An exploration of mechanisms for the transformation of 8-oxoguanine to guanidinohydantoin and spiroiminodihydantoin by density functional theory

The potential energy surface for formation of 2-amino-5-hydroxy-7,9-dihydropurine-6,8-dione (5-OH-OG), guanidinohydantoin (Gh) and spiroiminodihydantoin (Sp) from 8-oxoguanine (8-oxoG) has been mapped out using B3LYP density functional theory, the aug-cc-pVTZ and 6-31+G(d,p) basis sets and the IEF-polarizable continuum model (PCM) solvation model. Three pathways for formation of 5-OH-OG from 8-oxoG were evaluated: (A) stepwise loss of two electrons and two protons to form the quinonoid intermediate 2-amino-7,9-dihydro-purine-6,8-dione (8-oxoG(ox)) followed by hydration; (B) stepwise loss of two electrons and one proton and net addition of hydroxide, in which the key step is nucleophilic addition to the 8-oxoG radical cation; and (C) stepwise loss of one electron and one proton and addition of hydroxyl radical to the 8-oxoG radical cation. The data suggest that all three pathways are energetically feasible mechanisms for the formation of 5-OH-OG, however, Pathway A may be kinetically favored over Pathway B. Although lower in energy, Pathway C may be of limited biological significance since it depends on the local concentration of hydroxyl radical. Pathways for hydrolysis and decarboxylation of 5-OH-OG to form Gh via either a carboxylic acid or substituted carbamic acid intermediate have been evaluated with the result that cleavage of the N1-C6 bond is clearly favored over that of the C5-C6 bond. Formation of Sp from 5-OH-OG via stepwise proton transfer and acyl migration or ring opening followed by proton transfer and ring closure have also been explored and suggest that deprotonation of the hydroxyl group facilitates a 1,2 acyl shift. Results of the calculations are consistent with experimental studies showing dependence of the Gh/Sp product ratio on pH. Under neutral and basic conditions, the data predict that formation of Sp is kinetically favored over the pathways for formation of Gh. Under acidic conditions, Gh is predicted to be the kinetically favored product.     

On the determination of the number of periodic (or closed) solutions of a scalar differential equation with convexity

It is well known that a scalar differential equation , where f(t,x) is continuous, T-periodic in t and weakly convex or concave in x has no, one or two T-periodic solutions or a connected band of T-periodic solutions. The last possibility can be excluded if f(t,x) is strictly convex or concave for some t in the period interval. In this paper we investigate how the actual number of T-periodic solutions for a given equation of this type in principle can be determined, if f(t,x) is also assumed to have a continuous derivative . It turns out that there are three cases. In each of these cases we indicate the monotonicity properties and the domain of values for the function P(ξ)=S(ξ)−ξ, where S(ξ) is the Poincaré successor function. From these informations the actual number of periodic solutions can be determined, since a zero of P(ξ) represents a periodic solution.     

The characterization of structure by computer

A comprehensive approach to a computer-based system of structure characterization must include capabilities in both spectrum interpretation and structure generation, and a link between the two that is transparent to the user. Program CASE is undergoing development with these requirements in mind. Structure generation is based on the new concept of structure reduction, which appears to offer advantages in efficiency of execution over procedures based on structure assembly. An experimental version of the program possesses some problem-solving ability.     

Structure generation by reduction: a new strategy for computer-assisted structure elucidation

A problem common to computer programs for structure elucidation is the efficient and prospective use of the input information to constrain the structure generation process. The input may consist of potentially overlapping substructure requirements and alternative substructure interpretations of spectral data. Other useful information may be structural features that must not be present in the output structures. All of these may interact in a complex manner that is impossible to determine by use of a bond-by-bond structure assembly algorithm. A new method is described called structure reduction. In contrast to structure assembly, this method begins with a set of all bonds and removes inconsistent bonds as structure generation progresses. This results in a more efficient use of the input information and the ability to use potentially overlapping required substructures. Several examples illustrate the application of our computer program COCOA, which uses this method to solve real-world structure elucidation problems.     

Harnsarcine

Ohne Zusammenfassung     

A Necessary and Sufficient Condition for a Linear Differential System to be Strongly Monotone

In order to present the results of this note, we begin withsome definitions. Consider a differential system [formula] where IR is an open interval, and f(t, x), (t, x)IxRⁿ, is acontinuous vector function with continuous first derivativesf_r/x_s, r, s=1, 2, ..., n. Let D_xf(t, x), (t, x)IxRⁿ, denote the Jacobi matrix of f(t,x), with respect to the variables x₁, ..., x_n. Let x(t, t₀,x₀), tI(t₀, x₀) denote the maximal solution of the system (1)through the point (t₀, x₀)IxRⁿ. For two vectors x, yRⁿ, we use the notations x>y and x>>yaccording to the following definitions: [formula] An nxn matrix A=(a_rs) is called reducible if n2 and there existsa partition [formula] (p1, q1, p+q=n) such that [formula] The matrix A is called irreducible if n=1, or if n2 and A isnot reducible. The system (1) is called strongly monotone if for any t₀I, x₁,x₂Rⁿ [formula] holds for all t>t₀ as long as both solutions x(t, t₀, x_i),i=1, 2, are defined. The system is called cooperative if forall (t, x)IxRⁿ the off-diagonal elements of the nxn matrix D_xf(t,x) are nonnegative. 1991 Mathematics Subject Classification34A30, 34C99.     

An approach to automated partial structure expansion

An algorithm (ASSEMBLE) to construct all structures consistent with the structural implications of the chemical and spectroscopic properties of an unknown molecule is described. The design of ASSEMBLE takes cognizance of the need to supply some nonoverlapping substructure information in addition to the molecular formula, and the use of structural constraints that cannot be directly expressed as non-overlapping fragments. ASSEMBLE employs several heuristics (rules) intended to avoid the assembly of identical (isomorphic) graphs. To provide a non-redundant list of structures, duplicate structures are recognized and removed by a naming algorithm. ASSEMBLE also perceives different π-resonance forms as identical structures even when they are topologically non-equivalent.