On the Local and Superlinear Convergence of Quasi-Newton Methods

This paper presents a local convergence analysis for severalwell-known quasi-Newton methods when used, without line searches,in an iteration of the form to solve for x^* such that Fx^* = 0. The basic idea behind theproofs is that under certain reasonable conditions on x_o, Fand x_o, the errors in the sequence of approximations {H_k} toF'(x^*)^–1 can be shown to be of bounded deterioration inthat these errors, while not ensured to decrease, can increaseonly in a controlled way. Despite the fact that H_k is not shownto approach F'(x^*)^–1, the methods considered, includingthose based on the single-rank Broyden and double-rank Davidon-Fletcher-Powellformulae, generate locally Q-superlinearly convergent sequences{x_k}.     

PHOTOACTIVATION OF UROCANASE IN PSEUDOMONAS PUTIDA: POSSIBLE CONFORMATIONAL CHANGE DURING ACTIVATION

Earlier studies of urocanase indicated that it is converted to an inactive form in resting cells of Pseudomonas putida . When cell extracts are irradiated by ultraviolet (u.v.) light, the enzyme is activated[1]. The chromophore is closely associated with the enzyme [ 1 ,2]. The action spectrum for photoactivation showed that, although near-u.v. light was effective, the most efficient wavelengths were at 275–280 nm[3]. The study we present here suggests that urocanase undergoes a conformational change upon photoactivation.     

Further Accurate Representations of Partial Differential Equations by Finite-difference Methods

A fourth-order finite-difference scheme recently introducedfor the solution of second-order partial differential equationsis developed. The resulting scheme retains all the advantagesof the original, but is more satisfactory in that the simultaneousalgebraic equations to be solved are more amenable to solutionby numerical techniques in many cases. Some numerical solutionsof the Navier-Stokes equations are considered.     

Accurate Representations of Partial Differential Equations by Finite-difference Schemes

A Specialized method introduced some years ago for obtainingfinite-difference approximations to both ordinary and partialdifferential equations is developed to give representationsof higher accuracy. A numerical example is considered whichis based on a model solution of the two-dimensional Navier-Stokesequations for the flow of an incompressible fluid.     

KAPPA FUNCTION AS A UNIFYING FRAMEWORK FOR DISCRETE POPULATION MODELING

This paper develops a unified way to describe the various generalized discrete‐time nonlinear dynamical models with density dependence, Allee effects, and parasitoids. We show how the kappa function can be used to describe the probabilities involved in intra‐ or interspecific encounters, namely, (i) the probability of surviving to the next generation in the absence of parasitoids or Allee effects, (ii) the encounter probability associated with Allee effects, and (iii) the probability of escaping parasitism in the presence of parasitoids. Having introduced a phenomenological framework of modeling via the kappa function, we then provide a realistic mechanism through stochastic encounters, responsible for generating the kappa function to any of the three involved probabilities. The unified modeling through the kappa function yields insights into how abundances influence species interactions. It is now straightforward to use this unified modeling to analyze and investigate its consequences in species dynamics.     

A computational study of the electron detachment energies of Al2As2 − and Al3As3 −

Ab initio and density functional theory calculations are reported for the low-lying electronic states of Al₂As₂ ^?, Al₂As₂, Al₃As₃ ^?, and Al₃As₃. The ²B_2g ground electronic state of Al₂As₂ ^? has a rhombic structure with the Al atoms occupying the shorter diagonal. In contrast, the As atoms occupy the shorter diagonal of the ground state rhombic structure of Al₂As₂. Electron detachment energies computed for Al₂As₂ ^? are presented and discussed. The adiabatic electron affinity of Al₂As₂ ^? is calculated to be 2.1 eV at the CCSD(T) level, using B3LYP and MP2 optimized geometries. The ground states of both Al₃As₃ ^? (²A₁′) and Al₃As₃ (¹A₁′) have planar hexagonal D_3h geometry. Electron detachment energies computed for the anion are reported. At the CCSD(T)//B3LYP level, the electron affinity of Al₃As₃ is calculated to be 2.47 eV.     

An Asymptotic Matching Condition for Unsteady Boundary-Layer Flows Governed by the Navier-Stokes Equations

It is shown that one condition only, derived from one of Green'sidentities, is necessary to determine the matching of innerand outer expansions in solving problems involving the initialflows of a viscous fluid. This condition has been named an integralcondition, and when it has been satisfied, in the form of aset of conditions for the spectral components, the inner solutionis obtained by a straightforward integration procedure and theouter solution is obtained merely by substituting the innersolution in an integral. Two examples of the method are considered,including that of flow past a suddenly started circular cylinderand flow due to a suddenly started rotating sphere.     

The Solution of Two-Dimensional Oseen Flow Problems Using Integral Conditions

A general method of solving Oseen's linearized equations fortwo-dimensional steady flow of a viscous incompressible fluidpast a cylinder in an unbounded field is developed. The analysisis developed in terms of the scalar vorticity and stream functionand it is shown that the vorticity for Oseen flow problems canbe obtained separately from the stream function. The determinationof the vorticity can be effected using conditions of an integralcharacter deduced from the no-slip condition at the cylindersurface together with the conditions at large distances. Theindependent determination of the vorticity seems to be a newstep in Oseen theory. The method enables one to obtain manyproperties of the flow in terms ofthe Reynolds number by usingonly the vorticity without the necessity of finding the streamfunction. The use of integral conditions makes the detailedcalculations straightforward, systematic, and elementary. Themethod is tested by applying it to the case of uniform flowpast an elliptic cylinder at an arbitrary angle of incidenceand also to cases of symmetrical and asymmetrical flows pastcircular cylinders. The leading approximation for small Reynoldsnumber is obtained where possible. In the case of flow pasta rotating cylinder, the only possible solution is the Oseensolution for the nonrotating case with the addition of a potentialvortex.     

ELECTROSTATIC EFFECTS IN THE PHOTOREDUCTION OF FLAVINS BY EDTA

The anaerobic photoreduction of riboflavin, flavin mononucleotide, N(3)-carboxymethylriboflavin, N(3)-methyl-lumiflavin, and lumiflavin by EDTA was studied in aqueous solution over the pH range 2.5–10. The electrostatic effects of the electron donor-acceptor pair produce a secondary effect on the reactivity, and this effect can be predicted from the product of the charges (Z_D x Z_A). The trianonic and tetraanonic species of EDTA have nitrogens which are free from intramolecular hydrogen bonding, and these species are potentially the most reactive. However, in some pH regions the electrostatic effect can become the dominant factor when both the electron donor and acceptor become negatively charged. The excited states of flavins are susceptible to charge effects whether the charge is localized on the side chain or involves the isoalloxazine ring system.