Periodic solutions of semilinear partial differential equations of parabolic type

Summary In this paper we obtain necessary and sufficient conditions for the existence of solutions of a class of periodic-Dirichlet problems for parabolic- partial differential equations. The structure of the solution set and the asymptotic behaviour of the solution is also studied.Entrata in Redazione il 17 giugno 1983.     

Two applications of the natural map

Anstract Using a method which has been recently introduced by Besson, Courtois and Gallot we give new simple proofs of Ahlfors’ measure theorem and of Canary’s estimate of the Hausdorff-dimension of the limit set of a Kleinian group in terms of the volume of the convex-core.      

The introduction of logarithms into Spain

During the first half of the 17th century, logarithms were taught by some professors in Spain, but knowledge of this subject remained scanty until the publication of Architectura civil by Juan Caramuel (1678) and especially of Trigonometria española by José Zaragoza (1672). Logarithms were considered only as an aid for computation up to the second half of the 18th century. Only when the infinitesimal calculus became more widely spread in Spanish mathematics, analytical interpretations of logarithms were also taken into account in books such as Elementos de matemáticas by Benito Bails (1776).     

Sequencing games with repeated players

Two classes of one machine sequencing situations are considered in which each job corresponds to exactly one player but a player may have more than one job to be processed, so called RP(repeated player) sequencing situations. In max-RP sequencing situations it is assumed that each player’s cost function is linear with respect to the maximum completion time of his jobs, whereas in min-RP sequencing situations the cost functions are linear with respect to the minimum completion times. For both classes, following explicit procedures to go from the initial processing order to an optimal order for the coalition of all players, equal gain splitting rules are defined. It is shown that these rules lead to core elements of the associated RP sequencing games. Moreover, it is seen that min-RP sequencing games are convex. We thank two referees for their valuable suggestions for improvement. Financial support for P. Calleja has been given by the Ministerio de Educación y Ciencia and FEDER under grant SEJ2005-02443/ECON, and by the Generalitat de Catalunya through a BE grant from AGAUR and grant 2005SGR00984.     

A Highly Sensitive Kinetic Spectrophotometric System and Its Analytical Potential for Chromatographic Detection of Metal Ions

Micelles,microemulsions.vesicles,etc.,areorganicmicroheterogeneousmedia.Useofthesemediainanalyticalreactionsfordevelopingnewkinetic-baseddeterminationsorimprovingpreviouslyestablishedkineticmethodshasbeenreported"2.Inrecentyears,amixedmicellarmediumc...     

Fusel oil as precursor for aroma generation by biotransformation using lipase

The feasibility of using mixtures of C4 and C5 chain-length aliphatic alcohols from fusel oil as the bulk organic media for lipase-mediated synthesis of laurate esters was assessed. Reaction mixtures consisted of lauric acid, lipase, solvent (if added), and appropriate amount of fusel oil (previously dehydrated with inorganic salts and molecular sieves). The influence of the reaction conditions such as substrate concentrations and temperature were investigated. Increased molar ratio of acyl donor to acyl acceptor allowed the esterification to proceed with no need for solvent addition.     

Copper‐catalyzed Clauson–Kass pyrroles synthesis in aqueous media

An efficient and convenient copper‐catalyzed Clauson–Kass reaction of 2,5‐dimethoxytetrahydrofuran with amines in aqueous media has been developed, providing a wide range of N‐substituted pyrroles in good yields. It is noteworthy that the Clauson–Kass reaction of 2,5‐dimethoxytetrahydrofuran with p‐phenylenediamine or m‐phenylenediamine proceeds smoothly to afford the corresponding monopyrroles and bispyrroles with high selectivity in impressive yields. A plausible mechanism for the formation of N‐substituted pyrroles has been proposed. Copyright © 2012 John Wiley & Sons, Ltd.     

Resolution and uniqueness of estimated parameters of a model of thin filament regulation in solution

The estimation of chemical kinetic rate constants for any non-trivial model is complex due to the nonlinear effects of second order chemical reactions. We developed an algorithm to accomplish this goal based on the Damped Least Squares (DLS) inversion method and then tested the effectiveness of this method on the McKillop–Geeves (MG) model of thin filament regulation. The kinetics of MG model is defined by a set of nonlinear ordinary differential equations (ODEs) that predict the evolution of troponin–tropomyosin–actin and actin–myosin states. The values of the rate constants are estimated by integrating these ODEs numerically and fitting them to a series of stopped-flow pyrene fluorescence transients of myosin-S1 fragment binding to regulated actin in solution. The accuracy and robustness of the estimated rate constants are evaluated for DLS and two other methods, namely quasi-Newton (QN) and simulated annealing (SA). The comparison of these methods revealed that SA provides the best estimates of the model parameters because of its global optimization scheme. However it converges slowly and does quantify the uniqueness of the estimated parameters. On the other hand the QN method converges rapidly but only if the initial guess of the parameters is close to the optimum values, otherwise it diverges. Overall, the DLS method proves to be the most convenient method. It converges fast and was able to provide excellent estimates of kinetic parameters. Furthermore, DLS provides the model resolution matrix, which quantifies the interdependence of model parameters thereby evaluating the uniqueness of their estimated values. This property is essential for estimating of the dependence of the model parameters on experimental conditions (e.g. Ca²⁺ concentration) when it is assessed from noisy experimental data such as pyrene fluorescence from stopped-flow transients. The advantages of the DLS method observed in this study should be further examined in other physicochemical systems to firmly establish the observed effectiveness of DSL vs. the other parameter estimation methods.