Influence of self-quenching of the benzene triplet state on estimates of naphthalene T2→T1 internal conversion rates

Self-quenching of the benzene triplet state is shown to be important under the conditions employed by Ladwig and Liu to estimate the T₂ lifetime of naphthalene derivatives. The appropriate kinetic expressions, which reinforce the validity of their experimental approach, are presented and their data corrected for the self-quenching process. The corrected data indicate a slightly larger deuterium effect and somewhat shorter T₂ lifetimes than previously estimated.     

Lyapunov Functions for General Nonuniform Dichotomies

For nonautonomous linear equations x′ = A(t)x, we give a complete characterization of the existence of exponential behavior in terms of Lyapunov functions. In particular, we obtain an inverse theorem giving explicitly Lyapunov functions for each exponential dichotomy. The main novelty of our work is that we consider a very general type of nonuniform exponential dichotomy. This includes for example uniform exponential dichotomies, nonuniform exponential dichotomies and polynomial dichotomies. We also consider the case of different growth rates for the uniform and the nonuniform parts of the dichotomy. As an application of our work, we establish in a very direct manner the robustness of nonuniform exponential dichotomies under sufficiently small linear perturbations.     

Frequencies of digits under trigonometric perturbations

We study the Hausdorff dimension of a class of sets of real numbers defined in terms of frequencies of digits in some integer base m, with the frequencies related by trigonometric perturbations. We show in particular that the Hausdorff dimension is analytic in the parameter determining the perturbation, and we obtain estimates for the coefficients of the corresponding power series in terms of m. We also compute the first terms of the series.     

Time and work generalised precedence relationships in project scheduling with pre-emption: An application to the management of Service Centres

In this paper we present an application of project scheduling concepts and solution procedures for the solution of a complex problem that comes up in the daily management of many company Service Centres. The real problem has been modelled as a multi-mode resource-constrained project scheduling problem with pre-emption, time and work generalised precedence relationships with minimal and maximal time lags between the tasks and due dates. We present a complete study of work GPRs which includes proper definitions, a new notation and all possible conversions amongst them. Computational results that show the efficiency of the proposed hybrid genetic algorithm and the advantages of allowing pre-emption are also presented.     

Analytic invariant manifolds for sequences of diffeomorphisms

We obtain real analytic invariant manifolds for trajectories of maps assuming only the existence of a nonuniform exponential behavior. We also consider the more general case of sequences of maps, which corresponds to a nonautonomous dynamics with discrete time. We emphasize that the maps that we consider are defined in a real Euclidean space, and thus, one is not able to obtain the invariant manifolds from a corresponding procedure to that in the nonuniform hyperbolicity theory in the context of holomorphic dynamics. We establish the existence both of stable (and unstable) manifolds and of center manifolds. As a byproduct of our approach we obtain an exponential control not only for the trajectories on the invariant manifolds, but also for all their derivatives.     

Characterizing efficiency without linear structure: a unified approach

In this paper, we study a general optimization problem without linear structure under a reflexive and transitive relation on a nonempty set E, and characterize the existence of efficient points and the domination property for a subset of E through a generalization of the order-completeness condition introduced earlier. Afterwards, we study the abstract optimization problem by using generalized continuity concepts and establish various existence results. As an application, we extend and improve several existence results given in the literature for an optimization problem involving set-valued maps under vector and set criteria. The work of the first author was partially supported by CONICYT-Chile through FONDECYT 107-0689 and FONDAP-Matemáticas Aplicadas II; whereas that of the second and third author were supported in part by Ministerio de Educación y Ciencia (Spain), project MTM2006-02629 and by Junta de Castilla y León (Spain) Project VA027B06.     

Neutron diffraction data and molecular dynamics simulations of the molten mixture Ag(Br0.7I0.3)

The structure factors of the ionic liquid mixture Ag(Br(0.7)I(0.3)) at three temperatures, 723, 923, and 1023 K, as well as of the pure molten AgI at 923 K and the pure molten AgBr at 773 and 923 K, were studied experimentally and by means of molecular dynamics simulations. The experiments were carried out using the high intensity total scattering time-of-flight spectrometer, HIT-II, at the KENS spallation neutron source in Japan. The experimental data are very reliable, with the possible exception of the small momentum transfer region, whose accessibility is limited by neutron energy and detector positions. The simulations made use of the semiempirical rigid ion potentials of the Vashishta-Rahman [Phys. Rev. Lett. 40, 1337 (1978)] type using a new set of parameters appropriate for the mixture. Within the known constraints of the pairwise rigid ion potentials, the simulated structure factors are in fair agreement with experiment. The results for the pair distribution functions suggest that the molten mixture retains the superionic character found in previous calculations of both the AgI and AgBr melts. This suggestion is confirmed by the results for the self-diffusion coefficients. Values obtained for the ionic conductivities are also presented.     

Determination of the biogenic amines in musts and wines before and after malolactic fermentation using 6-aminoquinolyl-N-hydroxysuccinimidyl carbamate as the derivatizing agent

An accurate, rapid and sensitive high-performance liquid chromatographic (HPLC) method is reported for the determination of four biogenic amines in red and white wine samples. The method involves derivatization with 6-aminoquinolyl-N-hydroxysuccinimidyl carbamate (AQC) followed by liquid chromatography gradient elution analysis without any other sample pretreatment. The procedure developed permitted the determination of the four amines in 40 min. The relative standard deviation (RSD) values ranged from 3.1% to 6.1% in peak areas and the response was linear (R2>0.994) in a range from 0.1 to 4 mg/l. Leaving aside putrescine in Tempranillo wines, the malolactic fermentation did not exert any effect on the concentration of these compounds. On the contrary, the influence of the grape variety was important, and Tempranillo wines showed higher levels of tyramine and histamine and lesser of putrescine and cadaverine (p<0.05) than wines made with Cabernet Sauvignon.     

The "triamino-analogue" of methyl allocholate; a rigid, functionalised scaffold for supramolecular chemistry

Cholic acid has been converted into triamine with the all-trans polycyclic allocholanoyl skeleton and co-directed, axial amino groups; the potential of this system as a scaffold is illustrated by conversion to a preorganised anion receptor.