A descent hybrid conjugate gradient method based on the memoryless BFGS update

In this work, we present a new hybrid conjugate gradient method based on the approach of the convex hybridization of the conjugate gradient update parameters of DY and HS+, adapting a quasi-Newton philosophy. The computation of the hybrization parameter is obtained by minimizing the distance between the hybrid conjugate gradient direction and the self-scaling memoryless BFGS direction. Furthermore, a significant property of our proposed method is that it ensures sufficient descent independent of the accuracy of the line search. The global convergence of the proposed method is established provided that the line search satisfies the Wolfe conditions. Our numerical experiments on a set of unconstrained optimization test problems from the CUTEr collection indicate that our proposed method is preferable and in general superior to classic conjugate gradient methods in terms of efficiency and robustness.     

A homogenization approach to flashing ratchets

The paper continues the program of the authors to develop a mathematical framework to understand and characterize the notion of “asymmetric” potentials, which has been introduced to explain how molecular motors work, considering flashing ratchets, i.e., molecules diffusing in a potential with periodic switches. The mathematical model is a Fokker–Planck equation with a space–time periodic potential and diffusion of order of magnitude compatible with the period of the potential. After performing a homogenization analysis of the problem the “asymmetric” potentials are characterized by the property that the solution, which models the molecule density, concentrates on one end of the domain. Finally explicit examples are presented exhibiting that the concentration phenomena (motor effect) takes place are presented. The proof uses techniques from the theory of viscosity solutions for the Hamilton–Jacobi equation which, in the homogenization limit, defines the effective hamiltonian.     

Stabilizing an uncertain production system

Consider a production system that consists ofm machines each of which can produce parts ofn types. When machinek is used, it produces a part of typei with probabilityp _ki . Requests arrive for parts, one at a time. With probability _i an arriving request is for a part of typei. The requests must be served without waiting. Thus, if a requested part is not available, it must be produced. We find necessary and sufficient conditions for the existence of a strategy (a choice of the machines to be used) which makes the inventory of parts stable and we provide such a strategy.Two variations of this model are also considered: the case of batch arrivals of requests, and that of a system where the requests can be queued.     

Two-generator subgroups of soluble groups and their Fitting subgroups

For soluble groups, the Fitting length is bounded by a function of the maximum order of the Fitting subgroups of 2-generator subgroups.     

Modelling of discontinuities through dipole distribution

An indirect boundary element method using dipole distribution is employed in order to model discontinuities inside the flow region. The problem of flow under a dam is treated with a sheet-pile in its foundation. The discontinuity across the sheet-pile is demonstrated, a general boundary element procedure for a mixed problem is outlined and the coefficients of the linear system are given in analytical form. Very good agreement with existing analytical results is obtained.     

Cloning and Characterization of a Biotic-Stress-Inducible Glutathione Transferase from Phaseolus vulgaris

Glutathione transferases (GSTs, EC 2.5.1.18) are ubiquitous proteins in plants that play important roles in stress tolerance and in the detoxification of toxic chemicals and metabolites. In this study, we systematically examined the catalytic diversification of a GST isoenzyme from Phaseolus vulgaris (PvGST) which is induced under biotic stress treatment (Uromyces appendiculatus infection). The full-length cDNA of this GST isoenzyme (termed PvGSTU3-3) with complete open reading frame, was isolated using RACE-RT and showed that the deduced amino acid sequence shares high homology with the tau class plant GSTs. PvGSTU3-3 catalyzes several different reactions and exhibits wide substrate specificity. Of particular importance is the finding that the enzyme shows high antioxidant catalytic function and acts as hydroperoxidase, thioltransferase, and dehydroascorbate reductase. In addition, its K _m for GSH is about five to ten times lower compared to other plant GSTs, suggesting that PvGSTU3-3 is able to perform efficient catalysis under conditions where the concentration of reduced glutathione is low (e.g., oxidative stress). Its ability to conjugate GSH with isothiocyanates may provide an additional role for this enzyme to act as a regulator of the released isothiocyanates from glucosinolates as a response of biotic stress. Molecular modeling showed that PvGSTU3-3 shares the same overall fold and structural organization with other plant cytosolic GSTs, with major differences at their hydrophobic binding sites (H-sites) and some differences at the level of C-terminal domain and the linker between the C- and N-terminal domains. PvGSTU3-3, in general, exhibits restricted ability to bind xenobiotics in a nonsubstrate manner, suggesting that the biological role of PvGSTU3-3, is restricted mainly to the catalytic function. Our findings highlight the functional and catalytic diversity of plant GSTs and demonstrate their pivotal role for addressing biotic stresses in Phaseolus vulgaris.     

The renormalization constants of QED in unitary approximation

A unitary approximation for the time-evolution operator given through the exponential representation is used to calculate the renormalization constants of QED. The results obtained by this method are the same as the renormalization group improvement of the usual perturbation series taking into account terms up to the second order ine.     

Which, if any, hydrates will crystallise? Predicting hydrate formation of two dihydroxybenzoic acids

A study of two dihydroxybenzoic acid isomers shows that computational methods can be used to predict hydrate formation, the compound:water ratio and hydrate crystal structures. The calculations also help identify a novel hydrate found in the solid form screening that validates this study.     

Use of Time-Resolved Fluorescence Analysis to Assess Molecular Mobility and Ionic Conductivity in Nanocomposite Organic-Inorganic Gels

This work is a short review of studies on nanocomposite organic-inorganic gels by stretched-exponential analysis of fluorescence decay profiles. Emphasis is given to the conditions which allow maximum probe mobility and minimum confinement conditions with the aim to assess ionic conductivity in these materials and with the purpose to employ them with dye-sensitized photoelectrochemical solar cells and other analogous systems.