General variable neighborhood search for the continuous optimization

We suggest a new heuristic for solving unconstrained continuous optimization problems. It is based on a generalized version of the variable neighborhood search metaheuristic. Different neighborhoods and distributions, induced from different metrics are ranked and used to get random points in the shaking step. We also propose VNS for solving constrained optimization problems. The constraints are handled using exterior point penalty functions within an algorithm that combines sequential and exact penalty transformations. The extensive computer analysis that includes the comparison with genetic algorithm and some other approaches on standard test functions are given. With our approach we obtain encouraging results.     

Assay of free captopril in human plasma as monobromobimane derivative,using RPLC/(+)ESI/MS/MS: validation aspects and bioequivalence evaluation

A sensitive method for determination of free captopril as monobromobimane derivative in plasma samples is discussed. The internal standard (IS) was 5‐methoxy‐1H‐benzimidazole‐2‐thiol. Derivatization with monobromobimane immediately after blood collection and plasma preparation prevents oxidation of captopril to the corresponding disulfide compound and enhances the ionization yield. Consequently, derivatization enhances sample stability and detection sensitivity. Addition of the internal standard was made immediately after plasma preparation. The internal standard was also derivatized by monobromobimane, as it contains a thiol functional group. Preparation of plasma samples containing captopril and IS derivatives was based upon protein precipitation through addition of acetonitrile, in a volumetric ratio 1:2. The reversed‐phase liquid chromatographic separation was achieved on a rapid resolution cartridge Zorbax SB‐C₁₈, monitored through positive electrospray ionization and tandem MS detection using the multiple‐reaction monitoring mode. Transitions were 408–362 amu for the captopril derivative and 371–260 amu for the internal standard derivative. The kinetics of captopril oxidation to the corresponding disulfide compound in plasma matrix was also studied using the proposed method. A linear log–log calibration was obtained over the concentration interval 2.5–750 ng/mL. A low limit of quantitation in the 2.5 ng/mL range was obtained. The analytical method was fully validated and successfully applied in a three‐way, three‐period, single‐dose (50 mg), block‐randomized bioequivalence study for two pharmaceutical formulations (captopril LPH 25 and 50 mg) against the comparator Capoten 50 mg. Copyright © 2009 John Wiley & Sons, Ltd.     

Rheology of interfacial layers

The response of interfacial layers to deformations in size and shape depends on their composition. The corresponding main mechanical quantities are elasticity and viscosity of dilation and shear, respectively. Hence, the interfacial rheology represents a kind of two-dimensional equivalent to the traditional bulk rheology. Due to growing interest in the quantitative understanding of foams and emulsions, more works are dedicated to studies on interfacial rheology. This overview presents the theoretical basis for traditional and recently developed experimental tools and discusses their application to different interfacial systems. While dilational rheology provides information on the composition of mixed interfacial layers, the shear rheology gives answers essentially on structures formed at an interface. The most frequently used methods at present are the oscillating drop and bubble tensiometry methods for dilational deformations and oscillating ring/bicone rheometers for shear deformations.     

Minimum general sum-connectivity index of unicyclic graphs

The general sum-connectivity index of a graph G is defined as χ _α (G) = ∑_edges (d _u + d _v ) ^α , where d _u denotes the degree of vertex u in G and α is a real number. In this report, we determine the minimum and the second minimum values of the general sum-connectivity indices of n-vertex unicyclic graphs for non-zero α ≥ −1, and characterize the corresponding extremal graphs.     

A recipe for finding good solutions to MINLPs

Finding good (or even just feasible) solutions for Mixed-Integer Nonlinear Programming problems independently of the specific problem structure is a very hard but practically important task, especially when the objective and/or the constraints are nonconvex. With this goal in mind, we present a general-purpose heuristic based on Variable Neighborhood Search, Local Branching, a local Nonlinear Programming algorithm and Branch-and-Bound. We test the proposed approach on MINLPLib, comparing with several existing heuristic and exact methods. An implementation of the proposed heuristic is freely available and can employ all NLP/MINLP solvers with an AMPL interface as the main search tools.     

Nonequilibrium phase transition in a periodically driven XY spin chain

We present a general formulation of Floquet states of periodically time-dependent open Markovian quasifree fermionic many-body systems in terms of a discrete Lyapunov equation. Illustrating the technique, we analyze periodically kicked XY spin-? chain which is coupled to a pair of Lindblad reservoirs at its ends. A complex phase diagram is reported with reentrant phases of long range and exponentially decaying spin-spin correlations as some of the system's parameters are varied. The structure of phase diagram is reproduced in terms of counting nontrivial stationary points of Floquet quasiparticle dispersion relation.     

Effect of partial fluorination on the Lewis sites of microcrystalline γ-alumina studied by adsorption of pyridine as a probe molecule: A quantum chemical cluster model study

The influence of fluorination of microcrystalline γ-alumina on the acidity of Lewis sites was studied by quantum chemical cluster model approach. B3LYP and HF/6-31++G(d,p) levels of theory were employed, considering the standard and counterpoise-corrected potential energy surfaces (PESs). Explicit inclusion of dynamical electron correlation effects along with the elimination of the basis set superposition effects in geometry optimization and harmonic vibrational analysis were found to be crucial to reproduce the experimental trends in the shifts of the pyridine ν_19b and ν_8a modes upon fluorination. The acidity of surface-exposed Al-sites was found to increase upon fluorination, which is manifested as a ~ 10% increase of the interaction energies, and also in the characteristics of the electronic density and density Laplacian at the intermolecular bond critical point. Bader analysis of the electronic density has shown that pyridine adsorption on pure and fluorinated γ-alumina can be classified as non-covalent interaction.     

Robustness of dual divergence estimators for models satisfying linear constraints

We consider new classes of estimators and test statistics for models satisfying linear constraints with unknown parameter. These procedures are based on minimization of divergences through duality techniques. We prove that, for various divergences, the new approach provides robust estimation and test procedures, unlike the empirical likelihood method. We give general results using the influence function approach, which we exemplify in detail in the case of the Cressie–Read divergences. It is found that the Hellinger distance is one of the divergences that leads to robust procedures.     

On Picard iterations for strongly accretive and strongly pseudo-contractive Lipschitz mappings

In this note, we speed up the convergence of the Picard sequence of iterations for strongly accretive and strongly pseudo-contractive mappings. Our results improve the results of Chidume [C.E. Chidume, Picard iteration for strongly accretive and strongly pseudo-contractive Lipschitz maps, ICTP Preprint no. IC2000098; C.E. Chidume, Iterative Algorithms for Non-expansive Mappings and Some of Their Generalizations, in: Nonlinear Analysis and Applications: To V. Lakshmikantham on his 80th Birthday, vol. 1, 2, Kluwer Acad. Publ, Dordrecht, 2003, pp. 383–429], and Liu [L. Liu, Approximation of fixed points of a strictly pseudo-contractive mapping, Proc. Amer. Math. Soc. 125 (2) (1997) 1363–1366], and some other known results. The technique of the proof, presented in this paper, is different from the technique used by Chidume.     

Gradient methods for multiple state optimal design problems

We optimise a distribution of two isotropic materials α I and β I (α < β) occupying the given body in R ^d . The optimality is described by an integral functional (cost) depending on temperatures u ₁, . . . , u _m of the body obtained for different source terms f ₁, . . . ,f _m with homogeneous Dirichlet boundary conditions. The relaxation of this optimal design problem with multiple state equations is needed, introducing the notion of composite materials as fine mixtures of different phases, mathematically described by the homogenisation theory. The necessary conditions of optimality are derived via the Gateaux derivative of the cost functional. Unfortunately, there could exist points in which necessary conditions of optimality do not give any information on the optimal design. In the case m < d we show that there exists an optimal design which is a rank-m sequential laminate with matrix material α I almost everywhere on Ω. Contrary to the optimality criteria method, which is commonly used for the numerical solution of optimal design problems (although it does not rely on a firm theory of convergence), this result enables us to effectively use classical gradient methods for minimising the cost functional.