Multi-hump bright solitons in a Schrödinger–mKdV system

We consider the problem of energy transport in a Davydov model along an anharmonic crystal medium obeying quartic longitudinal interactions corresponding to rigid interacting particles. The Zabusky and Kruskal unidirectional continuum limit of the original discrete equations reduces, in the long wave approximation, to a coupled system between the linear Schrödinger (LS) equation and the modified Korteweg–de Vries (mKdV) equation. Single- and two-hump bright soliton solutions for this LS–mKdV system are predicted to exist by variational means and numerically confirmed. The one-hump bright solitons are found to be the anharmonic supersonic analogue of the Davydov's solitons while the two-hump (in both components) bright solitons are found to be a novel type of soliton consisting of a two-soliton solution of mKdV trapped by the wave function associated to the LS equation. This two-hump soliton solution, as a two component solution, represents a new class of polaron solution to be contrasted with the two-soliton interaction phenomena from soliton theory, as revealed by a variational approach and direct numerical results for the two-soliton solution.     

A note on polynomial chaos expansions for designing a linear feedback control for nonlinear systems

This paper presents a polynomial chaos-based framework for designing optimal linear feedback control laws for nonlinear systems with stochastic parametric uncertainty. The spectral decomposition of the original stochastic dynamical model in an orthogonal polynomial basis, prescribed by the Wiener–Askey scheme, provides a deterministic model from which the optimal linear control law is designed. Optimality of the proposed control law is proved by solving the Hamilton–Jacobi–Bellman equation, and asymptotic stability of the controlled nonlinear systems is guaranteed in the Lyapunov sense. We are especially interested in synchronization of chaotic systems. For this reason, the control strategy is applied in the trajectory tracking of periodic orbits for the Duffing oscillator and the Rössler system with uncertain stochastic parameters and initial conditions. The results are verified with Monte Carlo simulations.     

Nonfunctionalized Gold Nanoparticles: Synthetic Routes and Synthesis Condition Dependence

Since Faraday first described gold sol synthesis, synthetic routes to nanoparticles, as well as their applications, have experienced a huge growth. Variations in synthesis conditions such as pH, temperature, reduction, and the stabilizing agent used will determine the morphology, size, monodispersity, and stability of nanoparticles obtained, allowing for modulation of their physical and chemical properties. Although many studies have been made about the synthesis and characterization of individual nanosystems of interest, to our knowledge the common, general traits that all those synthesis share have not been previously compiled. In this review, we aim to offer a global vision of some of the most relevant synthetic procedures reported up to date, with a special focus on nonfunctionalized gold nanoparticle synthetic routes in aqueous media, and to display a broad overview of the influence that synthesis conditions have on the shape, stability, and reactivity of nanoparticle systems.     

Characterizingω 1 and the long line by their topological elementary reflections

Given a topological space 〈X, T〉 ∈M, an elementary submodel of set theory, we defineX _Mto beX ∩M with the topology generated by {U ∩M : U ∈T ∩M}. We prove that it is undecidable whetherX _Mhomeomorphic toω ₁ impliesX =X _M,yet it is true in ZFC that ifX _Mis homeomorphic to the long line, thenX =X _M.The former result generalizes to other cardinals of uncountable confinality while the latter generalizes to connected, locally compact, locally hereditarily LindelöfT ₂ spaces.     

Comparison of micellar electrokinetic chromatography, liquid chromatography, and microbiologic assay for analysis of cephalexin in oral suspensions

Two well-accepted methodologies, based on a microbiologic assay (MA) and liquid chromatography (LC), and a novel methodology using micellar electrokinetic chromatography (MEKC), were compared for the determination of cephalexin in commercially available and simulated samples of oral suspensions. The MA, described in the Brazilian Pharmacopeia, was performed with a strain of Staphylococcus aureus ATCC 6538 as the test organism, following the cylinder-plate method. The LC analysis followed the European Pharmacopoeia, 3rd Ed., and was used with minor modifications. The MEKC analysis was based on a previous work of the group. Estimates of the repeatability relative standard deviations of the MA, LC, and MEKC methods in the analysis of a commercial sample were 0.34, 0.42, and 0.37%, respectively. The recovery obtained with LC was 99.90 +/- 1.11%; for MEKC, it was 100.09 +/- 0.56%. Although the 3 methodologies were statistically equivalent for the determination of cephalexin in oral suspensions, MA gave suitable repeatability despite being nonspecific and time-consuming. MEKC provided faster analysis and higher column efficiency, whereas LC presented superior sensitivity. The results indicated that MEKC can be used as an alternative method to MA and LC in routine quality control laboratories.     

An FT-IR study of sarcoplasmic reticulum solubilization by triton X-100

Low concentrations of the non-ionic detergent Triton X-100 increase the activity of sarcoplasmic reticulum Ca⁺⁺-ATPase without major changes in protein conformation, according to FT-IR spectroscopy in H₂O and D₂O. At higher surfactant concentrations the enzyme activity is inhibited, while changes in protein conformation are seen: The proportion of unordered structure increases at the expenses of-turns and parallel-sheet.     

Parameters for the calculation of the ring current and atomic magnetic anisotropy contributions to magnetic shielding constants: Nucleic acid bases and intercalating agents

The values of the non-zero elements of the diamagnetic and paramagnetic parts of the atomic magnetic susceptibility tensors are reported for nucleic acid bases and for the conjugated parts of some intercalating agents. These quantities are necessary for the computation of the contribution of the local magnetic anisotropy to the intermolecular shielding which is produced by this type of molecule. The intensities of the ring currents as well as the radii of the conjugated rings are reported for these compounds so that the contribution of the magnetic anisotropy of these molecules to the chemical shift of any nucleus located at any point in space may be computed in an NMR study.     

Heavy-Atom Tunneling in Bicyclo[4.1.0]hepta-2,4,6-trienes

Heavy-atom tunneling limits the lifetime and observability of bicyclo[4.1.0]hepta-2,4,6-triene, a key intermediate in the rearrangement of phenylcarbene. Bicyclo[4.1.0]hepta-2,4,6-triene had been proposed as the primary intermediate of the rearrangement of phenylcarbene, but despite many efforts evaded its characterization even in cryogenic matrices. By introducing fluorine substituents into the ortho-positions of the phenyl ring of phenylcarbene, the highly strained cyclopropene 1,5-difluorobicyclo[4.1.0]hepta-2,4,6-triene becomes stable enough to be characterized in argon matrices. However, even at 3 K this cyclopropene is only metastable and rearranges via heavy-atom tunneling to the corresponding cycloheptatetraene. Calculations suggest that fluorination is necessary to slow down the tunneling rearrangement of the bicycloheptatriene. The parent bicycloheptatriene rapidly rearranges via heavy-atom tunneling and therefore cannot be detected under matrix isolation conditions.