On certain arithmetic functions involving the greatest common divisor

The paper deals with asymptotics for a class of arithmetic functions which describe the value distribution of the greatest-common-divisor function. Typically, they are generated by a Dirichlet series whose analytic behavior is determined by the factor ζ²(s)ζ(2s − 1). Furthermore, multivariate generalizations are considered.     

Smart dampers control in a Remoissenet–Peyrard substrate potential

A model of spring-block on a moving plate with a nonlinear periodic substrate potential whose shape can be varied continuously as a function of a shape parameter is investigated. The dynamical study of the system for different values of the shape parameter involves the analysis of phase space, the construction of bifurcation diagrams, and the computation of the largest Lyapunov exponent. A smart damper associated with drag coefficient is proposed to reduce stick-slip and chaotic motions. The domain of validity of the control method is derived.     

Study of benznidazole–cyclodextrin inclusion complexes, cytotoxicity and trypanocidal activity

The current chemotherapy for Chagas disease is still based on benznidazole, which has low solubility, but complexation with cyclodextrins provides a way of increasing the solubility. The objective of this work was to characterize the inclusion complexes formed between benznidazole (BNZ) and randomly 2-methyled-β-cyclodextrin (RM-β-CD) in aqueous solution and study cytotoxicity and trypanocidal. BNZ:RM-β-CD solution complex systems were prepared and characterized using the phase solubility diagram, nuclear magnetic resonance and a photostability assays, also to investigate the in vitro trypanocidal activity with epimastigote forms of Trypanossoma cruzi and the study of cytotoxicity against mammal cells. The phase-solubility diagram displayed an A _L-type feature, providing evidence of the formation of soluble inclusion complexes. The continuous variation method showed the existence of a complex with 1:1 stoichiometry. Toxicity assays demonstrated that inclusion complexes were able to reduce the toxic effects caused by benznidazole alone and that this did not interfere with the trypanocidal activity of the benznidazole. The use of inclusion complexes benznidazole:cyclodextrin is thus a promising alternative for the development of a safe and stable liquid formulation and a new option for the treatment of Chagas disease.     

Crystal structure of 1-methyl-3-([2,2-dimethyl-4,6-dioxo-1,3-dioxane-5-ylidene]methyl)urea

The crystal structure of 1-Methyl-3-([2,2-dimethyl-4,6-dioxo-1,3-dioxane-5-ylidene]methyl)urea (C₉H₁₂N₂O₅) has been determined by single crystal X-ray diffraction analysis. The crystals are monoclinic, a = 5.3179(2), b = 18.6394(6), c =10.8124(3) Å, β = 100.015(2)°, Z = 4, sp. gr. P2₁/c, R = 0.0381 for 2537 reflections with I > 2σ(I). Except for C(CH₃)₂ group, the molecule is planar. The structure is stabilized by inter- and intramolecular N-H...O hydrogen bonds and weak C-H...O interactions.     

Synthesis and Photochromic Properties of Configurationally Varied Azobenzene Glycosides

Spatial orientation of carbohydrates is a meaningful parameter in carbohydrate recognition processes. To vary orientation of sugars with temporal and spatial resolution, photosensitive glycoconjugates with favorable photochromic properties appear to be opportune. Here, a series of azobenzene glycosides were synthesized, employing glycoside synthesis and Mills reaction, to allow “switching” of carbohydrate orientation by reversible E/Z isomerization of the azobenzene N=N double bond. Their photochromic properties were tested and effects of azobenzene substitution as well as the effect of anomeric configuration and the orientation of the sugars 2-hydroxy group were evaluated.     

Ground-state correlation properties of charged bosons trapped in strongly anisotropic harmonic potentials

We study systems of a few charged bosons contained within a strongly anisotropic harmonic trap. A detailed examination of the ground-state correlation properties of two-, three-, and four-particle systems is carried out within the framework of the single-mode approximation of the transverse components. The linear correlation entropy of the quasi-1D systems is discussed in dependence on the confinement anisotropy and compared with a strictly 1D limit. Only at weak interaction the correlation properties depend strongly on the anisotropy parameter.     

A majorization inequality for Wright-convex functions revisited

We give an elementary proof of a majorization inequality concerning Wright-convex functions.