Special Issue: 18th International conference on mathematical optimization theory and operations research (MOTOR 2019)

Journal of Global Optimization -     

How One can Repair Non-integrable Kahan Discretizations. II. A Planar System with Invariant Curves of Degree 6

Mathematical Physics, Analysis and Geometry - In this paper, we develop the dressing method to study the modified Camassa-Holm equation with the help of reciprocal transformation and the associated...     

A non‐iterative implicit algorithm for the solution of advection–diffusion equation on a sphere

A numerical algorithm for the solution of advection–diffusion equation on the surface of a sphere is suggested. The velocity field on a sphere is assumed to be known and non‐divergent. The discretization of advection–diffusion equation in space is carried out with the help of the finite volume method, and the Gauss theorem is applied to each grid cell. For the discretization in time, the symmetrized double‐cycle componentwise splitting method and the Crank–Nicolson scheme are used. The numerical scheme is of second order approximation in space and time, correctly describes the balance of mass of substance in the forced and dissipative discrete system and is unconditionally stable. In the absence of external forcing and dissipation, the total mass and L₂‐norm of solution of discrete system is conserved in time. The one‐dimensional periodic problems arising at splitting in the longitudinal direction are solved with Sherman–Morrison's formula and Thomas's algorithm. The one‐dimensional problems arising at splitting in the latitudinal direction are solved by the bordering method that requires a prior determination of the solution at the poles. The resulting linear systems have tridiagonal matrices and are solved by Thomas's algorithm. The suggested method is direct (without iterations) and rapid in realization. It can also be applied to linear and nonlinear diffusion problems, some elliptic problems and adjoint advection–diffusion problems on a sphere. Copyright © 2015 John Wiley & Sons, Ltd.     

Encapsulation-Controlled Photoisomerization of a Styryl Derivative: Stereoselective Formation of the Anti Z-Isomer in the Cucurbit[7]uril Cavity

The photochemical isomerization of a styrylpyridinium dye ( SP ) bearing an unsymmetrically attached benzo-15-crown-5 ether has been studied in aqueous solution in the absence and presence of cucurbit[7]uril (CB[7]). The detailed analysis of the UV/Vis and NMR spectra showes that the isomeric composition of the photostationary mixtures of SP can be modulated by the host-guest complexation with CB[7]. It was found that steric hindrance caused by encapsulation of SP in the host cavity induces the exclusive formation of the anti conformer of Z- SP in contrast with the mixture of both anti and syn conformers obtained during photoisomerization of the dye without CB[7]. Remarkably, the displacement of anti Z- SP from CB[7] does not lead to the transformation of the anti Z-isomer into the syn Z-isomer pointing out the conformational memory of the system. The results provide an interesting example of the supramolecular stereorecognition by the achiral CB[7] host.     

Apodization‐Assisted Subdiffraction Near‐Field Localization in 2D Phase Diffraction Grating

Conventional phase diffraction gratings can be used to localize the incoming optical radiation in the near‐field region. A new design of the binary phase diffraction grating is proposed with embedded pupil opaque mask inside each stripe. By means of numerical simulations, it is shown that with this masked phase grating the spatial resolution of the near‐field localization can be substantially improved and brought even beyond the solid immersion limit (λ/2n). Moreover, due to anomalous apodization effect, the subdiffraction field localization is accompanied by intensity enhancement as compared to the non‐masked design. The pupil mask rearranges the optical fluxes within the stripes and promotes the Fano resonances excitation in the periodic step lattice. This can be important for advancing the phase grating‐based super‐resolution technologies, including subdiffraction imaging, interferometry, and surface fabrication.     

Spectral Photoluminescent Parameters of Barley Seeds (Hordéum vulgáre) Infected with Fusarium ssp

We needed effective and sustainable technologies for better microbiological control of crops, including Fusarium. However, photoluminescent UV–Vis methods are potential for diagnosing plant diseases with Fusarium. It has not been sufficiently studied despite the application of these methods for other biological researches. The excitation spectrum of the seeds during infection shifts to the shorter wavelength and a new maximum appears in the region λ ≈ 232 nm. The photoluminescence of infected seeds increases with excitation by radiation of wavelengths λ_e,1 = 232 nm, λ_e,2 = 362 nm and λ_e,3 = 424 nm by 1.33–3.14 times, and λ_e,3 = 424 nm—decreases by 1.1 times. Statistical moments μ₃ and μ₄, asymmetry and kurtosis change only with short-wave excitation. When analyzing the decomposition of the frequency spectrum into Gaussian curves, the most informative ratio is the ratio of right-handed and left-handed Gaussians under excitation λ_e,2 = 362 nm and λ_e,3 = 424 nm. The ratios of their maxima change during infection by 1.36–3.2 times, and for excitation by radiation λ_e,2, the frequency boundaries of Gaussians change. The results of measurements and calculations provide a basis for the development of a method and device for photoluminescence diagnostics of fusarium seeds in UV–Vis ranges.     

Site-Selective C−H Alkenylation of N-Heteroarenes by Ligand-Directed Co/Al and Co/Mg Cooperative Catalysis**

We report herein the design and development of Co/Al and Co/Mg bimetallic catalysts, supported by a phosphine/secondary phosphine oxide (PSPO) bifunctional ligand, for the site-selective C−H alkenylation of nitrogen-containing heteroarenes with alkynes. These catalysts enable the alkenylation of pyridine, pyridone, and imidazo[1,2-a]pyridine derivatives at the C−H site proximal to the Lewis basic nitrogen or oxygen atom, which represents a selectivity profile distinct from that of the previously developed cobalt-diphosphine/aluminum catalyst. The alkenylated products were obtained in moderate to good yields using various heterocycles and differently substituted internal alkynes. Kinetic isotope effect experiments suggest the irreversibility of the C−H activation step, the relevance of which to the rate-limiting step depends on the reaction conditions. Density functional theory calculations indicate that ligand-to-ligand hydrogen transfer is the common mechanism of C−H activation.