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We construct a multi-parametric family of quasi-rational solutions to the focusing NLS equation, presenting a profile of multiple rogue waves. These solutions have also been used by us to construct a large family of smooth, real localized rational solutions of the KP-I equation quite different from the multi-lumps solutions first constructed in Bordag et al. (1977). The physical relevance of both equations is very large. From the point of view of geosciences,the focusing NLS equation is relevant to the description of surface waves in deep water, and the KP-I equation occurs in the description of capillary gravitational waves on a liquid surface, but also when one considers magneto-acoustic waves in plasma (Zhdanov, 1984) etc. In addition, there are plenty of equations of physical importance, having their origin in fiber optics, hydrodynamics, plasma physics and many other areas, which are gauge equivalent to the NLS equation or to the KP-I equation. Therefore our results can be easily extended to a large number of systems of physical interest to be discussed in separate publications.

The authors argue that a market monetary approach to environmental management is not effective. In this regard, the article proposes theoretical background and practical recommendations for creating a global ecology management system based on the operational assessment of the current environmental impact magnitude. This system allows calculating the environmental value of products, as well as a number of key indicators of environmental performance, which are direct analogues of economic performance indicators. The proposed economic approach, based on the use of accounting methods, provides an opportunity to establish a mathematically accurate correlation between the economic and environmental results of economic and other related activities.The application of carbon emission data for selecting the “cleanest” type of generator that provides the least amount of total globally significant CO 2 emissions has been analyzed as an example.

The highlights of the 24th International Exposition Glass World held in Moscow are briefly cited. About 100 companies from 12 countries of the world participated. New manufacturing and quality-control technologies of glass products and the main structural components of glass furnaces and methods of their high-quality production are demonstrated at the exposition. Examples of the most successful enterprises in the glass industry are given.

Recent advancements in experimental and computational methods for RNA secondary structure detection have revealed the crucial role of RNA structural elements in diverse molecular processes within living cells. It has been demonstrated that the secondary structure of the entire viral genome is often responsible for performing crucial functions in the viral life cycle and also influences virus evolution. To investigate the role of viral RNA secondary structure, alongside experimental techniques, the use of bioinformatics tools is important for analyzing various secondary structure patterns, including hairpin loops, internal loops, multifurcations, external loops, bulges, stems, and pseudoknots. Here, we have introduced a Python package for analyzing RNA secondary structure elements in viral genomes, which includes the recognition of common secondary structure patterns, the generation of descriptive statistics for these structural elements, and the provision of their basic properties. We applied the developed package to analyze the secondary structures of complete viral genomes collected from the literature, aiming to gain insights into viral function and evolution. Both the package and the collection of secondary structures of viral genomes are available at http://github.com/KazanovLab/RNAsselem .

Identifying, counting and measuring particles is an important component of many research studies. Images with particles are usually processed by hand using a software ruler. Automated processing, based on conventional image processing methods (edge detection, segmentation, etc.) are not universal, can only be used on good-quality images and need to set a number of parameters empirically. In this paper, we present results from the application of deep learning to automated recognition of metal nanoparticles deposited on highly oriented pyrolytic graphite on images obtained by scanning tunneling microscopy (STM). We used the Cascade Mask-RCNN neural network. Training was performed on a dataset containing 23 STM images with 5157 nanoparticles. Three images containing 695 nanoparticles were used for verification. As a result, the trained neural network recognized nanoparticles in the verification set with 0.93 precision and 0.78 recall. Predicted contour refining with 2D Gaussian function was a proposed option. The accuracies for mean particle size calculated from predicted contours compared with ground truth were in the range of 0.87–0.99. The results were compared with outcomes from other generally available software, based on conventional image processing methods. The advantages of deep learning methods for automatic particle recognition were clearly demonstrated. We developed a free open-access web service “ParticlesNN” based on the trained neural network, which can be used by any researcher in the world.

Abstract We consider nonlocal symmetries that all or all even (all odd) equations of the AKNS hierarchy have. We construct examples of solutions simultaneously satisfying several nonlocal equations of the AKNS hierarchy. We present a detailed study of single-phase solutions.

We generalize the celebrated results of Bernhard Riemann and Gaston Darboux: we give necessary and sufficient conditions for a bilinear form to be flat. More precisely, we give explicit necessary and sufficient conditions for a tensor field of type (0, 2) which is not necessary symmetric or skew-symmetric, and is possibly degenerate, to have constant entries in a local coordinate system.

Abstract We consider a simplest two-dimensional reduction of the remarkable three-dimensional Hirota–Ohta system. The Lax pair of the Hirota–Ohta system was extended to a Lax triad by adding extra third linear equation, whose compatibility conditions with the Lax pair of the Hirota–Ohta imply another remarkable systems: the Kulish–Sklyanin system (KSS) together with its first higher commuting flow, which we can call the vector complex mKdV. This means that any common particular solution of both these two-dimensional integrable systems yields a corresponding particular solution of the three-dimensional Hirota–Ohta system. Using the Zakharov–Shabat dressing method, we derive the \\(N\\)-soliton solutions of these systems and analyze their interactions, i.e., explicitly derive the shifts of the relative center-of-mass coordinates and the phases as functions of the discrete eigenvalues of the Lax operator. Next, we relate Hirota–Ohta-type system to these nonlinear evolution equations and obtain its \\(N\\)-soliton solutions.

Ribavirin and its analogues exhibit an in vitro antiproliferative effect in cancer cells. In this work, we studied the biological activities of a number of alkyl/aryloxymethyl derivatives of ribavirin’s aglycon—1,2,4-triazole-3-carboxamide. Alkyl/arylxymethyl derivatives of 1,2,4-triazole-3-carboxamide with substitutions at the fifth or first position of the triazole ring, were synthesized and their antiproliferative and antimicrobial effects were assessed. For both series, the presence of an antiproliferative effect was investigated, and 1-alkyl/aryloxymethyl derivatives were shown an antimicrobial potential against a Gram-positive bacteria Micrococcus luteus and Gram-negative bacterium Pseudomonas aeruginosa. The obtained results showed that the n-decyloxymethyl derivatives induced leukemia cell death at low micromolar concentrations. We confirmed that n-decyloxymethyl derivatives of ribavirin inhibited the cell cycle progression and induced an accumulation of leukemia cells in the subG1-phase. The molecular docking results suggest that alkyl/aryloxymethyl derivatives may act by inhibiting translation initiation, due to interference with eIF4E assembly. The outcome results revealed that active derivatives (1- or 5-n-decyloxymethyl-1,2,4-triazole-3-carboxamides) can be considered as a lead compound for anticancer treatments.

We show that the set of Finsler metrics on a manifold contains an open everywhere dense subset of Finsler metrics with infinite-dimensional holonomy groups.