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This paper proposes a novel method for the prevention of the unbounded oscillation of an aircraft wings under the flexural torsion flutter. The paper introducing the novel multiagent method for control of an aircraft wing, assuming that the wing surface consists of controlled "feathers" (agents). Theoretical evaluation of the approach demonstrates its high ability to prevent flexural-torsional vibrations of an aircraft. Since the model expands the possibilities for damping the wing oscillations, which potentially allows an increase in aircraft speed without misgiving of flutter. The study exhibits that timing is the main limitation of dampening vibrations. A new method for controlling an aircraft wing is suggested to increase the maximal flight speed of an aircraft without flutter occurrence via a novel model of the bending-torsional vibrations of an airplane wing with controlled feathers on its surface and new control laws based on the Speed-Gradient methodology. Provided experiments demonstrate the theoretical and advantages of the multiagent approach to "feathers" movement control., Comment: submitted to Mathematics. arXiv admin note: substantial text overlap with arXiv:2012.04582

This paper proposes a novel method for prevention of the increasing oscillation of an aircraft wing under the flexural torsion flutter. The paper introduces the novel multi-agent method for control of an aircraft wing, assuming that the wing surface consists of controlled 'feathers' (agents). Theoretical evaluation of the approach demonstrates its high ability to prevent flexural-torsional vibrations of an aircraft. Our model expands the possibilities for damping the wing oscillations, which potentially allows an increase in aircraft speed without misgiving of flutter. The study shows that the main limitation is the time, during which the system is able to damp vibrations to a safe level and keep them. The relevance of this indicator is important because of the rather fast process of increasing wing oscillations during flutter. In this paper, we suggest a new method for controlling an aircraft wing, with the use of which it becomes theoretically possible to increase the maximum flight speed of an aircraft without flutter occurrence. A mathematical model of the bending-torsional vibrations of an airplane wing with controlled feathers on its surface is presented. Based on the Speed-Gradient method a new control laws are synthesized., Comment: 21 pages, 4 figures

A model of scientific citation distribution is given. We apply it to understand the role of the Hirsch index as an indicator of scientific publication importance in Mathematics and some related fields. The proposed model is based on a generalization of such well-known distributions as geometric and Sibuja laws included now in a family of distributions. Real data analysis of the Hirsch index and corresponding citation numbers is given.

Metagenome, a mixture of different genomes (as a rule, bacterial), represents a pattern, and the analysis of its composition is, currently, one of the challenging problems of bioinformatics. In the present study, the possibility of evaluating metagenome composition by DNA-marker methods is investigated. These methods are based on using primers, short nucleic acid fragments. Each primer picks out of the tested genome the fragment set specific just for this genome, which is called its spectrum (for the given primer) and is used for identifying the genome. The DNA-marker method, applied to a metagenome, also gives its spectrum, which, obviously, represents the union of the spectra of all genomes belonging to the metagenome. Thus each primer provides a projection of the genomes and of the metagenome onto the corresponding spectra set. Here we propose to apply the random projection (random primer) approach for analyzing metagenome composition and present some estimates of the method effectiveness for the case of Random Amplified Polymorphic DNA (RAPD) technology., Comment: 18 pages, 4 figures

In the paper there is given a connection between one special case of cluster analysis, deconvolution problem, and classical moment problem. Namely, the methods used there are applied to solve deconvolution problem for the case of one known distribution and another one concentrated in unknown finite number of points. These results can be applied to estimate a number of clusters for the case of scale or location mixture of identical distributions. keywords: number of clusters, deconvolution problem, classical moment problem, scale and location mixtures.

The article presents the theoretical foundations of the algorithm for calculating the number of different genomes in the medium under study and of two algorithms for determining the presence of a particular (known) genome in this medium. The approach is based on the analysis of the compositional spectra of subsequently sequenced samples of the medium. The theoretical estimations required for the implementation of the algorithms are obtained.

In this research, we consider a mixture of genome fragments of a certain bacteria set. The problem of mixture separation is studied under the assumption that all the genomes present in the mixture are completely sequenced or are close to those already sequenced. Such assumption is relevant, e.g., in regular observations of ecological or biomedical objects, where the possible set of microorganisms is known and it is only necessary to follow their concentrations.

HoPLLS (Hierarchy of protein loop-lock structures) (http://leah.haifa.ac.il/~skogan/Apache/mydata1/main.html) is a web server that identifies closed loops - a structural basis for protein domain hierarchy. The server is based on the loop-and-lock theory for structural organisation of natural proteins. We describe this web server, the algorithms for the decomposition of a 3D protein into loops and the results of scientific investigations into a structural "alphabet" of loops and locks., Comment: 11 pages, 4 figures