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- Голубятников Владимир Петрович

# Голубятников Владимир Петрович

доктор физико-математических наук, профессор- Article. Golubyatnikov V. P. A cobordism theory // Siberian Mathematical Journal. Maik Nauka/Interperiodica Publishing. Russian Federation. - P.187-191. - ISSN 00374466. - EISSN 15739260.
- Article. Golubyatnikov V. P. Bordism rings with split normal bundles // Russian Mathematical Surveys. Turpion - Moscow Ltd.. United Kingdom. - P.172-176. - ISSN 00360279. - EISSN 14684829.
- Article. Golubyatnikov V. P., Pestov L. N. Trajectories of a dynamical system determined by a one-parameter group of conformal mappings of R3 // Siberian Mathematical Journal. Maik Nauka/Interperiodica Publishing. Russian Federation. - P.52-56. - ISSN 00374466. - EISSN 15739260.
- Article. Golubyatnikov V. P. Manifolds with split (into halves) stable normal bundles in phase spaces // Functional Analysis and its Applications. Maik Nauka/Interperiodica Publishing. Russian Federation. - P.139-140. - ISSN 00162663. - EISSN 15738485.
- Article. Golubyatnikov V. P. Unique determination of visible bodies from their projections // Siberian Mathematical Journal. Maik Nauka/Interperiodica Publishing. Russian Federation. - P.761-764. - ISSN 00374466. - EISSN 15739260.
- Article. Golubyatnikov V. P. Bordism rings with split normal bundles. II // Siberian Mathematical Journal. Maik Nauka/Interperiodica Publishing. Russian Federation. - P.699-704. - ISSN 00374466. - EISSN 15739260.
- Article. Golubyatnikov V. P. Unioue recoverability of convex compact sets from their projections // Siberian Mathematical Journal. Maik Nauka/Interperiodica Publishing. Russian Federation. - P.1043-1045. - ISSN 00374466. - EISSN 15739260.
- Article. Golubyatnikov V. P. On unique recoverability of convex and visible compacta from their projections // The question is: Under what conditions does the congruence of the projections of two compacta on every two-dimensional plane imply the congruence of the compacta themselves? The results are extended to the cases of (n-2)-visible and (n-2)-convex compacta, and even to the case when it is known the projections of the compacta are merely similar. © 1992 American Mathematical Society.
- Article. Golubyatnikov V. P. Stability problems in certain inverse problems of reconstruction of convex compacta from their projections - To Mikhail Mikhailovich Lavrent'ev on his sixtieth birthday anniversary // Siberian Mathematical Journal. Maik Nauka/Interperiodica Publishing. Russian Federation. - P.409-415. - ISSN 00374466. - EISSN 15739260.
- Article. Golubyatnikov V. P. Inverse problem for the Hamilton-Jacobii equation // Journal of Inverse and Ill-Posed Problems. Walter de Gruyter GmbH & Co. KG. Germany. - P.407-410. - ISSN 09280219. - EISSN 15693945. Sufficient conditions are given for the solvability of an inverse problem of determining the Hamiltonian and solving the corresponding Hamilton-Jacobi equation, provided that the phase function w(x, t) is known for t = 0 and t = T. © VSP 1995
- Article. Golubyatnikov V. P. On unique reconstructibility of convex and visible compact sets from their projections. II // Siberian Mathematical Journal. Maik Nauka/Interperiodica Publishing. Russian Federation. - P.265-269. - ISSN 00374466. - EISSN 15739260.
- Article. Golubyatnikov V. P. An inverse problem for the Hamilton-Jacobi equation on a closed manifold // Siberian Mathematical Journal. Maik Nauka/Interperiodica Publishing. Russian Federation. - P.235-238. - ISSN 00374466. - EISSN 15739260.
- Article. Golubyatnikov V. P. On the unique determination of compact convex sets from their projections. The complex case // Siberian Mathematical Journal. Maik Nauka/Interperiodica Publishing. Russian Federation. - P.678-681. - ISSN 00374466. - EISSN 15739260.
- Article. Golubyatnikov V. P., Kleshchev A. G., Malinovskii V. K., Novikov V. N. Relaxation spectra of liquids in the coupling-mode theory: Comparison with experimental data in the two-mode approximation // Doklady Physics. Maik Nauka/Interperiodica Publishing. Russian Federation. - P.514-516. - ISSN 10283358. - EISSN 15626903.
- ConferencePaper. Golubyatnikov V. P., Pekmen U., Karaca I., Ozyilmaz E., Tantay B. On reconstruction of surfaces from their apparent contours and the stationary phase observations // The main results of the paper concern a classical problem: if two surfaces in the Euclidean space have congruent projections on any plane, how different can they be? We consider the apparent contours of the smooth hypersurfaces as the projection data and formulate some sufficient conditions of coincidence of the shapes of two hypersurfaces, if the shapes of their apparent contours on any 2-dimensional plane coincide. We also obtain new results on reconstruction of smooth surfaces from observations of the wavefronts generated by these surfaces. © 1999 IEEE.
- Article. Golubyatnikov V. P., Kleshchev A. G., Malinovskii V. K., Novikov V. N. Liquid relaxation spectra in mode coupling theory: Comparison with experiment in a two-mode approximation // Doklady Akademii Nauk. Izdatel'stva Nauka. Russian Federation. - P.617-619. - ISSN 08695652.
- ConferencePaper. Pickalov V. V., Kazantzev D. I., Ayupova N. B., Golubyatnikov V. P. Considerations on iterative algorithms for fan-beam tomography scheme // © 2014 International Society for Industrial Process Tomography. Problems of tomography with too few views require sophisticated iterative algorithms which employ a priori information on unknown objects. So, we elaborate a fan beam version of the Gerchberg- Papoulis tomography algorithm, based on modification of the Central Slice Theorem to the case of the fan beam tomography. Numerical simulations of this modification are presented; this was carried out with the help of special non-linear change of the variables.
- Article. Golubyatnikov V. P., Gaidov Yu A., Kleshchev A. G., Volokitin E. P. Modeling of asymmetric gene networks functioning with different types of regulation // Biophysics. Maik Nauka/Interperiodica Publishing. Russian Federation. - P.61-65. - ISSN 00063509. We find conditions of existence of closed trajectories and describe their bifurcations for two broad classes of 3D asymmetric gene network models corresponding to two different regulation mechanisms. These results can be generalized to the case of gene networks of mixed types, where this regulation is effected either at the stages of initiation of mRNA and protein synthesis or at the stages of their degradation, and both different regulation mechanisms can appear in the same gene network. Description of the Andronov-Hopf bifurcation in these models is given as well. © 2006 Pleiades Publishing, Ltd.
- Article. Akinina E. V., Bednarzhevskii S. S., Golubyatnikov V. P., Nazin A. G., Smirnov G. I., Shevchenko N. G. Modeling calibration functions for the technologies of system analysis of quality and certification of biomaterials // Journal of Applied and Industrial Mathematics. Maik Nauka/Interperiodica Publishing. Russian Federation. - P.406-409. - ISSN 19904789. - EISSN 19904797. Possibilities are considered of using the modern methods of computer modeling for the technologies of system analysis of quality and certification of biomaterials. The practical methods and algorithms are described to calculate the adequate calibration models from a collection of the standard samples based on the application of the international standard ISO 11095. Applications of numerical simulation methods are investigated for construction of calibration functions under variation of the initial data concerning standard samples within the intervals of their attested values. It is shown that the proposed technology of finding the optimal calibration from a collection of adequate models allows us to improve the precision of the ecoanalytical measurements of the composition of toxic micro-impurities in biomedia. © Pleiades Publishing, Ltd. 2007.
- Article. Golubyatnikov V. P. On convexity of a planar domain with a pair of concave tomography projections // Siberian Advances in Mathematics. Springer Verlag. Germany. - P.85-90. - ISSN 10551344. - EISSN 19348126. We describe simple sufficient conditions on tomography-type measurements of a planar set which imply convexity of this set. The cases of partial convexity and higher-dimensional sets are considered as well. © Allerton Press, Inc. 2009.
- Article. Golubyatnikov V. P., Rovenski V. Y. Some extensions of the class of k-convex bodies // Siberian Mathematical Journal. Maik Nauka/Interperiodica Publishing. Russian Federation. - P.820-829. - ISSN 00374466. - EISSN 15739260. We study interrelations between some classes of bodies in Euclidean spaces. We introduce circular projections in normed linear spaces and the classes of bodies related with some families of these projections. Investigation of these bodies more general than k-convex and k-visible bodies allows us to generalize some classical results of geometric tomography and find their new applications. © 2009 Springer Science+Business Media, Inc.
- Article. Golubyatnikov V. P., Golubyatnikov I. V., Likhoshvai V. A. On the existence and stability of cycles in five-dimensional models of gene networks // Numerical Analysis and Applications. Maik Nauka/Interperiodica Publishing. Russian Federation. - P.329-335. - ISSN 19954239. - EISSN 19954247. Sufficient conditions for the existence and stability of closed trajectories in five-dimensional nonlinear dynamical systems that model gene networks with negative feedback are obtained. © 2010 Pleiades Publishing, Ltd.
- Article. Golubyatnikov V. P., Golubyatnikov I. V. On multidimensional models of gene network functioning // Journal of Applied and Industrial Mathematics. Maik Nauka/Interperiodica Publishing. Russian Federation. - P.343-347. - ISSN 19904789. - EISSN 19904797. Some sufficient conditions are obtained for the existence of closed trajectories of the odd-dimensional nonlinear dynamical systems that model gene networks with negative feedbacks. © 2011 Pleiades Publishing, Ltd.
- Article. Golubyatnikov V. P., Golubyatnikov I. V. On periodic trajectories in odd-dimensional gene network models // Russian Journal of Numerical Analysis and Mathematical Modelling. Walter de Gruyter GmbH & Co. KG. Germany. - P.397-412. - ISSN 09276467. We prove a theorem on the existence of periodic trajectories in phase portraits of odd-dimensional nonlinear dynamical systems modelling gene networks regulated by negative feedbacks. Also, we find certain sufficient conditions of the existence of stable cycles there. Some generalizations and applications of these results are given as well. © 2011 de Gruyter.
- Article. Golubyatnikov Vladimir, Rovenski Vladimir Determination of sets with positive reach by their projection type images // Journal of Inverse and Ill-Posed Problems. Walter de Gruyter GmbH & Co. KG. Germany. - P.407-428. - ISSN 09280219. - EISSN 15693945. We introduce new classes of sets extending the class of convex bodies. We show strong inclusions between these classes of bodies. In the case of bodies in Euclidean spaces, we obtain a new characterization of sets with positive reach, prove the Helly type theorem for them, and find applications to geometric tomography. We investigate the problem of determination of sets with positive reach by their projection-type images, and generalize corresponding stability theorems by H. Groemer. © de Gruyter 2011.
- Article. Bukharina T. A., Golubyatnikov V. P., Golubyatnikov I. V., Furman D. P. Model investigation of central regulatory contour of gene net of D. melanogaster macrochaete morphogenesis // Russian Journal of Developmental Biology. Consultants Bureau. United States. - P.49-53. - ISSN 10623604. Morphogenesis of drosophila macrochaete functioning as mechanoreceptors includes several steps, each of which has their own genetic support described in terms of gene nets. Mechanoreceptor develops from one parental cell (Sensory Organ Precursor cell-SOP cell), the determination of which has a critical role in macrochaete development. The highest content of AS-C proneural proteins with respect to surrounding cells that initiate a neural way of cellular development and by means of it mechanoreceptor morphogenesis is typical for SOP cell. The key object of gene net providing parental cell determination consists of gene complex achaete-scute (AS-C). This complex activity is controlled by central regulatory contour (CRC). Besides AS-C, CRC includes the following genes: hairy, senseless (sens), charlatan (chn), scratch (scrt), daughterless (da), extramacrochaete (emc), and groucho (gro). The system of direct relation and feedback and induction and repression relations between CRC components are realized via the coding by these genes proteins. A mathematical model of CRC functioning as a regulator of proneural AS-C protein content in SOP cell determining successful passing of the main phase of morphogenesis of D. melanogaster mechanoreceptor is discussed. © 2012 Pleiades Publishing, Ltd.
- Article. Bukharina T. A., Golubyatnikov V. P., Golubyatnikov I. V., Furman D. P. Mathematical modeling of the first phase of morphogenesis of mechanoreceptors in D. melanogaster // Journal of Applied and Industrial Mathematics. Maik Nauka/Interperiodica Publishing. Russian Federation. - P.145-149. - ISSN 19904789. - EISSN 19904797. The mechanoreceptors (in particular, macrochaetes) of drosophila pass three stages in its development (morphogenesis) whose genetic support is described in terms of gene networks. The key object of the gene networks of macrochaete morphogenesis is the achaete-scute (AS-C) complex of genes. Each mechanoreceptor develops from one parent cell distinguished by high concentration of the AS-C protein. The activity of this complex, which ensures the protein concentration critical for initiating morphogenesis, is determined by the central regulatory contour which includes a system of interactions among certain objects of the networks (genes and their products). © 2012 Pleiades Publishing, Ltd.
- Article. Akinshin A. A., Golubyatnikov V. P., Golubyatnikov I. V. On some multidimensional models of gene network functioning // Journal of Applied and Industrial Mathematics. Maik Nauka/Interperiodica Publishing. Russian Federation. - P.296-301. - ISSN 19904789. - EISSN 19904797. We obtain some sufficient conditions for the nonuniqueness of cycles in nonlinear dynamical systems considered as the models of gene network functioning. The constructive methods for the determination of these cycles and the invariant surfaces containing the mare described as well. © 2013 Pleiades Publishing, Ltd.
- Article. Ayupova N. B., Golubyatnikov V. P. On the uniqueness of a cycle in an asymmetric three-dimensional model of a molecular repressilator // Journal of Applied and Industrial Mathematics. Maik Nauka/Interperiodica Publishing. Russian Federation. - P.153-157. - ISSN 19904789. - EISSN 19904797. Some sufficient conditions are established for the nonlinear dynamical systems of dimension 3 that simulate the functioning of a molecular repressilator to have exactly one cycle. Some constructive method is described for finding an invariant surface that contains this cycle. © 2014 Pleiades Publishing, Ltd.
- Article. Batenkov D. V., Golubyatnikov V. P., Yomdin Y. N. Integral Geometry Problems with Incomplete Data // Journal of Mathematical Sciences. Plenum Publishers. United States. - P.25-39. - ISSN 10723374. © 2014, Springer Science+Business Media New York. We consider nonlinear problems of reconstructing multidimensional objects from incomplete data of distant measurements expressed as integral transformations. Based on the Prony system for the class of D-finite objects, we obtain constructive solutions.
- ConferencePaper. Gaidov Yu A., Golubyatnikov V. P. On cycles and other geometric phenomena in phase portraits of some nonlinear dynamical systems // © Springer International Publishing Switzerland 2014. We show existence of cycles in some special nonlinear 4-D and 5-D dynamical systems and construct in their phase portraits invariant surfaces containing these cycles. In the 5D case, we demonstrate non-uniqueness of the cycles. Some possible mechanisms of this non-uniqueness are described as well.
- ArticleInPress. Batenkov D. V., Golubyatnikov V. P., Yomdin Y. N. Integral Geometry Problems with Incomplete Data // Journal of Mathematical Sciences. Plenum Publishers. United States. - ISSN 10723374. We consider nonlinear problems of reconstructing multidimensional objects from incomplete data of distant measurements expressed as integral transformations. Based on the Prony system for the class of D-finite objects, we obtain constructive solutions. © 2014 Springer Science+Business Media New York.
- Article. Golubyatnikov Vladimir P., Bukharina Tatyana A., Furman Dagmara P. A model study of the morphogenesis of D. melanogaster mechanoreceptors: The central regulatory circuit // Journal of Bioinformatics and Computational Biology. Imperial College Press. United Kingdom. - ISSN 02197200. © 2015 Imperial College Press. Macrochaetes (large bristles) are sensor organs of the Drosophila peripheral nervous system with a function of mechanoreceptors. An adult mechanoreceptor comprises four specialized cells: shaft (trichogen), socket (tormogen), neuron, and glial cell (thecogen). All these cells originate from a single cell, the so-called sensor organ precursor (SOP) cell. Separation of the SOP cell from the encompassing cells of the imaginal disc initiates a multistage process of sensory organ development. A characteristic feature of the SOP cell is the highest amount of the proneural proteins AS-C as compared with the encompassing ectodermal cells. The accumulation of proneural proteins and maintenance of their amount in the SOP cell at a necessary level is provided by the gene network with the achaete-scute gene complex (AS-C) as its key component. The activity of this complex is controlled by the central regulatory circuit (CRC). The CRC comprises the genes hairy, senseless (sens), charlatan (chn), scratch (scrt), daughterless (da), extramacrochaete (emc), and groucho (gro), coding for the transcription factors involved in the system of direct links and feedbacks and implementation of activation-repression relationships between the CRC components. The gene phyllopod (phyl), involved in degradation of the AS-C proteins, is also associated with the CRC functioning. In this paper, we propose a mathematical model for the CRC functioning as a regulator of the amount of proneural AS-C proteins in the SOP cell taking into account their degradation. The modeling has demonstrated that a change in the amount of proneural proteins in the SOP cell is stepwise rather than strictly monotonic. This prediction can be tested experimentally.
- Article. Ayupova N. B., Golubyatnikov V. P. On two classes of nonlinear dynamical systems: The four-dimensional case // Siberian Mathematical Journal. Maik Nauka/Interperiodica Publishing. Russian Federation. - P.231-236. - ISSN 00374466. - EISSN 15739260. © 2015, Pleiades Publishing, Ltd. We consider two four-dimensional piecewise linear dynamical systems of chemical kinetics. For one of them, we give an explicit construction of a hypersurface that separates the attraction basins of two stable equilibrium points and contains an unstable cycle of this system. For the other system, we prove the existence of a trajectory not contained in the attraction basin of the stable cycle of this system described earlier by Glass and Pasternack. The homotopy types of the phase portraits of these two systems are compared.
- Article. Golubyatnikov V. P., Kalenykh A. E. Structure of Phase Portraits of Nonlinear Dynamical Systems // Journal of Mathematical Sciences. Plenum Publishers. United States. - P.475-483. - ISSN 10723374. © 2016, Springer Science+Business Media New York.We consider phase portraits of some piecewise linear dynamical systems of chemical kinetics. We construct an invariant piecewise linear surface that consists of eight planar polygons and is formed by the trajectories which do not enter the attraction basin of a stable cycle. We prove that the dynamical system does not have cycles on this surface. Bibliography: 26 titles. Illustrations: 1 figure.
- Article. Bukharina T. A., Golubyatnikov V. P., Furman D. P. Gene network controlling the morphogenesis of D. melanogaster macrochaetes: An expanded model of the central regulatory circuit // Russian Journal of Developmental Biology. Consultants Bureau. United States. - P.288-293. - ISSN 10623604. © 2016, Pleiades Publishing, Inc.The drosophila macrochaetes act as mechanoreceptors, the sensory organs of the peripheral nervous system. Each mechanoreceptor consists of four specialized cells, namely, the shaft, socket, neuron, and sheath. All these cells develop from a single cell referred to as the sensory organ precursor (SOP) cell. The SOP cell segregates from the surrounding cells of imaginal disc, thereby launching multistage sensory organ development. A characteristic feature of the SOP cell is the highest content of the proneural proteins Achaete and Scute (ASC) as compared with the surrounding cells. The pattern of changes in the content of proneural proteins in the SOP cell is determined by a gene network with the achaete-scute (AS-C) gene complex as its key component. The activity of this complex is controlled by the central regulatory circuit (CRC), containing the genes hairy, senseless (sens), charlatan (chn), scratch (scrt), daughterless (da), extramacrochaete (emc), and groucho (gro), encoding the transcription factors involved in the system of feedforwards and feedbacks and implementing the activation–repression of CRC components, as well as the gene phyllopod (phyl), an adaptor protein that controls the degradation of ASC proteins. A mathematical model describing the CRC functioning in the SOP cell as a regulator of the content of ASC proneural proteins is proposed.
- Article. Ayupova N. B., Golubyatnikov V. P. A three-cell model of the initial stage of development of a proneural cluster // Journal of Applied and Industrial Mathematics. Maik Nauka/Interperiodica Publishing. Russian Federation. - P.168-173. - ISSN 19904789. - EISSN 19904797. © 2017, Pleiades Publishing, Ltd. We construct a 9-dimensional nonlinear dynamical system that simulates the initial stage of interaction of three adjacent cells in the proneural cluster of Drosophila melanogaster. We describe the conditions of existence of three stable equilibrium points in the phase space of this system, list its other equilibrium points, and provide a biological interpretation.
- Article. Ayupova N. B., Golubyatnikov V. P., Kazantsev M. V. On the existence of a cycle in an asymmetric model of a molecular repressilator // Numerical Analysis and Applications. Maik Nauka/Interperiodica Publishing. Russian Federation. - P.101-107. - ISSN 19954239. - EISSN 19954247. © 2017, Pleiades Publishing, Ltd. In this paper, a nonlinear six-dimensional dynamic system, which is a model of functioning of a simple molecular repressilator, is considered. Sufficient conditions for the existence of a cycle C in the phase portrait of this system are found. An invariant neighborhood of C, which retracts to C, is constructed.