PD Dr. Tatiana Latychevskaia

PD at the University of Zurich, Department of Physics

Google Scholar, Web of Science Researcher ID D-3099-2013

Biography: Tatiana Latychevskaia studied physics at Peter the Great St. Petersburg Polytechnic University in Russia and obtained Master degree in 1996, her Master thesis project was in optical holography. For one year, she was employed as a teaching assistant at the Department of Theoretical Physics, teaching undergraduate students classes in classical mechanics, quantum mechanics, and electrodynamics. In 1997, she joined the group of Prof. Urs Wild in Physical Chemistry Laboratory, ETH Zurich, where she completed her doctoral thesis in 2001. Thesis subject: experimental detection of single molecule fluorescence at low-temperature (1.4 K) and measuring the Stark effect on single molecules. In 2001, Tatiana Latychevskaia joined the group of Prof. Hans-Werner Fink, Physics Department at the University of Zurich, where she was developing low-energy electron (20 - 300 eV) lensless coherent imaging techniques (diffraction and holography) for imaging of single biomolecules and nano-scale objects. In 2017 –2018, she was working in the group of Prof. Carbone, Institute of Physics, EPFL Lausanne. Complete CV.

Our current research topics are: novel high-resolution 3D diffraction and imaging methods, iterative phase retrieval, coherent diffraction imaging, holography, convergent beam electron diffraction, 2D materials. Some selected topics:

Convergent beam electron diffraction on 2D materials

Algorithms for wavefront propagation, digital holography and iterative phase retrieval

3D curved light beams

Gold nanoparticles: Motion simulation

Students of the University of Zurich are welcome to contact us for Bachelor and Master projects.

PHY427 Electron microscopy Lectures

PHY425 Modern Microscopy with Light and Electrons

Optical Society of America (OSA) Outstanding Reviewer 2022 Award 

Photonics Outstanding Reviewer 2021 Award

2023

• Controlling topological states in bilayer graphene Latychevskaia T
  Nature Nanotechnology ~ (2023).
  DOI:10.1038/s41565-023-01454-8
• Fourier Transform Holography: A Lensless Imaging Technique, Its Principles and Applications Mustafi S, Latychevskaia T
  Photonics 10(2), 153 (2023).
  DOI:10.3390/photonics10020153
• Coherent imaging with low-energy electrons, quantitative analysis Latychevskaia T
  Ultramicroscopy 253, 113807 (2023).
  DOI:10.1016/j.ultramic.2023.113807
• Potentials of individual atoms by convergent beam electron diffraction Latychevskaia T, Woods CR, Wang YB, Holwill M, Prestat E, Mustafi S, Haigh SJ, Novoselov KS
  Carbon 201, 244-250 (2023).
  DOI:10.1016/j.carbon.2022.09.003

2022

• Low-dose shift- and rotation-invariant diffraction recognition imaging Latychevskaia T, Kohli A
  Scientific Reports 12, 11202 (2022).
  DOI: 10.1038/s41598-022-15486-y
• Imaging defects in two-dimensional crystals by convergent-beam electron diffraction Latychevskaia T, Huang P, Novoselov K
  Physical Review B 105, 184113 (2022).
  DOI: 10.1103/PhysRevB.105.184113

2021

• Bragg holography of nano-crystals Latychevskaia T, Cassidy C, Shintake T
  Ultramicroscopy 230, 113376 (2021).
  DOI: 10.1016/j.ultramic.2021.113376
• Three-dimensional structure from single two-dimensional diffraction intensity measurement Latychevskaia T
  Physical Review Letters 127(6), 063601 (2021).
  DOI: 10.1103/PhysRevLett.127.063601
• Holographic convergent electron beam diffraction (CBED) imaging of two-dimensional crystals Latychevskaia T, Haigh S. J., Novoselov K. S. 
  Surface Review and Letters 28(8), 2140001 (2021).
  DOI: 10.1142/S0218625X21400011
• Phase retrieval methods applied to coherent imaging Latychevskaia T
  Advances in Imaging and Electron Physics 218, 1 (2021).
  DOI: 10.1016/bs.aiep.2021.04.001
• Symmetry of diffraction patterns of two-dimensional crystal structures Latychevskaia T, Zan R, Morozov S, Novoselov K
  Ultramicroscopy 228, 113336  (2021).
  DOI: 10.1016/j.ultramic.2021.113336
• Wavefront modulation and beam shaping into arbitrary three-dimensional intensity distributions Latychevskaia T
  Photonics 8(6), 179 (2021).
  DOI: 10.3390/photonics8060179
• Three-dimensional volumetric deconvolution in coherent optics and holography Latychevskaia T
  Applied Optics 60(5), 1304 (2021).
  DOI: 10.1364/AO.412736

2020

• Holographic reconstruction of the interlayer distance of bilayer two-dimensional crystal samples from their convergent beam electron diffraction patterns Latychevskaia T, Zou YC, Woods CR, Wang YB, Holwill M, Prestat E, Haigh SJ, Novoselov KS
  Ultramicroscopy 219, 113020 (2020).
  DOI: 10.1016/j.ultramic.2020.113020
• Holography and Coherent Diffraction Imaging with Low-(30–250 eV) and High-(80–300 keV) Energy Electrons: History, Principles, and Recent Trends Latychevskaia T
  Materials 13, 3089 (2020).
  DOI: 10.3390/ma13143089"Congrats on your excellent review in Materials!" by John Spence
• Convergent beam electron diffraction of multilayer van der Waals structures Latychevskaia T, Woods CR, Wang YB, Holwill M, Prestat E, Haigh SJ, Novoselov KS
  Ultramicroscopy 212, 112976 (2020).
  DOI: 10.1016/j.ultramic.2020.112976

2019

• Iterative phase retrieval for digital holography (invited) Latychevskaia T
  Journal of the Optical Society of America 36, D31 (2019).
  DOI: 10.1364/JOSAA.36.000D31
• Reconstruction of missing information in diffraction patterns and holograms by iterative phase retrieval Latychevskaia T
  Optics Communications 452, 56 (2019).
  DOI: 10.1016/j.optcom.2019.07.021
• Inelastic scattering and solvent scattering reduce dynamical diffraction in biological crystals Latychevskaia T, Abrahams JP
  Acta Crystallographica Section B 75, 52 (2019).
  DOI: 10.1107/S2052520619009661
• Direct visualization of charge transport in suspended (or free-standing) DNA strands by low-energy electron microscopy Latychevskaia T, Escher C, Andregg W, Andregg M, Fink HW
  Scientific Reports 9, 8889 (2019).
  DOI: 10.1038/s41598-019-45351-4
• Lateral and axial resolution criteria in incoherent and coherent optics and holography, near- and far-field regimes Latychevskaia T
  Applied Optics 58, 3597 (2019).
  DOI: 10.1364/AO.58.003597
• Ultrafast holography enabled by quantum interference of ultrashort electrons Madan I, Vanacore GM, Pomarico E, Berruto G, Lamb RJ, McGrouther D, Lummen TTA, Latychevskaia T, García de Abajo FJ, Carbone F
  Science Advances 5, eaav8358 (2019).
  DOI: 10.1126/sciadv.aav8358
• Local photo-mechanical stiffness revealed in gold nanoparticles supracrystals by ultrafast small-angle electron diffraction Mancini GF, Pennacchio F, Latychevskaia T, Reguera J, Stellacci F, Carbone F
  Structural Dynamics 6, 024304 (2019).
  DOI: 10.1063/1.5091858
• Moiré structures in twisted bilayer graphene studied by transmission electron microscopy Latychevskaia T, Escher C, Fink HW
  Ultramicroscopy 197, 46 (2019).
  DOI: 10.1016/j.ultramic.2018.11.009
• Stacking transition in rhombohedral graphite Latychevskaia T, Son KS, Yang YP, Chancellor D, Brown M, Ozdemir S, Madan I, Berruto G, Carbone F, Mishchenko A, Novoselov KS
  Frontiers of Physics 14, 13608 (2019).
  DOI: 10.1007/s11467-018-0851-6
• Convergent and divergent beam electron holography and reconstruction of adsorbates on free-standing two-dimensional crystals Latychevskaia T, Woods CR, Wang YB, Holwill M, Prestat E, Haigh SJ, Novoselov KS
  Frontiers of Physics 14, 13606 (2019).
  DOI: 10.1007/s11467-018-0851-6

2018

• Investigating Skyrmions Using Lorentz Transmission Electron Microscopy Huang P, Jayaraman R, Mancini GF, Kruchkov A, Cantoni M, Murooka Y, Latychevskaia T, McGrouther D, Baldini E, White JS, Magrez A, Giamarchi T, Carbone F, Rønnow HM
  MICROSCOPY AND MICROANALYSIS 24, 932 (2018).
  DOI: 10.1017/S1431927618005159
• Three-dimensional double helical DNA structure directly revealed from its X-ray fiber diffraction pattern by iterative phase retrieval Latychevskaia T, Fink HW
  Optics Express 26, 30991 (2018).
  DOI: 10.1364/OE.26.030991
• Iterative phase retrieval in coherent diffractive imaging: practical issues Latychevskaia T
  Applied Optics 57, 7187 (2018).
  DOI: 10.1364/AO.57.007187
• Algorithms and image formation in orbital tomography Kliuiev P, Latychevskaia T, Zamborlini G, Jugovac M, Osterwalder J, Hengsberger M, Castiglioni L
  Physical Review B 98, 085426 (2018).
  DOI: 10.1103/PhysRevB.98.085426
• Convergent beam electron holography for analysis of van der Waals heterostructures Latychevskaia T, Woods CR, Wang YB, Holwill M, Prestat E, Haigh SJ, Novoselov KS
  PNAS 115, 7473 (2018).
  DOI: 10.1073/pnas.1722523115
• Metal adsorption and nucleation on free-standing graphene by low-energy electron point source microscopy Lorenzo M, Escher C, Latychevskaia, Fink HW
  Nano Letters 18, 3421 (2018).
  DOI: 10.1021/acs.nanolett.8b00359

2017

• Resolution enhancement in in-line holography by numerical compensation of vibrations Latychevskaia T, Fink HW
  Optics Express 25, 20109 (2017).
  DOI: 10.1364/OE.25.020109
• Imaging the potential distribution of charged adsorbates on graphene by low-energy electron holography Latychevskaia T, Wicki F, Escher C, Fink HW
  Ultramicroscopy 182, 276 (2017).
  DOI: 10.1016/j.ultramic.2017.07.019
• Three-dimensional surface topography of graphene by divergent beam electron diffraction Latychevskaia T, Hsu WH, Chang WT, Lin CY, Hwang IS
  Nature Communications 8, 14440 (2017).
  DOI: 10.1038/ncomms14440
• Spatial coherence of electron beams from field emitters and its effect on the resolution of imaged objects Latychevskaia T
  Ultramicroscopy 175, 121 (2017).
  DOI: 10.1016/j.ultramic.2016.11.008
• Imaging proteins at the single-molecule level Longchamp JN, Rauschenbach S, Abb S, Escher C, Latychevskaia T, Kern K, Fink HW
  PNAS 114, 1474 (2017).
  DOI: 10.1073/pnas.1614519114

2016

• Application of iterative phase-retrieval algorithms to ARPES orbital tomography Kliuiev P, Latychevskaia T, Osterwalder J, Hengsberger M, Castiglioni L
  New Journal of Physics 18, 093041 (2016).
  DOI: 10.1088/1367-2630/18/9/093041
• Resolution enhancement by extrapolation of coherent diffraction images: a quantitative study about the limits and a numerical study of non-binary and phase objects Latychevskaia T, Chushkin Y, Fink HW
  Journal of Microscopy 264, 2 (2016).
  DOI: 10.1111/jmi.12408
• Direct observation of individual charges and their dynamics on graphene by low-energy electron holography Latychevskaia T, Wicki F, Longchamp JN, Escher C, Fink HW
  Nano Letters 16, 5469 (2016).
  DOI: 10.1021/acs.nanolett.6b01881
• Mapping unoccupied electronic states of freestanding graphene by angle-resolved low-energy electron transmission Wicki F, Longchamp JN, Latychevskaia T, Escher C, Fink HW
  Physical Review B 94, 075424 (2016).
  DOI: 10.1103/PhysRevB.94.075424
• Creating Airy beams employing a transmissive spatial light modulator Latychevskaia T, Schachtler D, Fink HW
  Applied Optics 55, 6095 (2016).
  DOI: 10.1364/AO.55.006095
• Inverted Gabor holography principle for tailoring arbitrary shaped three-dimensional beams Latychevskaia T, Fink HW
  Scientific Reports 6, 26312 (2016).
  DOI: 10.1038/srep26312
• Order/disorder dynamics in a dodecanethiol-capped gold nanoparticles supracrystal by small-angle ultrafast electron diffraction Mancini GF, Latychevskaia T, Pennacchio F, Reguera J, Stellacci F, Carbone F
  Nano Letters 16, 2705 (2016).
  DOI: 10.1021/acs.nanolett.6b00355
• Invariant time-dependent exchange perturbation theory and its application to the particles collision problem Orlenko EV, Latychevskaia T, Evstafev AV, Orlenko FE
  Highlights in Theoretical Chemistry 11, 41 (2016).
  DOI: 10.1007/s00214-015-1646-2

2015

• Imaging outside the box: Resolution enhancement in X-ray coherent diffraction imaging by extrapolation of diffraction patterns Latychevskaia T, Chushkin Y, Zontone F, Fink HW
  Applied Physics Letters 107, 183102 (2015).
  DOI: 10.1063/1.4934879
• Filming the formation and fluctuation of skyrmion domains by cryo-Lorentz transmission electron microscopy Rajeswari J, Huang P, Mancini GF, Murooka Y, Latychevskaia T, McGrouther D, Cantoni M, Baldini E, White JS, Magrez A, Giamarchi T, Ronnow HM, Carbone F
  PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA 112, 14212 (2015).
  DOI: 10.1073/pnas.1513343112
• The role of the coherence in the cross-correlation analysis of diffraction patterns from two-dimensional dense mono-disperse systems Latychevskaia T, Mancini GF, Carbone F
  Scientific Report 5, 16573 (2015).
  DOI: 10.1038/srep16573
• Holography and coherent diffraction with low-energy electrons: A route towards structural biology at the single molecule level Latychevskaia T, Longchamp JN, Escher C, Fink HW
  Ultramicroscopy 159, 395 (2015).
  DOI: 10.1016/j.ultramic.2014.11.024
• Terahertz in-line digital holography of human hepatocellular carcinoma tissue Rong L, Latychevskaia T, Chen C, Wang D, Yu Z, Zhou X, Li Z, Huang H, Wang Y, Zhou Z
  Scientific Reports 5, 8445 (2015).
  DOI: 10.1038/srep08445
• Low-energy electron holographic imaging of individual tobacco mosaic virions Longchamp JN, Latychevskaia T, Escher C, Fink HW
  Applied Physics Letters 107, 133101 (2015).
  DOI: 10.1063/1.4931607
• Invariant time-dependent exchange perturbation theory and its application to the particles collision problem Orlenko EV, Latychevskaia T, Evstafev AV, Orlenko FE
  Theoretical Chemistry Accounts 134, 1 (2015).
  DOI: 10.1007/s00214-015-1646-2
• Atomically resolved structural determination of graphene and its point defects via extrapolation assisted phase retrieval Latychevskaia T, Fink HW
  Applied Physics Letters 106, 021908 (2015).
  DOI: 10.1063/1.4906089
• Practical algorithms for simulation and reconstruction of digital in-line holograms Latychevskaia T, Fink HW
  Applied Optics 54, 2424 (2015).
  DOI: 10.1364/AO.54.002424
• Reconstruction of purely absorbing, absorbing and phase-shifting, and strong phase-shifting objects from their single-shot in-line holograms Latychevskaia T, Fink HW
  Applied Optics 54, 3932 (2015).
  DOI: 10.1364/AO.54.003925

2014

• Holographic time-resolved particle tracking by means of three-dimensional volumetric deconvolution Latychevskaia T, Fink HW
  Optics Express 22, 20994 (2014).
  DOI: 10.1364/OE.22.020994
• On artefact-free reconstruction of low-energy (30-250 eV) electron holograms Latychevskaia T, Escher C, Longchamp JN, Fink HW
  Ultramicroscopy 145, 22 (2014).
  DOI: 10.1016/j.ultramic.2013.11.012
• Terahertz in-line digital holography of dragonfly hindwing: amplitude and phase reconstruction at enhanced resolution by extrapolation Rong L, Latychevskaia T, Wang D, Zhou X, Huang H, Li Z, Wang Y
  Optics Express 22, 17236 (2014).
  DOI: 10.1364/OE.22.017236
• Low-energy electron holographic imaging of ultraclean graphene-supported gold-nanorods Longchamp JN, Escher C, Latychevskaia T, Fink HW
  Ultramicroscopy 145, 80 (2014).
  DOI: 10.1016/j.ultramic.2013.10.018

2013

• Pulsed electron holography Germann M, Latychevskaia T, Escher C, Fink HW
  Applied Physics Letters 102, 203115 (2013).
  DOI: 10.1063/1.4807661
• Coherent diffraction and holographic imaging of individual biomolecules using low-energy electrons Latychevskaia T, Longchamp JN, Escher C, Fink HW
  Advancing Methods for Biomolecular Crystallography. NATO Science for Peace and Security Series A: Chemistry and Biology ~, 331 (2013).
  DOI: 10.1007/978-94-007-6232-9_29
• Resolution enhancement in digital holography by self-extrapolation of holograms Latychevskaia T, Fink HW
  Optics Express 21, 7726 (2013).
  DOI: 10.1364/OE.21.007726
• Graphene unit cell imaging by holographic coherent diffraction Longchamp JN, Latychevskaia T, Escher C, Fink HW
  Physical Review Letters 110, 255501 (2013).
  DOI: 10.1103/PhysRevLett.110.255501
• Coherent microscopy at resolution beyond diffraction limit using post-experimental data extrapolation Latychevskaia T, Fink HW
  Applied Physics Letters 103, 204105 (2013).
  DOI: 10.1063/1.4831985

2012

• When holography meets coherent diffraction imaging Latychevskaia T, Longchamp JN, Fink HW
  Optics Express 20, 28871 (2012).
  DOI: 10.1364/OE.20.028871
• Non-destructive imaging of an individual protein Longchamp JN, Latychevskaia T, Escher C, Fink HW
  Applied Physics Letters 101, 093701 (2012).
  DOI: 10.1063/1.4748113
• Low-energy electron transmission imaging of clusters on free-standing graphene Longchamp JN, Latychevskaia T, Escher C, Fink HW
  Applied Physics Letters 101, 113117 (2012).
  DOI: 10.1063/1.4752717

2011

• Novel Fourier-domain constraint for fast phase retrieval in coherent diffraction imaging Latychevskaia T, Longchamp JN, Fink HW
  Optics Express 19, 19330 (2011).
  DOI: 10.1364/OE.19.019330
• Individual filamentous phage imaged by electron holography Stevens GB, Krüger M, Latychevskaia T, Lindner P, Plückthun A, Fink HW
  Eurropean Biophysics Journal 40, 1197 (2011).
  DOI: 10.1007/s00249-011-0743-y

2010

• Nondestructive imaging of individual biomolecules Germann M, Latychevskaia T, Escher C, Fink HW
  Physical Review Letters 104, 095501 (2010).
  DOI: 10.1103/PhysRevLett.104.095501
• Off-axis and inline electron holography: Experimental comparison Latychevskaia T, Formanek P, Koch CT, Lubk A
  Ultramicroscopy 110, 472 (2010).
  DOI: 10.1016/j.ultramic.2009.12.007
• Depth-resolved holographic reconstructions by three-dimensional deconvolution Latychevskaia T, Gehri F, Fink HW
  Optics Express 18, 22527 (2010).
  DOI: 10.1364/OE.18.022527
• Graphene as a transparent conductive support for studying biological molecules by transmission electron microscopy Nair RR, Blake P, Blake JR, Zan R, Anissimova S, Bangert U, Golovanov AP, Morozov SV, Latychevskaia T, Geim AK, Novoselov KS
  Applied Physics Letters 97, 153102 (2010).
  DOI: 10.1063/1.3492845

2009

• Simultaneous reconstruction of phase and amplitude contrast from a single holographic record Latychevskaia, Fink HW
  Optics Express 17, 10697 (2009).
  DOI: 10.1364/OE.17.010697

2007

• Solution to the twin image problem in holography Latychevskaia, Fink HW
  Physical Review Letters 98, 233901 (2007).
  DOI: 10.1103/PhysRevLett.98.233901

2006

• Resorcin[4]arene cavitand-based molecular switches Azov VA, Beeby A, Cacciarini M, Cheetham AG, Diederich F, Frei M, Gimzewski JK, Gramlich V, Hecht B, Jaun B, Latychevskaia T, Lieb A, Lill Y, Marotti F, Schlegel A, Schlittler RR, Skinner PJ, Seiler P, Yamakoshi Y
  Advanced Functional Materials 16, 147 (2006).
  DOI: 10.1002/adfm.200500181
• Direct evidence for conduction pathways in a solid electrolyte Escher C, Latychevskaia T, Fink HW, Pohl DW
  Physical Review Letters 97, 136601 (2006).
  DOI: 10.1103/PhysRevLett.97.136601
• A single-molecule study of polycrystalline microstructure by fluorescence polarization spectroscopy Latychevskaia T, Renn A, Wild UP
  Journal of Luminescence 118, 111 (2006).
  DOI: 10.1016/j.jlumin.2005.08.008
• A quantum mechanical scheme to reduce radiation damage in electron microscopy Okamoto H, Latychevskaia T, Fink HW
  Applied Physics Letters 88, 164103 (2006).
  DOI: 10.1063/1.2191096
• Axisymmetric liquid hanging drops Meister EC, Latychevskaia T
  Journal of Chemical Education 83, 117 (2006).
  DOI: 10.1021/ed083p117

2003

• Single molecule spectroscopy Latychevskaia T, Liang KK, Hayashi M, Chang CH, Renn A, Wild UP, Hsu JH, Chang TC, Lin SH
  Journal of the Chinese Chemical Society 50, 477 (2003).
  DOI: 10.1002/jccs.200300075

2002

• Theory of the Stark effect on single molecular spectroscopy Hayashi M, Chiang CH, Liang KK, Shiu YJ, Chang CH, Wu DY, Li FY, Chang TC, Wild UP, Latychevskaia T, Lin SH
  Journal of the Chinese Chemical Society 49, 797 (2002).
  DOI: 10.1002/jccs.200200114
• Higher-order Stark effect on single-molecules Latychevskaia T, Renn A, Wild UP
  Chemical Physics 282, 109 (2002).
  DOI: 10.1016/S0301-0104(02)00621-3

2000

• Radio-frequency Stark effect modulation of single-molecule lines Kador L, Latychevskaia T, Renn A, Wild UP
  Journal of Luminescence 86, 189 (2000).
  DOI: 10.1016/S0022-2313(00)00162-9

1999

• Detection and spectroscopy of single molecules in rare gas matrices: dibenzanthanthrene in krypton and xenon Sepiol J, Starukhin A, Kolos R, Latychevskaia T, Jasny J, Renn A, Wild UP
  Chemical Physics Letters 311, 29 (1999).
  DOI: 10.1016/S0009-2614(99)00753-8
• Imaging and spectroscopy of terrylene molecules isolated in vapor-deposited n-alkane matrices Sepiol J, Starukhin A, Latychevskaia T, Jasny J, Renn A, Wild UP
  Chemical Physics 247, 35 (1999).
  DOI: 10.1016/S0301-0104(99)00099-3
• Absorption spectroscopy on single molecules in solids Kador L, Latychevskaia T, Renn A, Wild UP
  Journal of Chemical Physics 111, 8755 (1999).
  DOI: 10.1063/1.480222
• Advanced holographic nondestructive testing system for residual stress analysis Kniazkov A, Onischenko YT, Dovgalenko GE, Salamo GJ, Latychevskaia T
  Proceedings of SPIE 3678, 73 (1999).
  DOI: 10.1117/12.347399

1998

• Recording and reconstruction of reflection and transmission holograms with a cw laser diode Krylov VN, Mikhailov VN, Weitzel KT, Latychevskaia T, Sizov VN, Renn A, Wild UP
  SPIE Proceedings 3293, 131 (1999).
  DOI: 10.1117/12.303646
• Pulse recording of slanted fringe holograms in DuPont photopolymer Mikhailov VN, Weitzel TK, Latychevskaia T, Krylov V, Wild UP
  SPIE Proceedings 3294, 132 (1999).
  DOI: 10.1117/12.304533
• The method of exchange perturbation theory as applied to magnetic ordering in high-Tc materials Orlenvko, EV, Latychevskaia T
  Journal of Experimental and Theoretical Physics 86, 2129 (1999).
  DOI: 10.1134/1.558587