Persons: Tsar'kov, Igor' Germanovich

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Tsar'kov, Igor' Germanovich

Total publications:	115 (113)
in MathSciNet:	81 (80)
in zbMATH:	74 (73)
in Web of Science:	59 (58)
in Scopus:	69 (69)
Cited articles:	94
Citations:	958
Talks:	13

Number of views:
This page:	7061
Abstract pages:	44910
Full texts:	20389
Talk pages:	3140
Video records:	118

Professor

Doctor of physico-mathematical sciences (1996)

Speciality:

01.01.01 (Real analysis, complex analysis, and functional analysis)

Birth date:

5.01.1960

E-mail:

Keywords:

approximations, smooth approximations, extension of maps.

Main publications:

Ogranichennye chebyshevskie mnozhestva v konechnomernykh banakhovykh prostranstvakh // Matematicheskie zametki. T. 36, # 1. 1984. S. 73–87.
O kompaktnykh i slabo kompaktnykh chebyshevskikh mnozhestvakh v lineinykh normirovannykh prostranstvakh // Trudy MIAN. T. 189. 1989. S. 169–184.
Neravenstvo tipa Dzheksona dlya abstraktnykh funktsii // Matematicheskii sbornik. T. 180, # 5. 1989. S. 121–123.
O globalnom suschestvovanii neyavnoi funktsii // Matematicheskii sbornik. T. 184, # 7. 1993. S. 79–116.
Sglazhivanie abstraktnykh funktsii // Matematicheskii sbornik. T. 185, # 11. 1994. S. 119–144.

https://www.mathnet.ru/eng/person8789

List of publications on Google Scholar

https://mathscinet.ams.org/mathscinet/MRAuthorID/212301

https://elibrary.ru/author_items.asp?authorid=7947

ISTINA

https://istina.msu.ru/workers/1227900

https://orcid.org/0000-0002-5943-3711

https://www.scopus.com/authid/detail.url?authorId=6602443197

List of publications:

scientific publications

by years

by types

by times cited

common list

		Citations (Crossref Cited-By Service + Math-Net.Ru)

1.	A. R. Alimov, I. G. Tsar'kov, “Approximaively weakly compact sets”, Mat. Sb.

2026
2.	I. G. Tsar'kov, “Approximative compactness for piecewise approximatively compact sets”, Mat. Zametki, 119:5 (2026) (to appear)

2025
3.	I. G. Tsar'kov, “Properties of at most countable unions of pairwise disjoint sets in asymmetric spaces”, Sb. Math., 216:2 (2025), 257–269
4.	I. G. Tsar'kov, “Solarity of boundedly weakly compact sets”, Math. Notes, 117:4 (2025), 650–655
5.	A. R. Alimov, I. G. Tsar'kov, “Stability of approximation in classical problems of geometric approximation theory”, Izv. Math., 89:6 (2025), 1087–1107
6.	I. G. Tsar'kov, “Density of points of continuity of the distance function for union of half-spaces in asymmetric spaces”, Math. Notes, 118:3 (2025), 614–623
7.	A. R. Alimov, I. G. Tsar'kov, “Projection closed sets and Efimov–Stechkin spaces”, Trudy Inst. Mat. i Mekh. UrO RAN, 31, no. 3, 2025, 20–35
8.	I.G.Tsar'kov, “Convexity of weakly compact sets in normed linear spaces”, Russ. J. Math. Phys., 32:3 (2025), 585–589
9.	I.G.Tsar'kov, “Solarity of boundedly ae-compact sets”, Russ. J. Math. Phys., 32:2 (2025), 410-415
10.	I. G. Tsarkov, “Svoistva solnechnosti dlya kusochno approksimativno kompaktnykh mnozhestv”, Matem. trudy, 28:4 (2025), 174–186
11.	I. G. Tsar'kov, “Solarity of Deutsch boundedly compact sets”, Russ. J. Math. Phys., 32:4 (2025), 827-832

2024
12.	I. G. Tsar'kov, “$\theta$-metric function in the problem of minimization of functionals”, Izv. Math., 88:2 (2024), 369–388
13.	A. R. Alimov, I. G. Tsar'kov, “Chebyshev sets that are unions of planes”, Russian Math. Surveys, 79:2 (2024), 361–362
14.	A. R. Alimov, I. G. Tsar'kov, “Chebyshev unions of planes, and their approximative and geometric properties”, J. Approx. Theory, 298 (2024), 106009, 12 pp.	9 ^[x]
15.	A. R. Alimov, I. G. Tsar'kov, “Chebyshev sets composed of subspaces in asymmetric normed spaces”, Izv. Math., 88:6 (2024), 1032–1049
16.	I. G. Tsar'kov, “Uniformly convex cone spaces and properties of convex sets in them”, Math. Notes, 116:4 (2024), 831–840
17.	A. R. Alimov, I. G. Tsar'kov, “Classical concepts of approximation theory in asymmetric CLUR-spaces”, Math. Notes, 116:3 (2024), 408–420
18.	A. R. Alimov, I. G. Tsar'kov, “Connectedness and approximative properties of sets in asymmetric spaces”, Filomat, 38:9 (2024), 3243–3259	3 ^[x]
19.	I. G. Tsar'kov, “Convexity of $\delta$-suns and $\gamma$-suns in asymmetric spaces”, Russ. J. Math. Phys., 31:2 (2024), 325-334	8 ^[x]
20.	I. G. Tsar'kov, “Properties of Sets in Asymmetric Spaces”, Lobachevskii Journal of Mathematics, 45:6 (2024), 2971–2974
21.	A. R. Alimov, I. G. Tsarkov, “Monotonno lineino svyaznye mnozhestva v geometricheskoi teorii priblizheniya i ee prilozheniyakh”, Matematika i teoreticheskie kompyuternye nauki, 2:2 (2024), 30-46
22.	I.G Tsar'kov., “Relations between various types of suns in asymmetric spaces”, Russ. J. Math. Phys., 31 (2024), 562-567	1 ^[x]
23.	I. G. Tsar'kov, “Local and global suns”, Russ. J. Math. Phys., 31:4 (2024), 765–773	3 ^[x]

2023
24.	I. G. Tsar'kov, “Continuous selections of set-valued mappings and approximation in asymmetric and semilinear spaces”, Izv. Math., 87:4 (2023), 835–851
25.	I. G. Tsar'kov, “Chebyshev Sets with Piecewise Continuous Metric Projection”, Math. Notes, 113:6 (2023), 840–849
26.	A. R. Alimov, K. S. Ryutin, I. G. Tsar'kov, “Existence, uniqueness, and stability of best and near-best approximations”, Russian Math. Surveys, 78:3 (2023), 399–442
27.	I. G. Tsar'kov, “Kuhn–Tucker Type Theorems in Cone and Linear Normed Spaces”, Math. Notes, 114:6 (2023), 1373–1382
28.	I. G. Tsar'kov, “Connectedness in asymmetric spaces”, J. Math. Anal. Appl., 527:1 (2023), 127381, 14 pp.
29.	A. R. Alimov, I. G. Tsar'kov, “Max-solar properties of sets in normed and asymmetrically normed spaces”, J. Convex Analysis, 30:1 (2023), 159–174
30.	I. G. Tsar'kov, “Estimates of the Chebyshev radius in terms of the MAX-metric function and the MAX-projection operator”, Russian J. Math. Phys., 30:1 (2023), 128-134	8 ^[x]
31.	I. G. Tsar'kov, “Reflexivity for spaces with extended norm”, Russ. J. Math. Phys., 30:3 (2023), 399 - 417	3 ^[x]
32.	I. G. Tsar'kov, “Smoothness of solutions of the eikonal equation and regular points of their level surfaces”, Russ. J. Math. Phys., 30:2 (2023), 259 - 269	8 ^[x]

2022
33.	I. G. Tsar'kov, “Solarity and connectedness of sets in the space $C[a,b]$ and in finite-dimensional polyhedral spaces”, Sb. Math., 213:2 (2022), 268–282
34.	I. G. Tsar'kov, “Continuity of a Metric Function and Projection in Asymmetric Spaces”, Math. Notes, 111:4 (2022), 616–623
35.	I. G. Tsar'kov, “Approximative and structural properties of sets in asymmetric spaces”, Izv. Math., 86:6 (2022), 1240–1253
36.	Alexey R. Alimov, Igor' G. Tsar'kov, “Ball-complete sets and solar properties of sets in asymmetric spaces”, Result. Math., 77 (2022), 86, 1 pp.	23 ^[x]
37.	A. R. Alimov, I. G. Tsar'kov, “Some Classical Problems of Geometric Approximation Theory in Asymmetric Spaces”, Math. Notes, 112:1 (2022), 3–16
38.	I. G. Tsar'kov, “Uniformly and locally convex asymmetric spaces”, Sb. Math., 213:10 (2022), 1444–1469
39.	A. R. Alimov, I. G. Tsarkov, “$\overset{\circ}B$-complete sets: approximative and structural properties”, Siberian Math. J., 63 (2022), 412–420
40.	Alexey R. Alimov, Igor' G. Tsar'kov, “Suns, moons, and $\mathring B$-complete sets in asymmetric spaces”, Set-Valued Var. Anal., 30 (2022), 1233–1245	26 ^[x]
41.	I. G. Tsar'kov, “Density of the Points of Continuity of the Metric Function and Projection in Asymmetric Spaces”, Math. Notes, 112:6 (2022), 1017–1024
42.	A. R. Alimov, I. G. Tsar'kov, “Classical problems of rational approximation”, Dokl. Math., 106:2 (2022), 305–307
43.	I. G. Tsar'kov, “Properties of Chebyshev generalized rational fractions in $L^1$”, Russian. J. Math. Phys., 29 (2022), 583-587	5 ^[x]
44.	A. R. Alimov, I. G. Tsar'kov, “Solarity and proximinality in generalized rational approximation in spaces $C(Q)$ and $L^p$”, Russian. J. Math. Phys., 29 (2022), 291–305	16 ^[x]
45.	I. G. Tsar'kov, “Geometry of the singular set of hypersurfaces and the eikonal equation”, Russian. J. Math. Phys., 2022, 240-248	11 ^[x]
46.	I. G. Tsar'kov, “Uniformly and locally convex asymmetric spaces”, Russian. J. Math. Phys., 29:1 (2022), 141-14	11 ^[x]

2016
47.	I. G. Tsar'kov, “Local and global continuous $\varepsilon$-selection”, Izv. Math., 80:2 (2016), 442–461

2021
48.	A. R. Alimov, I. G. Tsar'kov, “Smoothness of subspace sections of the unit balls of $C(Q)$ and $L^1$”, J. Approx. Theory, 65 (2021), 105552, 8 pp.	10 ^[x]
49.	I. G. Tsar'kov, “Properties of Monotone Connected Sets”, Math. Notes, 109:5 (2021), 819–827
50.	I. G. Tsar'kov, “Uniform Convexity in Nonsymmetric Spaces”, Math. Notes, 110:5 (2021), 773–783
51.	A. R. Alimov, I. G. Tsar'kov, “Approximatively Compact Sets in Asymmetric Efimov–Stechkin Spaces and Convexity of Almost Suns”, Math. Notes, 110:6 (2021), 947–951
52.	I. G. Tsar'kov, “Properties of Suns in the Spaces L1 and C(Q)”, Russian. J. Math. Phys., 28 (2021), 398-405	14 ^[x]

2020
53.	I. G. Tsar'kov, “The Geometry of a Singular Set of Hypersurfaces and the Eikonal Equation”, Math. Notes, 108:3 (2020), 426–433
54.	I. G. Tsar'kov, “Approximative properties of sets and continuous selections”, Sb. Math., 211:8 (2020), 1190–1211

2019
55.	I. G. Tsar'kov, “Smooth solutions of the eikonal equation and the behaviour of local minima of the distance function”, Izv. Math., 83:6 (2019), 1234–1258
56.	I. G. Tsar'kov, “Local Approximation Properties of Sets and Continuous Selections on Them”, Math. Notes, 106:6 (2019), 995–1008
57.	A. R. Alimov, I. G. Tsar'kov, “Chebyshev centres, Jung constants, and their applications”, Russian Math. Surveys, 74:5 (2019), 775–849
58.	I. G. Tsar'kov, “Weakly monotone sets and continuous selection in asymmetric spaces”, Sb. Math., 210:9 (2019), 1326–1347
59.	I. G. Tsar'kov, “Metric Max-Distance Function in Max-Approximation Problems”, Russ. J. Math. Phys., 26:2 (2019), 219-226	2 ^[x]

2018
60.	I. G. Tsar'kov, “Continuous selections for metric projection operators and for their generalizations”, Izv. Math., 82:4 (2018), 837–859
61.	I. G. Tsar'kov, “New Criteria for the Existence of a Continuous $\varepsilon$-Selection”, Math. Notes, 104:5 (2018), 727–734
62.	I. G. Tsar'kov, “Continuous selections in asymmetric spaces”, Sb. Math., 209:4 (2018), 560–579
63.	I. G. Tsar'kov, “Stability of the relative Chebyshev projection in polyhedral spaces”, Trudy Inst. Mat. i Mekh. UrO RAN, 24, no. 4, 2018, 235–245
64.	I. G. Tsar'kov, “Weakly monotone sets and continuous selection from a near-best approximation operator”, Proc. Steklov Inst. Math., 303 (2018), 227–238
65.	I. G. Tsar'kov, “Smoothing of Real-Valued Functions on Uniformly Smooth Spaces”, Russ. J. Math. Phys., 25 (2018), 409-414

2017
66.	I. G. Tsar'kov, “Continuous selection for set-valued mappings”, Izv. Math., 81:3 (2017), 645–669

2020
67.	I. G. Tsar'kov, “Some applications of geometric theory of approximations”, Journal of Mathematical Sciences, 245:1 (2020), 64–82

2017
68.	I. G. Tsar'kov, “Continuous $\varepsilon$-Selection and Monotone Path-Connected Sets”, Math. Notes, 101:6 (2017), 1040–1049
69.	I. G. Tsar'kov, “Singular sets of surfaces”, Russ. J. Math. Phys., 24 (2017), 263–271	13 ^[x]
70.	I. G. Tsar'kov, “Properties of C^1-solution to the eikonal equation”, Lobachevskii J Math, 38:4 (2017), 762-765	9 ^[x]

2016
71.	I. G. Tsar'kov, “Local and global continuous $\varepsilon$-selection”, Izv. Math., 80:2 (2016), 442–461
72.	A. R. Alimov, I. G. Tsar'kov, “Connectedness and solarity in problems of best and near-best approximation”, Russian Math. Surveys, 71:1 (2016), 1–77
73.	I. G. Tsar'kov, “Continuous $\varepsilon$-selection”, Sb. Math., 207:2 (2016), 267–285
74.	A. R. Alimov, I. G. Tsar'kov, “Connectedness and other geometric properties of suns and Chebyshev sets”, J. Math. Sci., 217:6 (2016), 683–730

2011
75.	V. V. Arestov, V. I. Berdyshev, N. I. Chernykh, T. V. Demina, N. N. Kholschevnikova, S. V. Konyagin, Yu. N. Subbotin, S. A. Telyakovskii, I. G. Tsar'kov, V. A. Yudin, “Exposition of the lectures by S. B. Stechkin on approximation theory”, Eurasian Math. J., 2:4 (2011), 5–155	3 ^[x]
76.	I. G. Tsar'kov, “Stability of Unique Solvability of Quasilinear Equations Given Additional Data”, Math. Notes, 90:6 (2011), 894–919
77.	I. G. Tsar'kov, “Properties of Sets Admitting Stable $\varepsilon$-Selections”, Math. Notes, 89:4 (2011), 572–576
78.	I. G. Tsar'kov, “Approximative compactness and nonuniqueness in variational problems, and applications to differential equations”, Sb. Math., 202:6 (2011), 909–934

2010
79.	N. N. Andreev, S. V. Konyagin, A. G. Sergeev, Yu. N. Subbotin, S. A. Telyakovskii, N. N. Kholshchevnikova, I. G. Tsar'kov, “International conference “Approximation theory” (Moscow, 23–26 august 2010)”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 4, 2010, 314–315

2009
80.	I. G. Tsar'kov, “Stability of the unique solvability for some differential equations”, Proc. Steklov Inst. Math. (Suppl.), 264, suppl. 1 (2009), S185–S198

2008
81.	V. I. Berdyshev, V. A. Kaminsky, S. V. Konyagin, B. P. Osilenker, M. V. Samokhin, S. A. Telyakovskii, I. G. Tsar'kov, V. A. Shmatkov, “Alexandr L'vovich Garkavi (obituary)”, Russian Math. Surveys, 63:3 (2008), 547–549

2006
82.	I. G. Tsar'kov, “Local Smoothing of Uniformly Smooth Maps”, Funct. Anal. Appl., 40:3 (2006), 200–206
83.	I. G. Tsar'kov, “Stability of Unique Solvability in an Ill-Posed Dirichlet Problem”, Math. Notes, 79:2 (2006), 268–282

2005
84.	I. G. Tsar'kov, “Smoothing of Hilbert-valued uniformly continuous maps”, Izv. Math., 69:4 (2005), 149–160
85.	I. G. Tsar'kov, “Localization of smooth and smoothing of uniformly continuous mappings”, Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 2, S196–S210

2004
86.	I. G. Tsar'kov, “Nonunique Solvability of Certain Differential Equations and Their Connection with Geometric Approximation Theory”, Math. Notes, 75:2 (2004), 259–271

1999
87.	I. G. Tsar'kov, E. T. Shavgulidze, “Smooth Isometric Immersions into the Infinite-Dimensional Sphere”, Funct. Anal. Appl., 33:3 (1999), 239–240
88.	I. G. Tsar'kov, “Extension of Hilbert-valued Lipschitz mappings”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1999, no. 6, 9–16

1997
89.	M. I. Karlov, I. G. Tsar'kov, “Convexity and connectedness of Chebyshev sets and suns”, Fundam. Prikl. Mat., 3:4 (1997), 967–978
90.	I. G. Tsar'kov, “Smoothing of functions in finite-dimensional Banach spaces”, Izv. Math., 61:1 (1997), 207–223
91.	I. G. Tsar'kov, “Smoothing of Functions on a Hilbert Ball”, Proc. Steklov Inst. Math., 219 (1997), 403–412

1996
92.	I. G. Tsar'kov, “On $\epsilon$-selections”, Dokl. Akad. Nauk, 349:6 (1996), 747–748
93.	I. G. Tsar'kov, “On smooth selections from sets of almost Chebyshev centers”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1996, no. 2, 92–94

1995
94.	I. G. Tsar'kov, “Polynomial Approximation of Vector Functions”, Funct. Anal. Appl., 29:3 (1995), 222–223
95.	I. G. Tsar'kov, “On the extension and smoothing of vector-valued functions”, Izv. Math., 59:4 (1995), 847–879
96.	I. G. Tsar'kov, “Some topics on the continuation and smoothing of vector functions”, Math. Notes, 58:6 (1995), 1327–1335
97.	I. G. Tsar'kov, “Right inverse operators and $\varepsilon$-selections”, Russian Math. Surveys, 50:2 (1995), 453–454
98.	I. G. Tsar'kov, “Some theorems on function smoothing”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1995, no. 1, 79–81
99.	I. G. Tsar'kov, “Extension theorems and approximation of functions in Banach spaces”, Dokl. Math., 50:2 (1995), 348–350

1994
100.	I. G. Tsar'kov, “Linear methods in some smoothing problems”, Math. Notes, 56:6 (1994), 1255–1270

1995
101.	I. G. Tsar'kov, “Smoothing of abstract functions”, Russian Acad. Sci. Sb. Math., 83:2 (1995), 405–430

1993
102.	I. G. Tsar'kov, “Smoothing of uniformly continuous mappings in $L_p$ spaces”, Math. Notes, 54:3 (1993), 957–967

1994
103.	I. G. Tsar'kov, “On global existence of an implicit function”, Russian Acad. Sci. Sb. Math., 79:2 (1994), 287–313

1992
104.	I. G. Tsar'kov, “Theorems on the global existence of an implicit function and their applications”, Dokl. Math., 45:3 (1992), 638–640

1994
105.	I. G. Tsar'kov, “Widths and Jackson's type inequality for abstract functions”, Proc. Steklov Inst. Math., 198 (1994), 209–221

1990
106.	I. G. Tsar'kov, “Properties of the sets that have a continuous selection from the operator $P^\delta$”, Math. Notes, 48:4 (1990), 1052–1058
107.	I. G. Tsar'kov, “Continuity of the metric projection, structural and approximate properties of sets”, Math. Notes, 47:2 (1990), 218–227

1989
108.	I. G. Tsar'kov, “Local ‘homogeneity’ of sets of uniqueness”, Mat. Zametki, 45:5 (1989), 121–123

1990
109.	I. G. Tsar'kov, “The inequality of Jackson type for abstract functions”, Math. USSR-Sb., 67:1 (1990), 117–142
110.	I. G. Tsar'kov, “Compact and weakly compact Chebyshev sets in linear normed spaces”, Proc. Steklov Inst. Math., 189 (1990), 199–215

1988
111.	I. G. Tsar'kov, “Compact and weakly compact Chebyshev sets in linear normed spaces”, Dokl. Math., 37:3 (1988), 629–631
112.	S. V. Konyagin, I. G. Tsar'kov, “On smoothing of maps in normed spaces”, Russian Math. Surveys, 43:4 (1988), 213–214

1986
113.	I. G. Tsar'kov, “Relations between certain classes of sets in Banach spaces”, Math. Notes, 40:2 (1986), 597–610
114.	S. V. Konyagin, I. G. Tsar'kov, “Efimov–Stechkin spaces”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1986, no. 5, 20–27

1984
115.	I. G. Tsar'kov, “Bounded Chebyshev sets in finite-dimensional Banach spaces”, Math. Notes, 36:1 (1984), 530–537

Presentations in Math-Net.Ru

1.	Слабо компактные и компактные по Дойчу множества в теории приближений. Приложения к экспоненциальным суммам I. G. Tsar'kov, A. R. Alimov Seminar on Theory of Functions of Real Variables November 14, 2025 18:30
2.	Приближение набором множеств. Кусочно аппроксимативно компактные чебышёвские множества. Солнечность ограниченно слабо компактных множеств I. G. Tsar'kov, A. R. Alimov Seminar on Theory of Functions of Real Variables November 7, 2025 18:30
3.	Mach disks and caustic reflections, caustics, application to astrophysics I. G. Tsar'kov Weekly Mathematics Research Seminars at ADA University March 1, 2022 16:00
4.	Caustics, applications in natural sciences. Mach disks, reflection caustics. I. G. Tsar'kov Geometric Theory of Optimal Control October 6, 2021 16:45
5.	Caustics, Mach disks, application to astrophysics I. G. Tsar'kov International Conference "Approximation Theory and Applications" Dedicated to the 100th Anniversary S. B. Stechkin September 9, 2021 12:30
6.	Mach disks and caustic reflections, caustics, application to astrophysics I. G. Tsar’kov Mathematical Physics, Dynamical Systems and Infinite-Dimensional Analysis – 2021 July 6, 2021 16:10
7.	Законы преломления и отражения в неевклидовых пространствах, каустика, приложения к астрофизике I. G. Tsar'kov Differential equations, analysis and control: theory and applications March 15, 2021 18:25
8.	Решение задач о гладких C^1-решений уравнения эйконала, принцип отражения, зеркала I. G. Tsar'kov, A. R. Alimov Geometric Theory of Optimal Control March 14, 2018 18:30
9.	Экстремумы функции-расстояния, уравнение эйконала и связанные с ним геометрические задачи I. G. Tsar'kov Differential equations, analysis and control: theory and applications February 12, 2018 18:25
10.	Гладкие решения уравнения эйконала и поведение локальных минимумов функции расстояния I. G. Tsar'kov Seminar on Theory of Functions of Real Variables December 1, 2017 18:30
11.	Слабо монотонные множества относительно определяющих множеств. Связь с непрерывными $(r,\varepsilon)$-выборками I. G. Tsar'kov Seminar on Approximation Theory November 2, 2017 10:30
12.	Достаточные условия существования непрерывной $\varepsilon$-выборки I. G. Tsar'kov International conference on Function Spaces and Approximation Theory dedicated to the 110th anniversary of S. M. Nikol'skii May 25, 2015 17:55

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