# zbMATH — the first resource for mathematics

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 Author ID: zhuk.vladimir-vasilievich Published as: Zhuk, V.; Zhuk, V. V.; Zhuk, Vladimir; Zhuk, Vladimir Vasilievich; Zuk, V. V. Homepage: http://www.math.spbu.ru/analysis/members/zhuk/ External Links: MGP · Math-Net.Ru · Wikidata · ORCID
 Documents Indexed: 167 Publications since 1965, including 4 Books
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#### Co-Authors

 85 single-authored 27 Natanson, Garal’d Isidorovich 27 Vinogradov, Oleg Leonidovich 9 Dodonov, N. Yu. 6 Babushkin, Max V. 4 Bure, Vladimir M. 2 Dron’, Vera O. 2 Khavin, Viktor Petrovich 2 Pudovkin, A. A. 2 Zhuk, A. S. 1 Faĭnshmidt, V. L. 1 Goluzina, E. G. 1 Iljina, Anna V. 1 Kuźmina, Galina Vasil’evna 1 Kuzyutin, V. F. 1 Malozemov, Vasily Nikolaevich 1 Petrosyan, Leon Aganesovich 1 Pimenov, S. Yu. 1 Puerov, G. Yu. 1 Shirokov, Nikolaĭ Alekseevich 1 Tumka, Oleg A. 1 Yeung, David Wing-Kay
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#### Serials

 34 Journal of Mathematical Sciences (New York) 29 Vestnik Leningradskogo Universiteta. Matematika, Mekhanika, Astronomiya 24 Vestnik Leningrad University. Mathematics 11 Soviet Mathematics. Doklady 11 Vestnik St. Petersburg University. Mathematics 10 Problemy Matematicheskogo Analiza 5 Izvestiya Vysshikh Uchebnykh Zavedeniĭ, Matematika 3 Mathematical Notes 3 Zapiski Nauchnykh Seminarov POMI 3 Doklady Mathematics 2 Matematicheskie Zametki 2 Siberian Mathematical Journal 2 Sibirskiĭ Matematicheskiĭ Zhurnal 2 Vestnik Leningradskogo Universiteta. Seriya 1. Matematika, Mekhanika, Astronomiya 2 Russian Academy of Sciences. Doklady. Mathematics 2 St. Petersburg Mathematical Journal 2 Matematicheskiĭ Zhurnal 2 Voprosy Mekhaniki i Protsessov Upravleniya 1 Analysis Mathematica 1 Russian Mathematical Surveys 1 Studia Scientiarum Mathematicarum Hungarica 1 Vestnik Sankt-Peterburgskogo Universiteta. Seriya 1. Matematika, Mekhanika, Astronomiya 1 Trudy Sankt-Peterburgskogo Matematicheskogo Obshchestva
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#### Fields

 107 Approximations and expansions (41-XX) 90 Harmonic analysis on Euclidean spaces (42-XX) 17 Real functions (26-XX) 8 Numerical analysis (65-XX) 5 Functional analysis (46-XX) 4 History and biography (01-XX) 2 Functions of a complex variable (30-XX) 2 Sequences, series, summability (40-XX) 1 Operator theory (47-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

#### Citations contained in zbMATH

54 Publications have been cited 180 times in 107 Documents Cited by Year
Approximation of periodic functions. (Approksimatsiya periodicheskikh funktsij). Zbl 0521.42003
Zhuk, V. V.
1982
Approximation of functions and numerical integration. Zbl 0942.41500
Zhuk, V. V.; Kuzyutin, V. F.
1995
Trigonometrical Fourier series and elements of approximation theory. Textbook. (Trigonometricheskie ryady Fur’e i ehlementy teorii approksimatsii. Uchebnoe posobie). Zbl 0535.42010
Zhuk, V. V.; Natanson, G. I.
1983
Functions of class Lip 1 and S. N. Bernstein polynomials. Zbl 0667.41004
Zhuk, V. V.
1989
Some sharp inequalities between best approximations and moduli of continuity. Zbl 0231.42004
Zhuk, V. V.
1971
Sharp estimates for deviations of linear approximation methods for periodic functions by linear combinations of moduli of continuity of different order. Zbl 1050.41018
Vinogradov, O. L.; Zhuk, V. V.
2003
Estimates for functionals with a known moment sequence in terms of deviations of Steklov type means. Zbl 1303.41006
Vinogradov, O. L.; Zhuk, V. V.
2011
Some orthogonalities in approximation theory. Zbl 1127.42005
Zhuk, A. S.; Zhuk, V. V.
2004
On approaching the differentiable periodic functions by linear methods. Zbl 0412.42003
Zhuk, V. V.; Natanson, G. I.
1977
Estimates for functionals with a known, finite set of moments, in terms of moduli of continuity, and behavior of constants, in the Jackson-type inequalities. Zbl 1275.41016
Vinogradov, O. L.; Zhuk, V. V.
2013
Strong approximation of periodic functions. Zbl 0721.42002
Zhuk, V. V.
1989
On the theory of cubic periodic splines with equidistant nodes. Zbl 0531.41010
Zhuk, V. V.; Natanson, G. I.
1984
Approximation of periodic functions by Fejer’s sums and the de la Vallee- Poussin integral. Zbl 0288.41013
Zhuk, V. V.
1974
Some sharp inequalities between uniform best approximations of periodic functions. Zbl 0239.42003
Zhuk, V. V.
1971
The rate of decrease of constants in Jackson type inequalities in dependence of the order of the continuity modulus. Zbl 1303.41007
Vinogradov, O. L.; Zhuk, V. V.
2011
Approximation of periodic functions by Steklov averages in $$L_{2}$$. Zbl 1202.41021
Dron’, V. O.; Zhuk, V. V.
2007
On approximate characteristics of functions of many variables occurring in saturation classes of continuity moduli of different orders. Zbl 1114.41014
Dodonov, N. Yu.; Zhuk, V. V.
2006
On the approximation of periodic functions by linear approximation methods. Zbl 1125.42003
Zhuk, A. S.; Zhuk, V. V.
2006
Uniform approximation of nonperiodic functions defined on the entire axis. Zbl 1099.41021
Dodonov, N. Yu.; Zhuk, V. V.
2004
On uniform approximation in $$\mathbb R^2$$ of continuous functions of two variables with bounded variation in the sense of Hardy. Zbl 1099.41015
Dodonov, N. Yu.; Zuk, V. V.
2004
Sharp Kolmogorov-type inequalities for moduli of continuity and best approximations by trigonometric polynomials and splines. Zbl 1078.42001
Vinogradov, O. L.; Zhuk, V. V.
2002
Seminorms and moduli of continuity of higher orders. Zbl 0981.42500
Zhuk, V. V.
1993
On the question of approximation of functions by means of positive operators. Zbl 0436.41011
Zhuk, V.; Natanson, G.
1977
On the problem of constants in direct theorems of the approximation theory for differentiable functions. Zbl 0362.41013
Zhuk, V. V.
1976
On the representation of a periodic function by a bounded semiadditive operator. Zbl 0167.05201
Zhuk, V. V.
1966
Voronovskaya-Bernstein type asymptotic formulas in strong form. Zbl 1357.41017
Zhuk, V. V.; Babushkin, Max V.; Pudovkin, A. A.
2016
Some inequalities for trigonometric polynomials and Fourier coefficients. Zbl 1337.42001
Zhuk, V. V.; Puerov, G. Yu.
2015
Estimates for functionals with a known finite set of moments in terms of high order moduli of continuity in spaces of functions defined on a segment. Zbl 1305.41015
Vinogradov, O. L.; Zhuk, V. V.
2014
Linear methods in the proof of Jackson type inequalities and applications to estimates of functionals with two known moments. Zbl 1302.41017
Vinogradov, O. L.; Zhuk, V. V.
2014
Jackson type inequalities for deviations of the Riesz averages and applications to estimates of functionals with two known moments. Zbl 1301.41012
Vinogradov, O. L.; Zhuk, V. V.
2014
Estimates for the best approximations of a periodic function by linear combinations of values of the function and its primitives. Zbl 1282.42004
Zhuk, V. V.
2013
Inequalities of the type of the generalized Jackson theorem for the best approximations. Zbl 1280.41014
Zhuk, V. V.
2013
Estimates for functionals with a known finite set of moments in terms of deviations of operators constructed with the use of the Steklov averages and finite differences. Zbl 1262.41010
Vinogradov, O. L.; Zhuk, V. V.
2012
Estimates for functionals by deviations of the Riesz sums in seminormed spaces. Zbl 1205.41027
Dodonov, N. Yu.; Zhuk, V. V.
2009
Extensions to the Jackson-type and Landau-Kolmogorov-type sharp inequalities for derivatives of low order. Zbl 1096.41012
Vinogradov, O. L.; Zhuk, V. V.
2003
Estimates of errors of quadrature formulas by linear combinations of the uniform norm and oscillation of derivatives with both sharp constants. Zbl 1050.26022
Vinogradov, O. L.; Zhuk, V. V.
2003
Seminorms and continuity modules for functions defined on a segment. Zbl 1071.41008
Zhuk, V. V.; Natanson, G. I.
2001
Sharp estimates for the deviation of the mean value of a periodic function in terms of moduli of continuity of higher order. Zbl 0992.42001
Vinogradov, O. L.; Zhuk, V. V.
2001
Estimates for the deviation of the mean-value of a function by the moduli of continuity of its odd derivatives with the smallest constant and step. Zbl 1043.42002
Vinogradov, O. L.; Zhuk, V. V.
2000
Approximation of functions on standard simplexes. Zbl 0928.41003
Zhuk, V. V.; Natanson, G. I.
1996
Functions of class Lip 1 and S. N. Bernstein polynomials. Zbl 0723.41006
Zhuk, V. V.
1989
Some remarks on periodic equidistant splines. Zbl 0586.41008
Zhuk, V. V.; Natanson, G. I.
1985
On the theory of cubic periodic splines with equidistant nodes. Zbl 0549.41011
Zhuk, V. V.; Natanson, G. I.
1984
On a certain approximation method. Zbl 0481.42003
Zhuk, V. V.
1981
On constants in direct problems of approximation theory. Zbl 0431.42002
Zhuk, V. V.; Natanson, G. I.
1980
On the question of the approximation of functions defined on a closed interval in the integral metric. Zbl 0429.41028
Zhuk, V. V.; Natanson, G. I.
1979
Über die Approximation stetiger periodischer Funktionen durch lineare Methoden der Summation von Fourierreihen. Zbl 0304.41013
Zhuk, V. V.
1974
Über gewisse genaue Ungleichungen zwischen den besten Approximationen und Stetigkeitsmoduln. Zbl 0275.41012
Zhuk, V. V.
1974
Some sharp inequalities between best approximations and moduli of continuity. Zbl 0243.42001
Zhuk, V. V.
1972
Saturation theory converse problem. Zbl 0194.09201
Zhuk, V. V.; Natanson, G. I.
1969
Über die Ordnung der Approximation einer stetigen $$2\pi$$-periodischen Funktion nach linearen Methoden. Zbl 0188.13301
Zhuk, V. V.
1969
Approximation of periodic functions by linear methods of summing their Fourier series. Zbl 0193.02904
Zhuk, V. V.
1967
Über die Approximation einer $$2\pi$$-periodischen Funktion durch die Werte eines gewissens beschränkten halbadditiven Operators. II. Zbl 0172.34602
Zhuk, V. V.
1967
Some modifications of the concept of modulus of smoothness and their applications. Zbl 0147.05503
Zhuk, V. V.
1965
Voronovskaya-Bernstein type asymptotic formulas in strong form. Zbl 1357.41017
Zhuk, V. V.; Babushkin, Max V.; Pudovkin, A. A.
2016
Some inequalities for trigonometric polynomials and Fourier coefficients. Zbl 1337.42001
Zhuk, V. V.; Puerov, G. Yu.
2015
Estimates for functionals with a known finite set of moments in terms of high order moduli of continuity in spaces of functions defined on a segment. Zbl 1305.41015
Vinogradov, O. L.; Zhuk, V. V.
2014
Linear methods in the proof of Jackson type inequalities and applications to estimates of functionals with two known moments. Zbl 1302.41017
Vinogradov, O. L.; Zhuk, V. V.
2014
Jackson type inequalities for deviations of the Riesz averages and applications to estimates of functionals with two known moments. Zbl 1301.41012
Vinogradov, O. L.; Zhuk, V. V.
2014
Estimates for functionals with a known, finite set of moments, in terms of moduli of continuity, and behavior of constants, in the Jackson-type inequalities. Zbl 1275.41016
Vinogradov, O. L.; Zhuk, V. V.
2013
Estimates for the best approximations of a periodic function by linear combinations of values of the function and its primitives. Zbl 1282.42004
Zhuk, V. V.
2013
Inequalities of the type of the generalized Jackson theorem for the best approximations. Zbl 1280.41014
Zhuk, V. V.
2013
Estimates for functionals with a known finite set of moments in terms of deviations of operators constructed with the use of the Steklov averages and finite differences. Zbl 1262.41010
Vinogradov, O. L.; Zhuk, V. V.
2012
Estimates for functionals with a known moment sequence in terms of deviations of Steklov type means. Zbl 1303.41006
Vinogradov, O. L.; Zhuk, V. V.
2011
The rate of decrease of constants in Jackson type inequalities in dependence of the order of the continuity modulus. Zbl 1303.41007
Vinogradov, O. L.; Zhuk, V. V.
2011
Estimates for functionals by deviations of the Riesz sums in seminormed spaces. Zbl 1205.41027
Dodonov, N. Yu.; Zhuk, V. V.
2009
Approximation of periodic functions by Steklov averages in $$L_{2}$$. Zbl 1202.41021
Dron’, V. O.; Zhuk, V. V.
2007
On approximate characteristics of functions of many variables occurring in saturation classes of continuity moduli of different orders. Zbl 1114.41014
Dodonov, N. Yu.; Zhuk, V. V.
2006
On the approximation of periodic functions by linear approximation methods. Zbl 1125.42003
Zhuk, A. S.; Zhuk, V. V.
2006
Some orthogonalities in approximation theory. Zbl 1127.42005
Zhuk, A. S.; Zhuk, V. V.
2004
Uniform approximation of nonperiodic functions defined on the entire axis. Zbl 1099.41021
Dodonov, N. Yu.; Zhuk, V. V.
2004
On uniform approximation in $$\mathbb R^2$$ of continuous functions of two variables with bounded variation in the sense of Hardy. Zbl 1099.41015
Dodonov, N. Yu.; Zuk, V. V.
2004
Sharp estimates for deviations of linear approximation methods for periodic functions by linear combinations of moduli of continuity of different order. Zbl 1050.41018
Vinogradov, O. L.; Zhuk, V. V.
2003
Extensions to the Jackson-type and Landau-Kolmogorov-type sharp inequalities for derivatives of low order. Zbl 1096.41012
Vinogradov, O. L.; Zhuk, V. V.
2003
Estimates of errors of quadrature formulas by linear combinations of the uniform norm and oscillation of derivatives with both sharp constants. Zbl 1050.26022
Vinogradov, O. L.; Zhuk, V. V.
2003
Sharp Kolmogorov-type inequalities for moduli of continuity and best approximations by trigonometric polynomials and splines. Zbl 1078.42001
Vinogradov, O. L.; Zhuk, V. V.
2002
Seminorms and continuity modules for functions defined on a segment. Zbl 1071.41008
Zhuk, V. V.; Natanson, G. I.
2001
Sharp estimates for the deviation of the mean value of a periodic function in terms of moduli of continuity of higher order. Zbl 0992.42001
Vinogradov, O. L.; Zhuk, V. V.
2001
Estimates for the deviation of the mean-value of a function by the moduli of continuity of its odd derivatives with the smallest constant and step. Zbl 1043.42002
Vinogradov, O. L.; Zhuk, V. V.
2000
Approximation of functions on standard simplexes. Zbl 0928.41003
Zhuk, V. V.; Natanson, G. I.
1996
Approximation of functions and numerical integration. Zbl 0942.41500
Zhuk, V. V.; Kuzyutin, V. F.
1995
Seminorms and moduli of continuity of higher orders. Zbl 0981.42500
Zhuk, V. V.
1993
Functions of class Lip 1 and S. N. Bernstein polynomials. Zbl 0667.41004
Zhuk, V. V.
1989
Strong approximation of periodic functions. Zbl 0721.42002
Zhuk, V. V.
1989
Functions of class Lip 1 and S. N. Bernstein polynomials. Zbl 0723.41006
Zhuk, V. V.
1989
Some remarks on periodic equidistant splines. Zbl 0586.41008
Zhuk, V. V.; Natanson, G. I.
1985
On the theory of cubic periodic splines with equidistant nodes. Zbl 0531.41010
Zhuk, V. V.; Natanson, G. I.
1984
On the theory of cubic periodic splines with equidistant nodes. Zbl 0549.41011
Zhuk, V. V.; Natanson, G. I.
1984
Trigonometrical Fourier series and elements of approximation theory. Textbook. (Trigonometricheskie ryady Fur’e i ehlementy teorii approksimatsii. Uchebnoe posobie). Zbl 0535.42010
Zhuk, V. V.; Natanson, G. I.
1983
Approximation of periodic functions. (Approksimatsiya periodicheskikh funktsij). Zbl 0521.42003
Zhuk, V. V.
1982
On a certain approximation method. Zbl 0481.42003
Zhuk, V. V.
1981
On constants in direct problems of approximation theory. Zbl 0431.42002
Zhuk, V. V.; Natanson, G. I.
1980
On the question of the approximation of functions defined on a closed interval in the integral metric. Zbl 0429.41028
Zhuk, V. V.; Natanson, G. I.
1979
On approaching the differentiable periodic functions by linear methods. Zbl 0412.42003
Zhuk, V. V.; Natanson, G. I.
1977
On the question of approximation of functions by means of positive operators. Zbl 0436.41011
Zhuk, V.; Natanson, G.
1977
On the problem of constants in direct theorems of the approximation theory for differentiable functions. Zbl 0362.41013
Zhuk, V. V.
1976
Approximation of periodic functions by Fejer’s sums and the de la Vallee- Poussin integral. Zbl 0288.41013
Zhuk, V. V.
1974
Über die Approximation stetiger periodischer Funktionen durch lineare Methoden der Summation von Fourierreihen. Zbl 0304.41013
Zhuk, V. V.
1974
Über gewisse genaue Ungleichungen zwischen den besten Approximationen und Stetigkeitsmoduln. Zbl 0275.41012
Zhuk, V. V.
1974
Some sharp inequalities between best approximations and moduli of continuity. Zbl 0243.42001
Zhuk, V. V.
1972
Some sharp inequalities between best approximations and moduli of continuity. Zbl 0231.42004
Zhuk, V. V.
1971
Some sharp inequalities between uniform best approximations of periodic functions. Zbl 0239.42003
Zhuk, V. V.
1971
Saturation theory converse problem. Zbl 0194.09201
Zhuk, V. V.; Natanson, G. I.
1969
Über die Ordnung der Approximation einer stetigen $$2\pi$$-periodischen Funktion nach linearen Methoden. Zbl 0188.13301
Zhuk, V. V.
1969
Approximation of periodic functions by linear methods of summing their Fourier series. Zbl 0193.02904
Zhuk, V. V.
1967
Über die Approximation einer $$2\pi$$-periodischen Funktion durch die Werte eines gewissens beschränkten halbadditiven Operators. II. Zbl 0172.34602
Zhuk, V. V.
1967
On the representation of a periodic function by a bounded semiadditive operator. Zbl 0167.05201
Zhuk, V. V.
1966
Some modifications of the concept of modulus of smoothness and their applications. Zbl 0147.05503
Zhuk, V. V.
1965
all top 5

#### Cited by 77 Authors

 35 Zhuk, Vladimir Vasil’evich 25 Vinogradov, Oleg Leonidovich 8 Dodonov, N. Yu. 5 Babushkin, Max V. 4 Bure, Vladimir M. 4 Ligun, A. A. 4 Trynin, Aleksandr Yur’evich 3 Kryakin, Yuri V. 3 Sucu, Sezgin 3 Varma, Serhan 2 Babenko, Aleksandr Grigor’evich 2 Dron’, Vera O. 2 Gladkaya, A. V. 2 Ịçöz, Gürhan 2 Pichugov, S. A. 2 Puerov, G. Yu. 2 Sharapudinov, Idris Idrisovich 2 Skopina, Maria A. 1 Aliukov, S. V. 1 Andrianov, P. A. 1 Ansari, Khursheed Jamal 1 Besov, Oleg Vladimirovich 1 Boos, A. 1 Cao, Jiading 1 Cui, Dezao 1 Davydov, Oleg V. 1 Deepmala, Vandana 1 Deo, Naokant 1 Dhamija, Minakshi 1 Doronin, V. G. 1 Gairola, Asha Ram 1 Gavrilyuk, V. T. 1 Gilewicz, Jacek 1 Gonska, Heinz Herbert 1 Gorbachëv, Dmitriĭ Viktorovich 1 Hahn, Lothar 1 Ikhsanov, L. N. 1 Il’yasov, Niyazi Aladdin ogly 1 Ivanov, Valeriĭ Ivanovich 1 Ivanov, Valeriy Ivanovich 1 Khatri, Kejal 1 Kivinukk, Andi 1 Konyagin, Sergeĭ Vladimirovich 1 Kowalczyk, Stanisław 1 Magomed-Kasumov, M. G. 1 Martins-Filho, Carlos 1 Mertens, Hans Jochen 1 Mishra, Lakshmi Narayan 1 Mishra, Vishnu Narayan 1 Mursaleen, Mohammad 1 Mynbaev, Kairat T. 1 Nessel, Rolf Joachim 1 Nosenko, Yuri L. 1 Pérez-Palomares, Ana 1 Petukhov, Alexander P. 1 Pimenov, S. Yu. 1 Ponomarev, Stanislav P. 1 Pudovkin, A. A. 1 Saidusaynov, M. S. 1 Saksa, Anna 1 Savchuk, V. V. 1 Scherer, Karl 1 Shabozov, Mirgand Shabozovich 1 Shakirov, Iskander Asgatovich 1 Sharapudinov, T. I. 1 Shevchuk, Igor A. 1 Trigub, Roal’d Mikhaĭlovich 1 Tumka, Oleg A. 1 Umakhanov, Aĭvar Yarakhmedovich 1 Vakarchuk, Sergei Borisovich 1 Vakarchuk, Sergey B. 1 Vinogradov, L. 1 Weisz, Ferenc 1 Xu, Aimin 1 Zabutnaya, Valentina I. 1 Zastavnyĭ, Viktor Petrovich 1 Zeltser, Maria
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#### Cited in 24 Serials

 45 Journal of Mathematical Sciences (New York) 18 Mathematical Notes 5 Ukrainian Mathematical Journal 5 Journal of Approximation Theory 5 St. Petersburg Mathematical Journal 3 Computers & Mathematics with Applications 3 Applied Mathematics and Computation 3 Siberian Mathematical Journal 3 Vestnik St. Petersburg University. Mathematics 2 Russian Mathematics 2 Proceedings of the Steklov Institute of Mathematics 1 Analysis Mathematica 1 Journal of Mathematical Analysis and Applications 1 Calcolo 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Statistics & Probability Letters 1 Computational Mathematics and Modeling 1 Zapiski Nauchnykh Seminarov POMI 1 Abstract and Applied Analysis 1 Lobachevskii Journal of Mathematics 1 Proceedings of the National Academy of Sciences, India. Section A. Physical Sciences 1 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 1 Proceedings of the Estonian Academy of Sciences 1 Afrika Matematika
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#### Cited in 12 Fields

 75 Approximations and expansions (41-XX) 54 Harmonic analysis on Euclidean spaces (42-XX) 8 Real functions (26-XX) 8 Functional analysis (46-XX) 3 Functions of a complex variable (30-XX) 3 Special functions (33-XX) 3 Operator theory (47-XX) 2 Numerical analysis (65-XX) 1 Integral transforms, operational calculus (44-XX) 1 Statistics (62-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX)

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