Vladimir Mikhailets

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All published works

Action	Title	Year	Authors
+	Differential systems in Sobolev spaces with generic inhomogeneous boundary conditions	2024	Vladimir Mikhailets Olena Atlasiuk
+ PDF Chat	Differential systems in Sobolev spaces with generic inhomogeneous boundary conditions	2024	Vladimir Mikhailets Olena Atlasiuk
+	Еліптичні оператори і крайові задачі у просторах узагальненої гладкості	2024	Vladimir Mikhailets A. A. Murach Iryna Chepurukhina
+ PDF Chat	Elliptic operators and boundary problems in spaces of generalized smoothness	2024	Vladimir Mikhailets Aleksandr Murach Iryna Chepurukhina
+ PDF Chat	Unconditional convergence of eigenfunction expansions for abstract and elliptic operators	2024	Vladimir Mikhailets Aleksandr Murach
+ PDF Chat	The solvability of inhomogeneous boundary-value problems in Sobolev spaces	2024	Vladimir Mikhailets Olena Atlasiuk
+	A New Look at Old Theorems of Fejér and Hardy	2024	Vladimir Mikhailets Aleksandr Murach Oksana Tsyhanok
+	On Differential Systems in Sobolev Spaces with Generic Inhomogeneous Boundary Conditions	2024	Olena Atlasiuk Vladimir Mikhailets
+ PDF Chat	On the Solvability of Fredholm Boundary-Value Problems in Fractional Sobolev Spaces	2023	Vladimir Mikhailets Olena Atlasiuk T. B. Skorobohach
+	Про розв'язність фредгольмових крайових задач у дробових просторах Соболєва	2023	Vladimir Mikhailets Olena Atlasiuk T. B. Skorobohach
+	On Differential Systems in Sobolev spaces with Generic Inhomogeneous Boundary Conditions	2023	Olena Atlasiuk Vladimir Mikhailets
+	A new look at old theorems of Fejér and Hardy	2023	Vladimir Mikhailets Aleksandr Murach Oksana Tsyhanok
+	The solvability of inhomogeneous boundary-value problems in Sobolev spaces	2023	Vladimir Mikhailets Olena Atlasiuk
+	Unconditional convergence of eigenfunction expansions for abstract and elliptic operators	2023	Vladimir Mikhailets Aleksandr Murach
+	Povzner–Wienholtz-Type Theorems for Sturm–Liouville Operators with Singular Coefficients	2022	Vladimir Mikhailets Andrii Goriunov Volodymyr Molyboga
+	On the solvability of Fredholm boundary-value problems in fractional Sobolev spaces	2022	Vladimir Mikhailets Olena Atlasiuk Tetiana Skorobohach
+	Fredholm Boundary-Value Problem in Sobolev–Slobodetsky Spaces	2021	Vladimir Mikhailets T. B. Skorobohach
+ PDF Chat	Фредгольмовi крайові задачі з параметром у просторах Соболєва—Слободецького	2021	Vladimir Mikhailets Т.Б. Скоробогач
+	Фредгольмові крайові задачі в просторах Соболєва – Слободецького	2021	Vladimir Mikhailets T. B. Skorobodach
+	An extended Hilbert scale and its applications	2021	Vladimir Mikhailets Aleksandr Murach Tetiana Zinchenko
+ PDF Chat	Parabolic problems in generalized Sobolev spaces	2021	Valerii Los Vladimir Mikhailets Aleksandr Murach
+	Parabolic boundary-value problems and generalized Sobolev spaces	2021	Valerii Los Vladimir Mikhailets Aleksandr Murach
+	Povzner-Wienholtz-type theorems for Sturm-Liouville operators with singular coefficients	2021	Andrii Goriunov Vladimir Mikhailets Volodymyr Molyboga
+ PDF Chat	On Fredholm parameter-dependent boundary-value problems in Sobolev spaces	2020	Olena Atlasiuk Vladimir Mikhailets
+ PDF Chat	None	2020	Olena Atlasiuk Vladimir Mikhailets
+ PDF Chat	On solvability of inhomogeneous boundary-value problems in Sobolev - Slobodetskiy spaces	2020	Vladimir Mikhailets T. B. Skorobohach
+	Continuity in a parameter of solutions to boundary-value problems in Sobolev spaces	2020	Olena Atlasiuk Vladimir Mikhailets
+	Parabolic problems in generalized Sobolev spaces.	2019	Valerii Los Vladimir Mikhailets Aleksandr Murach
+ PDF Chat	Fredholm One-Dimensional Boundary-Value Problems with Parameters in Sobolev Spaces	2019	Olena Atlasiuk Vladimir Mikhailets
+ PDF Chat	Fredholm One-Dimensional Boundary-Value Problems in Sobolev Spaces	2019	Olena Atlasiuk Vladimir Mikhailets
+ PDF Chat	Correction to: Continuity in the Parameter for the Solutions of One-Dimensional Boundary-Value Problems for Differential Systems of Higher Orders in Slobodetskii Spaces	2019	Hanna Masliuk Vladimir Mikhailets
+ PDF Chat	Sobolev-Like Hilbert Spaces Induced by Elliptic Operators	2019	Tetiana Kasirenko Vladimir Mikhailets Aleksandr Murach
+	On Linear Boundary-Value Problems for Differential Systems in Sobolev spaces	2019	Olena Atlasiuk Vladimir Mikhailets
+ PDF Chat	On the solvability of inhomogeneous boundary-value problems in Sobolev spaces	2019	Olena Atlasiuk Vladimir Mikhailets
+	Parabolic problems in generalized Sobolev spaces	2019	Valerii Los Vladimir Mikhailets Aleksandr Murach
+ PDF Chat	On spectral gaps of the Hill—Schrödinger operator with singular potential	2018	Vladimir Mikhailets Volodymyr Molyboga
+	Schr\"odinger operators with measure-valued potentials: semiboundedness and spectrum	2018	Vladimir Mikhailets Volodymyr Molyboga
+	Limit Theorems for the Solutions of Boundary-Value Problems	2018	Vladimir Mikhailets O. B. Pelekhata Nadya Reva
+	Schrödinger operators with measure-valued potentials: semiboundedness and spectrum	2018	Vladimir Mikhailets Volodymyr Molyboga
+ PDF Chat	On the Kiguradze theorem for linear boundary-value problems	2017	Vladimir Mikhailets O. B. Pelekhata Nadya Reva
+	On Kiguradze theorem for linear boundary value problems	2017	Vladimir Mikhailets O. B. Pelekhata Nadya Reva
+	Regularity of solutions to general parabolic problems in Hörmander spaces	2017	Valerii Los Vladimir Mikhailets Aleksandr Murach
+	Parameter-dependent one-dimensional boundary-value problems in Sobolev spaces	2017	Yevheniia Hnyp Vladimir Mikhailets Aleksandr Murach
+	Localization principles for Schrödinger operator with a singular matrix potential	2017	Vladimir Mikhailets Aleksandr Murach Viktor Novikov
+	On Kiguradze theorem for linear boundary value problems	2017	Vladimir Mikhailets O. B. Pelekhata Nadya Reva
+	Parameter-dependent one-dimensional boundary-value problems in Sobolev spaces	2017	Yevheniia Hnyp Vladimir Mikhailets Aleksandr Murach
+ PDF Chat	An isomorphism theorem for parabolic problems in Hörmander spaces and its applications	2016	Valerii Los Vladimir Mikhailets Aleksandr Murach
+	A criterion for continuity in a parameter of solutions to generic boundary-value problems for higher-order differential systems	2016	Vladimir Mikhailets Aleksandr Murach Vitalii Soldatov
+	Continuity in a parameter of solutions to generic boundary-value problems	2016	Vladimir Mikhailets Aleksandr Murach Vitalii Soldatov
+	General parabolic initial-boundary value problems in Hörmander spaces	2016	Valerii Los Vladimir Mikhailets Aleksandr Murach
+	Continuity in a parameter of solutions to generic boundary-value problems	2016	Vladimir Mikhailets Aleksandr Murach Vitalii Soldatov
+	A criterion for continuity in a parameter of solutions to generic boundary-value problems for higher-order differential systems	2016	Vladimir Mikhailets Aleksandr Murach Vitalii Soldatov
+	Continuity in a parameter of solutions to generic boundary-value problems	2016	Vladimir Mikhailets Aleksandr Murach Vitalii Soldatov
+	An isomorphism theorem for parabolic problems in H\"ormander spaces and its applications	2015	Valerii Los Vladimir Mikhailets Aleksandr Murach
+	Fredholm Boundary-Value Problems with Parameter in Sobolev Spaces	2015	E. V. Gnyp T. I. Kodlyuk Vladimir Mikhailets
+	Spectral gaps of the Hill--Schrödinger operators with distributional potentials	2015	Vladimir Mikhailets Volodymyr Molyboga
+	Spectral gaps of the Hill--Schrödinger operators with distributional potentials	2015	Vladimir Mikhailets Volodymyr Molyboga
+	An isomorphism theorem for parabolic problems in Hörmander spaces and its applications	2015	Valerii Los Vladimir Mikhailets Aleksandr Murach
+	Limit theorems for general one-dimensional boundary-value problems	2014	Vladimir Mikhailets Ganna A. Chekhanova
+	Fredholm boundary-value problems with a parameter on the spaces C<sup>(n)</sup>[a, b]	2014	Vladimir Mikhailets Ganna A. Chekhanova
+ PDF Chat	Interpolation Hilbert Spaces Between Sobolev Spaces	2014	Vladimir Mikhailets Aleksandr Murach
+ PDF Chat	Hörmander Spaces, Interpolation, and Elliptic Problems	2014	Vladimir Mikhailets Aleksandr Murach
+	Uniform estimates for the semi-periodic eigenvalues of the singular differential operators	2014	Vladimir Mikhailets Volodymyr Molyboga
+	Extended Sobolev Scale and Elliptic Operators	2013	Vladimir Mikhailets Aleksandr Murach
+	Limit theorems for one-dimensional boundary-value problems	2013	T. I. Kodlyuk Vladimir Mikhailets Nadya Reva
+	Solutions of one-dimensional boundary-value problems with a parameter in Sobolev spaces	2013	Tatiana I. Kodliuk Vladimir Mikhailets
+	Schrödinger operators with complex singular potentials	2013	Vladimir Mikhailets Volodymyr Molyboga
+	Remarks on Schrödinger operators with singular matrix potentials	2013	Vladimir Mikhailets Volodymyr Molyboga
+	The Refined Sobolev Scale, Interpolation, and Elliptic Problems	2012	Vladimir Mikhailets Aleksandr Murach
+	On the spectrum of singular perturbations of operators on the circle	2012	Vladimir Mikhailets Volodymyr Molyboga
+	On the unconditional almost-everywhere convergence of general orthogonal series	2012	Vladimir Mikhailets Aleksandr Murach
+ PDF Chat	Regularization of two-term differential equations with singular coefficients by quasiderivatives	2012	A. S. Goryunov Vladimir Mikhailets
+	Formally self-adjoint quasi-differential operators and boundary value problems	2012	Andrii Goriunov Vladimir Mikhailets Konstantin Pankrashkin
+ PDF Chat	Smoothness of Hill’s Potential and Lengths of Spectral Gaps	2012	Vladimir Mikhailets Volodymyr Molyboga
+ PDF Chat	The refined Sobolev scale, interpolation and elliptic problems	2012	Vladimir Mikhailets Aleksandr Murach
+ PDF Chat	О спектре сингулярных возмущений операторов на окружности	2012	Vladimir Mikhailets Vladimir Mikhailets Владимир Николаевич Молибога Volodymyr Molyboga
+	The Refined Sobolev Scale, Interpolation, and Elliptic Problems	2012	Vladimir Mikhailets Aleksandr Murach
+	General forms of the Menshov-Rademacher, Orlicz, and Tandori theorems on orthogonal series	2011	Vladimir Mikhailets Aleksandr Murach
+	Regularization of binomial differential equations with singular coefficients	2011	Andrii Goriunov Vladimir Mikhailets
+	Interpolation Hilbert spaces for a couple of Sobolev spaces	2011	Vladimir Mikhailets Aleksandr Murach
+	Continuous parameter dependence for solutions of one-dimensional boundary value problems	2011	Tanya Kodliuk Vladimir Mikhailets Nadya Reva
+	Regularization of binomial differential equations with singular coefficients	2011	Andrii Goriunov Vladimir Mikhailets
+	Hörmander Spaces, Interpolation, and Elliptic Problems	2011	Vladimir Mikhailets A. A. Murach
+	General forms of the Menshov-Rademacher, Orlicz, and Tandori theorems on orthogonal series	2011	Vladimir Mikhailets Aleksandr Murach
+ PDF Chat	Resolvent convergence of Sturm—Liouville operators with singular potentials	2010	Andrii Goriunov Vladimir Mikhailets
+	Regularization of singular Sturm-Liouville equations	2010	Andrii Goriunov Vladimir Mikhailets
+	Smoothness of Hill's potential and lengths of spectral gaps	2010	Vladimir Mikhailets Volodymyr Molyboga
+	Mark Grigorievich Krein (on his 100th birthday anniversary)	2009	V. M. Adamyan Damir Z. Arov Yu. M. Berezansky V. I. Gorbachuk М. Л. Горбачук Vladimir Mikhailets А. М. Самойленко
+	Hill's potentials in Hörmander spaces and their spectral gaps	2009	Vladimir Mikhailets Volodymyr Molyboga
+	Elliptic Problems and Hörmander Spaces	2009	Vladimir Mikhailets Aleksandr Murach
+	Elliptic problems and Hörmander spaces	2009	Vladimir Mikhailets Aleksandr Murach
+	SPECTRAL GAPS OF THE ONE-DIMENSIONAL SCHR¨ ODINGER OPERATORS WITH SINGULAR PERIODIC POTENTIALS	2008	Vladimir Mikhailets Volodymyr Molyboga Ostrovskii Theorem
+	Elliptic boundary-value problem in a two-sided improved scale of spaces	2008	Vladimir Mikhailets Aleksandr Murach
+	Spectral gaps of the one-dimensional Schrödinger operators with singular periodic potentials	2008	Vladimir Mikhailets Volodymyr Molyboga
+	One-dimensional Schrödinger operators with singular periodic potentials	2008	Vladimir Mikhailets Volodymyr Molyboga
+ PDF Chat	Elliptic Systems of Pseudodifferential Equations in the Refined Scale on a Closed Manifold	2008	Vladimir Mikhailets Aleksandr Murach
+ PDF Chat	Singularly perturbed periodic and semiperiodic differential operators	2007	Vladimir Mikhailets Volodymyr Molyboga
+	Improved scales of spaces and elliptic boundary-value problems. III	2007	Vladimir Mikhailets Aleksandr Murach
+	Regular elliptic boundary-value problem in a two-sided refined scale of spaces	2007	Vladimir Mikhailets Aleksandr Murach
+	Elliptic systems of pseudodifferential equations in a refined scale on a closed manifold	2007	Vladimir Mikhailets Alexandr A. Murach
+	Interpolation with a function parameter and refined scale of spaces	2007	Vladimir Mikhailets Aleksandr Murach
+	Regular elliptic boundary-value problem for a homogeneous equation in a two-sided improved scale of spaces	2006	Vladimir Mikhailets Aleksandr Murach
+	Improved scales of spaces and elliptic boundary-value problems. II	2006	Vladimir Mikhailets Aleksandr Murach
+	Improved scales of spaces and elliptic boundary-value problems. I	2006	Vladimir Mikhailets Aleksandr Murach
+	Elliptic Operators in a Refined Scale of Functional Spaces	2005	Vladimir Mikhailets Aleksandr Murach
+	Common Eigenvalue Problem and Periodic Schrödinger Operators	1999	Vladimir Mikhailets Alexander V. Sobolev
+	The structure of the continuous spectrum of a one-dimensional Schrödinger operator with point interactions	1996	Vladimir Mikhailets
+ PDF Chat	Структура непрерывного спектра одномерного оператора Шрeдингера с точечными взаимодействиями	1996	Vladimir Mikhailets Vladimir Mikhailets
+	Spectral properties of the one-dimensional Schrödinger operator with point intersections	1995	Vladimir Mikhailets
+	A discreteness criterion for the spectrum of a one-dimensional Schr�dinger operator with?-interactions	1995	Vladimir Mikhailets
+	Point interactions on the line	1993	Vladimir Mikhailets
+	A precise estimate of the remainder of an asymptotic spectral series of general elliptic boundary-value problems	1989	Vladimir Mikhailets
+	Spectral analysis of elliptic differential equations in Hilbert space	1986	Vladimir Mikhailets
+	Distribution of eigenvalues of operators which are nearly self-adjoint	1981	Vladimir Mikhailets
+	A REFINEMENT OF THE ASYMPTOTIC FORMULAE FOR THE SPECTRUM OF THE LAPLACE OPERATOR IN DOMAINS OF THE FORM<i>G</i>=<i>G</i><sub>1</sub>×<i>G</i><sub>2</sub>	1978	Vladimir Mikhailets
+	Asymptotics of the eigenvalues of a Sturm?Liouville equation with variable operator coefficients	1977	Vladimir Mikhailets
+	Asymptotic representation of the eigenvalues of the third boundary-value problem for the sturm ? liouville operator equation	1976	Vladimir Mikhailets
+	On solvable and sectorial boundary problems for the Sturm-Liouville operator equations	1975	Vladimir Mikhailets
+	On the nature of the spectrum of self-adjoint extensions of operators admitting separation of variables	1974	Vladimir Mikhailets

Common Coauthors

Coauthor	Papers Together
Aleksandr Murach	45
Volodymyr Molyboga	19
Olena Atlasiuk	16
Valerii Los	9
Andrii Goriunov	7
Nadya Reva	6
Vitalii Soldatov	5
O. B. Pelekhata	4
T. B. Skorobohach	4
Oksana Tsyhanok	2
Ganna A. Chekhanova	2
T. I. Kodlyuk	2
Iryna Chepurukhina	2
Yevheniia Hnyp	2
Hanna Masliuk	1
Tetiana Zinchenko	1
V. I. Gorbachuk	1
М. Л. Горбачук	1
Ostrovskii Theorem	1
A. A. Murach	1
Alexander V. Sobolev	1
Т.Б. Скоробогач	1
Damir Z. Arov	1
Tetiana Kasirenko	1
А. М. Самойленко	1
Tatiana I. Kodliuk	1
E. V. Gnyp	1
Tetiana Skorobohach	1
A. A. Murach	1
Yu. M. Berezansky	1
Viktor Novikov	1
Alexandr A. Murach	1
T. B. Skorobodach	1
A. S. Goryunov	1
Владимир Николаевич Молибога	1
Tanya Kodliuk	1
Konstantin Pankrashkin	1
V. M. Adamyan	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Linear Partial Differential Operators	1963	Lars Hörmander	22
+	Fredholm Boundary-Value Problems with Parameter in Sobolev Spaces	2015	E. V. Gnyp T. I. Kodlyuk Vladimir Mikhailets	18
+	Solutions of one-dimensional boundary-value problems with a parameter in Sobolev spaces	2013	Tatiana I. Kodliuk Vladimir Mikhailets	17
+	The analysis of linear partial differential operators	1990	Lars Hörmander	16
+ PDF Chat	Perturbation Theory for Linear Operators	1995	Tosio Kato	14
+	Improved scales of spaces and elliptic boundary-value problems. II	2006	Vladimir Mikhailets Aleksandr Murach	13
+	Limit theorems for one-dimensional boundary-value problems	2013	T. I. Kodlyuk Vladimir Mikhailets Nadya Reva	13
+	Boundary-value problems for systems of ordinary differential equations	1988	И. Т. Кигурадзе	13
+	Non-Homogeneous Boundary Value Problems and Applications	1973	J. L. Lions Enrico Magenes	12
+ PDF Chat	Fredholm One-Dimensional Boundary-Value Problems with Parameters in Sobolev Spaces	2019	Olena Atlasiuk Vladimir Mikhailets	12
+ PDF Chat	Resolvent convergence of Sturm—Liouville operators with singular potentials	2010	Andrii Goriunov Vladimir Mikhailets	12
+	Numerical Solution of Boundary Value Problems for Ordinary Differential Equations	1995	Uri M. Ascher Robert M. M. Mattheij Robert D. Russell	11
+	Continuous parameter dependence in linear systems of differential equations	1967	Z. Opial	11
+ PDF Chat	Characterisations of function spaces of generalised smoothness	2004	Walter Farkas Hans‐Gerd Leopold	11
+	Interpolation with a function parameter and refined scale of spaces	2007	Vladimir Mikhailets Aleksandr Murach	11
+ PDF Chat	Hörmander Spaces, Interpolation, and Elliptic Problems	2014	Vladimir Mikhailets Aleksandr Murach	11
+	CERTAIN SPACES OF GENERALIZED FUNCTIONS AND EMBEDDING THEOREMS	1965	L. R. Volevich B P Paneyakh	10
+	Continuity in a parameter of solutions to generic boundary-value problems	2016	Vladimir Mikhailets Aleksandr Murach Vitalii Soldatov	10
+	Expansions in eigenfunctions of selfadjoint operators	1968	Ю. М. Березанский Richard Bolstein	10
+	Expansions in Eigenfunctions of Selfadjoint Operators	1968	Ju. M. Berezanskiĭ	10
+	Elliptic Boundary Value Problems in the Spaces of Distributions	1996	Yakov Roitberg	10
+ PDF Chat	Fredholm One-Dimensional Boundary-Value Problems in Sobolev Spaces	2019	Olena Atlasiuk Vladimir Mikhailets	10
+ PDF Chat	Criteria of correctness of linear boundary value problems for systems of generalized ordinary differential equations	1996	Malkhaz Ashordia	9
+	Spaces of Functions of Generalized Smoothness	1987	G A Kaljabin П. И. Лизоркин	9
+	Theory of Function Spaces	1983	Hans Triebel	9
+	Improved scales of spaces and elliptic boundary-value problems. I	2006	Vladimir Mikhailets Aleksandr Murach	9
+	Elliptic Operators in a Refined Scale of Functional Spaces	2005	Vladimir Mikhailets Aleksandr Murach	9
+	Regular elliptic boundary-value problem for a homogeneous equation in a two-sided improved scale of spaces	2006	Vladimir Mikhailets Aleksandr Murach	9
+	Parameter-dependent one-dimensional boundary-value problems in Sobolev spaces	2017	Yevheniia Hnyp Vladimir Mikhailets Aleksandr Murach	9
+	Some limit theorems for ordinary differential systems	1967	William T. Reid	8
+ PDF Chat	The interpolation of quadratic norms	1967	William F. Donoghue	8
+	Limit theorems for general one-dimensional boundary-value problems	2014	Vladimir Mikhailets Ganna A. Chekhanova	8
+	The Analysis of Linear Partial Differential Operators II: Differential Operators with Constant Coefficients	1983	Lars Hörmander	8
+	Elliptic Boundary Problems	1997	M. S. Agranovich	7
+ PDF Chat	Formally self-adjoint quasi-differential operators	1975	Anton Zettl	7
+	Continuity envelopes of spaces of generalised smoothness, entropy and approximation numbers	2004	Dorothee D. Haroske Susana D. Moura	7
+	Extended Sobolev Scale and Elliptic Operators	2013	Vladimir Mikhailets Aleksandr Murach	7
+	Hardy-Sobolev spaces and Besov spaces with a function parameter	1988	Fernando Cobos Dicesar Lass Fernandez	7
+	Elliptic Operators on Closed Manifolds	1994	M. S. Agranovich	7
+	Limit Theorems for the Solutions of Boundary-Value Problems	2018	Vladimir Mikhailets O. B. Pelekhata Nadya Reva	7
+	On the regularity properties of solutions of elliptic differential equations	1956	Felix E. Browder	6
+ PDF Chat	The refined Sobolev scale, interpolation and elliptic problems	2012	Vladimir Mikhailets Aleksandr Murach	6
+	Elliptic pseudodifferential operators in the improved scale of spaces on a closed manifold	2007	Aleksandr Murach	6
+	Theory of function spaces	1983	Hans Triebel	6
+	Boundary Value Problems for Operator Differential Equations	1991	В. И. Горбачук М. Л. Горбачук	6
+	Methods of Modern Mathematical Physics	1972	Michael C. Reed Barry Simon	6
+ PDF Chat	Error bounds for spectral enhancement which are based on variable Hilbert scale inequalities	2010	Markus Hegland	6
+	Properties of solutions of ordinary differential equations in banach space	1963	Shmuel Agmon Louis Nirenberg	6
+	Sturm-liouville operators with singular potentials	1999	А. М. Савчук А. А. Шкаликов	6
+	CONVERGENCE PROBLEMS OF MULTIPLE TRIGONOMETRIC SERIES AND SPECTRAL DECOMPOSITIONS. I	1976	Sh. A. Alimov В. А. Ильин Е. М. Никишин	6