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Academic Staff

Liu, Tai-Ping

Liu, Tai-Ping

Distinguished Visiting Chair

Research Fields: Nonlinear partial differential equations, shock wave theory, kinetic theory,

Email : tpliu@math.sinica.edu.tw

Extension : 704

Dr. Liu's research interests center around Nonlinear partial differential equations, shock wave theory, and kinetic theory.

 

  • Ph.D. The University of Michigan 1973
  • M.S. Oregon State University 1970
  • B.S. National Taiwan University 1968

  • Distinguished Research Fellow Institute of Mathematics, Academia Sinica, R.O.C. 2006 - Present
  • Distinguished Research Fellow Institute of Mathematics,Academia Sinica, R.O.C. 2000-2005

  • 2012, Galileo Galilei Medal , City if Padova
  • 2009, Cataldo e Angiola Agostinelli International Prize
  • 2006, TWAS membership
  • 1992, Member, Academia Sinica, Nankang, Rep. of China
  • 1982-83, Guggenheim Fellowship
  • 1979-81, Sloan Fellowship
  • 1976-Present, NSF Grant
  • Honorary professor, City University of Hong Kong
  • Honorary professor, Chinese Academy of Sciences, Beijing
  • Adjunct professor, Zhejiang University, Hangzhou

  • (with Jiang J.-C.) "Boltzmann collision operator for the infinite range potential: a limit problem.", 36 (6), 1639-1677, 2019
  • (with Yu S.-H.) "Multi-dimensional wave propagation over a Burgers shock profile.", Archive for Rational Mechanics and Analysis, 229 (1), 231-337, 2018
  • (with Yu S.-H.) "Multi-dimensional wave propagation over a Burgers shock profile", Archive for Rational Mechanics and Analysis, 229, 231-337, 2018
  • "Hopf-Cole transformation", Bull. Inst. Math. Acad. Sin. (N.S.), 12 (1), 71-101, 2017
  • (with Chen, I-Kun; Funagane, Hitoxhi; and Takata, Shigeru) "Singularity of the velocity distribution function in molecular velocity space. ", Comm. Math. Phys., 341 (1), 105-134, 2016
  • (with Noh, Se Eun) "Wave propagation for the compressible Navier-Stokes equations. ", J. Hyperbolic Differ. Equ. , 12 (2), 385-445, 2015
  • (with Zeng, Yanni) "Shock waves in conservation laws with physical viscosity. ", Mem. Amer. Math. Soc., 234 (1105), 2015
  • (with Yu, Shih-Hsien) "Boundary wave propagator for compressible Navier-Stokes equations. ", Found. Comput. Math., 14 (6), 1287-1335, 2014
  • (with Yu, Shih-Hsien) "Fujita equation with boundary effect", Bull. Inst. Math. Acad. Sin. (N.S.), 9 (2), 267-282, 2014
  • "Equilibrating effects of boundary and collision in rarefied gases. ", Comm. Math. Phys., 318 (2), 421-480, 2014
  • (with Chen, I-Kun and Takata, Shigeru) "Boundary singularity for thermal transpiration problem of the linearized Boltzmann equation", Arch. Ration. Mech. ANal., 212 (2), 575-595, 2014
  • "Aspects of dissipation for compressible fluids and kinetic theory", Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 371 (2005), 2013
  • (with Yu, Shih-Hsien) "Invariant manifolds for steady Boltzmann equation and applications", Archive Rational Mechanics and Analysis, 209 (3), 869-997, 2013
  • (with Kuo, Hung-Wen and Tsai, Li-Cheng) "Free molecular flow with boundary effect", Comm. Math. Phys., 318 (2), 375-409, 2013
  • (with Yu S.-H.) "Dirichlet-Neumann kernel for hyperbolic-dissipative system in half-space", Bull. Inst. Math. Acad. Sin. (N.S.), 7 (4), 477-543, 2012
  • "Multi-dimensional gas flow: some historical perspectives", Bull. Inst. Math. Acad. Sin. (N.S.), 6 (3), 269-291, 2011
  • (with Yu S.-H.) "On boundary relation for some dissipative systems", Bull. Inst. Math. Acad. Sin. (N.S.), 6 (3), 245-267, 2011
  • (with Yu, Shih-Hsien) "Solving Boltzmann equation, Part I: Green's function", Bull. Inst. Math. Acad. Sin. (N.S.) , 6 (1), 115-243, 2011
  • (with Yu S.-H.) "Viscous rarefaction waves", Bull. Inst. Math. Acad. Sin. (N.S.), 5 (2), 123-179, 2010
  • (with S.-H. Yu; Y. Zeng) "Viscous Conservation Laws, Part I: Scalar Laws", Bull. Inst. Math., Acad. Sin. (N.S.), 5 (3), 233-310, 2010
  • (with Kuo, Hung-Wen; Noh, Se Eun) "Mixture lemma", Bull. Inst. Math., Acad. Sin. (N.S.), 5 (1), 1-10, 2010
  • (with Zeng, Yanni) "On Green's function for hyperbolic-parabolic systems ", Acta Math. Sci. Ser. B Engl. Ed., 29 (6), 1556-1572, 2009
  • (with S.-H., Yu) " Boltzmann equation, boundary effects. ", Discrete Contin. Dyn. Syst., 24 (1), 145-157, 2009
  • (with S.-H., Yu) " Viscous shock wave tracing, local conservation laws, and pointwise estimates ", Bull. Inst. Math. Aca. (N.S.) , 4 (3), 167-210, 2009
  • (with Y., Zeng) "Time-asymptotic behavior of wave propagation around a viscous shock profile. ", Comm. Math. Phys., 290 (1), 23-82, 2009
  • (with Yu, Shih-Hsien) "Diffusion under gravitational and boundary effects.", Bull. Inst. Math. Acad. Sin. (N.S.) , 3 (1), 167-210, 2008
  • (with Elling, Volker) "Supersonic flow onto a solid wedge.", Comm. Pure Appl. Math. , 61 (10), 1347-1448, 2008
  • (with Yu, Shih-Hsien) "Initial-boundary value problem for one-dimensional wave solutions of the Boltzmann equation. ", Comm. Pure Appl. Math., 60 (3), 295-356, 2007
  • (with Lee, Ming-Yi; Yu, Shih-Hsien) "Large-time behavior of solutions for the Boltzmann equation with hard potentials. ", Comm. Math. Phys., 269 (1), 17-37, 2007
  • (with Chen, Chiun-Chuan; Chen, I-Kun; Sone, Yoshio) "Thermal transpiration for the linearized Boltzmann equation. ", Comm. Pure Appl. Math., 60 (2), 147-163, 2007
  • (with S.-H. Yu) "Green's function of Boltzmann equation, 3-D ", Bull. Inst. Math. Acad. Sin. (N.S.) , 1 (1), 1-78, 2006
  • (with T. Yang, S.-H. Yu, H.-J. Zhao) "Nonlinear stability of rarefaction waves for the Boltzmann equation. ", Arch. Rational Mech. Anal., 181 (2), 333-371, 2006
  • (with V. Elling) "The ellipticity principle for self-similar potential flows. ", J. Hyperbolic Differ. Equ., 2 (4), 909-917, 2005
  • (with C.-Y., Lan;H.-E., Lin;S.-H. Yu) "Propagation of viscous shock waves away from the boundary.", SIAM J. Math. Anal., 36 (2), 580-617, 2004
  • (with C.-C. Chen and T. Yang) "Existence of boundary layer solutions to the Boltzmann equation", Anal. Appl. (Singap.), 2 (4), 337-363, 2004
  • (with Yu, Shih-Hsien) "(with ) The Green's function and large-time behavior of solutions for one-dimensional Boltzmann equation", Comm. Pure. Appl. Math., 57 (12), 1543-1608, 2004
  • (with Yang, Tong; Yu, Shih-Hsien) "Energy method for Boltzmann equation", Phys. D, 188 (3月4日), 178-192, 2004
  • (with Yu, Shih-Hsien) "Boltzmann equation: micro-macro decompositions and positivity of shock profiles", Comm. Math. Phys., 246 (1), 133-179, 2004
  • (with T. Ruggeri) "Entropy production and admissibility of shocks", Acta Math. Appl. Sin. Engl. Ser., 19, 1-12, 2003
  • (with Y. Deng, T. Yang, and T. Yao) "Solutions with vacuum for Euler-Poisson equations", Arch. Rational Mech. Anal., 164 (3), 261-285, 2002
  • (with T. Yang) "Weak Solutions to General Systems of Hyperbolic Conservation Laws", Comm. Math. Phys., 230 (2), 289-327, 2002
  • "Shock waves. Proceedings of the International Congress of Mathematicians", Higher Ed. Press (Beijing), 0, 185-188, 2002
  • (with T. Yang and Y. Zheng) "Some nonlinear functionals for scalar conservation laws", Methods Appl. Anal., 8 (4), 609-622, 2001
  • "Hyperbolic and Viscous Conservation Laws. CBMS-NSF Regional Conference Series in Applied Mathematics, 72. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2000. ", 2000
  • (with S.H. Yu) "145Hyperbolic conservation laws and dynamic systems", Discrete Contin. Dynam. Systems, 6 (1), 143-145, 2000
  • "L1 stability for systems of hyperbolic conservation laws.'' Nonlinear partial differential equations (Evanston, IL, 1998), 183-192, Contemp. Math., 238, Amer. Math. Soc., Providence, RI, 1999. ", Yang, Tong, 1999
  • (with W.-C. Lien) "Nonlinear stability of a self-similar 3-dimensional gas flow", Comm. Math. Phys., 204 (3), 525-549, 1999
  • (with W.-C. Lien) "Nonlinear stability of a self-similar 3-dimensional gas flow", Comm. Math. Phys., 204 (3), 525-549, 1999
  • (with S.-H. Yu) "Nonlinear stability of weak detonation waves for a combustion model", Comm. Math. Phys., 204, 551-586, 1999
  • (with T. Yang) "Well-posedness theory for hyperbolic conservation l aws, Comm. Pure Appl. Math. LII", Comm. Pure Appl. Math., 0, 1553-1586, 1999
  • (with S.-H. Yu) "Continuum shock profiles for discrete conservation laws, II. Stability. Comm. Pure Appl. Math. LII (1999), 1047-1073. ", 1999
  • (with T. Yang) "A generalized entropy for scalar conservation laws", Comm. Pure Appl. Math., 0, 1427-1442, 1999
  • (with Yang, Tong) "Well-posedness theory for system of hyperbolic conservation laws. Hyperbolic problems: theory, numerics, applications, Vol.II, (Z�rich,1998), 681-691, Internat. Ser. Numer. Math., 130, Birkh酳ser, Basel, 1999. ", 0, 1998/1999
  • (with A. Bressan and T. Yang) "L1 stability estimates for nxn conservatiob laws", Archive Rational Mech. Anal., 1998
  • (with SIAM J. Math. Anal.) "Behaviours of solutions for the Burgers equation with boundary corresponding to rarefaction waves", A. Matsumura and K. Nishihar, 29, 293-308, 1998
  • (with T. Yang) "L1 stability of conservation laws with coinciding Hugoniot and characteristic curves", Indiana Univ. Math. J. , 1998
  • (with T. Yang) "(with ) L1 stability of 2x2 systems of hyperbolic conservation laws", J. Amer. Math. Soc., 729-772, 1998
  • (with Z. Xin and T. Yang) "Vacuum states for compressible flow", Disc. Cont. Dyn. Ana., 4, 1-32, 1998
  • "Zero dissipation and stability of shock waves", Methods and Appl. Analysis, 5, 81-94, 1998
  • (with W. Wang) "The pointwise estimates of diffusion wave for the Navier-Stokes systems in odd dimensions", Comm. Math. Phys., 196, 145-173, 1998
  • (with S.-H. Yu) "Continuum shock profiles for discrete conservation laws, I. Construction", Comm. Pure Appl. Math., 1998
  • (with Y. Zeng) "Compressible Navier-Stokes equations with zero heat conductivity", J. D. E., 1998
  • "Regularization of solution operators for quasilinear hyperbolic-parabolic partial differential equations", J. Partial Differential Equations, 10 (4), 347-354, 1997
  • (with T. Yang) "L1 stability of constant states for hyperbolic conservation laws", Methods and Appl. Analysis, 4, 339-355, 1997
  • (with K. Nishihara) "Asymptotic behaviour for scalar viscous conservation law with boundary effect", J.D.E., 133, 296-320, 1997
  • (with Z. Xin) "Pointwise decay to contact continuities for viscous conservation laws", Asian J. Math., 1, 34-84, 1997
  • (with T. Yang) "Compressible Euler equations with vacuum", J.D.E., 140, 223-237, 1997
  • "Pointwise convergence to shock waves for viscous conservaton laws, Comm. Pure Appl. Math. L (1997)", Comm. Pure Appl. Math. , 0, 1113-1182, 1997
  • (with S. Yu) "Propagation of Burgers stationary shocks under boundary effect", Archive Rational Mech. Anal., 139, 57-82, 1997
  • (with Y. Zeng) "Large time behavior of solutions of general quasilinear hyperbolic-parabolic systems of conservation laws", Memoirs, Amer. Math. Soc., 599, 1997
  • (with D. Li and D. Tan) "Stability of strong detonation travelling waves to combustion model", J. Math. Anal. Appl., 201, 516-531, 1996
  • "Gas flows with damping and vacuum", Japan J. Indus. and Appl. Math., 13, 25-32, 1996
  • "Stability and viscosity criterion of shocks. Proceedings of the VIII International Conference on Waves and Stability in Continuous Media, Part I (Palermo, 1995). Rend. Circ. Mat. Palermo (2) Suppl. No. 45, part I (1996), 357--366. ", 1996
  • (with K. Zumbrum) "On nonlinear stability of general undercompressive viscous shock waves", Comm. Math. Phys., 175, 319-345, 1995
  • (with K. Zumbrun) "Nonlinear stability of an undercompressive shock for complex Burgers equation", Comm. Math. Physics, 168, 163-186, 1995
  • (with L. Ying) "Nonliner stability strong detonations for a combustion model", SIAM J. of Math. Anal., 26, 519-528, 1995
  • "Nonlinear hyperbolic-dissipative partial differential equations. Recent mathematical methods in nonlinear wave propagation (Montecatini Terme, 1994), 103--136, Lecture Notes in Math., 1640, Springer, Berlin, 1996. ", Recent mathematical methods in nonlinear wave propagation , 1994/1996
  • (with Bolliat, G.) "Dafermos, C. M.; Lax, P. D. Recent mathematical methods in nonlinear wave propagation. Lectures given at the 1st C.I.M.E. Session held in Montecatini Terme, May 23--31, 1994. ", 1994-05
  • (with G.-Q. Chen and D. Levermore) "Hyperbolic conservation laws with stiff relaxation terms and entropy", Comm. Pure Applied Math., 47, 787-830, 1994
  • "Nonlinear evolutionary partial differential equations.", Proceedings of the International Conference held in Beijing, 21-25, 1993-06
  • (with Hsiao, Ling) "Nonlinear diffusive phenomena of nonlinear hyperbolic systems. A Chinese summary appears in Chinese Ann. Math. Ser. A 14 (1993), no. 6, 740. Chinese Ann. Math. Ser. B 14 (1993), no. 4, 465--480. ", 1993
  • "Nonlinear waves for viscous conservation laws", Nonlinear evolutionary partial differential equations, 65-74, 1993
  • (with L. Hsiao) "Nonlinear diffusive phenomena of nonlinear hyperbolic systems", Chin.Ann. Math., 14, 465-480, 1993
  • (with P. Le Floch) "Existence theory for nonlinear hyperbolic systems in nonconservative form", Forum Math., 5, 261-280, 1993
  • (with H. Freistühler) "Nonlinear stability of overcompressive shock waves in a rotationally invariant system of viscious conservation laws", Comm. Math. Physics, 153, 147-158, 1993
  • (with G.-Q. Chen) "Zero relaxation and dissipation limits for hyperbolic conservation laws ", Comm. Pure Appl. Math., 46, 755-781, 1993
  • (with L. Hsiao) "(with ) Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping", Comm. Math. Phys., 143, 599-605, 1992
  • (with Z. Xin) "Stability of viscous shock waves associated with a nonstrictly hyperbolic conservantion law, Comm. Pure Appl. Math., XLV (1992), 361-388. ", 1992
  • "Interaction of nonlinear hyperbolic waves, Nonlinear Analysis", Academia Sinica, R.O.C., World Scientific , 171-184, 1991
  • "Nonlinear hyperbolic-parabolic p.d.e., Nonlinear Analysis", Academia Sinica, R.O.C., World Scientific, 161-170, 1991
  • "Viscosity criterion for hyperbolic conservation laws", Proc. SIAM. Ed. M. Shearer, 1991
  • (with T. Zheng) "A scalar combustion model", Arch. Rational Mech. Anal., 114, 297-312, 1991
  • "On the viscosity criterion for hyperbolic conservation laws. Viscous profiles and numerical methods for shock waves (Raleigh, NC, 1990), 105-114. ", 1990
  • (with S. Hsu) "Nonlinear singular Sturm-Liouville problem and application to transonic flow through a nozzle", Comm. Pure Appl. Math., 43, 31-61, 1990
  • (with Z. Xin) "Over compressive shock waves nonlinear evolution equations that change types, ed. B. Keyfitz and M. Shearer", IMA volumes in Math Appls., 27, 139-145, 1990
  • "Nonlinear hyperbolic waves. Nonlinear hyperbolic equations in applied sciences. Rend. Sem. Mat. Univ. Politec. Torino 1988, Special Issue, 269--277 (1989). ", 1989
  • "Nonlinear analysis. Papers from the conference held in Taipei, June 19--24, 1989 ", 1989
  • "Geometric theory of shock waves. Multidimensional hyperbolic problems and computations (Minneapolis, MN, 1989), 198-202. ", 1989
  • (with D. Hoff) "The inviscid limit for the Navier-Stokes equations of compressible, instropic flow with shock data", Indiana Univ. J., 38, 861-915, 1989
  • (with Hsu, Sze-Bi) "Local uniqueness of interior layer solution and its related stability property.", Nonlinear analysis (Taipei), 51-60, 1989
  • "Quasilinear hyperbolic-parabolic partial differential equations", Algebra, analysis and geometry (Taipei), 185-197, 1988
  • (with Z. Xin) "Nonlinear stability of rarefaction waves for compressible Navier--Stokes equations", Comm. Math. Phys., 451-465, 1988
  • "Nonlinear waves for viscoelasticity with fading memory ", J. Diff. Equ., 76, 26-46, 1988
  • "Nonlinear resonance for quasilinear hyperbolic equation", J. Math. Phys., 28, 2593-2602, 1987
  • "Hyperbolic conservation laws with relaxation", Comm. Math. Phys., 108, 153-175, 1987
  • "Pointwise convergence to $N$-waves for hyperbolic conservation laws", Bulletin, Inst. Math., Academia Sinica, 15, 1-17, 1987
  • "Hyperbolic conservation laws and related topics. Partial differential equations of hyperbolic type and applications, 113--139, World Sci. Publishing, Singapore, 1987. ", 1987
  • (with I-L. Chern) "Convergence to diffusion waves of solutions for viscous conservation laws", Comm. Math. Phys., 110, 503-517, 1987
  • (with R. Caflisch) "Stability of shock waves for the Broadwell equations", Comm. Math. Phys., 39, 565-594, 1986
  • "Shock waves for compressible Navier-Stokes equations are stable", Comm. Pure Appl. Math., 39, 565-594, 1986
  • (with L. P. Huang) "Piecewise steady elements and Godunov-type difference scheme for duct flow", Comp. & Maths. with Appls., 12, 377-388, 1986
  • "Shock waves and diffusion waves. Nonlinear systems of partial differential equations in applied mathematics, Part 1 (Santa Fe, N.M., 1984), 283--291, Lectures in Appl. Math., 23, Amer. Math. Soc., Providence, RI, 1986. ", 1986
  • "Nonlinear stability of shock waves for viscous conservation laws, Memoirs", Amer. Math. Soc., 328, 1985
  • "Nonlinear stability of shock waves for viscous conservation laws", Amer. Math. Soc. (N.S.) , 12 (2), 233-236, 1985
  • (with C. H. Wang) "On a system of nonstrictly hyperbolic system", J.D.E., 57, 1-14, 1985
  • "Stability of nonlinear waves. Metastability and incompletely posed problems", Minneapolis, Minn., 259-267, 1985
  • (with H. Galz) "The asymptotic analysis of wave interactions and numerical calculations of transonic nozzle flow", Advances Appl., 5, 111-146, 1984
  • (with M. Pierre) "Source-solutions and asymptotic behavior in conservation law", J. Diff. Equ., 51, 419-441, 1984
  • (with C. Li) "Asymptotic states for hyperbolic conservation laws with a moving source", Advances in Appl. Math., 4, 353-379, 1983
  • "Resonance for quasilinear hyperbolic equation", Bulletin Amer. Math. Soc., 6, 463-465, 1982
  • (with A. Chorin and Z. H. Teng) "Riemann problems for reacting gas with applications to transitions", SIAM J. Appl. Math., 42, 964-981, 1982
  • "Nonlinear stability and instability of transonic flows through a nozzle", Comm. Math. Phys., 83, 243-260, 1982
  • "Transonic gas flow in a duct of varying area", Arch. Rat. Mech. and Anal., 80, 1-18, 1982
  • "Admissible solutions of hyperbolic conservation laws, Memoirs", Amer. Math. Soc., 240, 1981
  • (with Conlon, Joseph G.) "Admissibility criteria for hyperbolic conservation laws", Indiana Univ. Math. J., 30 (5), 641-652, 1981
  • (with J. Smoller) "On the vacuum state for isentropic gas dynamics equations", Advances in Math., 1, 345-359, 1980
  • "probleme du vide pour les equations de la dynamique des gaz isentropiques. (French) [The problem of the vacuum for equations in isentropic gas dynamics] Nonlinear partial differential equations and their applications. Collège de France Seminar, Vol. II (Paris, 1979/1980), 319--326, 395.", 1979/1980
  • "A system of quasilinear hyperbolic partial differential equations. Trends in applications of pure mathematics to mechanics, Vol. III (Edinburgh, 1979), 179-189. ", 1979
  • "Quasilinear hyperbolic systems68", Comm. Math. Phys., 68, 142-172, 1979
  • "Development of singularities in the nonlinear waves for quasilinear hyperbolic partial differential equations", J. Diff. Equations,, 33, 92-111, 1979
  • (with S. Antman) "Traveling waves in hyperelastic rods", Quarterly of Appl. Math., 36, 377-399, 1979
  • "The free piston problem for gas dynamics", J. of Diff. Equations, 39, 175-191, 1978
  • "Invariants and asymptotic behavior of solution of a conservation law ", Proceedings of A.M.S., 71, 227-231, 1978
  • "Asymptotic behavior of solutions of general systems of nonlinear hyperbolic conservation laws", Indiana Univ. J., 27, 211-253, 1978
  • "The deterministic version of the Glimm scheme", Comm. Math. Phys., 57, 135-148, 1977
  • "Linear and nonlinear large-time behaviors of solutions of hyperbolic conservation laws", Comm. Pure Appl. Math., 30, 767-796, 1977
  • "Large-time behavior of solutions of initial and initial-boundary value problem of general system of hyperbolic conservation laws", Comm. Math. Phys., 55, 163-177, 1977
  • "Decay to N-waves of solutions of general systems of nonlinear hyperbolic conservation laws", Comm. Pure Appl. Math, 30, 586-611, 1977
  • "Initial-boundary value problems for gas dynamics", Arc. Rat. Mech. and Anal., 64, 137-168, 1977
  • "Solutions in the large for equations of nonisentropic gas dynamics", Indiana Univ. J., 26, 144-177, 1977
  • "The entropy condition and the admissibility of shocks", J. of Math. Anal. and Applications, 53, 75-88, 1976
  • "Shock waves in nonisentropic gas flow", J. Diff. Equations, 22, 442-452, 1976
  • "Uniqueness theorem of the Cauchy problem for general 2 X 2 conservation laws", J. Diff. Eqs., 20, 369-388, 1976
  • "Existence and uniqueness theorems for Riemann problems", Transactions of A.M.S., 212, 375-382, 1975
  • "The Riemann Problem for general systems of conservation laws", J. Diff. Equations, 18, 218-234, 1975
  • "The Riemann problem for general 2 X 2 conservation Laws ", Transactions of A.M.S., 199, 89-112, 1974
  • (with S. Cox) "Zero-memory limit for a viscoelasticity model with Riemann data (preprint). "
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