Publications by Zvi Artstein

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Hebrew version:
  • הקשר המתמטי: המתמטיקה של הטבע, הטבע של המתמטיקה, והזיקה לאבולוציה. ספרי עליית הגג וידיעות ספרים, תל אביב, 2014

    Translation to English:
  • Mathematics and the Real World: The Remarkable role of Evolution in the Making of Mathematics, Prometheus Books, Amherst NY, 2014 (translated from Hebrew by Alan Hercberg)

    Translation to Italian:
  • Matematica E Mondo Reale: Il ruolo decisivo della'evoluzione nella costruzione matematica del mondo, Bollati Boringhieri, Bologna, 2017 (traduzione di Simonetta Frediani)

    Translation to Japanese:
  • 数学がいまの数学になるまで , Maruzen Publishing Company Ltd., 2018 (translated by Yoshiaki Ueno, translation supervised by Takushiro Ochiai)

    • Papers


    1. Values of games with denumerably many players. International J. of Game Theory 1 (1971), 27-37. [Abstract]

    2. Set-valued measures. Transactions American Mathematical Society 165 (1972), 103-125. [Abstract]

    3. Trajectories and the attainable set of an abstract linear control system. Mathematical Systems Theory 7 (1973), 265-280. [Abstract]

    4. On a variational problem. J. Mathematical Analysis and Applications 45 (1974), 404-415. [Abstract]

    5. On the calculus of closed set-valued functions. Indiana University Mathematics J. 24 (1974), 433-441. [Abstract]

    6. The maximum amplitude cost functional in linear systems. J. Mathematical Analysis and Applications 50 (1975), 341-349. [Abstract]

    7. Continuous dependence on parameters: On the best possible results. J. Differential Equations 19 (1975), 214-225. [Abstract]

    8. Weak convergence of set-valued functions and control. SIAM J. Control 13 (1975), 865-878. [Abstract]

    9. Continuous dependence of solutions of Volterra integral equations. SIAM J. Mathematical Analysis 6 (1975), 446-456. [Abstract]

    10. (with J.A. Burns): Integration of compact set-valued functions. Pacific J. of Mathematics 58 (1975), 297-307. [Abstract]

    11. Continuous dependence of solutions of operator equations I. Transactions American Mathematical Society 231 (1977), 143-166. [Abstract]

    12. On continuous dependence of fixed points of condensing maps. Dynamical Systems, an International Symposium, L. Cesari, J.K. Hale and J.P. LaSalle eds., Academic Press, New York, 1976, Vol. 2, pp. 73-75. [Abstract]

    13. (with R.A. Vitale): A strong law of large numbers for random compact sets. Annals of Probability 3 (1975), 879-882. [Abstract]

    14. Lyapunov convexity theorem and Riemann-type integrals. Indiana University Mathematics J. 25 (1976), 717-72 . [Abstract]

    15. Topological dynamics of an ordinary differential equation. J. Differential Equations 23 (1977), 216-223. [Abstract]

    16. Topological dynamics of ordinary differential equations and Kurzweil equations. J. Differential Equations 23 (1977), 224-243. [Abstract]

    17. The limiting equations of nonautonomous ordinary differential equations. J. Differential Equations 25 (1977), 184-202. [Abstract]

    18. (with E.F. Infante): On the asymptotic stability of oscillators with unbounded damping. Quarterly of Applied Mathematics 34 (1976), 195-199. [Abstract]

    19. Limiting equations and stability of nonautonomous ordinary differential equations. An appendix in The Stability of Dynamical Systems, by J.P. LaSalle, Regional Conference Series in Appl. Math. 25, SIAM Publications, 1976. [Abstract]

    20. On the limiting equations and invariance of time-dependent difference equations. Stability of Dynamical Systems, J. Graef ed., Marcel-Dekker, New York, 1977, pp. 3-9. [Abstract]

    21. Uniform asymptotic stability via the limiting equations. J. Differential Equations 27 (1978), 172-189. [Abstract]

    22. Relaxed controls and the dynamics of control systems. SIAM J. on Control and Optimization 16 (1978), 689-701. [Abstract]

    23. A note on Fatou's lemma in several dimensions. J. Mathematical Economics 6 (1979), 277-282. [Abstract]

    24. Generalized solutions to continuous-time allocation processes. Econometrica 48 (1980), 899-922. [Abstract]

    25. Discrete and continuous bang-bang and facial spaces, or: Look for the extreme points. SIAM Review 22 (1980), 172-185. (Reprinted in: Games and Economic Theory (Hart and Neyman, eds.), Univ. of Michigan Press, Ann Harbor, 1995, pp. 449-462.) [Abstract]

    26. (with G. Karakostas): Convergence in the delay population equation. SIAM J. on Applied Mathematics 38 (1980), 261-272. [Abstract]

    27. (with Y. Greenberg): Exhaustion time in continuous allocation processes. J. Mathematical Analysis and Applications 78 (1980), 378-395. [Abstract]

    28. (with S. Hart): Law of large numbers for random sets and allocation processes. Mathematics of Operations Research 6 (1981), 485-492. [Abstract]

    29. (with G. Tadmor): Linear systems with indirect controls: The underlying measures. SIAM J. on Control and Optimization 20 (1982), 96-111. [Abstract]

    30. (with G. Tadmor): The underlying measures of linear systems with indirect controls. Proceedings IEEE Conference on Decision and Control, San Diego 1981, pp. 1018-1021. [Abstract]

    31. (with M. Slemrod): Trajectories joining critical points. J. Differential Equations 44 (1982), 40-62. [Abstract]

    32. Stability, observability and invariance. J. Differential Equations 44 (1982), 224-248. [Abstract]

    33. Linear systems with delayed controls: A reduction. IEEE Transactions on Automatic Control AC-27 (1982), 869-879. [Abstract]

    34. (with G. Schechtman): Positive definite forms generated by integrals and weak limits. J. Mathematical Analysis and Applications 92 (1983), 114-118. [Abstract]

    35. Uniform controllability via the limiting systems. Applied Mathematics and Optimization 9 (1982), 111-131. [Abstract]

    36. Irregular cobweb dynamics. Economics Letters 11 (1983), 15-17. [Abstract]

    37. Stabilization with relaxed controls. Nonlinear Analysis 7 (1983), 1163-1173. [Abstract]

    38. Convergence rates for the optimal values of allocation processes. Mathematics of Operations Research 9 (1984), 348-355. [Abstract]

    39. Convergence of sums of random sets. Stochastic Geometry, Geometric Statistics and Stereology, R. Ambertzumian and W. Weil, eds., Teubner-Texte zur Math. 65, Teubner Verlag, 1984, pp. 34-42. [Abstract]

    40. Distributions of random sets and random selections. Israel J. of Mathematics 46 (1983), 313-324. [Abstract]

    41. (with G.C. Hansen): Convexification in limit laws of random sets in Banach spaces. Annals of Probability 13 (1985), 307-309. [Abstract]

    42. Limit laws for multifunctions applied to an optimization problem. Multifunctions and Integrands, Stochastic Analysis, Approximation and Optimization, G. Salinetti, ed., Lecture Notes in Math. 1091, Springer Verlag, Berlin, 1984, pp. 66-79. [Abstract]

    43. On dense univalued representations of multivalued maps. Rendiconti del Circolo Matematico di Palermo, Ser. II, Tom. 33 (1984), 340-350. [Abstract]

    44. (with A. Leizarowitz): Tracking periodic signals with the overtaking criterion. IEEE Transactions on Automatic Control AC-30 (1985), 1123-1126. [Abstract]

    45. On Liapunov functions for time-varying and for controlled equations. Differential Equations: Qualitative Theory, B. Sz.-Nagy and L. Hatvani, eds., North Holland, Amsterdam, 1986, pp. 61-103. [Abstract]

    46. (with K. Prikry): Caratheodory selections and the Scorza-Dragoni property. J. Mathematical Analysis and Applications 127 (1987), 540-547. [Abstract]

    47. (with R. J-B Wets): Approximating the integral of a multifunction. J. Multivariate Analysis 24 (1988), 285-308. [Abstract]

    48. Piecewise linear approximations of set-valued maps. J. Approximation Theory 56 (1989), 41-47. [Abstract]

    49. (with R. J-B Wets): Decentralized allocation of resources among many produces. J. Mathematical Economics 18 (1989), 303-324. [Abstract]

    50. A variational convergence that yields chattering systems. Annales Institut H. Poincare, Analyse Non Lineare, supp. an Vol. 6 (1989), pp. 49-71. [Abstract]

    51. Chattering linear systems: A model of rapidly oscillating coefficients. Math. of Control Signals Systems 2 (1989), 359-380. [Abstract]

    52. Yet another proof of the Lyapunov convexity theorem. Proceedings American Mathematical Society 108 (1990), 89-91. [Abstract]

    53. Parameterized integration of multifunctions with applications to control and optimization. SIAM J. Control and Optimization 27 (1989), 1369-1380. (Reprinted in: Games and Economic Theory (S. Hart and A. Neyman, eds.), Univ. of Michigan Press, Ann Harbor, 1995, pp. 437-448.) [Abstract]

    54. Rapid oscillations, chattering systems, and relaxed controls. SIAM J. Control and Optimization 27 (1989), 940-948. [Abstract]

    55. On collective limit sets. Qualitative Theory of Differential Equations, B. Sz.-Nagy and L. Hatvani, eds., North Holland, Amsterdam, 1989, pp. 23-36. [Abstract]

    56. Extensions of Lipschitz selections and an application to differential inclusions. Nonlinear Analysis 16 (1991), 701-704. [Abstract]

    57. Sensitivity to sigma-fields of information in stochastic allocation. Stochastics and Stochastics Reports 36 (1991), 41-63. [Abstract]

    58. (with T. Rzezuchowski): A note on Olech's lemma. Studia Mathematica 98 (1991), 91-94. [Abstract]

    59. Chattering variational limits of control systems. Forum Mathematicum 5 (1993), 369-403. [Abstract]

    60. (with R. J-B Wets): Sensors and information in optimization under stochastic uncertainty. Mathematics of Operation Research 18 (1993), 523-547. [Abstract]

    61. Chattering limit for a model of harvesting in a rapidly changing environment. Applied Mathematics and Optimization 28 (1993), 133-147. [Abstract]

    62. Integral-like operator equations with time-varying parameters, and variational convergence. The Second Colloquium on Differential Equations, D. Bainov and V. Covachev, eds., World Scientific, Singapore, 1992, pp. 1-14. [Abstract]

    63. (with R. J-B Wets): Stability results for stochastic programs and sensors, allowing for discontinuous objective functions. SIAM J. Optimization 4 (1994), 537-550. [Abstract]

    64. Sensitivity with respect to the underlying information in stochastic programs. J. of Computational and Applied Mathematics 56 (1994), 127-136. [Abstract]

    65. First order approximations for differential inclusions. Set-Valued Analysis 2 (1994), 7-17. [Abstract]

    66. Probing for information in two-stage stochastic programming and the associated consistency. Asymptotic Statistics, P. Mandl and M. Huskova, eds., Springer-Verlag, Berlin, 1994, pp. 21-33. [Abstract]

    67. (with A. Vigodner): Singularly perturbed ordinary differential equations with dynamic limits. Proceedings of the Royal Society of Edinburgh 126A (1996), 541-569. [Abstract]

    68. (with R. J-B Wets): Consistency of minimizers and the SLLN for stochastic programs. J. Convex Analysis 2 (1995), 1-17. [Abstract]

    69. A calculus for set-valued maps and set-valued evolution equations. Set-valued Analysis 3 (1995), 213-261. [Abstract]

    70. Examples of stabilization with hybrid feedback. In: Hybrid Systems III: Verification and Control, R. Alur, T.A. Henzinger and E.D. Sontag eds., Lecture Notes in Computer Science 1066, Springer-Verlag, Berlin, 1996, pp. 173-185. [Abstract]

    71. (with V. Gaitsgory): Tracking fast trajectories along a slow dynamics: A singular perturbations approach. SIAM J. Control and Optimization 35 (1997), 1487-1507. [Abstract]

    72. Necessary conditions for continuous dependence. Dynamics of Continuous Discrete Impulsive Systems 3 (1997), 509-516. [Abstract]

    73. (with V. Gaitsgory): Linear-quadratic tracking of coupled slow and fast targets. Math. Control Signals and Systems 10 (1997), 1-30. [Abstract]

    74. Stability in the presence of singular perturbations. Nonlinear Analysis 34 (1998), 817-827. [Abstract]

    75. Singularly perturbed ordinary differential equations with nonautonomous fast dynamics. J. Dynamics and Differential Equations 11 (1999) 297-318. [Abstract]

    76. Gains and costs of information in stochastic programming. Annals of Operations Research 85 (1999), 129-152. [Abstract]

    77. (with M. Slemrod): Phase separation of the slightly viscous Cahn-Hilliard equation in the singular perturbation limit. Indiana University Mathematics J. 47 (1998), 1147-1166. [Abstract]

    78. Invariant measures of differential inclusions applied to singular perturbations. J. Differential Equations 152 (1999), 289-307. [Abstract]

    79. Relaxed multifunctions and Young multimeasures. Set-Valued Analysis 6 (1998), 237-255. [Abstract]

    80. Variational limits constrained by measure-valued multifunctions. Calculus of Variations and Optimal Control, A. Ioffe, S. Reich and I. Shafrir Eds., Chapman & Hall, London, 1999, pp. 1-23. [Abstract]

    81. (with V. Gaitsgory): The value function of singularly perturbed control systems. Applied Mathematics and Optimization 41 (2000), 425-445. [Abstract]

    82. (with M. Slemrod): On singularly perturbed retarded functional differential equations. J. Differential Equations 171 (2001), 88-109. [Abstract]

    83. (with M. Slemrod): The singular perturbation limit of an elastic structure in a rapidly flowing nearly invicid fluid. Quarterly of Applied Mathematics 59 (2001), 543-555. [Abstract]

    84. Compact convergence of sigma-fields and relaxed conditional expectation. Probability Theory and Related Fields 120 (2001), 369-394. [Abstract]

    85. Invariant measures of set-valued maps. J. Mathematical Analysis and Applications 252 (2000), 696-709. [Abstract]

    86. The chattering limit of singularly perturbed optimal control problems. Proceedings of CDC-2000, IEEE 39th IEEE Conference on Decision and Control, Sydney 2000, pp. 564-569. [Abstract]

    87. Projections on convex sets in the relaxed limit. Set-Valued Analysis 9 (2001), 13-34. [Abstract]

    88. (with Michael Grinfeld): Ergodicity and mixing via Young measures. Ergodic Theory and Dynamical Systems 22 (2002), 1001-1015. [Abstract]

    89. On singularly perturbed ordinary differential equations with measure-valued limits. Mathematica Bohemica 127 (2002), 139-152. [Abstract]

    90. (with Arie Leizarowitz): Singularly perturbed control systems with one-dimensional fast dynamics. SIAM J. Control and Optimization 41 (2002), 641-658. [Abstract]

    91. (with Cristian Contantin Popa): Convexity and the natural best approximation in spaces of Young measures. J. Convex Analysis 10 (2003), 169-184. [Abstract]

    92. An occupational measure solution to a singularly perturbed optimal control problem. Control and Cybernetics 31 (2002), 623-642. [Abstract]

    93. Relaxation in singularly perturbed control systems. Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, USA, 2002, pp 4330-4335. [Abstract]

    94. (with V. Gaitsgory): Convergence to compact convex sets in infinite dimensions. J. Mathematical Analysis and Applications 284 (2003), 471-480. [Abstract]

    95. Switching systems induced by singular perturbations. Functional Differential Equations 10 (2003), 19-44. [ Abstract]

    96. Controlled switching in singularly perturbed systems. Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, USA, 2003, pp. 2756-2761. [Abstract]

    97. (with Cristian Contantin Popa): Orlicz-Young structures of Young measures. Acta Applicandae Mathematicae 80 (2004), 1-33. [Abstract]

    98. On impulses induced by singular perturbations. In: Optimal Control, Stabilization, and Nonsmooth Analysis, M. de Queiroz, M. Malisoff and P. Wolenski, Eds., Lecture Notes in Control and Information Sciences 301, Springer-Verlag, Heidelberg, 2004, pp. 61-72. [Abstract]

    99. Invariant measures and their projections in nonautonomous dynamical systems. Stochastics and Dynamics 4 (2004), 439-459. [Abstract]

    100. Distributional convergence in planar dynamics and singular perturbations. J. Differential Equations 201 (2004), 250-286. [Abstract]

    101. (with Gera Weiss): State nullification by memoryless output feedback. Math. Control Signals Systems 17 (2005), 38-56. [Abstract]

    102. On the value function of singularly perturbed optimal control systems. Proceedings of the 43rd IEEE Conference on Decision and Control, Paradise Island, Bahamas 2004, pp. 432-437. [Abstract]

    103. Bang-bang controls in the singular perturbations limit. Control and Cybernetics 34 (2005), 645-663. [Abstract]

    104. A Young measures approach to averaging. In Differential Equations, Chaos and Variational Problems, V. Staicu Ed., Progress in Nonlinear Differential Equations and Their Applications, Vol. 75, 15-28, Birkhäuser Verlag, Basel, 2007. [Abstract]

    105. Averaging of time-varying differential equations revisited. J. Differential Equations 243 (2007), 146-167. [Abstract]

    106. (with Sasa V. Rakovic) Feedback and invariance under uncertainty via set-iterates. Automatica 44 (2008), 520-525. [Abstract]

    107. (with Jasmine Linshiz and Edriss S. Titi) Young measure approach to computing slowly advancing fast oscillations. Multiscale Modeling and Simulation 6 (2007), 1085-1097. [Abstract]

    108. (with Ioannis G. Kevrekidis, Marshall Slemrod and Edriss S. Titi) Slow observables of singularly perturbed differential equations. Nonlinearity 20 (2007), 2463-2481, on line at: http://stacks.iop.org/0951-7715/20/2463 [Abstract]

    109. Sensitivity of control systems with respect to measure-valued coefficients. In Geometric Control and Nonsmooth Analysis, F. Ancona et al. Eds., Worldscientific, London, 2008, pp. 65-81. [Abstract]

    110. (with Jonathan Ronen) On stabilization of switched linear systems. Systems and Control Letters 57 (2008), 919-926. [Abstract]

    111. Pontryagin maximum principle for coupled slow and fast systems. Control and Cybernetics 38 (2009), 1003-1019. [Abstract]

    Recent Publications


    1. (with Sasa V. Rakovic) Set-invariance under output-feedback: A set-dynamics approach. International Journal of Systems Science 42 (2011), 539-555. [Abstract]

    2. Averaging of ordinary differential equations with slowly varying averages. Discrete and Continuous Dynamical Systems Series B, 14 (2010), 353-365. [Abstract]

    3. Applied Platonism. EMS Newsletter, March 2010, 23-24. (E-reprinted in the Philosophy of Mathematics section of http://www.mathematics-in-europe.eu) [Abstract]

    4. Analysis and control of coupled slow and fast systems: A review. Proceedings of DINCON'2010, 9th Brazilian Conference on Dynamics, Control and Their Applications, pp. 1254-1263 (http://www.sbmac.org.br/dincon/). [Abstract]

    5. Pontryagin Maximum Principle revisited with feedbacks. European Journal of Control 17 (2011), 46-54. [Abstract]

    6. (with Ido Bright) Periodic optimization suffices for infinite horizon planar optimal control. SIAM J. Control and Optimization 48 (2010), 4963-4986. [Abstract]

    7. Sensitivity estimates via Lyapunov functions and Lyapunov metrics. In Optimization Theory and Related Topics, Contemporary Mathematics, vol. 568, Amer. Math. Soc., Providence, RI, 2012, pp. 1-17. [Abstract]

    8. (with C. William Gear, Ioannis G. Kevrekidis, Marshall Slemrod and Edriss S. Titi) Analysis and computation of a discrete KdV-Burgers type equation with fast dispersions and slow diffusion. SIAM J. Numerical Analysis 49 (2011), 2124-2143. [Abstract]

    9. (with Ido Bright) On the velocity of planar trajectories. Nonlinear Differential Equations and Applications NoDEA, 20 (2013), 177–185. [Abstract]

    10. Intuition versus logische Strenge (in German). Alles Mathematik, Von Pythagoras zu Big Data, 4. Auflage, Martin Aigner and Ehrhard Behrends, Herausgeber, Springer Spektrum, 2016, pp. 457-470. [Abstract]

    11. Asymptotic stability of singularly perturbed differential equations. Journal of Differential Equations 262 (2017), 1603-1616. [Abstract]

    12. (with Ruhama Even and Avital Elbaum-Cohen),The Rothschild-Weizmann Master Program for Practicing Mathematics Teachers. In K-12 Mathematics Education in Israel: Issues and Innovations, Nitsa Movshovitz-Hadar Ed., Series on Mathematics Education Volume 13, World Scientific, Singapore, 2018, Chapter 25, pp.235-242. [Abstract]

    13. (with Sabyasachi Chatterjee and Amit Acharya), Computing Singularly Perturbed Differential Equations, J. of Computational Physics 354 (2018), 417-446. [Abstract]

    14. A variational problem determined by probability measures. Optimization 68 (2019), 81-98. [Abstract]

    15. Invariance principle in the singular perturbations limit. Discrete and Continuous Dynamical Systems Series-B 24 (2019), 3653-3666. [Abstract]

    16. Convexity and closure in optimal allocations determined by decomposable measures. Vietnam J. Mathematics 47 (2019), 563-577. [Abstract]

    17. Interval-decomposability of continuous functions, and convexity. J. Convex Analysis 27 (2020), 31- 48. [Abstract]

    18. Convexification estimates for Minkowski averages in infinite dimensions. Pure and Applied Functional Analysis 6 (2021), 709-718. [Abstract]

    19. The pendulum under vibrations revisited. Nonlinearity 34 (2021), 394-410. [Abstract]

    20. Linear singularly perturbed systems without slow-fast split. Computational Optimization and Applications, to appear. [Abstract]

    21. (with Alon Shapira) Samplings from the values of random convex sets. Journal of Convex Analyis 30 (2023), 441-452. [Abstract]

    22. (with Gerald Beer) Making continuous functions Lipschitz. Rocky Mountain J. of Mathematics, to appear. [Abstract]



    Drafts


    1. What to teach and how to teach mathematics: A proposal for a reform (in Hebrew). [Proposal for reform]




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