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On the 70th birthday of Boris Vasil’evich Pal’tsev

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Pal’tsev’s Selected Works

  1. “A Multidimensional Analog of the Morera Theorem,” Sib. Mat. Zh. 4, 1376–1389 (1963).

  2. “On Decomposition of Solutions of the Dirichlet Problem and the Mixed Problem for the Biharmonic Equation in Series with Respect to Solutions of Decomposing Problems,” Zh. Vychisl. Mat. Mat. Fiz. 6, 43–51 (1966).

  3. “The Method of a Small Parameter in a Boundary Value Problem for an Oseen System,” Zh. Vychisl. Mat. Mat. Fiz. 7, 1144–1166 (1967).

  4. “Convergence of the Method of Successive Approximations with Splitting of Boundary Conditions in the Solution of a Boundary Value Problem for the Navier-Stokes Equations,” Zh. Vychisl. Mat. Mat. Fiz. 10, 785–788 (1970).

  5. “Asymptotic Behavior of the Eigenvalues of Convolution Integral Operators on a Finite Interval with Kernels Whose Fourier Transforms Are Rational,” Dokl. Akad. Nauk SSSR 194, 774–777 (1970).

  6. “Expansion in Eigenfunctions of Integral Convolution Operators on a Finite Interval with Kernels Whose Fourier Transforms Are Rational: “Weakly” Nonself-Adjoint Regular Kernels,” Izv. Akad. Nauk SSSR, Ser. Mat. 36, 591–634 (1972).

  7. “On Domain Decomposition in Solving Boundary Value Problems for Poisson’s Equation in Domains of Complex Geometry,” Zh. Vychisl. Mat. Mat. Fiz. 13, 1441–1458 (1973) (with E. I. Matveeva).

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  8. “The Asymptotics of the Spectrum and Eigenfunctions of Convolution Operators on a Finite Interval with Kernel Having a Homogeneous Fourier Transform,” Dokl. Akad. Nauk SSSR 218, 28–31 (1974).

  9. “A Continuity Condition for the Canonical Solution Matrix of Hilbert’s Problem,” Dokl. Akad. Nauk SSSR 226, 1271–1274 (1976).

  10. “Normal Solvability of some Integral Equations of the First Kind on an Interval,” Sib. Mat. Zh. 18, 195–211 (1977).

  11. “On the Dirichlet Problem for a Pseudodifferential Equation Encountered in the Theory of Random Processes,” Izv. Akad. Nauk SSSR, Ser. Mat. 41, 1348–1387 (1977).

  12. “Boundary Value Problems for the St. Venant System of Equations on a Plane,” Zh. Vychisl. Mat. Mat. Fiz. 19, 708–725 (1979) (with V. F. Baklanovskaya and I. I. Chechel’).

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  13. “Convolution Equations on a Finite Interval for a Class of Symbols Having Powerlike Asymptotics at Infinity,” Izv. Akad. Nauk SSSR, Ser. Mat. 44, 322–393 (1980).

  14. “A Generalization of the Wiener-Hopf Method for Convolution Equations on a Finite Interval with Symbols Having Powerlike Asymptotics at Infinity,” Mat. Sb. 113, 355–399 (1980).

  15. “A Method for Constructing a Canonical Matrix of Solutions of a Hilbert Problem Arising in the Solution of Convolution Equations on a Finite Interval,” Izv. Akad. Nauk SSSR, Ser. Mat. 45, 1332–1390 (1981).

  16. “On the Canonical Solution Matrix of the Linear Junction Problem with a Piecewise Continuous Matrix Coefficient on an Elementary Piecewise Smooth Curve,” Dokl. Akad. Nauk SSSR 297, 1054–1058 (1987).

  17. “Norm estimates for Singular Integral Operators in L p Spaces with Weights Satisfying Muckenhoupt’s Condition,” Sib. Mat. Zh. 28, 185–198 (1987).

  18. “On Conditions Guaranteeing Continuity up to the Contour and Power Behavior in Neighborhoods of Nodal Points of Solutions of a Homogeneous Linear Junction Problem with a Piecewise Continuous Matrix Coefficient,” Dokl. Akad. Nauk SSSR 299, 558–562 (1988).

  19. “The Multigrid Method Applied to a Finite-Element Scheme for a Two-Dimensional Stokes-Type System,” Zh. Vychisl. Mat. Mat. Fiz. 30, 1797–1804 (1990) (with I. I. Chechel’).

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  20. “On Rapidly Converging Modifications of Dorodnitsyn’s Method for a Two-Dimensional Stokes-Type System with a Small Parameter,” in Problems in Applied Mathematics and Informatics, Part I: Mechanics and Mathematical Physics (Vychisl. Tsentr Akad. Nauk SSSR, Moscow, 1992), pp. 108–124 (with N. A. Meller and I. I. Chechel’).

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  21. “Fast-Converging Iterative Methods with Splitting of Boundary Conditions for a Multidimensional Stokes-Type System: Periodic “Flows” between Parallel Walls, Dokl. Akad. Nauk 325, 926–931 (1992).

  22. “Fast-Converging Iterative Methods with Incomplete Splitting of Boundary Conditions for a Multidimensional Singularly Perturbed Stokes-Type System,” Mat. Sb. 185(4), 101–150 (1994).

  23. “On Rapidly Convergent Iterative Methods with Complete Boundary Condition Splitting for a Multidimensional Singularly Perturbed System of Stokes Type,” Mat. Sb. 185(9), 109–138 (1994).

  24. “On Convergence Conditions for Iterative Methods with Complete Splitting of Boundary Conditions for a Stokes System in a Sphere and Spherical Layer,” Zh. Vychisl. Mat. Mat. Fiz. 35, 935–963 (1995).

  25. “Mixed Problem with Nonhomogeneous Boundary Conditions in Lipschitz Domains for Second-Order Elliptic Equations with a Parameter,” Mat. Sb. 187(4), 59–116 (1996).

  26. “A Rapidly Convergent Iterative Domain-Decomposition Method for Boundary-Value Problems for a Second-Order Elliptic Equation with a Parameter,” Zh. Vychisl. Mat. Mat. Fiz. 36, 26–45 (1996) (with N. A. Meller and I. I. Chechel’).

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  27. “Algorithms Based on Bilinear Finite Elements for Iterative Methods with Split Boundary Conditions for a Stokes-Type System on a Strip under the Periodicity Condition,” Zh. Vychisl. Mat. Mat. Fiz. 37, 799–815 (1997) [Comput. Math. Math. Phys. 37, 775–791 (1997)] (with I. I. Chechel’).

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  28. “Real Properties of Bilinear Finite-Element Implementations of Methods with the Splitting of Boundary Conditions for a Stokes-Type System,” Zh. Vychisl. Mat. Mat. Fiz. 38, 247–261 (1998) [Comput. Math. Math. Phys. 38, 238–251 (1998)] (with I. I. Chechel’).

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  29. “On Some Methods for Enhancing the Convergence Rate for the Higher Harmonics of Bilinear Finite-Element Implementations of Iterative Methods with Boundary-Condition Splitting for a Stokes-Type System,” Zh. Vychisl. Mat. Mat. Fiz. 38, 956–970 (1998) [Comput. Math. Math. Phys. 38, 916–929 (1998)] (with I. I. Chechel’).

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  30. “On Methods with Splitting of Boundary Conditions for a Stokes-Type System in Circularly Symmetric Domains,” in Proceedings of International Conference Dedicated to the 75th Birthday of Corresponding Member of the RAS, Professor L.D. Kudryavtsev (Ross. Univ. Druzhby Narodov, Moscow, 1998), Vol. 2, pp. 124–128 [in Russian].

  31. “On Some Finite-Element Implementations of Iterative Methods with Splitting of Boundary Conditions for Stokes and Stokes-Type Systems in a Spherical Layer: Axially Symmetric Case,” Zh. Vychisl. Mat. Mat. Fiz. 39, 98–123 (1999) [Comput. Math. Math. Phys. 39, 92–117 (1999)] (with N. A. Meller and E. G. Khlyupina).

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  32. “On Two-Sided Estimates Uniform with Respect to the Real Argument and Index for Modified Bessel Functions,” Mat. Zametki 65, 681–692 (1999).

  33. “Bilinear Finite-Element Implementations of Iterative Methods with Incomplete Splitting of Boundary Conditions for a Stokes-type System on a Rectangle,” Zh. Vychisl. Mat. Mat. Fiz. 39, 1838–1864 (1999) [Comput. Math. Math. Phys. 39, 1755–1780 (1999)] (with I. I. Chechel’).

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  34. “On the Spectral and Approximating Properties of Cubic Finite-Element Approximations of the Laplace and First-Derivative Operators: The Periodic Case,” Zh. Vychisl. Mat. Mat. Fiz. 40, 754–774 (2000) [Comput. Math. Math. Phys. 40, 718–738 (2000)] (with V. O. Belash).

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  35. “Exact Estimates of the Convergence Rate of Iterative Methods with Splitting of the Boundary Conditions for the Stokes-Type System in a Layer with the Periodicity Condition,” Zh. Vychisl. Mat. Mat. Fiz. 40, 1823–1837 (2000) [Comput. Math. Math. Phys. 40, 1751–1764 (2000)] (with I. I. Chechel’).

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  36. “Optimization of Relaxation Parameter Values in a One-Step Version of an Iterative Method with Splitting of Boundary Conditions for the Stokes System in a Spherical Layer,” Vestn. Ross. Univ. Druzhby Narodov 8(2), 74–90 (2001).

  37. “Bicubic Finite-Element Implementations of Methods with Splitting of Boundary Conditions for a Stokes-Type System in a Strip under the Periodicity Condition,” Zh. Vychisl. Mat. Mat. Fiz. 42, 197–221 (2002) [Comput. Math. Math. Phys. 42, 188–210 (2002)] (with V. O. Belash).

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  38. “Approach of Separating Streamlines to a Contour in Plane-Parallel Viscous Fluid Flow,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 2, 76–89 (2002). (with Yu. D. Shmyglevskii).

  39. “On convergence Rate of Some Iterative Methods for Bilinear and Bicubic Finite Element Schemes for the Dissipative Helmholtz Equation with Large Values of a Singular Parameter,” Russ. J. Numer. Anal. Math. Model. 17, 485–520 (2002) (with V. O. Belash and I. I. Chechel’).

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  40. “Asymptotic Behavior of the Spectra of Convolution Integral Operators on a Finite Interval with Homogeneous Polar Kernels,” Izv. Ross. Akad. Nauk, Ser. Mat. 67(4), 67–155 (2003).

  41. “On Fast-Converging Iterative Methods with Splitting of Boundary Conditions for Solving Boundary Value Problems for Linearized and Nonlinear Navier-Stokes Equations,” Proceedings of the 2nd International Conference on Function Spaces, Differential Operators, and Issues of Mathematical Education Dedicated to the 80th Birthday of the Corresponding Member of the Russian Academy of Sciences, Professor L.D. Kudryavtsev (Fizmatlit, Moscow, 2003), pp. 286–301 (with V. O. Belash, N. A. Meller, I. I. Chechel’, and E. G. Khlyupina).

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  42. “Finite-Element Linear Second-Order Accurate (up to the Poles) Approximations of Laplace-Beltrami, Gradient, and Divergence Operators on a Sphere in ℝ3 in the Axisymmetric Case,” Dokl. Akad. Nauk 395, 308–315 (2004) [Dokl. Math. 69, 200–207 (2004)] (with I. I. Chechel’).

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  43. “Second-Order Accurate (up to the Axis of Symmetry) Finite-Element Implementations of Iterative Methods with Splitting of Boundary Conditions for Stokes and Stokes-Type Systems in a Spherical Layer,” Zh. Vychisl. Mat. Mat. Fiz. 45, 846–889 (2005) [Comput. Math. Math. Phys. 45, 816–857 (2005)] (with I. I. Chechel’).

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  44. “Department of Computational Methods (Achievements over 50 Years)” Fifty Years of the Computing Center of the Russian Academy of Sciences: History, People, and Achievements (Vychisl. Tsentr Ross. Akad. Nauk, Moscow, 2005), pp. 53–80 (with A. A. Abramov, A. I. Aleksandrovich, and N. B. Konyukhova).

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  45. “Second-Order Accurate Method with Splitting of Boundary Conditions for Solving the Stationary Axially Symmetric Navier-Stokes Problem in Spherical Gaps,” Zh. Vychisl. Mat. Mat. Fiz. 45, 2232–2250 (2005) [Comput. Math. Math. Phys. 45, 2148–2165 (2005)] (with I. I. Chechel’).

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  46. “On the Convergence Rate and Optimization of a Numerical Method with Splitting of Boundary Conditions for the Stokes System in a Spherical Layer in the Axisymmetric Case: Modification for Wide Layers,” Zh. Vychisl. Mat. Mat. Fiz. 46, 858–886 (2006) [Comput. Math. Math. Phys. 46, 820–847 (2006)] (with I. I. Chechel’).

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  47. “Numerical Study of the Basic Stationary Spherical Couette Flows at Low Reynolds Numbers,” Zh. Vychisl. Mat. Mat. Fiz. 47, 693–716 (2007) [Comput. Math. Math. Phys. 47, 664–686 (2007)] (with A. V. Stavtsev and I. I. Chechel’).

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  48. “Improved Bicubic Finite-Element Approximation of the Neumann Problem for Poisson’s Equation,” Dokl. Akad. Nauk 419, 458–465 (2008) [Dokl. Math. 77, 258–264 (2008)] (with A. V. Stavtsev and I. I. Chechel’).

  49. “On an Iterative Method with Splitting of Boundary Conditions for Solving the Dirichlet Initial-Boundary Value Problem for the Nonstationary Stokes System,” Abstracts of Papers of the International Conference Dedicated to the 100th Birthday of S.L. Sobolev (Sobolev Inst. of Mathematics, Novosibirsk, 2008), p. 540.

  50. “On an Method with Splitting of Boundary Condition for Solving the Dirichlet Boundary Value Problem for the Nonstationary Stokes System and Its Numerical Implementations,” Mathematics in Applications: Abstracts of Papers of the All-Russia Conference Dedicated to the 80th Birthday of S.K. Godunov (Sobolev Inst. of Mathematics, Novosibirsk, 2009), pp. 201–202 (with M. B. Solov’ev).

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  51. “On an Iterative Method with Splitting of Boundary Condition as Applied to the Dirichlet Initial-Boundary Value Problem for the Stokes System,” Dokl. Akad. Nauk 432(5) (2010) [Dokl. Math. 81, (2010)].

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  1. Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

    M. K. Kerimov

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Original Russian Text © M.K. Kerimov, 2010, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2010, Vol. 50, No. 7, pp. 1171–1178.

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Kerimov, M.K. On the 70th birthday of Boris Vasil’evich Pal’tsev. Comput. Math. and Math. Phys. 50, 1113–1119 (2010). https://doi.org/10.1134/S0965542510070018

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