NUMBER-THEORETIC METHOD IN APPROXIMATE ANALYSIS

number-theoretic method, uniform distribution, nonuniform grid, parallelepipedal nets, algebraic nets, hyperbolic dzeta-function of lattices, algebraic theory of polynomials Tue, given an algebraic irrationality, the classification of purely real algebraic irrationalities

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46. Dobrovol’skaya, L. P., Dobrovol’skii, M. N., Dobrovol’skii, N. M. & Dobrovol’skii, N. N. 2014, “On Hyperbolic Zeta Function of Lattices”, Continuous and Distributed Systems. Solid Mechanics and Its Applications, vol. 211, pp. 23–62.

47. Dobrovol’skaya, L. P., Dobrovol’skii, N. M., Dobrovol’skii, N. N., Ogorodnichuk, N. K., Rebrov, E. D. & Rebrova, I. YU. 2012, “Some questions of the number-theoretic method in the approximate analysis”, Trudy X mezhdunarodnoj konferentsii “Аlgebra i teoriya chisel: sovremennye problemy i prilozheniya” Uchenye zapiski Orlovskogo gosudarstvennogo universiteta [Proceedings of the X international conference "Algebra and number theory: modern problems and applications"scientific notes of Orel state University], no. 6, part 2, pp. 90-98.

48. Dobrovol’skaya, L. P., Dobrovol’skii, M. N., Dobrovol’skii, N. M., Dobrovol’skii, N. N., & Rebrova, I. YU. 2013, “Some questions of the number-theoretic method in the approximate analysis”, Izvestie Saratovskogo universiteta. Novaya seriya. Seriya: Matematika. Mekhanika. Informatika, vol.13, no. 4(2), pp. 47-52.

49. Dobrovol’skaya, L. P., Dobrovol’skii, N. M. & Simonov, А.S. 2008, “On the error of approximate integration over modified grids”, Chebyshevskij sbornik, vol. 9, no. 1(25), pp. 185–223.

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74. Dobrovol’skii, N. M. 2001, “Multidimensional number-theoretic grids and lattices and their applications to approximate analysis”, Sbornik IV Mezhdunarodnaya konferentsiya “Sovremennye problemy teorii chisel i ee prilozheniya”, posvyashhennaya 180-letiyu P. L. Chebysheva i 110-letiyu I. M. Vinogradova (A collection of the IV international conference “Modern problems of number theory and its applications”, dedicated to 180th anniversary of P. L. Chebyshev and 110th anniversary of I. M. Vinogradov), Tula, Russia, 10-15 September, pp. 54–80.

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84. Dobrovol’skii, N. M. & Van’kova, V.S. 1993, “On a regular P-ary meshes”, Matematicheskie zametki, vol. 54, no. 6, pp. 22–32.

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86. Dobrovol’skii, N. M., Van’kova, V.S. & Kozlova, S. L. 1990, “The hyperbolic Zeta function of algebraic lattices”, Dep. v VINITI, no. 2327– B90.

87. Dobrovol’skii, N. M., Van’kova, V.S. & Penton, M.M. 1989, “Algorithm for constructing optimal modified Hammersley-Roth grids”, Sovremennye problemy informatiki, vychislitel’noj tekhniki i avtomatizatsii: Tezisy dokladov Vsesoyuznoj konferentsii, Tula, Russia, pp. 92–95.

88. Dobrovol’skii, N. M., Dobrovol’skii, N. N. 2015, “On minimal polynomials of residual fractions for algebraic irrationalities”, Chebyshevskij sbornik, vol. 16, no. 3, pp. 147–182.

89. Dobrovol’skii, N. M., Dobrovol’skii, N. N., Balaba, I. N., Rebrova, I. YU., Sobolev, D.K. & Soboleva, V.N. 2016, “Generalized Pisot Numbers and Matrix Decomposition”, Advances in Dynamical Systems and Control, Springer Switzerland.

90. Dobrovol’skii, N. M., Dobrovol’skii, N. N., Sobolev, D.K. & Soboleva, V.N. 2017, “Classification of pure-real algebraic irrationalities”, Chebyshevskij sbornik, vol. 18, no. 2, pp. 98–128.

91. Dobrovol’skii, N. M., Dobrovol’skii, N. N., Sobolev, D.K., Soboleva, V.N., Dobrovol’skaya, L. P. & Bocharova, O. E. 2016, “On the hyperbolic Hurwitz Zeta function ”, Chebyshevskij sbornik, vol. 17, no. 3, pp. 72–105.

92. Dobrovol’skii, N. M., Dobrovol’skii, N. N., Soboleva, V.N., Sobolev, D.K. & Yushina, E.I. 2015, “Hyperbolic dzeta-function of lattices of quadratic fields”, Chebyshevskij sbornik, vol. 16, no. 4, pp. 100–149.

93. Dobrovol’skii, N. M., Dobrovol’skii, N. N. & Yushina, E.I. 2012, “On the matrix form of Galois ’ theorem on purely periodic continued fractions”, Chebyshevskij sbornik, vol. 13, no. 3, pp. 47–52.

94. Dobrovol’skii, N. M., Esayan, А.R., Pikhtil’kov, S.А., Rodionova, O.V. & Ustyan, А.E. 1999, “On a single algorithm for finding optimal coefficients”, Izvestiya TulGU. Seriya Matematika. Mekhanika. Informatika, vol. 5, no. 1, pp. 51–71.

95. Dobrovol’skii, N. M., Esayan, А.R. & Rebrova, I. YU. 1998, “On a recursive algorithm for lattices”, Teoriya priblizhenij i garmonicheskij analiz: Tezisy doklada Mezhdunarodnoj konferentsii (Approximation theory and harmonic analysis: proceedings of the International conference), Tula, Russia.

96. Dobrovol’skii, N. M., Esayan, А.R. & Rebrova, I. YU. 1998, “On a recursive algorithm for lattices”, Izvestiya TulGU. Seriya Matematika. Mekhanika. Informatika, vol. 5, no. 3, pp. 38–51.

97. Dobrovol’skii, N. M., Esayan, А.R. & Yafaeva, R. R. 2002, “On grids of Smolyak S. A.”, Sovremennye problemy matematiki, mekhaniki, informatiki: Tezisy dokladov Vserossijskoj nauchnoj konferentsii, Tula, Russia, pp. 18–20.

98. Dobrovol’skii, N. M. & Klepikova, N.L. 1990, “Table of optimal coefficients for approximate calculation of multiple integrals”, Institut obshhej fiziki АN SSSR, Moscow, USSR.

99. Dobrovol’skii, N. M. & Korobov, N. M. 2001, “The optimal coefficients for mixed meshes”, Chebyshevskij sbornik, vol. 2, pp. 41–53.

100. Dobrovol’skii, N. M. & Korobov, N. M. 2002, “On the error estimation of quadrature formulas with optimal parallelepipedal grids”, Chebyshevskij sbornik, vol. 3, no. 1(3), pp. 41–48.

101. Dobrovol’skii, N. M. & Manokhin, E.V. 1998, “Banach spaces of periodic functions”, Izvestiya TulGU. Seriya Matematika. Mekhanika. Informatika, vol. 4, no. 3, pp. 56–67.

102. Dobrovol’skii, N. M., Manokhin, E.V., Rebrova, I. YU. & Аkkuratova, S.V.1999, “On some properties of normed spaces and algebras of nets”, Izvestiya TulGU. Seriya Matematika. Mekhanika. Informatika, vol. 5, no. 1, pp. 100–113.

103. Dobrovol’skii, N. M., Rebrova, I. YU. & Roshhenya, А.L. 1998, “Continuity of the hyperbolic Zeta function of lattices”, Matematicheskie zametki, vol. 63, no. 4, pp. 522–526.

104. Dobrovol’skii, N. M. & Rodionova, O. V.1996, “Quadrature formulas with generalized parallelepipedal grids”, Sovremennye problemy teorii chisel i ee prilozheniya: Sbornik tezisov dokladov III Mezhdunarodnoj konferentsii [Modern problems of number theory and its applications: proceedings of the third International conference], Tula, Russia, pp. 47–48.

105. Dobrovol’skii, N. M. & Rodionova, O. V.1996, “Quadrature formulas with generalized parallelepipedal grids”, Izvestiya TulGU. Seriya Matematika. Mekhanika. Informatika, vol. 2, no. 1, pp. 71–77.

106. Dobrovol’skii, N. M. & Rodionova, O. V.1998, “On one finite Fourier series and its applications”, Izvestiya TulGU. Seriya Matematika. Mekhanika. Informatika, vol. 4, no. 3, pp. 68–79.

107. Dobrovol’skii, N. M. & Roshhenya, А.L. 1995, “On the number of lattice points in a hyperbolic cross”, Аlgebraicheskie, veroyatnostnye, geometricheskie, kombinatornye i funktsional’nye metody v teorii chisel: Sbornik tezisov doklada II Mezhdunarodnoj konferentsii [Algebraic, probabilistic, geometric, combinatorial and functional methods in number theory: Proceedings of the II international conference], Voronezh, Russia, p. 53.

108. Dobrovol’skii, N. M. & Roshhenya, А.L. 1996, “On the analytic continuation of the hyperbolic Zeta function of rational lattices”, Sovremennye problemy teorii chisel i ee prilozheniya: Sbornik tezisov doklada III Mezhdunarodnoj konferentsii [Modern problems of number theory and its applications: Proceedings of the III international conference], Tula, Russia, p. 49.

109. Dobrovol’skii, N. M. & Roshhenya, А.L. 1996, “On continuity of the hyperbolic Zeta function of lattices”, Izvestiya TulGU. Seriya Matematika. Mekhanika. Informatika, vol. 2, no. 1, pp. 77–87.

110. Dobrovol’skii, N. M., Sobolev, D.K. & Soboleva, V.N. 2013, “On a matrix decomposition of the reduced cubic irrational”, Chebyshevskij sbornik, vol. 14, no. 1, pp. 34–55.

111. Dobrovol’skii, N. N. 2003, “On the number of integer points in a hyperbolic cross at the values of 1 6 t < 21”, Izvestiya TulGU. Seriya Matematika. Mekhanika. Informatika, vol. 9, no. 1, pp. 91–95.

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