{"id":3657,"date":"2014-11-20T11:35:33","date_gmt":"2014-11-20T07:35:33","guid":{"rendered":"http:\/\/www.imm.az\/exp\/?page_id=3657"},"modified":"2019-02-05T10:43:54","modified_gmt":"2019-02-05T06:43:54","slug":"%d0%b8%d1%81%d0%bc%d0%b0%d0%b8%d0%bb%d0%be%d0%b2-%d0%b2%d1%83%d0%b3%d0%b0%d1%80-%d1%8d%d0%bb%d1%8c%d0%bc%d0%b0%d0%bd","status":"publish","type":"page","link":"https:\/\/www.imm.az\/exp\/%d1%81%d0%be%d1%82%d1%80%d1%83%d0%b4%d0%bd%d0%b8%d0%ba%d0%b8\/%d0%b8%d1%81%d0%bc%d0%b0%d0%b8%d0%bb%d0%be%d0%b2-%d0%b2%d1%83%d0%b3%d0%b0%d1%80-%d1%8d%d0%bb%d1%8c%d0%bc%d0%b0%d0%bd\/","title":{"rendered":"\u0418\u0441\u043c\u0430\u0438\u043b\u043e\u0432 \u0412\u0443\u0433\u0430\u0440 \u042d\u043b\u044c\u043c\u0430\u043d"},"content":{"rendered":"

\u041e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u043d\u0430\u0443\u0447\u043d\u044b\u0435 \u0434\u043e\u0441\u0442\u0438\u0436\u0435\u043d\u0438\u044f<\/strong><\/p>\n

1) \u041f\u043e\u043b\u0443\u0447\u0435\u043d\u044b \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u044b\u0435 \u0438 \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u044b\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u044f \u0434\u043b\u044f \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u043c\u043d\u043e\u0433\u0438\u0445 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u043c\u0438 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f\u043c\u0438 \u0440\u0438\u0434\u0436 \u0444\u0443\u043d\u043a\u0446\u0438\u0439;<\/p>\n

2) \u0414\u043e\u043a\u0430\u0437\u0430\u043d\u0430 \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u0447\u0435\u0431\u044b\u0448\u0435\u0432\u0441\u043a\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \u0434\u043b\u044f \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0430\u043b\u044c\u043d\u043e\u0441\u0442\u0438 \u0441\u0443\u043c\u043c\u044b \u0440\u0438\u0434\u0436 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u043a \u0437\u0430\u0434\u0430\u043d\u043d\u043e\u0439 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438;<\/p>\n

3) \u041f\u043e\u043b\u0443\u0447\u0435\u043d\u044b \u044f\u0432\u043d\u044b\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0434\u043b\u044f \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u0442\u043e\u0447\u043d\u043e\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043f\u043e\u0433\u0440\u0435\u0448\u043d\u043e\u0441\u0442\u0438 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u044f \u0438 \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0442\u0438\u0432\u043d\u043e\u0433\u043e \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u0438\u044f \u043d\u0430\u0438\u043b\u0443\u0447\u0448\u0435 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u044e\u0449\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0437\u0430\u0434\u0430\u0447\u0430\u0445 \u0440\u0430\u0432\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0433\u043e \u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u043e\u0433\u043e \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u043c\u043d\u043e\u0433\u0438\u0445 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 \u0441\u0443\u043c\u043c\u0430\u043c\u0438 \u0440\u0438\u0434\u0436 \u0444\u0443\u043d\u043a\u0446\u0438\u0439;<\/p>\n

4) \u0414\u043e\u043a\u0430\u0437\u0430\u043d\u043e, \u0447\u0442\u043e \u0435\u0441\u043b\u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u044b\u0435 \u043d\u0430 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u043e\u043c \u043a\u043e\u043c\u043f\u0430\u043a\u0442\u043d\u043e\u043c \u0445\u0430\u0443\u0441\u0434\u043e\u0440\u0444\u043e\u0432\u043e\u043c \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435, \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u043c\u0438 \u0441\u0443\u043f\u0435\u0440\u043f\u043e\u0437\u0438\u0446\u0438\u044f\u043c\u0438, \u0442\u043e \u0432\u0441\u044f\u043a\u0430\u044f \u0440\u0430\u0437\u0440\u044b\u0432\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u0430\u044f \u043d\u0430 \u044d\u0442\u043e\u043c \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 \u0442\u0430\u043a\u0436\u0435 \u0438\u043c\u0435\u0435\u0442 \u0442\u0430\u043a\u043e\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0435.<\/p>\n

5) \u0440\u0435\u0448\u0435\u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u0442\u0435\u043e\u0440\u0438\u0438 \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0430\u0446\u0438\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u043c\u043d\u043e\u0433\u0438\u0445 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445, \u0441\u0432\u044f\u0437\u0430\u043d\u043d\u0430\u044f \u0441 \u0442\u0435\u043e\u0440\u0435\u043c\u043e\u0439 \u0413\u043e\u043b\u043e\u043c\u0431\u0430.<\/p>\n

\u0420\u044f\u0434 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u0432 \u0432\u043a\u043b\u044e\u0447\u0435\u043d\u044b \u0432 \u043a\u043d\u0438\u0433\u0443 “Allan Pinkus, Ridge Functions, Cambridge University Press, 2015, 218 pp.”\u00a0 \u041f\u043e \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u043c \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0430\u043c \u0431\u044b\u043b \u0441\u0434\u0435\u043b\u0430\u043d \u043f\u0440\u0438\u0433\u043b\u0430\u0448\u0435\u043d\u043d\u044b\u0439 \u0434\u043e\u043a\u043b\u0430\u0434 \u0432 \u041e\u043a\u0441\u0444\u043e\u0440\u0434\u0441\u043a\u043e\u043c \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0435 (\u0441\u043c. https:\/\/www.maths.ox.ac.uk\/node\/24710<\/a>)<\/p>\n

\u0421\u043f\u0438\u0441\u043e\u043a \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0445 \u043d\u0430\u0443\u0447\u043d\u044b\u0445 \u0440\u0430\u0431\u043e\u0442 \u0437\u0430 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u0435 \u043f\u044f\u0442\u044c \u043b\u0435\u0442<\/strong><\/p>\n

    \n
  1. (with N. Guliyev) On the approximation by single hidden layer feedforward neural networks with fixed weights,\u00a0Neural Networks<\/em>98<\/strong>(2018), 296-304,\u00a0https:\/\/doi.org\/10.1016\/j.neunet.2017.12.007<\/a><\/li>\n
  2. A note on the criterion for a best approximation by superpositions of functions,\u00a0Studia Mathematica<\/em>240\u00a0<\/strong>(2018), no. 2, 193-199,\u00a0https:\/\/doi.org\/10.4064\/sm170314-9-4<\/a><\/li>\n
  3. (with A. Asgarova) On the representation by sums of algebras of continuous functions,\u00a0Comptes Rendus Mathematique<\/em>355\u00a0<\/strong>(2017), no. 9, 949-955,\u00a0https:\/\/doi.org\/10.1016\/j.crma.2017.09.015<\/a><\/li>\n
  4. \n

    A note on the equioscillation theorem for best ridge function approximation,\u00a0Expositiones Mathematicae<\/em>\u00a035\u00a0<\/strong>(2017), no. 3, 343-349,\u00a0https:\/\/doi.org\/10.1016\/j.exmath.2017.05.003<\/a><\/p>\n

      \n
    1. (with A. Asgarova) Diliberto\u2013Straus algorithm for the uniform approximation by a sum of two algebras,\u00a0Proceedings – Mathematical Sciences<\/em>127\u00a0<\/strong>(2017), no. 2, 361-374,\u00a0http:\/\/dx.doi.org\/10.1007\/s12044-017-0337-4<\/a><\/li>\n
    2. (with E. Savas) Measure theoretic results for approximation by neural networks with limited weights,\u00a0Numerical Functional Analysis and Optimization<\/em>38<\/strong>(2017), no. 7, 819-830,\u00a0http:\/\/dx.doi.org\/10.1080\/01630563.2016.1254654<\/a><\/li>\n
    3. Approximation by sums of ridge functions with fixed directions, (Russian)\u00a0Algebra i Analiz<\/em>28<\/strong>(2016), no. 6,\u00a020\u201369,\u00a0http:\/\/mi.mathnet.ru\/eng\/aa1513<\/a>\u00a0English transl.\u00a0St. Petersburg Mathematical Journal<\/em>\u00a028<\/strong>\u00a0(2017), 741-772,\u00a0https:\/\/doi.org\/10.1090\/spmj\/1471<\/a><\/li>\n
    4. On the uniqueness of representation by linear superpositions,\u00a0Ukrainskii Matematicheskii Zhurnal<\/em>68<\/strong>(2016), no. 12, 1620-1628. English transl.\u00a0Ukrainian Mathematical Journal<\/em>\u00a068\u00a0<\/strong>(2017), no. 12, 1874-1883,\u00a0https:\/\/doi.org\/10.1007\/s11253-017-1335-5<\/a><\/li>\n
    5. (with N. Guliyev)\u00a0A single hidden layer feedforward network with only one neuron in the hidden layer can approximate any univariate function,\u00a0Neural Computation\u00a0<\/em>28<\/strong>(2016), no. 7,\u00a01289\u20131304,\u00a0http:\/\/dx.doi.org\/10.1162\/NECO_a_00849<\/a><\/li>\n
    6. (with R. Aliev) On a smoothness problem in ridge function representation,\u00a0Advances in Applied Mathematics<\/em>73<\/strong>(2016), 154\u2013169,\u00a0http:\/\/dx.doi.org\/10.1016\/j.aam.2015.11.002<\/a><\/li>\n
    7. Approximation by ridge functions and neural networks with a bounded number of neurons,\u00a0Applicable Analysis<\/em>94<\/strong>(2015), no. 11, 2245-2260,\u00a0http:\/\/dx.doi.org\/10.1080\/00036811.2014.979809<\/a><\/li>\n
    8. On the approximation by neural networks with bounded number of neurons in hidden layers,\u00a0Journal of Mathematical Analysis and Applications<\/em>417\u00a0<\/strong>(2014), no. 2, 963\u2013969,\u00a0http:\/\/dx.doi.org\/10.1016\/j.jmaa.2014.03.092<\/a><\/li>\n
    9. (with A. Pinkus) Interpolation on lines by ridge functions,\u00a0Journal of Approximation Theory<\/em>175<\/strong>(2013), 91-113,\u00a0http:\/\/dx.doi.org\/10.1016\/j.jat.2013.07.010<\/a><\/li>\n<\/ol>\n

      14. Approximation by neural networks with weights varying on a finite set of directions,\u00a0Journal of Mathematical Analysis and\u00a0\u00a0<\/em><\/em>Applications<\/em>\u00a0389<\/strong>\u00a0(2012), Issue 1, 72-83,\u00a0http:\/\/dx.doi.org\/10.1016\/j.jmaa.2011.11.037<\/a><\/p>\n

        \n
      1. A note on the representation of continuous functions by linear superpositions,\u00a0Expositiones Mathematicae<\/em>30<\/strong>(2012), Issue 1, 96-101,\u00a0http:\/\/dx.doi.org\/10.1016\/j.exmath.2011.07.005<\/a><\/li>\n
      2. On the theorem of M Golomb,\u00a0Proceedings – Mathematical Sciences<\/em>119<\/strong>(2009), no. 1, 45-52,\u00a0http:\/\/dx.doi.org\/10.1007\/s12044-009-0005-4<\/a><\/li>\n
      3. On the representation by linear superpositions,\u00a0Journal of Approximation Theory<\/em>151<\/strong>(2008), Issue 2 , 113-125,\u00a0http:\/\/dx.doi.org\/10.1016\/j.jat.2007.09.003<\/a><\/li>\n
      4. On the approximation by compositions of fixed multivariate functions with univariate functions,\u00a0Studia Mathematica<\/em>183<\/strong>(2007), 117-126,\u00a0http:\/\/dx.doi.org\/10.4064\/sm183-2-2<\/a><\/li>\n
      5. On the best L\u2082 approximation by ridge functions,\u00a0Applied Mathematics E-Notes<\/em>,\u00a07<\/strong>(2007), 71-76,\u00a0http:\/\/www.math.nthu.edu.tw\/~amen\/<\/a><\/li>\n
      6. Representation of multivariate functions by sums of ridge functions,\u00a0Journal of Mathematical Analysis and Applications<\/em>331<\/strong>(2007), Issue 1, 184-190,\u00a0http:\/\/dx.doi.org\/10.1016\/j.jmaa.2006.08.076<\/a><\/li>\n
      7. Characterization of an extremal sum of ridge functions,\u00a0Journal of Computational and Applied Mathematics<\/em>205<\/strong>(2007), Issue 1, 105-115,\u00a0http:\/\/dx.doi.org\/10.1016\/j.cam.2006.04.043<\/a><\/li>\n
      8. Methods for computing the least deviation from the sums of functions of one variable, (Russian)\u00a0Sibirskii Matematicheskii Zhurnal<\/em>47<\/strong>(2006), no. 5, 1076 -1082; translation in\u00a0Siberian Mathematical Journal<\/em>\u00a047<\/strong>\u00a0(2006), no. 5, 883\u2013888,\u00a0http:\/\/dx.doi.org\/10.1007\/s11202-006-0097-3<\/a><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

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