{"id":3600,"date":"2014-11-14T11:00:34","date_gmt":"2014-11-14T07:00:34","guid":{"rendered":"http:\/\/www.imm.az\/exp\/?page_id=3600"},"modified":"2019-02-05T10:44:44","modified_gmt":"2019-02-05T06:44:44","slug":"ismayilov-vuqar-elman-oglu","status":"publish","type":"page","link":"https:\/\/www.imm.az\/exp\/%c9%99m%c9%99kdaslar\/ismayilov-vuqar-elman-oglu\/","title":{"rendered":"\u0130smay\u0131lov V\u00fcqar Elman o\u011flu"},"content":{"rendered":"

\u018fsas elmi nailiyy\u0259tl\u0259ri<\/strong><\/p>\n

1) \u00c7oxd\u0259yi\u015f\u0259nli funksiyalar\u0131n ridge funksiyalar\u0131n x\u0259tti kombinasiyalar\u0131 \u015f\u0259klind\u0259 g\u00f6st\u0259ril\u0259 bilm\u0259si \u00fc\u00e7\u00fcn z\u0259ruri v\u0259 kafi \u015f\u0259rtl\u0259r tap\u0131lm\u0131\u015fd\u0131r;
\n2) Ridge funksiyalar c\u0259minin verilmi\u015f k\u0259silm\u0259z funksiyaya ekstremal olmas\u0131 \u00fc\u00e7\u00fcn \u00c7eb\u0131\u015fev tipli teorem isbat edilmi\u015fdir;
\n3) M\u00fcnt\u0259z\u0259m v\u0259 kvadratik-inteqral metrikalarda \u00e7oxd\u0259yi\u015f\u0259nli funksiyan\u0131n ridge funksiyalar v\u0259 bird\u0259yi\u015f\u0259nli funksiyalar\u0131n c\u0259ml\u0259ri il\u0259 yax\u0131nla\u015fma x\u0259tas\u0131n\u0131 d\u0259qiq hesablamaq v\u0259 \u0259n yax\u015f\u0131 yax\u0131nla\u015fma ver\u0259n funksiyan\u0131 konstruktiv qurmaq \u00fc\u00e7\u00fcn a\u015fkar d\u00fcsturlar al\u0131nm\u0131\u015fd\u0131r;
\n4) Kompakt Hausdorf f\u0259zas\u0131nda t\u0259yin olunmu\u015f h\u0259r bir k\u0259silm\u0259z funksiyan\u0131n x\u0259tti superpozisiyalarla g\u00f6st\u0259ril\u0259 bilm\u0259 \u015f\u0259rti daxilind\u0259, bu f\u0259zada verilmi\u015f b\u00fct\u00fcn dig\u0259r funksiylar\u0131n da bel\u0259 g\u00f6st\u0259ri\u015f\u0259 malik olmas\u0131n\u0131n do\u011frulu\u011fu isbat edilmi\u015fdir.<\/p>\n

5) \u00c7oxd\u0259yi\u015f\u0259nli funksiyalar\u0131n yax\u0131nla\u015fmalar n\u0259z\u0259riyy\u0259sinin Qolomb teoremi il\u0259 ba\u011fl\u0131 problemi h\u0259ll edilmi\u015fdir.<\/p>\n

Bir \u00e7ox elmi n\u0259tic\u0259l\u0259ri Kembric Universitetind<\/a>\u0259 n\u0259\u015fr olunmu\u015f “Allan Pinkus, Ridge Functions, Cambridge University Press, 2015, 218 pp.” kitab\u0131na daxil edilmi\u015fdir. B\u0259zi n\u0259tic\u0259l\u0259ri \u00fczr\u0259 Oksford Universitetnd\u0259 d\u0259v\u0259tli m\u0259ruz\u0259 edilmi\u015fdir (bax: https:\/\/www.maths.ox.ac.uk\/node\/24710<\/a>)<\/p>\n

Son be\u015f ild\u0259 \u00e7ap olunmu\u015f \u0259sas elmi i\u015fl\u0259rinin siyah\u0131s\u0131<\/strong><\/p>\n

    \n
  1. (N. Quliyevl\u0259 birg\u0259) 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. (A. \u018fsg\u0259rova il\u0259 birg\u0259) 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. A note on the equioscillation theorem for best ridge function approximation,\u00a0Expositiones Mathematicae<\/em>35\u00a0<\/strong>(2017), no. 3, 343-349,\u00a0https:\/\/doi.org\/10.1016\/j.exmath.2017.05.003<\/a><\/li>\n<\/ol>\n
      \n
    1. (A. \u018fsg\u0259rova il\u0259 birg\u0259) 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. (E. Sava\u015fla birg\u0259) 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. (N. Quliyevl\u0259 birg\u0259)\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. (R. \u018fliyevl\u0259 birg\u0259) 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. (A. Pinkusla birg\u0259) 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 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","protected":false},"excerpt":{"rendered":"

        \u018fsas elmi nailiyy\u0259tl\u0259ri 1) \u00c7oxd\u0259yi\u015f\u0259nli funksiyalar\u0131n ridge funksiyalar\u0131n x\u0259tti kombinasiyalar\u0131 \u015f\u0259klind\u0259 g\u00f6st\u0259ril\u0259 bilm\u0259si \u00fc\u00e7\u00fcn z\u0259ruri v\u0259 kafi \u015f\u0259rtl\u0259r tap\u0131lm\u0131\u015fd\u0131r; 2) Ridge funksiyalar c\u0259minin verilmi\u015f k\u0259silm\u0259z funksiyaya ekstremal olmas\u0131 \u00fc\u00e7\u00fcn \u00c7eb\u0131\u015fev tipli teorem isbat edilmi\u015fdir; 3) M\u00fcnt\u0259z\u0259m v\u0259 kvadratik-inteqral metrikalarda \u00e7oxd\u0259yi\u015f\u0259nli funksiyan\u0131n ridge funksiyalar v\u0259 bird\u0259yi\u015f\u0259nli funksiyalar\u0131n c\u0259ml\u0259ri il\u0259 yax\u0131nla\u015fma x\u0259tas\u0131n\u0131 d\u0259qiq hesablamaq v\u0259 \u0259n yax\u015f\u0131 […]<\/p>\n","protected":false},"author":6,"featured_media":0,"parent":260,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","meta":{"footnotes":""},"_links":{"self":[{"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/pages\/3600"}],"collection":[{"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/comments?post=3600"}],"version-history":[{"count":6,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/pages\/3600\/revisions"}],"predecessor-version":[{"id":23345,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/pages\/3600\/revisions\/23345"}],"up":[{"embeddable":true,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/pages\/260"}],"wp:attachment":[{"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/media?parent=3600"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}