{"id":39575,"date":"2015-02-18T21:59:00","date_gmt":"2015-02-18T18:59:00","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles\/mathinfocontent012015-2\/"},"modified":"2019-06-18T21:58:31","modified_gmt":"2019-06-18T18:58:31","slug":"mathinfocontent012015-2","status":"publish","type":"post","link":"https:\/\/philosophy.azbuki.bg\/en\/matematics\/matharticles\/mathinfocontent012015-2\/","title":{"rendered":"Mathematics and Informatics, Number 1\/2015, Volume 58"},"content":{"rendered":"<p><strong><a name=\"top\">&nbsp;<\/a>CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 <\/strong><br \/><strong><\/p>\n<p><\/strong><strong>\u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u0427\u0415\u0421\u041a\u041e\u0422\u041e \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u041d\u0418\u0415 \u041f\u041e \u0421\u0412\u0415\u0422\u0410 \/ MATHEMATICAL EDUCATION WORLDWIDE<\/p>\n<p><\/strong><a href=\"#art01\"> \u041c. \u0412. \u041b\u043e\u043c\u043e\u043d\u043e\u0441\u043e\u0432 \u0418 \u0422\u0440\u0430\u0434\u0438\u0446\u0438\u0438 \u0423\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0441\u043a\u043e\u0433\u043e \u041e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f <br \/>[M. V. Lomonosov And The Traditions Of The University Education] <\/a>\/ <br \/><em>\u0422\u0430\u0442\u044c\u044f\u043d\u0430 \u0411\u0443\u0442\u043e\u0440\u0438\u043d\u0430 \/ \u0422atyana Butorina<\/em> &#8211; \u0441\u0442\u0440. 10<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2015\/02\/azbuki.bg_dmdocuments_MathInfo012015_Butorina.pdf\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p><strong><br \/>\u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u0422\u0415\u041b\u041d\u0418 \u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0418\u0418 \/ EDUCATIONAL TECHNOLOGY<br \/><\/strong><br \/><a href=\"#art02\"> XML \u043c\u043e\u0434\u0435\u043b \u0437\u0430 \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u043d\u043e \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u0438 \u0442\u0435\u043a\u0441\u0442\u043e\u0432\u0435 <br \/>[An XML Model for Automatic Generation of Program Texts] <\/a>\/ <br \/><em>\u041f\u0430\u0432\u0435\u043b \u0410\u0437\u044a\u043b\u043e\u0432 \/ Pavel Azalov<\/em> &#8211; \u0441\u0442\u0440. 19<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2015\/02\/azbuki.bg_dmdocuments_MathInfo012015_Azalov.pdf\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"#art03\">The Computer Improves the Steiner\u2019s Construction of the Malfatti Circles] <\/a> \/<br \/><em>Sava Grozdev, Deko Dekov<\/em> &#8211; \u0441\u0442\u0440. 40<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2015\/02\/azbuki.bg_dmdocuments_MathInfo012015_Grozdev_Dekov.pdf\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p><strong><br \/>\u041d\u0410\u0423\u0427\u041d\u041e\u2013\u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0418 \u0421\u0422\u0410\u0422\u0418\u0418 \/ EDUCATIONAL RESEARCH<\/p>\n<p><\/strong><a href=\"#art04\"> \u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0430 \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0446\u0438\u044f \u043d\u0430 \u043a\u0440\u0438\u0432\u0430 \u043d\u0430 \u0427\u0435\u0432\u0430 <br \/>[A Geometrical Construction of a Ceva Curve] \/ <br \/><em>Sava Grozdev, Veselin Nenkov <\/em><\/a>\/ Sava Grozdev, Veselin Nenkov &#8211; \u0441\u0442\u0440. 52<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2015\/02\/azbuki.bg_dmdocuments_MathInfo012015_Grozdev_Nenkov.pdf\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><strong>\u0412\u042a\u041f\u0420\u041e\u0421\u0418 \u041d\u0410 \u041f\u0420\u0415\u041f\u041e\u0414\u0410\u0412\u0410\u041d\u0415\u0422\u041e \/ EDUCATIONAL MATTERS<\/strong><\/p>\n<p><a href=\"#art05\"> \u0421\u0442\u0438\u043c\u0443\u043b\u0438\u0440\u0430\u043d\u0435 \u0430\u043a\u0442\u0438\u0432\u043d\u043e\u0441\u0442\u0442\u0430 \u043d\u0430 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0438\u0442\u0435 \u0432 \u043f\u0440\u043e\u0446\u0435\u0441\u0430 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u0447\u0440\u0435\u0437 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435 \u043d\u0430 \u0438\u043d\u0442\u0435\u0440\u0430\u043a\u0442\u0438\u0432\u043d\u0438 \u043c\u0435\u0442\u043e\u0434\u0438 <br \/>[Stimulating Students&#8217; Activity in the Teaching Process by Interactive Methods] <\/a>\/ <br \/><em>\u041b\u0438\u043b\u044f\u043d\u0430 \u041a\u0430\u0440\u0430\u043a\u0430\u0448\u0435\u0432\u0430-\u0419\u043e\u043d\u0447\u0435\u0432\u0430 \/ Lilyana Karakasheva-Yoncheva<\/em> &#8211; \u0441\u0442\u0440. 58<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2015\/02\/azbuki.bg_dmdocuments_MathInfo012015_Karakasheva-Yoncheva.pdf\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"#art06\">\u0420\u043e\u043b\u044f\u0442\u0430 \u043d\u0430 \u0435\u043c\u043e\u0446\u0438\u0438\u0442\u0435 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 \u043f\u0440\u0438 \u043c\u043e\u0442\u0438\u0432\u0430\u0446\u0438\u044f\u0442\u0430 \u0438\u043c \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 <br \/>[The Role of Students&#8217; Emotions in Their Motivation to Study Mathematics] <\/a>\/ <br \/><em>\u0420\u0443\u043c\u044f\u043d\u0430 \u041c\u0430\u0432\u0440\u043e\u0432\u0430, \u0417\u0430\u0440\u0430 \u0414\u0430\u043d\u0430\u0438\u043b\u043e\u0432\u0430 \/ Rumjana Mavrova, Zara Danailova<\/em> &#8211;&nbsp;\u0441\u0442\u0440.69<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2015\/02\/azbuki.bg_dmdocuments_MathInfo012015_Mavrova_Danailova.pdf\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"#art07\"> \u041a\u043e\u0433\u043d\u0438\u0442\u0438\u0432\u043d\u0438 \u0438\u0437\u043c\u0435\u0440\u0435\u043d\u0438\u044f \u043f\u0440\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0446\u0438\u0442\u0435 \u0441 \u0443\u0432\u0440\u0435\u0434\u0435\u043d\u043e \u0437\u0440\u0435\u043d\u0438\u0435<br \/>[Cognitive Dimensions to Blind Mathematicians] <\/a>\/ <br \/><em>\u041c\u0438\u043b\u0435\u043d \u0417\u0430\u043c\u0444\u0438\u0440\u043e\u0432 \/ Milen Zamfirov<\/em> &#8211;&nbsp;\u0441\u0442\u0440.77<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2015\/02\/azbuki.bg_dmdocuments_MathInfo012015_Zamfirov.pdf\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><strong>\u041a\u041e\u041d\u041a\u0423\u0420\u0421\u0418, \u041e\u041b\u0418\u041c\u041f\u0418\u0410\u0414\u0418, \u0421\u042a\u0421\u0422\u0415\u0417\u0410\u041d\u0418\u042f \/ COMPETITIONS AND OLYMPIADS<\/strong><\/p>\n<p><a href=\"#art08\">\u0410\u043d\u0430\u043b\u0438\u0437 \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438\u0442\u0435 \u0438 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u044f\u043d\u0435\u0442\u043e \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 \u043e\u0442 12-\u0442\u0438 \u043a\u043b\u0430\u0441 \u043d\u0430 \u041e\u0431\u043b\u0430\u0441\u0442\u043d\u0438\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0442\u0443\u0440\u043d\u0438\u0440 \u0432 \u0433\u0440. \u041a\u044a\u0440\u0434\u0436\u0430\u043b\u0438 \u2013 2014 \u0433. <br \/>[Analysis of the Problems and Performance of the Students from 12th Grade on the Regional Mathematics Tournament in Kardzhali &#8211; 2014] <\/a>\/ <br \/><em>\u0420\u043e\u0441\u0435\u043d \u041d\u0438\u043a\u043e\u043b\u0430\u0435\u0432, \u0419\u043e\u0440\u0434\u0430\u043d \u041f\u0435\u0442\u043a\u043e\u0432 \/ Rosen Nikolaev, Jordan Petkov<\/em> &#8211; \u0441\u0442\u0440.&nbsp;86<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2015\/02\/azbuki.bg_dmdocuments_MathInfo012015_Nikolaev_Petkov.pdf\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"#art09\">\u0414\u0432\u0430\u043d\u0430\u0434\u0435\u0441\u0435\u0442\u0430 \u041c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0430 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0430 \u043f\u043e \u043b\u0438\u043d\u0433\u0432\u0438\u0441\u0442\u0438\u043a\u0430 <br \/>[The Twelfth International Olympiad in Linguistics] <\/a>\/ <br \/><em>\u0418\u0432\u0430\u043d \u0414\u0435\u0440\u0436\u0430\u043d\u0441\u043a\u0438 \/ Ivan Derzhanski<\/em> &#8211; \u0441\u0442\u0440. 95<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2015\/02\/azbuki.bg_dmdocuments_MathInfo012015_Derzhanski.pdf\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><strong>\u041a\u041e\u041d\u041a\u0423\u0420\u0421\u041d\u0418 \u0417\u0410\u0414\u0410\u0427\u0418 \/ CONTEST PROBLEMS<\/strong><\/p>\n<p>Contest Problems of this Issue <br \/>[Contest Problems of the Issue] &#8211; \u0441\u0442\u0440. 100<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2015\/02\/azbuki.bg_dmdocuments_MathInfo012015_Grozdev_Nenkov_Contest.pdf\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p>\u0420\u0435\u0448\u0435\u043d\u0438\u044f \u043d\u0430 \u043a\u043e\u043d\u043a\u0443\u0440\u0441\u043d\u0438\u0442\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u0442 \u0431\u0440\u043e\u0439 2, 2014 <br \/>[Solutions of the Contest Problems from issue 2, 2014] &#8211;&nbsp;\u0441\u0442\u0440. 101<\/p>\n<p><strong>\u0412 \u041d\u041e\u0412\u0418\u0422\u0415 \u0411\u0420\u041e\u0415\u0412\u0415 \u041d\u0410 \u0421\u041f\u0418\u0421\u0410\u041d\u0418\u042f\u0422\u0410 \u041d\u0410 \u0418\u0417\u0414\u0410\u0422\u0415\u041b\u0421\u0422\u0412\u041e \u201e\u0410\u0417 \u0411\u0423\u041a\u0418\u201c \u0427\u0415\u0422\u0415\u0422\u0415 \/ <br \/>READ IN THE LATEST ISSUES OF \u201eAZ BUKI\u201c JOURNALS <\/strong>&#8211;&nbsp;\u0441\u0442\u0440.105<strong><\/p>\n<p>\u0423\u041a\u0410\u0417\u0410\u041d\u0418\u0415 \u0417\u0410 \u0410\u0412\u0422\u041e\u0420\u0418\u0422\u0415 \/ GUIDE FOR AUTHORS <\/strong>&#8211;&nbsp;\u0441\u0442\u0440. 107<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a name=\"art01\">&nbsp;<\/a>\u041c. \u0412. \u041b\u041e\u041c\u041e\u041d\u041e\u0421\u041e\u0412 \u0418 \u0422\u0420\u0410\u0414\u0418\u0426\u0418\u0418 \u0423\u041d\u0418\u0412\u0415\u0420\u0421\u0418\u0422\u0415\u0422\u0421\u041a\u041e\u0413\u041e \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u041d\u0418\u042f<\/strong><\/p>\n<p><strong>\u0422\u0430\u0442\u044c\u044f\u043d\u0430 \u0411\u0443\u0442\u043e\u0440\u0438\u043d\u0430<\/strong><\/p>\n<p>\u041d\u041e\u0426 \u041b\u043e\u043c\u043e\u043d\u043e\u0441\u043e\u0432\u0441\u043a\u0438\u0439 \u0438\u043d\u0441\u0442\u0438\u0442\u0443\u0442 \u0421\u0410\u0424\u0423 \u0438\u043c\u0435\u043d\u0438 \u041c. \u0412. \u041b\u043e\u043c\u043e\u043d\u043e\u0441\u043e\u0432\u0430<\/p>\n<p><strong>Abstract. <\/strong>\u0412 \u0434\u0430\u043d\u043d\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043d\u044b \u0442\u0440\u0430\u0434\u0438\u0446\u0438\u0438 \u043a\u043b\u0430\u0441\u0441\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0441\u043a\u043e\u0433\u043e \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u0432 \u0420\u043e\u0441\u0441\u0438\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0437\u0430\u043b\u043e\u0436\u0438\u043b \u043f\u0435\u0440\u0432\u044b\u0439 \u0440\u0443\u0441\u0441\u043a\u0438\u0439 \u0430\u043a\u0430\u0434\u0435\u043c\u0438\u043a \u041c. \u0412. \u041b\u043e\u043c\u043e\u043d\u043e\u0441\u043e\u0432. \u041e\u043d\u0438 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u044b \u043d\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0438 \u043a\u043b\u0430\u0441\u0441\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043e\u0431\u0440\u0430\u0437\u0446\u0430, \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u043c\u0438 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044f\u043c\u0438 \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0441\u0432\u0435\u0442\u0441\u043a\u043e\u0441\u0442\u044c \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f, \u0444\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u043e\u0441\u0442\u044c \u0438 \u043d\u0430\u0443\u0447\u043d\u043e\u0441\u0442\u044c.<\/p>\n<p><i>Keywords: <\/i>education, university, tradition, science, fundamental knowledge<\/p>\n<p><strong>\u041c. V. LOMONOSOV AND THE TRADITIONS OF THE UNIVERSITY EDUCATION<\/strong><\/p>\n<p><strong>\u0410bstract. <\/strong>The present paper considers the traditions of the classic university education in Russia, founded by the first Russian academician M. V. Lomonosov. They are based on a classic type education, whose main characteristics are secularity, fundamentality and scientific content.<\/p>\n<p><strong>Prof. \u0422atyana Butorina, Dsc.<br \/><\/strong>Lomonosov Institute, NAFU<br \/>Arhangelsk, Russia<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a name=\"art02\">&nbsp;<\/a>XML \u041c\u041e\u0414\u0415\u041b \u0417\u0410 \u0410\u0412\u0422\u041e\u041c\u0410\u0422\u0418\u0427\u041d\u041e \u0413\u0415\u041d\u0415\u0420\u0418\u0420\u0410\u041d\u0415 \u041d\u0410 \u041f\u0420\u041e\u0413\u0420\u0410\u041c\u041d\u0418 \u0422\u0415\u041a\u0421\u0422\u041e\u0412\u0415<\/strong><\/p>\n<p><strong>Pavel Azalov<\/strong><\/p>\n<p><i>\u041f\u0435\u043d\u0441\u0438\u043b\u0432\u0430\u043d\u0441\u043a\u0438 \u0434\u044a\u0440\u0436\u0430\u0432\u0435\u043d \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442<\/i><\/p>\n<p><strong>Abstract. <\/strong>\u041f\u0440\u0435\u0434\u043c\u0435\u0442 \u043d\u0430 \u0442\u0430\u0437\u0438 \u0441\u0442\u0430\u0442\u0438\u044f \u0435 \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u043d\u043e\u0442\u043e \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0438, \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0432\u0430\u0449\u0438 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u0438 \u0442\u0435\u043a\u0441\u0442\u043e\u0432\u0435. \u041f\u0440\u043e\u0446\u0435\u0434\u0443\u0440\u0430\u0442\u0430 \u0437\u0430 \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u043d\u043e \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0430\u043d\u0435 \u0438\u0437\u0438\u0441\u043a\u0432\u0430 \u043f\u0440\u0435\u0434\u0432\u0430\u0440\u0438\u0442\u0435\u043b\u043d\u043e \u0434\u0430 \u0441\u0435 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0438 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0435\u043d \u0448\u0430\u0431\u043b\u043e\u043d. \u0422\u043e\u0439 \u0441\u0435 \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u0438\u0440\u0430 \u043e\u0442 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0435\u043d \u0442\u0435\u043a\u0441\u0442, \u0441\u044a\u043e\u0431\u0440\u0430\u0437\u0435\u043d \u0441 \u0442\u0435\u043c\u0430\u0442\u0430, \u0430 \u0441\u044a\u0449\u043e \u0438 \u0441 \u0446\u0435\u043b\u0442\u0430, \u0437\u0430 \u043a\u043e\u044f\u0442\u043e \u0449\u0435 \u0441\u0435 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430 \u2013 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430\u043d\u0435\u0442\u043e \u043c\u0443 \u0432 \u0447\u0430\u0441, \u0437\u0430 \u0441\u0430\u043c\u043e\u043f\u043e\u0434\u0433\u043e\u0442\u043e\u0432\u043a\u0430 \u0438\u043b\u0438 \u0438\u0437\u043f\u0438\u0442. \u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438\u044f\u0442 \u043c\u043e\u0434\u0435\u043b \u0437\u0430 \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u043d\u043e \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0438 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430 XML \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u044f. \u0417\u0430 \u0446\u0435\u043b\u0442\u0430 \u0435 \u0432\u0435\u0432\u0435\u0434\u0435\u043d \u043d\u043e\u0432 XML \u0435\u0437\u0438\u043a, \u043d\u0430\u0440\u0435\u0447\u0435\u043d xGen. \u0421\u0438\u043d\u0442\u0430\u043a\u0441\u0438\u0441\u044a\u0442 \u043c\u0443 \u0435 \u0434\u0435\u0444\u0438\u043d\u0438\u0440\u0430\u043d \u0447\u0440\u0435\u0437 \u0435\u0437\u0438\u043a\u0430 DTD (Document Type Definition). \u0415\u0437\u0438\u043a\u044a\u0442 xGen \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0432\u0430 \u0434\u0430 \u0441\u0435 \u043e\u043f\u0438\u0441\u0432\u0430\u0442 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u0438 \u0442\u0435\u043a\u0441\u0442\u043e\u0432\u0435 \u0441 \u0440\u0430\u0437\u043d\u043e\u043e\u0431\u0440\u0430\u0437\u043d\u0430 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0430. \u0422\u043e\u0439 \u0435 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c \u043e\u0442 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u0438\u044f \u0435\u0437\u0438\u043a \u0437\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0438\u0440\u0430\u043d\u0435. \u0417\u0430 \u0434\u0430 \u0441\u0435 \u0438\u043b\u044e\u0441\u0442\u0440\u0438\u0440\u0430\u0442 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438\u0442\u0435 \u043d\u0430 \u0435\u0437\u0438\u043a\u0430 xGen, \u0432 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d \u0435\u0437\u0438\u043a\u044a\u0442 \u0437\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0438\u0440\u0430\u043d\u0435 C++. \u0421\u044a\u0449\u0435\u0441\u0442\u0432\u0435\u043d\u0430 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442 \u043d\u0430 xGen \u0435 \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u043d\u043e \u0434\u0430 \u043e\u0446\u0435\u043d\u044f\u0432\u0430 \u0442\u0440\u0443\u0434\u043d\u043e\u0441\u0442\u0442\u0430 \u043d\u0430 \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0430\u043d\u0438\u0442\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u0438. \u0414\u0435\u0444\u0438\u043d\u0438\u0440\u0430\u043d\u043e \u0435 \u043f\u043e\u043d\u044f\u0442\u0438\u0435\u0442\u043e \u0433\u0435\u043d\u0435\u0442\u0438\u0447\u0435\u043d \u043a\u043e\u0434, \u0441 \u043f\u043e\u043c\u043e\u0449\u0442\u0430 \u043d\u0430 \u043a\u043e\u0435\u0442\u043e \u0441\u0435 \u043e\u043f\u0438\u0441\u0432\u0430 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0430\u0442\u0430 \u043d\u0430 \u0432\u0441\u0435\u043a\u0438 \u043e\u0442 \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0430\u043d\u0438\u0442\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u0438. \u0427\u0440\u0435\u0437 \u0433\u0435\u043d\u0435\u0442\u0438\u0447\u0438\u044f \u043a\u043e\u0434 \u0441\u0435 \u0432\u0435\u0432\u0435\u0436\u0434\u0430 \u0447\u0430\u0441\u0442\u0438\u0447\u043d\u0430 \u043d\u0430\u0440\u0435\u0434\u0431\u0430 \u0432 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e\u0442\u043e \u043e\u0442 \u043f\u0440\u0438\u043c\u0435\u0440\u0438, \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0430\u043d\u0438 \u0432 \u0435\u0434\u043d\u0430 \u0438 \u0441\u044a\u0449\u0430 \u0441\u0435\u0441\u0438\u044f. \u041f\u043e \u0442\u043e\u0437\u0438 \u043d\u0430\u0447\u0438\u043d \u043f\u0440\u0438\u043c\u0435\u0440\u0438\u0442\u0435 \u043c\u043e\u0433\u0430\u0442 \u0434\u0430 \u0441\u0435 \u0440\u0430\u0437\u0434\u0435\u043b\u044f\u0442 \u0432 \u043e\u0442\u0434\u0435\u043b\u043d\u0438 \u043f\u043e\u0434\u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430, \u0430 \u0432\u0441\u044f\u043a\u043e \u043e\u0442 \u0442\u044f\u0445 \u0434\u0430 \u0441\u0435 \u043f\u043e\u0434\u0440\u0435\u0434\u0438 \u0432 \u043d\u0435\u043d\u0430\u043c\u0430\u043b\u044f\u0432\u0430\u0449\u0430 \u043f\u043e \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442 \u0440\u0435\u0434\u0438\u0446\u0430 \u043e\u0442 \u043f\u0440\u0438\u043c\u0435\u0440\u0438. \u0412 \u043a\u0440\u0430\u044f \u043d\u0430 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0434\u0430\u043d \u043f\u0440\u0438\u043c\u0435\u0440, \u0438\u043b\u044e\u0441\u0442\u0440\u0438\u0440\u0430\u0449 \u0446\u044f\u043b\u043e\u0441\u0442\u043d\u0438\u044f \u043f\u0440\u043e\u0446\u0435\u0441 \u043d\u0430 \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u0438 \u043f\u0440\u0438\u043c\u0435\u0440\u0438.<\/p>\n<p><i>Keywords: <\/i>automatic example generation, sequernce of problems, XML model, example-based learning<\/p>\n<p><strong>AN XML MODEL FOR AUTOMATIC GENERATION OF PROGRAM TEXTS<\/strong><\/p>\n<p><strong>Abstract. <\/strong>This paper discusses the automatic generation of examples, which are program texts. The procedure for the automatic example generation requires a program template to be created in advance. This template should be based on a specific program text corresponding to the topic in consideration and to the objectives of the teaching process. The generated examples could be used in class, for self-preparation, or in a variety of assignments. The proposed model for automatic example generation was developed by implementing an XML-related technology. A new XML language, xGen, was introduces. Its syntax was defined by using the DTD (Document Type Definition) language. The xGen language allows the description of program texts of diverse structures and is independent from the specific programming language of the program texts. In this paper, the possibilities of the xGen language are illustrated by using the C++ programming language. The possibility for complexity assessment of the generated examples represents an essential xGen feature. The notion of genetic code was also defined to be used when describing the structure of every generated example. The genetic code allows introducing a partial order relation in the set of the examples that are generated during the same computer session. In this way, the examples could be distributed in separate subsets. Each of these subsets is ordered in ascending order as a series of examples starting with the easiest example and ending with the most difficult example. A case study illustrating the overall process for automatic example generation is also presented in the end of the paper.<\/p>\n<p><strong>Dr. Pavel Azalov, Assoc. Prof.<br \/><\/strong>Pennsylvania State University<br \/>Hazleton Campus, U.S.A.<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a name=\"art03\">&nbsp;<\/a>THE COMPUTER IMPROVES THE STEINER\u2019S CONSTRUCTION OF THE MALFATTI CIRCLES<\/strong><\/p>\n<p><strong>Sava Grozdev, Deko Dekov<\/strong><\/p>\n<p><i>Institute of Mathematics and Informatics<\/i><\/p>\n<p><strong>Abstract. <\/strong>The computer program \u201cDiscoverer\u201d, created by the authors, is the first computer program, which is able easily to discover new theorems in Mathematics, and possibly, the first computer program,which is able easily to discover new knowledge in science. In this paper we give a detailed description of an improvement of the classical Steiner\u2019s solution of the construction of the Malfatti circles, discovered by the computer program \u201cDiscoverer\u201d. We use the theory of the complexity of the geometric constructions in order to obtain a numerical measure of the complexity of the solutions.<\/p>\n<p><i>Keywords:<\/i> computer-generated mathematics, Euclidean geometry, Discoverer, Malfatti&nbsp;circles, Steiner\u2019s solution.<\/p>\n<p><strong>\u041a\u041e\u041c\u041f\u042e\u0422\u042a\u0420\u042a\u0422 \u041f\u041e\u0414\u041e\u0411\u0420\u042f\u0412\u0410 \u041a\u041e\u041d\u0421\u0422\u0420\u0423\u041a\u0426\u0418\u042f\u0422\u0410 \u041d\u0410 \u0429\u0410\u0419\u041d\u0415\u0420 \u041d\u0410 \u041e\u041a\u0420\u042a\u0416\u041d\u041e\u0421\u0422\u0418\u0422\u0415 \u041d\u0410 \u041c\u0410\u041b\u0424\u0410\u0422\u0418<\/strong><\/p>\n<p><strong>Abstract. <\/strong>\u041a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0430\u0442\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0430 \u201c\u041e\u0442\u043a\u0440\u0438\u0432\u0430\u0442\u0435\u043b\u201d, \u0441\u044a\u0437\u0434\u0430\u0434\u0435\u043d\u0430 \u043e\u0442 \u0430\u0432\u0442\u043e\u0440\u0438\u0442\u0435, \u0435 \u043f\u044a\u0440\u0432\u0430\u0442\u0430 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0430, \u043a\u043e\u044f\u0442\u043e \u043c\u043e\u0436\u0435 \u043b\u0435\u0441\u043d\u043e \u0434\u0430 \u043e\u0442\u043a\u0440\u0438\u0432\u0430 \u043d\u043e\u0432\u0438 \u0442\u0435\u043e\u0440\u0435\u043c\u0438 \u0432 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\u0442\u0430, \u0438 \u043c\u043e\u0436\u0435 \u0431\u0438 \u043f\u044a\u0440\u0432\u0430\u0442\u0430 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0430, \u043a\u043e\u044f\u0442\u043e \u043c\u043e\u0436\u0435 \u0434\u0430 \u043f\u0440\u0430\u0432\u0438 \u043e\u0442\u043a\u0440\u0438\u0442\u0438\u044f \u0432 \u043d\u0430\u0443\u043a\u0430\u0442\u0430 \u0438\u0437\u043e\u0431\u0449\u043e. \u0412 \u0442\u0430\u0437\u0438 \u0441\u0442\u0430\u0442\u0438\u044f \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430\u043c\u0435 \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u043e \u043e\u043f\u0438\u0441\u0430\u043d\u0438\u0435 \u043d\u0430 \u0435\u0434\u043d\u043e \u043e\u043f\u0440\u043e\u0441\u0442\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u043a\u043b\u0430\u0441\u0438\u0447\u0435\u0441\u043a\u043e\u0442\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u043d\u0430 \u0429\u0430\u0439\u043d\u0435\u0440 \u0437\u0430 \u043f\u043e\u0441\u0442\u0440\u043e\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442\u0438\u0442\u0435 \u043d\u0430 \u041c\u0430\u043b\u0444\u0430\u0442\u0438, \u043e\u0442\u043a\u0440\u0438\u0442\u043e \u043e\u0442 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0430\u0442\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0430 \u201c\u041e\u0442\u043a\u0440\u0438\u0432\u0430\u0442\u0435\u043b\u201d. \u0418\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043c\u0435 \u0442\u0435\u043e\u0440\u0438\u044f\u0442\u0430 \u043d\u0430 \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u0442\u0430 \u043d\u0430 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438\u0442\u0435 \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u0438\u044f, \u0437\u0430 \u0434\u0430 \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u0447\u0438\u0441\u043b\u0435\u043d\u0430 \u043c\u044f\u0440\u043a\u0430 \u043d\u0430 \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u0442\u0430 \u043d\u0430 \u0440\u0435\u0448\u0435\u043d\u0438\u044f\u0442\u0430.<\/p>\n<p><strong>Prof. Sava Grozdev, DSc<br \/><\/strong>Institute of Mathematics and Informatics \u2013 BAS<br \/>Sofia, Bulgaria<\/p>\n<p><strong>Dr. Deko Dekov, Assoc. Professor<br \/><\/strong>Stara Zagora, Bulgaria<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a name=\"art04\">&nbsp;<\/a>\u0413\u0415\u041e\u041c\u0415\u0422\u0420\u0418\u0427\u041d\u0410 \u041a\u041e\u041d\u0421\u0422\u0420\u0423\u041a\u0426\u0418\u042f \u041d\u0410 \u041a\u0420\u0418\u0412\u0410 \u041d\u0410 \u0427\u0415\u0412\u0410<\/strong><\/p>\n<p><strong><sup>1<\/sup>\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, <sup>2<\/sup>\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432<br \/><\/strong><i><sup>1<\/sup>Institute of Mathematics and Informatics \u2013 BAS<br \/><\/i><i><sup>2<\/sup>\u0422\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438 \u043a\u043e\u043b\u0435\u0436, \u041b\u043e\u0432\u0435\u0447<\/i><\/p>\n<p><strong>Abstract.<\/strong> \u0412 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0441\u0442\u0430\u0442\u0438\u044f \u0435 \u043e\u043f\u0438\u0441\u0430\u043d\u0430 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0430 \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0446\u0438\u044f \u043d\u0430 \u043a\u0440\u0438\u0432\u0430\u0442\u0430 \u043d\u0430 \u0427\u0435\u0432\u0430, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0430 \u0432 (\u0413\u0440\u043e\u0437\u0434\u0435\u0432 &amp; \u041d\u0435\u043d\u043a\u043e\u0432, 2014) \u0447\u0440\u0435\u0437 \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u043d\u0438 \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0430.<\/p>\n<p><i>Keywords: <\/i>triangle, conic, Ceva circle, Ceva curve, conjugate lines, GSP.<\/p>\n<p><strong>A GEOMETRICAL CONSTRUCTION OF A CEVA CURVE<\/strong><\/p>\n<p><strong>Abstract. <\/strong>The present paper describes a geometrical construction of the Ceva curve, which is obtained in by analytical means.<\/p>\n<p><strong>Prof. Sava Grozdev, DSc<br \/><\/strong>Institute of Mathematics and Informatics \u2013 BAS<br \/>Sofia, Bulgaria<\/p>\n<p><strong>Dr. Veselin Nenkov, Assoc. Prof.<br \/><\/strong>Technical College Lovech<br \/>Lovech, Bulgaria<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a name=\"art05\">&nbsp;<\/a>\u0421\u0422\u0418\u041c\u0423\u041b\u0418\u0420\u0410\u041d\u0415 \u0410\u041a\u0422\u0418\u0412\u041d\u041e\u0421\u0422\u0422\u0410 \u041d\u0410 \u0421\u0422\u0423\u0414\u0415\u041d\u0422\u0418\u0422\u0415 \u0412 \u041f\u0420\u041e\u0426\u0415\u0421\u0410 \u041d\u0410 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415 \u0427\u0420\u0415\u0417 \u0418\u0417\u041f\u041e\u041b\u0417\u0412\u0410\u041d\u0415 \u041d\u0410 \u0418\u041d\u0422\u0415\u0420\u0410\u041a\u0422\u0418\u0412\u041d\u0418 \u041c\u0415\u0422\u041e\u0414\u0418<\/strong><\/p>\n<p><strong>\u041b\u0438\u043b\u044f\u043d\u0430 \u041a\u0430\u0440\u0430\u043a\u0430\u0448\u0435\u0432\u0430-\u0419\u043e\u043d\u0447\u0435\u0432\u0430<br \/><\/strong><i>Episkop Konstantin Preslavski Shumen University<\/i><\/p>\n<p><strong>Abstract. <\/strong>\u0420\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430\u0442 \u0441\u0435 \u043e\u0441\u043d\u043e\u0432\u043d\u0438\u0442\u0435 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438 \u043d\u0430 \u0438\u043d\u0442\u0435\u0440\u0430\u043a\u0442\u0438\u0432\u043d\u0430\u0442\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u0430 \u0441\u0440\u0435\u0434\u0430 \u0432\u044a\u0432 \u0432\u0438\u0441\u0448\u0435\u0442\u043e \u0443\u0447\u0438\u043b\u0438\u0449\u0435. \u041f\u043e\u043a\u0430\u0437\u0430\u043d\u0438 \u0441\u0430 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438\u0442\u0435 \u043d\u0430 \u0438\u043d\u0442\u0435\u0440\u0430\u043a\u0442\u0438\u0432\u043d\u0438\u0442\u0435 \u043c\u0435\u0442\u043e\u0434\u0438 \u0437\u0430 \u043f\u043e\u0432\u0438\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u043c\u043e\u0442\u0438\u0432\u0430\u0446\u0438\u044f\u0442\u0430 \u0438 \u0430\u043a\u0442\u0438\u0432\u043d\u043e\u0441\u0442\u0442\u0430 \u043d\u0430 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0438\u0442\u0435 \u0432 \u043f\u0440\u043e\u0446\u0435\u0441\u0430 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435. \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u043f\u043e-\u043f\u043e\u0434\u0440\u043e\u0431\u043d\u043e \u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0434\u0430\u043d \u0438\u043d\u0442\u0435\u0440\u0430\u043a\u0442\u0438\u0432\u043d\u0438\u044f\u0442 \u043c\u0435\u0442\u043e\u0434 \u201e\u043c\u043e\u0437\u044a\u0447\u043d\u0430 \u0430\u0442\u0430\u043a\u0430\u201c, \u043a\u0430\u0442\u043e \u0441\u0430 \u043f\u043e\u0441\u043e\u0447\u0435\u043d\u0438 \u043e\u0441\u043d\u043e\u0432\u043d\u0438 \u0438\u0437\u0438\u0441\u043a\u0432\u0430\u043d\u0438\u044f \u0438 \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u0438 \u0431\u0435\u043b\u0435\u0436\u043a\u0438 \u0437\u0430 \u043d\u0435\u0433\u043e\u0432\u043e\u0442\u043e \u043f\u0440\u0438\u043b\u0430\u0433\u0430\u043d\u0435 \u0432 \u0443\u0447\u0435\u0431\u043d\u0430\u0442\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0430. \u0418\u043b\u044e\u0441\u0442\u0440\u0438\u0440\u0430\u043d\u0430 \u0435 \u0443\u043f\u043e\u0442\u0440\u0435\u0431\u0430\u0442\u0430 \u043c\u0443 \u0432 \u0441\u0435\u043c\u0438\u043d\u0430\u0440\u043d\u0438\u0442\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u043f\u043e \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0434\u0438\u0441\u0446\u0438\u043f\u043b\u0438\u043d\u0438.<\/p>\n<p><i>Keywords: <\/i>interactive learning environments, interactive methods, interactive method \u201ebrainstorming\u201d, session seminar<\/p>\n<p><strong>STIMULATING STUDENTS\u2019 ACTIVITY IN THE TEACHING PROCESS BY INTERACTIVE METHODS<\/strong><\/p>\n<p><strong>Abstract .<\/strong>The paper considers basic features of the interactive educational environment in higher school. The possibilities of the interactive methods are shown for increasing the motivation and the activity of students in the teaching process. Special attention is paid to the interactive method of brainstorming together with some fundamental requirements and methodological notes for its application in the educational practice. Examples are given for its use in seminars in different mathematical disciplines.<\/p>\n<p><strong>Dr. Lilyana Karakasheva-Yoncheva<br \/><\/strong>Faculty of Mathematics and Informatics<br \/>Shumen University<br \/>Shumen, Bulgaria<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a name=\"art06\">&nbsp;<\/a>\u0420\u041e\u041b\u042f\u0422\u0410 \u041d\u0410 \u0415\u041c\u041e\u0426\u0418\u0418\u0422\u0415 \u041d\u0410 \u0423\u0427\u0415\u041d\u0418\u0426\u0418\u0422\u0415 \u041f\u0420\u0418 \u041c\u041e\u0422\u0418\u0412\u0410\u0426\u0418\u042f\u0422\u0410 \u0418\u041c \u0412 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415\u0422\u041e \u041f\u041e \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410<\/strong><\/p>\n<p><strong><sup>1<\/sup>\u0420\u0443\u043c\u044f\u043d\u0430 \u041c\u0430\u0432\u0440\u043e\u0432\u0430, <sup>2<\/sup>\u0417\u0430\u0440\u0430 \u0414\u0430\u043d\u0430\u0438\u043b\u043e\u0432\u0430<br \/><\/strong><sup>1<\/sup>University of Plovdiv \u201cPaisii Hilendarski\u201d<br \/><sup>2<\/sup>\u0420\u0435\u0433\u0438\u043e\u043d\u0430\u043b\u0435\u043d \u0438\u043d\u0441\u043f\u0435\u043a\u0442\u043e\u0440\u0430\u0442 \u043f\u043e \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u0442\u043e \u2013 \u041f\u043b\u043e\u0432\u0434\u0438\u0432<\/p>\n<p><strong>Abstract. <\/strong>\u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430 \u0435\u0434\u043d\u0430 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442 \u0437\u0430 \u043f\u043e\u0432\u0438\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u043c\u043e\u0442\u0438\u0432\u0430\u0446\u0438\u044f\u0442\u0430 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 \u0438 \u043f\u0440\u0435\u0434\u0438\u0437\u0432\u0438\u043a\u0432\u0430\u043d\u0435 \u043d\u0430 \u0435\u043c\u043e\u0446\u0438\u0438 \u0443 \u0442\u044f\u0445 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0447\u0440\u0435\u0437 \u0440\u0430\u0437\u043a\u0440\u0438\u0432\u0430\u043d\u0435 \u043d\u0430 \u0432\u0440\u044a\u0437\u043a\u0438 \u043c\u0435\u0436\u0434\u0443 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\u0442\u0430 \u0438 \u0445\u0443\u0434\u043e\u0436\u0435\u0441\u0442\u0432\u0435\u043d\u0430\u0442\u0430 \u043b\u0438\u0442\u0435\u0440\u0430\u0442\u0443\u0440\u0430. \u041f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u0430 \u0435 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0430 \u043d\u0430 \u0437\u0430\u043d\u044f\u0442\u0438\u0435-\u043a\u043e\u043d\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u044f \u0437\u0430 \u0441\u0432\u043e\u0431\u043e\u0434\u043d\u043e\u0438\u0437\u0431\u0438\u0440\u0430\u0435\u043c\u0430 \u043f\u043e\u0434\u0433\u043e\u0442\u043e\u0432\u043a\u0430 \u0438 \u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u0435\u043d \u043e\u043f\u0438\u0442 \u0437\u0430 \u0444\u043e\u0440\u043c\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0438\u043d\u0442\u0435\u0440\u0435\u0441 \u0438 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u043d\u0438 \u043c\u043e\u0442\u0438\u0432\u0438 \u0443 \u043f\u043e\u0434\u0440\u0430\u0441\u0442\u0432\u0430\u0449\u0438\u0442\u0435. \u0417\u0430 \u0446\u0435\u043b\u0442\u0430 \u0441\u0435 \u043f\u043e\u0441\u0442\u0430\u0432\u044f\u0442 \u0437\u0430\u0434\u0430\u0447\u0438 \u0437\u0430 \u043d\u0430\u043c\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u044f \u0437\u0430 \u0438\u043c\u0435\u043d\u0438\u0442\u0438 \u043f\u043e\u0435\u0442\u0438 \u0438 \u043f\u0438\u0441\u0430\u0442\u0435\u043b\u0438, \u043f\u043e\u0441\u0432\u0435\u0442\u0438\u043b\u0438 \u0447\u0430\u0441\u0442 \u043e\u0442 \u0442\u0432\u043e\u0440\u0431\u0438\u0442\u0435 \u0441\u0438 \u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\u0442\u0430.<\/p>\n<p><i>Keywords:<\/i> motivation, interest, emotion, art, fiction.<\/p>\n<p><strong>THE ROLE OF STUDENTS\u2018 EMOTIONS IN THEIR MOTIVATION TO STUDY MATHEMATICS<\/strong><\/p>\n<p><strong>Abstract. <\/strong>The paper considers a possibility to increase students\u2018 motivation and to induce emotions in them while studying mathematics by revealing connections between mathematics and literature. An elaboration of a workshop is proposed for self-chosen preparation and an attempt is realized to form interest and positive motives in adolescents. A task is given to find information about famous poets and writers who have dedicated a part of their work to mathematics.<\/p>\n<p><strong>Dr. Rumjana Mavrova, Assoc. Prof.<br \/><\/strong>Faculty of Mathematics and Informatics<br \/>University of Plovdiv<br \/>Plovdiv, Bulgaria<\/p>\n<p><strong>Mrs. Zara Danailova<br \/><\/strong>Senior expert of mathematics<br \/>Regional Inspectorate of Education<br \/>Plovdiv, Bulgaria<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a name=\"art07\">&nbsp;<\/a>\u041a\u041e\u0413\u041d\u0418\u0422\u0418\u0412\u041d\u0418 \u0418\u0417\u041c\u0415\u0420\u0415\u041d\u0418\u042f \u041f\u0420\u0418 \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u0426\u0418\u0422\u0415 \u0421 \u0423\u0412\u0420\u0415\u0414\u0415\u041d\u041e \u0417\u0420\u0415\u041d\u0418\u0415<\/strong><\/p>\n<p><strong>Milen Zamfirov<br \/><\/strong><em>Sofia University<\/em><\/p>\n<p><strong>Abstract. <\/strong>\u0418\u0441\u0442\u043e\u0440\u0438\u044f\u0442\u0430 \u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\u0442\u0430 \u043f\u043e\u0437\u043d\u0430\u0432\u0430 \u043c\u043d\u043e\u0433\u043e \u0441\u043b\u0435\u043f\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0446\u0438. \u0415\u0434\u0438\u043d \u0437\u0440\u044f\u0449 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a \u043e\u0431\u0438\u043a\u043d\u043e\u0432\u0435\u043d\u043e \u0440\u0430\u0431\u043e\u0442\u0438 \u0441\u0435\u0434\u043d\u0430\u043b, \u0434\u0440\u0430\u0441\u043a\u0430\u0439\u043a\u0438 \u0432\u044a\u0440\u0445\u0443 \u043b\u0438\u0441\u0442 \u0445\u0430\u0440\u0442\u0438\u044f. \u041a\u0430\u043a \u0440\u0430\u0431\u043e\u0442\u044f\u0442 \u0441\u043b\u0435\u043f\u0438\u0442\u0435 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0446\u0438? \u0422\u0435 \u043d\u0435 \u043c\u043e\u0433\u0430\u0442 \u0434\u0430 \u0440\u0430\u0437\u0447\u0438\u0442\u0430\u0442 \u043d\u0430 \u0441\u0442\u0435\u043d\u043e\u0433\u0440\u0430\u0444\u0438\u0440\u0430\u043d\u0438 \u043c\u0438\u0441\u043b\u0438, \u0445\u0440\u0443\u043c\u043d\u0430\u043b\u0438 \u0438\u0437\u0432\u0435\u0434\u043d\u044a\u0436 \u0438 \u043d\u0430\u0445\u0432\u044a\u0440\u043b\u044f\u043d\u0438 \u043d\u0430 \u043b\u0438\u0441\u0442\u0447\u0435 \u0445\u0430\u0440\u0442\u0438\u044f, \u0438\u043b\u0438 \u043d\u0430 \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0438, \u043d\u0430\u0434\u0440\u0430\u0441\u043a\u0430\u043d\u0438 \u043d\u0430\u0431\u044a\u0440\u0437\u043e \u043d\u0430 \u0440\u044a\u043a\u0430, \u043a\u044a\u0434\u0435\u0442\u043e \u201e\u0442\u043e\u0432\u0430\u201c \u0441\u0435 \u0438\u0437\u0432\u0435\u0436\u0434\u0430 \u043e\u0442 \u201e\u0442\u0430\u043c\u201c \u0438 \u201e\u043e\u043d\u043e\u0432\u0430\u201c \u043d\u0435 \u043f\u0430\u0441\u0432\u0430 \u0441 \u201e\u0442\u0443\u043a\u201c. \u0412\u044a\u043f\u0440\u0435\u043a\u0438 \u0432\u0441\u0438\u0447\u043a\u043e \u0432 \u043c\u043d\u043e\u0433\u043e \u0441\u043b\u0443\u0447\u0430\u0438 \u0441\u043b\u0435\u043f\u0438\u0442\u0435 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0446\u0438 \u0440\u0430\u0431\u043e\u0442\u044f\u0442 \u043f\u043e \u043f\u043e\u0447\u0442\u0438 \u0441\u044a\u0449\u0438\u044f \u043d\u0430\u0447\u0438\u043d \u043a\u0430\u043a\u0442\u043e \u0437\u0440\u044f\u0449\u0438\u0442\u0435.<\/p>\n<p><i>Keywords:<\/i> blind mathematicians, cognitive process, Boy\u2018s surface<\/p>\n<p><strong>COGNITIVE DIMENSIONS TO BLIND MATHEMATICIANS<\/strong><\/p>\n<p><strong>Abstract. <\/strong>The history of mathematics includes a number of blind mathematicians. A sighted mathematician generally works by sitting around scribbling on paper. So how do blind mathematicians work? They cannot rely on backof-the-envelope calculations, half-baked thoughts scribbled on restaurant napkins, or hand-waving arguments in which \u201cthis\u201d attaches \u201cthere\u201d and \u201cthat\u201d intersects \u201chere\u201d. Still, in many ways, blind mathematicians work in much the same way as sighted mathematicians do.<\/p>\n<p><strong>Dr. Milen Zamfirov, Assoc. Prof.<br \/><\/strong>Department of Special Education and Speech Therapy<br \/>Sofia University \u201cSt. Kliment Ohridski\u201c<br \/>Sofia, Bulgaria<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a name=\"art08\">&nbsp;<\/a>\u0410\u041d\u0410\u041b\u0418\u0417 \u041d\u0410 \u0417\u0410\u0414\u0410\u0427\u0418\u0422\u0415 \u0418 \u041f\u0420\u0415\u0414\u0421\u0422\u0410\u0412\u042f\u041d\u0415\u0422\u041e \u041d\u0410 \u0423\u0427\u0415\u041d\u0418\u0426\u0418\u0422\u0415 \u041e\u0422 XII \u041a\u041b\u0410\u0421 \u041d\u0410 \u041e\u0411\u041b\u0410\u0421\u0422\u041d\u0418\u042f \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u0427\u0415\u0421\u041a\u0418 \u0422\u0423\u0420\u041d\u0418\u0420 \u0412 \u041a\u042a\u0420\u0414\u0416\u0410\u041b\u0418 \u2013 2014 \u0413.<\/strong><\/p>\n<p><strong>\u0420\u043e\u0441\u0435\u043d \u041d\u0438\u043a\u043e\u043b\u0430\u0435\u0432, \u0419\u043e\u0440\u0434\u0430\u043d \u041f\u0435\u0442\u043a\u043e\u0432<br \/><\/strong><i>University of Economics \u2013 Varna<\/i><\/p>\n<p><strong>Abstract.<\/strong> \u0412 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0441\u0442\u0430\u0442\u0438\u044f \u0441\u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430\u0442 \u0437\u0430\u0434\u0430\u0447\u0438\u0442\u0435 \u0437\u0430 XII \u043a\u043b\u0430\u0441 \u043e\u0442 \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u043d\u0430 29.11.2014 \u0433. o\u0431\u043b\u0430\u0441\u0442\u0435\u043d \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0442\u0443\u0440\u043d\u0438\u0440 \u0432 \u0433\u0440. \u041a\u044a\u0440\u0434\u0436\u0430\u043b\u0438. \u041f\u0440\u0435\u0434\u043b\u0430\u0433\u0430\u0442 \u0441\u0435 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u0438 \u043f\u043e\u0434\u0445\u043e\u0434\u0438 \u0437\u0430 \u0442\u044f\u0445\u043d\u043e\u0442\u043e \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435. \u041d\u0430 \u0431\u0430\u0437\u0430 \u043d\u0430 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u0442\u0435 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438 \u0441\u0435 \u0430\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u0430 \u043d\u0438\u0432\u043e\u0442\u043e \u043d\u0430 \u043f\u043e\u0434\u0433\u043e\u0442\u043e\u0432\u043a\u0430 \u043d\u0430 \u0443\u0447\u0430\u0441\u0442\u043d\u0438\u0446\u0438\u0442\u0435 \u0432 \u0441\u044a\u0441\u0442\u0435\u0437\u0430\u043d\u0438\u044f \u043e\u0442 \u043f\u043e\u0434\u043e\u0431\u0435\u043d \u0442\u0438\u043f \u0438 \u0441\u0435 \u043f\u0440\u0430\u0432\u044f\u0442 \u043d\u044f\u043a\u043e\u0438 \u043f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u0437\u0430 \u0443\u0441\u044a\u0432\u044a\u0440\u0448\u0435\u043d\u0441\u0442\u0432\u0430\u043d\u0435 \u043d\u0430 \u0431\u044a\u0434\u0435\u0449\u0430\u0442\u0430 \u0440\u0430\u0431\u043e\u0442\u0430 \u0441 \u0438\u0437\u044f\u0432\u0435\u043d\u0438 \u0443\u0447\u0435\u043d\u0438\u0446\u0438 \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u0442\u0430 \u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\u0442\u0430.<\/p>\n<p><i>Keywords:<\/i> education, mathematics competition<\/p>\n<p><strong>ANALYSIS OF THE PROBLEMS AND PERFORMANCE OF THE STUDENTS FROM 12TH GRADE ON THE REGIONAL MATHEMATICS TOURNAMENT IN KARDZHALI \u2013 2014<\/strong><\/p>\n<p><strong>Abstract.<\/strong> The present paper discusses the tasks for the 12th grade in the Regional Mathematics Tournament in Kardzhali, held on 11.29.2014. Different approaches to their solutions are proposed. On the basis of the obtained results the authors analyze the level of preparation of participants in events of a similar type and make some suggestions for the improvement of the future work with outstanding students in mathematics.<\/p>\n<p><strong>Dr. Rosen Nikolaev, Assoc. Prof.<br \/><\/strong>University of Economics<br \/>Varna, Bulgaria<\/p>\n<p><strong>Dr. Jordan Petkov, Assist. Prof.<br \/><\/strong>University of Economics<br \/>Varna, Bulgaria<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a name=\"art09\">&nbsp;<\/a>\u0414\u0412\u0410\u041d\u0410\u0414\u0415\u0421\u0415\u0422\u0410 \u041c\u0415\u0416\u0414\u0423\u041d\u0410\u0420\u041e\u0414\u041d\u0410 \u041e\u041b\u0418\u041c\u041f\u0418\u0410\u0414\u0410 \u041f\u041e \u041b\u0418\u041d\u0413\u0412\u0418\u0421\u0422\u0418\u041a\u0410<\/strong><\/p>\n<p><strong><i>Ivan Derzhanski<br \/><\/i><\/strong><i>Institute of Mathematics and Informatics \u2013 BAS<\/i><\/p>\n<p><strong>Abstract. <\/strong>\u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u043f\u043e\u0441\u0432\u0435\u0442\u0435\u043d\u0430 \u043d\u0430 \u0414\u0432\u0430\u043d\u0430\u0434\u0435\u0441\u0435\u0442\u0430\u0442\u0430 \u043c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0430 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0430 \u043f\u043e \u043b\u0438\u043d\u0433\u0432\u0438\u0441\u0442\u0438\u043a\u0430. \u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438 \u0441\u0430 \u0437\u0430\u0434\u0430\u0447\u0438\u0442\u0435 \u043e\u0442 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0430\u0442\u0430 \u0438 \u0441\u0430 \u043f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u0438 \u0442\u0435\u0445\u043d\u0438 \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u043d\u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u044f.<\/p>\n<p><i>Keywords: <\/i>linguistics, International Linguistics Olympiad, mathematics<\/p>\n<p><strong>THE&nbsp;<\/strong><strong>TWELFTH INTERNATIONAL OLYMPIAD IN LINGUISTICS<\/strong><\/p>\n<p><strong>Abstract.<\/strong> The paper is dedicated to the Twelfth International Olympiad in Linguistics. The problems are presented and their methodological solutions are proposed.&nbsp;Methodological solutions are proposed.<br \/><strong><br \/>Dr. Ivan Derzhanski, Assoc. Prof.<br \/><\/strong>Institute of Mathematics and Informatics<br \/>Sofia, Bulgaria<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>","protected":false},"excerpt":{"rendered":"<p>&nbsp;CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u0427\u0415\u0421\u041a\u041e\u0422\u041e \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u041d\u0418\u0415 \u041f\u041e \u0421\u0412\u0415\u0422\u0410 \/ MATHEMATICAL EDUCATION WORLDWIDE \u041c. \u0412. \u041b\u043e\u043c\u043e\u043d\u043e\u0441\u043e\u0432 \u0418 \u0422\u0440\u0430\u0434\u0438\u0446\u0438\u0438 \u0423\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0441\u043a\u043e\u0433\u043e \u041e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f [M. V. Lomonosov And The Traditions Of The University Education] \/ \u0422\u0430\u0442\u044c\u044f\u043d\u0430 \u0411\u0443\u0442\u043e\u0440\u0438\u043d\u0430 \/ \u0422atyana Butorina &#8211; \u0441\u0442\u0440. 10 &nbsp;\u041e\u0442\u0432\u043e\u0440\u0438 \u043f\u044a\u043b\u043d\u0438\u044f \u0442\u0435\u043a\u0441\u0442 \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u0422\u0415\u041b\u041d\u0418 \u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0418\u0418 \/ EDUCATIONAL TECHNOLOGY XML \u043c\u043e\u0434\u0435\u043b \u0437\u0430 \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u043d\u043e \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u0438 \u0442\u0435\u043a\u0441\u0442\u043e\u0432\u0435 [An XML [&hellip;]<\/p>","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jnews-multi-image_gallery":[],"jnews_single_post":[],"jnews_primary_category":[]},"categories":[2882],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>&quot;\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430&quot;, \u043a\u043d\u0438\u0436\u043a\u0430 1, \u0433\u043e\u0434\u0438\u043d\u0430 LVIII, 2015 - \u0410\u0437-\u0431\u0443\u043a\u0438<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/newspaper.azbuki.bg\/matematics\/matharticles\/mathinfocontent012015-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"&quot;\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430&quot;, \u043a\u043d\u0438\u0436\u043a\u0430 1, \u0433\u043e\u0434\u0438\u043d\u0430 LVIII, 2015 - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"&nbsp;CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u0427\u0415\u0421\u041a\u041e\u0422\u041e \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u041d\u0418\u0415 \u041f\u041e \u0421\u0412\u0415\u0422\u0410 \/ MATHEMATICAL EDUCATION WORLDWIDE \u041c. \u0412. \u041b\u043e\u043c\u043e\u043d\u043e\u0441\u043e\u0432 \u0418 \u0422\u0440\u0430\u0434\u0438\u0446\u0438\u0438 \u0423\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0441\u043a\u043e\u0433\u043e \u041e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f [M. V. 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