{"id":41701,"date":"2017-04-28T13:24:56","date_gmt":"2017-04-28T10:24:56","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles2016-2\/2-lxx-2017\/"},"modified":"2019-06-24T17:33:14","modified_gmt":"2019-06-24T14:33:14","slug":"2-lxx-2017","status":"publish","type":"post","link":"https:\/\/vocedu.azbuki.bg\/en\/matematics\/matharticles2016-2\/2-lxx-2017\/","title":{"rendered":"Mathematics and Informatics, Number 2\/2017, Volume 60"},"content":{"rendered":"<p><strong><a name=\"top\"><\/a>\u00a0CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415<\/strong><\/p>\n<p>\u00a0<\/p>\n<p><strong>EDUCATIONAL MATTERS \/ \u041d\u0410\u0423\u0427\u041d\u041e-\u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0418 \u0421\u0422\u0410\u0422\u0418\u0418<\/strong><br \/><a href=\"#art01\">NDM-Philosophy of Education in the 21st Century <\/a><br \/><a href=\"#art01\">[NDM \u0444\u0438\u043b\u043e\u0441\u043e\u0444\u0438\u044f\u0442\u0430 \u043d\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u0442\u043e \u0432 \u0425\u0425I \u0432\u0435\u043a] <\/a><br \/>\/ Marga Georgieva, Sava Grozdev \u2013 \u0441\u0442\u0440. \/ page 111<br \/><a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art02\">\u0418\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0430\u0442\u0430 \u0433\u0440\u0430\u043c\u043e\u0442\u043d\u043e\u0441\u0442 \u2013 \u0441\u044a\u0449\u043d\u043e\u0441\u0442, \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0438 \u0438 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u0437\u0430 \u043f\u043e\u0432\u0438\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0430\u0442\u0430 \u0433\u0440\u0430\u043c\u043e\u0442\u043d\u043e\u0441\u0442 \u0447\u0440\u0435\u0437 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435 \u043d\u0430 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u0432 \u0443\u0447\u0438\u043b\u0438\u0449\u0435 <\/a><br \/><a href=\"#art02\">[Information Literacy \u2013 Nature, Problems and Opportunities for Improving Information Literacy Through the Use of Information Technology in School] <\/a><br \/>\/ \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u0414\u0437\u0438\u0432\u0435\u0432 \/ Vesselin Dzivev \u2013 \u0441\u0442\u0440. \/ page 123<br \/><a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art03\">\u0418\u0437\u043a\u0443\u0441\u0442\u0432\u0435\u043d\u0430 \u0438\u043c\u0443\u043d\u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0430 <\/a><br \/><a href=\"#art03\">[Artificial Immune System] <\/a><br \/>\/ \u0419\u043e\u0430\u043d\u043d\u0430 \u0418\u043b\u0438\u0435\u0432\u0430, \u0421\u0435\u043b\u0438\u043d \u0428\u0435\u043c\u0441\u0438\u0435\u0432\u0430, \u0421\u0432\u0435\u0442\u043b\u0430\u043d\u0430 \u0412\u044a\u043b\u0447\u0435\u0432\u0430, \u0421\u044e\u0437\u0430\u043d \u0424\u0435\u0438\u043c\u043e\u0432\u0430 \/ Joanna Ilieva, student, Selin Shemsieva, Svetlana Valcheva, student, Suzan Feimova \u2013 \u0441\u0442\u0440. \/ page 149<br \/><a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p><a href=\"#art04\">\u00a0<\/a><\/p>\n<p><a href=\"#art04\">\u041d\u044f\u043a\u043e\u0438 \u0438\u0434\u0435\u0438 \u0437\u0430 \u043f\u0440\u043e\u043f\u0435\u0434\u0435\u0432\u0442\u0438\u043a\u0430 \u043d\u0430 \u043f\u043e\u043d\u044f\u0442\u0438\u0435\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432 \u043d\u0430\u0447\u0430\u043b\u043d\u0438\u0442\u0435 \u043a\u043b\u0430\u0441\u043e\u0432\u0435 <\/a><br \/><a href=\"#art04\">[Some Ideas for Propaedeutics of the Concept of Function in Primary School] <\/a><br \/>\/ \u041a\u0430\u0442\u0438\u043d\u0430 \u0422\u043e\u043d\u0447\u0435\u0432\u0430, \u041c\u0430\u0440\u0433\u0430\u0440\u0438\u0442\u0430 \u0412\u044a\u0440\u0431\u0430\u043d\u043e\u0432\u0430 \/ Katina Toncheva, Margarita Varbanova \u2013 \u0441\u0442\u0440. \/ page 157<br \/><a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><strong><span style=\"font-size: 12.16px;\">EDUCATIONAL TECHNOLOGIES \/ \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u0422\u0415\u041b\u041d\u0418 \u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0418\u0418<\/span><\/strong><\/p>\n<p><a href=\"#art05\">\u0427\u0435\u0442\u0438\u0440\u0438\u043d\u0430\u0434\u0435\u0441\u0435\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 <\/a><br \/><a href=\"#art05\">[Fourteenth International Linguistics Olympiads] <\/a><br \/>\/ \u0418\u0432\u0430\u043d \u0414\u0435\u0440\u0436\u0430\u043d\u0441\u043a\u0438 \/ Ivan Derzhanski \u2013 \u0441\u0442\u0440. \/ page 174<br \/><a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art06\">\u0412\u0435\u0442\u0440\u0438\u043b\u0430 \u043e\u0442 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442\u0438 \u0432\u044a\u0432 \u0432\u043f\u0438\u0441\u0430\u043d\u0438 \u043c\u043d\u043e\u0433\u043e\u044a\u0433\u044a\u043b\u043d\u0438\u0446\u0438 <\/a><br \/><a href=\"#art06\">[Fans of Circles in Inscribed Polygons] <\/a><br \/>\/ \u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432 \/ Sava Grozdev, Veselin Nenkov \u2013 \u0441\u0442\u0440. \/ page 181<br \/><a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art07\">\u0411\u0435\u043b\u0435\u0436\u043a\u0430 \u0432\u044a\u0440\u0445\u0443 \u0442\u0435\u043e\u0440\u0435\u043c\u0430\u0442\u0430 \u0437\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u043d\u0438\u0442\u0435 \u0441\u0440\u0435\u0434\u043d\u0438 \u0438 \u043e\u0431\u0443\u0447\u0430\u0432\u0430\u0449\u0438\u044f \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440 \u043d\u0430 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0438\u0442\u0435 <\/a><br \/><a href=\"#art07\">[A Note On the Theorem of the Power Averages and the Educational Character of the Olympiads] <\/a><br \/>\/ \u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432 \/ Sava Grozdev, Veselin Nenkov \u2013 \u0441\u0442\u0440. \/ page 202<br \/><a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art08\">\u0412\u0442\u043e\u0440\u0438 \u043a\u043e\u043b\u0435\u0434\u0435\u043d \u043b\u0438\u043d\u0433\u0432\u0438\u0441\u0442\u0438\u0447\u0435\u043d \u0442\u0443\u0440\u043d\u0438\u0440 <\/a><br \/><a href=\"#art08\">[Second Christmas Linguistics Tournament] <\/a><br \/>\/ \u0418\u0432\u0430\u043d \u0414\u0435\u0440\u0436\u0430\u043d\u0441\u043a\u0438, \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u0417\u043b\u0430\u0442\u0438\u043b\u043e\u0432 \/ Ivan Derzhanski, Veselin Zlatilov \u2013 \u0441\u0442\u0440. \/ page 207<br \/><a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><strong>CONTEST PROBLEMS \/ \u041a\u041e\u041d\u041a\u0423\u0420\u0421\u041d\u0418 \u0417\u0410\u0414\u0410\u0427\u0418<\/strong><br \/>Contest Problems of this Issue <br \/>[Contest Problems of this Issue] <br \/>\u2013 \u0441\u0442\u0440. \/ page 214<br \/><a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p>\u0420\u0435\u0448\u0435\u043d\u0438\u044f \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438\u0442\u0435 \u043e\u0442 \u0431\u0440\u043e\u0439 3, 2016 <br \/>[Solutions of the Contest Problems from Issue 3, 2016] <br \/>\u2013 \u0441\u0442\u0440. \/ page 215<\/p>\n<p>\u00a0<\/p>\n<p><strong>READ IN THE LATEST ISSUES OF \u201eAZBUKI\u201c JOURNALS \/ \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<\/strong> <br \/>\u2013 \u0441\u0442\u0440. \/ page 218<\/p>\n<p>\u00a0<\/p>\n<p><strong>GUIDE FOR AUTHORS \/ \u0423\u041a\u0410\u0417\u0410\u041d\u0418\u042f \u0417\u0410 \u0410\u0412\u0422\u041e\u0420\u0418\u0422\u0415<\/strong> \u2013 \u0441\u0442\u0440. \/ page 220<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: left;\"><strong style=\"font-size: 12.16px;\"><span style=\"font-size: 12.16px;\"><a name=\"art01\"><\/a>NDM-PHILOSOPHY OF EDUCATION IN THE 21st CENTURY<\/span><\/strong><\/p>\n<p>\u00a0<\/p>\n<p>Marga Georgieva, University of Veliko Tarnovo <br \/>Sava Grozdev, University of Finance, Business and Entrepreneurship \u2013 Sofia<\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> The article is an attempt to demonstrate the universality of the so-called NDM-philosophy of education in the 21st century. A concept has been presented through various conceptual models targeted at optimization of the intellectual development of lifelong learners within the triad \u201cformal \u2013 non-formal \u2013 informal\u201d education. All this is realized through a proposed technological model based on an introduced NDM-approach in the context of mophodynamics as a science with interdisciplinary direction in the presence of the \u201cI-concept\u201d of mathematical modeling. The mathematical modeling is visualizing the harnessing the power of human thought in the present technological society, but having justified claims about what is happening in this context and in the future technological society.<br \/><em>Keywords:<\/em> NDM-philosophy, NDM-paradigm, NDM-environment, NDM-approach<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: left;\"><strong style=\"font-size: 12.16px;\"><a name=\"art02\"><\/a>\u0418\u041d\u0424\u041e\u0420\u041c\u0410\u0426\u0418\u041e\u041d\u041d\u0410\u0422\u0410 \u0413\u0420\u0410\u041c\u041e\u0422\u041d\u041e\u0421\u0422 \u2013 \u0421\u042a\u0429\u041d\u041e\u0421\u0422, \u041f\u0420\u041e\u0411\u041b\u0415\u041c\u0418 \u0418 \u0412\u042a\u0417\u041c\u041e\u0416\u041d\u041e\u0421\u0422\u0418 \u0417\u0410 \u041f\u041e\u0412\u0418\u0428\u0410\u0412\u0410\u041d\u0415 \u041d\u0410 \u0418\u041d\u0424\u041e\u0420\u041c\u0410\u0426\u0418\u041e\u041d\u041d\u0410\u0422\u0410 \u0413\u0420\u0410\u041c\u041e\u0422\u041d\u041e\u0421\u0422 \u0427\u0420\u0415\u0417 \u00a0\u0418\u0417\u041f\u041e\u041b\u0417\u0412\u0410\u041d\u0415 \u041d\u0410 \u0418\u041d\u0424\u041e\u0420\u041c\u0410\u0426\u0418\u041e\u041d\u041d\u0418 \u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0418\u0418 \u0412 \u0423\u0427\u0418\u041b\u0418\u0429\u0415<\/strong><\/p>\n<p>\u00a0<\/p>\n<p>\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u0414\u0437\u0438\u0432\u0435\u0432<br \/>Sofia University<\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u043e\u043f\u0438\u0441\u0432\u0430\u0442 \u0441\u044a\u0449\u043d\u043e\u0441\u0442\u0442\u0430 \u043d\u0430 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0430\u0442\u0430 \u0433\u0440\u0430\u043c\u043e\u0442\u043d\u043e\u0441\u0442, \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0438\u0442\u0435 \u043f\u0440\u0438 \u0432\u043d\u0435\u0434\u0440\u044f\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0430\u0442\u0430 \u0433\u0440\u0430\u043c\u043e\u0442\u043d\u043e\u0441\u0442 \u0432 \u0431\u044a\u043b\u0433\u0430\u0440\u0441\u043a\u0430\u0442\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u0438 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438\u0442\u0435 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0430 \u0433\u0440\u0430\u043c\u043e\u0442\u043d\u043e\u0441\u0442 \u0434\u0430 \u0441\u0435 \u0443\u0441\u0432\u043e\u044f\u0432\u0430 \u0447\u0440\u0435\u0437 \u043c\u043e\u0434\u0443\u043b \u201e\u0411\u0430\u0437\u0438 \u043e\u0442 \u0434\u0430\u043d\u043d\u0438\u201c \u0432 \u0447\u0430\u0441\u043e\u0432\u0435\u0442\u0435 \u043f\u043e \u201e\u0418\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438\u201c.<br \/><em>Keywords:<\/em> information literacy, computer systems and technologies, databases, secondary education, methodology of teaching, electronic education<\/p>\n<p><strong>INFORMATION LITERACY \u2013 NATURE, PROBLEMS AND OPPORTUNITIES \u00a0FOR \u00a0IMPROVING \u00a0INFORMATION LITERACY THROUGH THE USE OF INFORMATION TECHNOLOGY IN SCHOOL<\/strong><\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> The article describes the nature of information literacy, the essence problems in the implementation of information literacy in the Bulgarian educational system and the opportunities to master information literacy by the module \u201cDatabases\u201d in \u201cInformation Technology\u201d classes.<\/p>\n<p>\u00a0<\/p>\n<p>Mr. Vesselin Dzivev, PhD student<br \/>Faculty of Mathematics and Informatics<br \/>Sofia University<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: left;\"><strong><span style=\"font-size: 12.16px;\"><a name=\"art03\"><\/a>\u0418\u0417\u041a\u0423\u0421\u0422\u0412\u0415\u041d\u0410 \u0418\u041c\u0423\u041d\u041d\u0410 \u0421\u0418\u0421\u0422\u0415\u041c\u0410<\/span><\/strong><a href=\"#top\"><\/a><\/p>\n<p>\u0419\u043e\u0430\u043d\u043d\u0430 \u0418\u043b\u0438\u0435\u0432\u0430, \u0421\u0435\u043b\u0438\u043d \u0428\u0435\u043c\u0441\u0438\u0435\u0432\u0430, \u0421\u0432\u0435\u0442\u043b\u0430\u043d\u0430 \u0412\u044a\u043b\u0447\u0435\u0432\u0430, \u0421\u044e\u0437\u0430\u043d \u0424\u0435\u0438\u043c\u043e\u0432\u0430<br \/>\u041f\u041c\u0413 \u201e\u0411\u0430\u0431\u0430 \u0422\u043e\u043d\u043a\u0430\u201c \u2013 \u0420\u0443\u0441\u0435<\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> \u041d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0430 \u043e\u043f\u0438\u0441\u0432\u0430 \u0441\u044a\u0449\u043d\u043e\u0441\u0442\u0442\u0430 \u0438 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435\u0442\u043e \u043d\u0430 \u0438\u0437\u043a\u0443\u0441\u0442\u0432\u0435\u043d\u0438\u0442\u0435 \u0438\u043c\u0443\u043d\u043d\u0438 \u0441\u0438\u0441\u0442\u0435\u043c\u0438 \u043a\u0430\u0442\u043e \u043a\u043b\u0430\u0441 \u043e\u0442 \u0438\u0437\u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u043d\u0438 \u0441\u0438\u0441\u0442\u0435\u043c\u0438, \u0432\u0434\u044a\u0445\u043d\u043e\u0432\u0435\u043d\u0438 \u043e\u0442 \u043f\u0440\u0438\u043d\u0446\u0438\u043f\u0438\u0442\u0435 \u0438 \u043f\u0440\u043e\u0446\u0435\u0441\u0438\u0442\u0435 \u043d\u0430 \u0438\u043c\u0443\u043d\u043d\u0430\u0442\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u043f\u0440\u0438 \u0433\u0440\u044a\u0431\u043d\u0430\u0447\u043d\u0438\u0442\u0435 \u0436\u0438\u0432\u043e\u0442\u043d\u0438. \u0420\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430\u0442 \u0441\u0435 \u0447\u0435\u0442\u0438\u0440\u0438 \u043e\u0441\u043d\u043e\u0432\u043d\u0438 \u043c\u043e\u0434\u0435\u043b\u0430. \u0420\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0435\u043d \u0435 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u044a\u043c \u0437\u0430 \u0432\u0441\u0435\u043a\u0438 \u043e\u0442 \u0442\u044f\u0445 \u0432\u044a\u0437 \u043e\u0441\u043d\u043e\u0432\u0430 \u043d\u0430 \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u0438\u0442\u0435 \u0437\u0430 \u0438\u0437\u0443\u0447\u0430\u0432\u0430\u043d\u0435, \u0440\u0430\u0437\u043f\u043e\u0437\u043d\u0430\u0432\u0430\u043d\u0435 \u0438 \u0437\u0430\u043f\u043e\u043c\u043d\u044f\u043d\u0435 \u043d\u0430 \u0447\u0443\u0436\u0434\u0438\u0442\u0435 \u0442\u0435\u043b\u0430 \u0432 \u0434\u0430\u0434\u0435\u043d \u043e\u0440\u0433\u0430\u043d\u0438\u0437\u044a\u043c \u0441 \u0446\u0435\u043b \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430 \u0433\u0440\u0443\u043f\u0430 \u0437\u0430\u0434\u0430\u0447\u0438. \u0420\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0430\u0442\u0430 \u0435 \u043a\u043b\u0430\u0441\u0438\u0440\u0430\u043d\u0430 \u043d\u0430 \u043f\u044a\u0440\u0432\u043e \u043c\u044f\u0441\u0442\u043e \u0432 \u041d\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u043d\u0438\u044f \u043a\u0440\u044a\u0433 \u043d\u0430 \u041c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0438\u044f \u043a\u043e\u043d\u043a\u0443\u0440\u0441 MITE: \u201e\u041c\u0435\u0442\u043e\u0434\u043e\u043b\u043e\u0433\u0438\u044f \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u0432 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u0442\u043e\u201c.<br \/><em>Keywords:<\/em> algorithms, immune system, clonal selection, negative selection, dendritic cell<\/p>\n<p>\u00a0<\/p>\n<p><strong>ARTIFICIAL IMMUNE SYSTEM<\/strong><\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> This paper describes the basis and use of artificial immune systems as a class of computing systems inspired by the principles and processes of the immune system of the vertebrates. Four basic models are discussed. An algorithm is developed for each of them based on the concepts of learning, recognition and remembering foreign bodies in an organism in order to solve a specific group of tasks. <br \/>The paper is awarded First place in the National round of the International Project MITE: Methogology and Information Technologies in Education.<\/p>\n<p>\u00a0<\/p>\n<p>Ms. Joanna Ilieva, student; Ms. Selin Shemsieva, student; Ms. Svetlana Valcheva, student; Ms. Suzan Feimova, teacher<br \/>Mathematical School \u201cBaba Tonka\u201d \u2013 Ruse<\/p>\n<p>\u00a0<\/p>\n<p style=\"text-align: right;\"><strong><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/strong><\/p>\n<hr \/>\n<p style=\"text-align: left;\"><strong><span style=\"font-size: 12.16px;\"><a name=\"art04\"><\/a>\u041d\u042f\u041a\u041e\u0418 \u0418\u0414\u0415\u0418 \u0417\u0410 \u041f\u0420\u041e\u041f\u0415\u0414\u0415\u0412\u0422\u0418\u041a\u0410 \u041d\u0410 \u041f\u041e\u041d\u042f\u0422\u0418\u0415\u0422\u041e \u0424\u0423\u041d\u041a\u0426\u0418\u042f \u0412 \u041d\u0410\u0427\u0410\u041b\u041d\u0418\u0422\u0415 \u041a\u041b\u0410\u0421\u041e\u0412\u0415<\/span><\/strong><a href=\"#top\"><\/a><\/p>\n<p>\u00a0<\/p>\n<p>\u041a\u0430\u0442\u0438\u043d\u0430 \u0422\u043e\u043d\u0447\u0435\u0432\u0430, \u041c\u0430\u0440\u0433\u0430\u0440\u0438\u0442\u0430 \u0412\u044a\u0440\u0431\u0430\u043d\u043e\u0432\u0430<br \/>St. Cyril and St. Methodius University of Veliko Turnovo<\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> \u0412 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0430 \u0441\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438 \u043d\u044f\u043a\u043e\u0438 \u0438\u0434\u0435\u0438 \u0437\u0430 \u043f\u0440\u043e\u043f\u0435\u0434\u0435\u0432\u0442\u0438\u043a\u0430 \u043d\u0430 \u043f\u043e\u043d\u044f\u0442\u0438\u0435\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432 \u043d\u0430\u0447\u0430\u043b\u043d\u0438\u0442\u0435 \u043a\u043b\u0430\u0441\u043e\u0432\u0435. \u0420\u0430\u0437\u0433\u043b\u0435\u0434\u0430\u043d\u0438 \u0441\u0430 \u0430\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u0447\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438, \u043a\u043e\u0438\u0442\u043e \u0441\u0430 \u201e\u043d\u0430\u0434\u0433\u0440\u0430\u0434\u0435\u043d\u0438\u201c \u0441 \u0434\u043e\u043f\u044a\u043b\u043d\u0438\u0442\u0435\u043b\u043d\u0438 \u0432\u044a\u043f\u0440\u043e\u0441\u0438, \u0438 \u0441\u0430 \u043f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u0438 \u043f\u0440\u0438\u043c\u0435\u0440\u043d\u0438 \u0442\u0435\u0445\u043d\u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u044f. \u0426\u0435\u043b\u0442\u0430 \u0435 \u0434\u0430 \u0441\u0435 \u0441\u044a\u0437\u0434\u0430\u0434\u0430\u0442 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u0437\u0430 \u043f\u0440\u043e\u0432\u043e\u043a\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 \u043a\u044a\u043c \u0442\u044a\u0440\u0441\u0435\u043d\u0435 \u0438 \u0444\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u043c\u0435\u0436\u0434\u0443 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0438 \u0438 \u0438\u0437\u0432\u044a\u0440\u0448\u0432\u0430\u043d\u0435 \u043d\u0430 \u043e\u0431\u043e\u0431\u0449\u0430\u0432\u0430\u0449\u0438 \u0440\u0430\u0437\u0441\u044a\u0436\u0434\u0435\u043d\u0438\u044f \u043d\u0430 \u0431\u0430\u0437\u0430\u0442\u0430 \u043d\u0430 \u0443\u0447\u0435\u0431\u043d\u043e\u0442\u043e \u0441\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0432 \u043d\u0430\u0447\u0430\u043b\u043d\u0438\u0442\u0435 \u043a\u043b\u0430\u0441\u043e\u0432\u0435.<br \/><em>Keywords:<\/em>the concept of function, prop\u0430edeutics, primary school, arithmetic problems, relationships among variables, generalizations<\/p>\n<p>\u00a0<\/p>\n<p><strong>SOME IDEAS FOR PROPAEDEUTICS OF THE CONCEPT OF FUNCTION IN PRIMARY SCHOOL<\/strong><\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> The present paper considers some ideas for prop\u0430edeutics of the concept of function in primary school. Arithmetic problems are discussed, \u201cupgraded\u201d with additional questions and exemplary solutions are proposed. The aim is to create provoking possibilities for students to search and formulate relationships among variables, thus realizing generalizing reasoning on the base of the primary school curriculum.<\/p>\n<p>\u00a0<\/p>\n<p>Ms. Katina Toncheva, PhD student; Prof. Dr. Margarita Varbanova<br \/>Faculty of Mathematics and Informatics<br \/>University of Veliko Tarnovo<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: left;\"><strong><span style=\"font-size: 12.16px;\"><a name=\"art05\"><\/a>\u0427\u0415\u0422\u0418\u0420\u0418\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<\/span><\/strong><a href=\"#top\"><\/a><\/p>\n<p>\u00a0<\/p>\n<p>Ivan Derzhanski<br \/>Institute of Mathematics and Informatics \u2013 BAS<\/p>\n<p>\u00a0<\/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 \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u0430\u0442\u0430 \u043f\u0440\u0435\u0437 2016 \u0433. \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 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438\u0442\u0435 \u043d\u0430 \u0431\u044a\u043b\u0433\u0430\u0440\u0441\u043a\u0438\u0442\u0435 \u0443\u0447\u0430\u0441\u0442\u043d\u0438\u0446\u0438, \u0447\u0430\u0441\u0442 \u043e\u0442 \u0437\u0430\u0434\u0430\u0447\u0438\u0442\u0435 \u0438 \u0442\u0435\u0445\u043d\u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u044f.<br \/><em>Keywords:<\/em> linguistics, Olympiad, problem solution.<\/p>\n<p>\u00a0<\/p>\n<p><strong>FOURTEENTH INTERNATIONAL LINGUISTICS OLYMPIADS<\/strong><\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> The paper is dedicated to the International Linguistics Olympiad in 2016. What are presented are the results of the Bulgarian participants, some of the tasks and their solutions.<\/p>\n<p>\u00a0<\/p>\n<p>Dr. Ivan Derzhanski, Assoc. Prof.<br \/>Institute of Mathematics and Informati\u0441s<br \/>Bulgarian Academy of Sciences<\/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\"><\/a>\u0412\u0415\u0422\u0420\u0418\u041b\u0410 \u041e\u0422 \u041e\u041a\u0420\u042a\u0416\u041d\u041e\u0421\u0422\u0418 \u0412\u042a\u0412 \u0412\u041f\u0418\u0421\u0410\u041d\u0418 \u041c\u041d\u041e\u0413\u041e\u042a\u0413\u042a\u041b\u041d\u0418\u0426\u0418<\/strong><\/p>\n<p>\u00a0<\/p>\n<p>\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0412\u0438\u0441\u0448\u0435 \u0443\u0447\u0438\u043b\u0438\u0449\u0435 \u043f\u043e \u0437\u0430\u0441\u0442\u0440\u0430\u0445\u043e\u0432\u0430\u043d\u0435 \u0438 \u0444\u0438\u043d\u0430\u043d\u0441\u0438 \u2013 \u0421\u043e\u0444\u0438\u044f <br \/>\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432, \u0422\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438 \u043a\u043e\u043b\u0435\u0436 \u2013 \u041b\u043e\u0432\u0435\u0447<\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> \u0412 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0440\u0430\u0431\u043e\u0442\u0430 \u0435 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0430 \u0438\u043d\u0434\u0443\u043a\u0442\u0438\u0432\u043d\u0430\u0442\u0430 \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0446\u0438\u044f \u043d\u0430 \u0421\u0438\u043c\u0441\u044a\u043d\u043e\u0432\u0430 \u043f\u0440\u0430\u0432\u0430 \u0437\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u043b\u0435\u043d \u0432\u043f\u0438\u0441\u0430\u043d \u043c\u043d\u043e\u0433\u043e\u044a\u0433\u044a\u043b\u043d\u0438\u043a. \u0412 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442 \u043d\u0430 \u0442\u043e\u0432\u0430 \u0441\u0430 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438 \u0437\u0430\u0431\u0435\u043b\u0435\u0436\u0438\u0442\u0435\u043b\u043d\u0438 \u0437\u0430 \u0432\u043f\u0438\u0441\u0430\u043d\u0438\u044f \u043c\u043d\u043e\u0433\u043e\u044a\u0433\u044a\u043b\u043d\u0438\u043a \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442\u0438, \u043a\u043e\u0438\u0442\u043e \u043f\u0440\u0438\u0442\u0435\u0436\u0430\u0432\u0430\u0442 \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u043d\u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430. \u0420\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430\u043d\u0438\u0442\u0435 \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0446\u0438\u0438 \u0441\u0430 \u0438\u0437\u0432\u044a\u0440\u0448\u0435\u043d\u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u0442\u0430 \u043d\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0430\u0442\u0430 The Geometer\u2019s Sketchpad (GSP), \u0430 \u043d\u044f\u043a\u043e\u0438 \u043e\u0442 \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u043d\u0438\u0442\u0435 \u043f\u0440\u0435\u0441\u043c\u044f\u0442\u0430\u043d\u0438\u044f \u2013 \u0441 Maple.<br \/><em>Keywords:<\/em> inscribed polygon, The Geometer\u2019s Sketchpad, Maple<\/p>\n<p>\u00a0<\/p>\n<p><strong>FANS OF CIRCLES IN INSCRIBED POLYGONS<\/strong><\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> What is applied in the present paper is an inductive construction of Simson line for an arbitrary inscribed polygon. As a result notable circles for the inscribe polygon are obtained, which have interesting properties. The considered constructions are elaborated by means of the program \u201cThe Geometer\u2019s Sketchpad\u201d (GSP), while some of the analytical computations \u2013 by Maple.<\/p>\n<p>\u00a0<\/p>\n<p>Prof. Sava Grozdev, DSc.<br \/>University of Finance, Business and Entrepreneurship<\/p>\n<p>Dr. Veselin Nenkov, Assoc. Prof.<br \/>Technical College, Lovech<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: left;\"><strong><span style=\"font-size: 12.16px;\"><a name=\"art07\"><\/a>\u0411\u0415\u041b\u0415\u0416\u041a\u0410 \u0412\u042a\u0420\u0425\u0423 \u0422\u0415\u041e\u0420\u0415\u041c\u0410\u0422\u0410 \u0417\u0410 \u0421\u0422\u0415\u041f\u0415\u041d\u041d\u0418\u0422\u0415 \u0421\u0420\u0415\u0414\u041d\u0418\u0418 \u041e\u0411\u0423\u0427\u0410\u0412\u0410\u0429\u0418\u042f \u0425\u0410\u0420\u0410\u041a\u0422\u0415\u0420 \u041d\u0410 \u041e\u041b\u0418\u041c\u041f\u0418\u0410\u0414\u0418\u0422\u0415<\/span><\/strong><a href=\"#top\"><\/a><\/p>\n<p>\u00a0<\/p>\n<p>\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0412\u0438\u0441\u0448\u0435 \u0443\u0447\u0438\u043b\u0438\u0449\u0435 \u043f\u043e \u0437\u0430\u0441\u0442\u0440\u0430\u0445\u043e\u0432\u0430\u043d\u0435 \u0438 \u0444\u0438\u043d\u0430\u043d\u0441\u0438 \u2013 \u0421\u043e\u0444\u0438\u044f <br \/>\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432, \u0422\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438 \u043a\u043e\u043b\u0435\u0436 \u2013 \u041b\u043e\u0432\u0435\u0447<\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> \u041f\u043e\u0432\u043e\u0434 \u0437\u0430 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0431\u0435\u043b\u0435\u0436\u043a\u0430 \u0435 \u0437\u0430\u0434\u0430\u0447\u0430 3. \u0437\u0430 VIII \u043a\u043b\u0430\u0441 \u043e\u0442 \u043e\u0431\u043b\u0430\u0441\u0442\u043d\u0438\u044f \u043a\u0440\u044a\u0433 \u043d\u0430 \u041d\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u043d\u0430\u0442\u0430 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0430 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d \u043d\u0430 8 \u0444\u0435\u0432\u0440\u0443\u0430\u0440\u0438 2017 \u0433.<br \/><em>Keywords:<\/em> problem, solution, Olympiad, educational character<\/p>\n<p>\u00a0<\/p>\n<p><strong>A NOTE ON THE THEOREM OF THE POWER AVERAGES AND THE EDUCATIONAL CHARACTER OF THE OLYMPIADS<\/strong><\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> The present note is in connection with Problem 3 for 8th grade from the Regional round of the National Olympiad in Mathematics, held on February 8, 2017.<\/p>\n<p>\u00a0<\/p>\n<p>Prof. Sava Grozdev, DSc.<br \/>University of Finance, Business and Entrepreneurship<\/p>\n<p>\u00a0<\/p>\n<p>Dr. Veselin Nenkov, Assoc. Prof.<br \/>Technical College, Lovech<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: left;\"><strong><span style=\"font-size: 12.16px;\"><a name=\"art08\"><\/a>\u0412\u0422\u041e\u0420\u0418 \u041a\u041e\u041b\u0415\u0414\u0415\u041d \u041b\u0418\u041d\u0413\u0412\u0418\u0421\u0422\u0418\u0427\u0415\u041d \u0422\u0423\u0420\u041d\u0418\u0420<\/span><\/strong><a href=\"#top\"><\/a><\/p>\n<p>\u00a0<\/p>\n<p>\u0418\u0432\u0430\u043d \u0414\u0435\u0440\u0436\u0430\u043d\u0441\u043a\u0438, \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u0417\u043b\u0430\u0442\u0438\u043b\u043e\u0432<br \/>Institute of Mathematics and Informatics \u2013 BAS<\/p>\n<p>\u00a0<\/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 \u0437\u0430\u0434\u0430\u0447\u0438\u0442\u0435 \u0438 \u0442\u0435\u0445\u043d\u0438\u0442\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043e\u0442 \u0412\u0442\u043e\u0440\u0438\u044f \u043a\u043e\u043b\u0435\u0434\u0435\u043d \u0442\u0443\u0440\u043d\u0438\u0440 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430 \u043b\u0438\u043d\u0433\u0432\u0438\u0441\u0442\u0438\u043a\u0430, \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d \u043f\u0440\u0435\u0437 \u0434\u0435\u043a\u0435\u043c\u0432\u0440\u0438 2016 \u0433. \u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438 \u0441\u0430 \u0441\u044a\u0449\u043e \u0438 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438\u0442\u0435 \u043d\u0430 \u0443\u0447\u0430\u0441\u0442\u043d\u0438\u0446\u0438\u0442\u0435.<br \/><em>Keywords:<\/em> mathematical linguistics, problem, solution, result, ranking<\/p>\n<p>\u00a0<\/p>\n<p><strong>SECOND CHRISTMAS LINGUISTICS TOURNAMENT<\/strong><\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> The paper is dedicated to the problems and their solutions of the Linguistics Tournament that has taken place in December 2016. The results of the participants are presented too.<\/p>\n<p>\u00a0<\/p>\n<p>Dr. Ivan Derzhanski, Assoc. Prof., Mr. Veselin Zlatilov, PhD student<br \/>Institute of Mathematics and Informatics<br \/>Bulgarian Academy of Sciences<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: right;\">\u00a0<\/p>","protected":false},"excerpt":{"rendered":"<p>\u00a0CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \u00a0 EDUCATIONAL MATTERS \/ \u041d\u0410\u0423\u0427\u041d\u041e-\u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0418 \u0421\u0422\u0410\u0422\u0418\u0418NDM-Philosophy of Education in the 21st Century [NDM \u0444\u0438\u043b\u043e\u0441\u043e\u0444\u0438\u044f\u0442\u0430 \u043d\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u0442\u043e \u0432 \u0425\u0425I \u0432\u0435\u043a] \/ Marga Georgieva, Sava Grozdev \u2013 \u0441\u0442\u0440. \/ page 111 \u00a0 \u0418\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0430\u0442\u0430 \u0433\u0440\u0430\u043c\u043e\u0442\u043d\u043e\u0441\u0442 \u2013 \u0441\u044a\u0449\u043d\u043e\u0441\u0442, \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0438 \u0438 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u0437\u0430 \u043f\u043e\u0432\u0438\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0430\u0442\u0430 \u0433\u0440\u0430\u043c\u043e\u0442\u043d\u043e\u0441\u0442 \u0447\u0440\u0435\u0437 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435 \u043d\u0430 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u0432 \u0443\u0447\u0438\u043b\u0438\u0449\u0435 [Information Literacy \u2013 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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 2, \u0433\u043e\u0434\u0438\u043d\u0430 LX, 2017 - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"\u00a0CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \u00a0 EDUCATIONAL MATTERS \/ \u041d\u0410\u0423\u0427\u041d\u041e-\u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0418 \u0421\u0422\u0410\u0422\u0418\u0418NDM-Philosophy of Education in the 21st Century [NDM \u0444\u0438\u043b\u043e\u0441\u043e\u0444\u0438\u044f\u0442\u0430 \u043d\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u0442\u043e \u0432 \u0425\u0425I \u0432\u0435\u043a] \/ Marga Georgieva, Sava Grozdev \u2013 \u0441\u0442\u0440. \/ page 111 \u00a0 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