{"id":42029,"date":"2017-08-31T14:25:07","date_gmt":"2017-08-31T11:25:07","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles2016-2\/4-lxx-2017\/"},"modified":"2019-06-24T17:33:14","modified_gmt":"2019-06-24T14:33:14","slug":"4-lxx-2017","status":"publish","type":"post","link":"https:\/\/press.azbuki.bg\/en\/matematics\/matharticles2016-2\/4-lxx-2017\/","title":{"rendered":"Mathematics and Informatics, Number 4\/2017, Volume 60"},"content":{"rendered":"<p><strong><a name=\"top\"><\/a>CONTENTS \/ \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\">\u0417\u0430 \u0434\u043d\u0435\u0432\u043d\u0438\u044f \u0440\u0435\u0434 \u0432 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u0442\u043e <\/a><br \/><a href=\"#art01\">[For the Agenda in the Education]<\/a> <br \/>\/ \u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432 \/ Sava Grozdev &#8211; \u0441\u0442\u0440.\u00a0<span>335\u00a0<br \/><a href=\"https:\/\/press.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><br \/><\/span><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art02\">\u0413\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 \u043d\u0430 \u0442\u0435\u0441\u0442\u043e\u0432\u0435 <\/a><br \/><a href=\"#art02\">[Test Generator] <\/a><br \/>\/ \u0410\u043d\u0433\u0435\u043b \u0410\u043d\u0433\u0435\u043b\u043e\u0432, \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u0414\u0437\u0438\u0432\u0435\u0432 \/ Angel Angelov, Vesselin Dzivev &#8211; \u0441\u0442\u0440.\u00a0<span>344\u00a0<br \/><a href=\"https:\/\/press.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><br \/><\/span><\/p>\n<p>\u00a0<\/p>\n<p><strong>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<\/strong><br \/><a href=\"#art03\">\u041b\u043e\u0433\u0430\u0440\u0438\u0442\u043c\u0438\u0447\u043d\u0438 \u0438 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u0440\u0430\u043d\u0441\u0446\u0435\u043d\u0434\u0435\u043d\u0442\u043d\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f (II \u0447\u0430\u0441\u0442) <\/a><br \/><a href=\"#art03\">[Logarithmic and Trigonometric Functions in Transcendental Equations (part II)] <\/a><br \/>\/ \u0414\u0438\u0430\u043d\u0430 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432\u0430 \/ Diana Stefanova &#8211; \u0441\u0442\u0440.\u00a0<span>351\u00a0<br \/><a href=\"https:\/\/press.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><br \/><\/span><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art04\">\u041f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u043d\u0430 \u0432\u0440\u044a\u0437\u043a\u0430\u0442\u0430 \u043c\u0435\u0436\u0434\u0443 \u0441\u0440\u0435\u0434\u043d\u043e \u0430\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u0447\u043d\u043e \u0438 \u0441\u0440\u0435\u0434\u043d\u043e \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e \u0437\u0430 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u043d\u043e \u0434\u043e\u043a\u0430\u0437\u0432\u0430\u043d\u0435 \u043d\u0430 \u043d\u044f\u043a\u043e\u0438 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 <\/a><br \/><a href=\"#art04\">[An Application of the Relation Between Arithmetic Mean and Geometric Mean for Rational Proving Some Inequalities] <\/a><br \/>\/ \u0420\u0430\u0434\u0430\u043d \u041c\u0438\u0440\u044f\u043d\u043e\u0432, \u0419\u043e\u0440\u0434\u0430\u043d \u041f\u0435\u0442\u043a\u043e\u0432 \/ Radan Miryanov, Jordan Petkov &#8211; \u0441\u0442\u0440.\u00a0<span>363\u00a0<br \/><a href=\"https:\/\/press.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><br \/><\/span><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art05\">\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u043d\u0435 \u0431\u0440\u043e\u044f \u043d\u0430 \u043a\u043e\u0440\u0435\u043d\u0438\u0442\u0435 \u043d\u0430 \u0435\u0434\u0438\u043d \u043a\u043b\u0430\u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u0430\u043b\u0433\u0435\u0431\u0440\u0438\u0447\u043d\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043e\u0442 \u0442\u0440\u0435\u0442\u0430 \u0441\u0442\u0435\u043f\u0435\u043d <\/a><br \/><a href=\"#art05\">[Determining the Number of the Roots of a Class of Third Order Parametric Algebraic Equations ] <\/a><br \/>\/ \u0420\u043e\u0441\u0435\u043d \u041d\u0438\u043a\u043e\u043b\u0430\u0435\u0432, \u0422\u0430\u043d\u043a\u0430 \u041c\u0438\u043b\u043a\u043e\u0432\u0430 \/ Rosen Nikolaev, Tanka Milkova &#8211; \u0441\u0442\u0440.\u00a0<span>370\u00a0<br \/><a href=\"https:\/\/press.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><br \/><\/span><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art06\">Interesting Proofs of Some Algebraic Inequalities <\/a><br \/><a href=\"#art06\">\/ \u0160efket Arslanagi\u0107, Faruk Zejnulahi<\/a> &#8211; \u0441\u0442\u0440.\u00a0<span>377<br \/><a href=\"https:\/\/press.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><br \/><\/span><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art07\">Problems on the Brocard Circle <\/a><br \/><a href=\"#art07\">\/ Sava Grozdev, Hiroshi Okumura, Deko Dekov<\/a> &#8211; \u0441\u0442\u0440.\u00a0<span>382\u00a0<br \/><a href=\"https:\/\/press.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><br \/><\/span><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art08\">\u041d\u044f\u043a\u043e\u043b\u043a\u043e \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0446\u0438\u0438, \u043f\u043e\u0440\u043e\u0434\u0435\u043d\u0438 \u043e\u0442 \u043f\u0440\u0438\u043d\u0446\u0438\u043f\u0430 \u0437\u0430 \u0434\u0443\u0430\u043b\u043d\u043e\u0441\u0442 <\/a><br \/><a href=\"#art08\">[Some Constructions, Generated by the Duality Principle] <\/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 &#8211; \u0441\u0442\u0440.\u00a0<span>391\u00a0<br \/><a href=\"https:\/\/press.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><br \/><\/span><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art09\">\u041f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u043d\u0430 \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u0442\u0430 \u0430\u043b\u0433\u0435\u0431\u0440\u0430 \u0432 \u0438\u043a\u043e\u043d\u043e\u043c\u0438\u043a\u0430\u0442\u0430 <\/a><br \/><a href=\"#art09\">[Application of Linear Algebra in Economics] <\/a><br \/>\/ \u0412\u0435\u043b\u0438\u043a\u0430 \u041a\u0443\u043d\u0435\u0432\u0430, \u0417\u0430\u0445\u0430\u0440\u0438\u043d\u043a\u0430 \u0410\u043d\u0433\u0435\u043b\u043e\u0432\u0430 \/ Velika Kuneva, Zaharinka Angelova &#8211; \u0441\u0442\u0440.\u00a0<span>401\u00a0<br \/><a href=\"https:\/\/press.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><br \/><\/span><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art10\">\u0421\u043a\u043e\u0440\u043e\u0441\u0442\u0442\u0430 \u043d\u0430 \u0441\u0432\u0435\u0442\u043b\u0438\u043d\u0430\u0442\u0430 <\/a><br \/><a href=\"#art10\">[The Speed of Light] <\/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 &#8211; \u0441\u0442\u0440.\u00a0<span>410\u00a0<br \/><a href=\"https:\/\/press.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><br \/><\/span><\/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] &#8211; \u0441\u0442\u0440.\u00a0<span>420\u00a0<br \/><a href=\"https:\/\/press.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><br \/><\/span><\/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 5, 2016 <br \/>[Solutions of the Contest Problems from Issue 5, 2016] &#8211; \u0441\u0442\u0440.\u00a0<span>422\u00a0<br \/><a href=\"https:\/\/press.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><br \/><\/span><\/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 &#8211; <\/strong>\u0441\u0442\u0440.\u00a0426\u00a0<\/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>&#8211;\u00a0428\u00a0<\/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>\n<p><strong><a name=\"art01\"><\/a>\u0417\u0410 \u0414\u041d\u0415\u0412\u041d\u0418\u042f \u0420\u0415\u0414 \u0412 \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u041d\u0418\u0415\u0422\u041e<\/strong><\/p>\n<p style=\"text-align: right;\">\u00a0<\/p>\n<p>\u00a0<\/p>\n<p>Sava Grozdev<br \/>University of Finance, Business and Entrepreneurship<\/p>\n<p style=\"text-align: right;\">\u00a0<\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u0430\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u0430 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e\u0441\u0442\u0442\u0430 \u043e\u0442 \u0441\u044a\u0437\u0434\u0430\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u043d\u0430\u0443\u0447\u043d\u043e-\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u0430 \u0438\u043d\u0441\u0442\u0438\u0442\u0443\u0442\u0446\u0438\u044f, \u043a\u043e\u044f\u0442\u043e \u0434\u0430 \u0441\u0432\u044a\u0440\u0437\u0432\u0430 \u0443\u0442\u0432\u044a\u0440\u0434\u0435\u043d\u0438 \u043c\u0435\u0442\u043e\u0434\u0438\u043a\u0438 \u0438 \u0434\u0430 \u0441\u044a\u0437\u0434\u0430\u0432\u0430 \u043d\u043e\u0432\u0438 \u0432\u044a\u0432 \u0432\u0440\u044a\u0437\u043a\u0430 \u0441 \u0440\u0435\u0430\u043b\u043d\u0438\u0442\u0435 \u0438\u0437\u0438\u0441\u043a\u0432\u0430\u043d\u0438\u044f \u043d\u0430 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u043e\u0442\u043e \u043e\u0431\u0449\u0435\u0441\u0442\u0432\u043e.<br \/><em>Keywords:<\/em> information society; education; requirements; scientific-educational institution<\/p>\n<p>\u00a0<\/p>\n<p><strong>FOR THE AGENDA IN THE EDUCATION<\/strong><\/p>\n<p><strong>Abstract<\/strong>. The paper analyzes the necessity of a scientific-educational institution to connect approved methodologies and to create new ones in relation with the real requirements of the information society.<\/p>\n<p>\u00a0<\/p>\n<p>Prof. Sava Grozdev, DSc.<br \/>University of Finance, Business and Entrepreneurship<br \/>1, Gusla Str.<br \/>1618 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=\"art02\"><\/a>\u0413\u0415\u041d\u0415\u0420\u0410\u0422\u041e\u0420 \u041d\u0410 \u0422\u0415\u0421\u0422\u041e\u0412\u0415<\/strong><\/p>\n<p>\u0410\u043d\u0433\u0435\u043b \u0410\u043d\u0433\u0435\u043b\u043e\u0432, \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 \u043f\u0440\u043e\u0442\u043e\u0442\u0438\u043f \u043d\u0430 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0430, \u0441 \u043f\u043e\u043c\u043e\u0449\u0442\u0430 \u043d\u0430 \u043a\u043e\u044f\u0442\u043e \u0441\u0435 \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0430\u0442 \u0442\u0435\u0441\u0442\u043e\u0432\u0438 \u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b\u0438 \u043d\u0430 \u0445\u0430\u0440\u0442\u0438\u0435\u043d \u043d\u043e\u0441\u0438\u0442\u0435\u043b, \u043f\u0440\u0435\u0434\u043d\u0430\u0437\u043d\u0430\u0447\u0435\u043d\u0438 \u0437\u0430 \u0434\u0438\u0430\u0433\u043do\u0441\u0442\u0438\u0446\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0437\u043d\u0430\u043d\u0438\u044f\u0442\u0430, \u0443\u043c\u0435\u043d\u0438\u044f\u0442\u0430 \u0438 \u043a\u043e\u043c\u043f\u0435\u0442\u0435\u043d\u0446\u0438\u0438\u0442\u0435 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 <br \/>(\u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430 \u0438\u043b\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 \u043a\u043b\u0430\u0441\u043d\u043e-\u0443\u0440\u043e\u0447\u043d\u0430 \u0444\u043e\u0440\u043c\u0430 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435. \u0421 \u043f\u043e\u043c\u043e\u0449\u0442\u0430 \u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0430\u0442\u0430 \u0443\u0447\u0438\u0442\u0435\u043b\u044f\u0442 \u043c\u043e\u0436\u0435 \u0434\u0430 \u043f\u043e\u0434\u0433\u043e\u0442\u0432\u0438 \u0438 \u0440\u0430\u0437\u043f\u0435\u0447\u0430\u0442\u0430 (\u043d\u0430 \u0445\u0430\u0440\u0442\u0438\u044f, \u0432 \u0440\u0430\u043c\u043a\u0438\u0442\u0435 \u043d\u0430 \u0435\u0434\u043d\u043e \u043c\u0435\u0436\u0434\u0443\u0447\u0430\u0441\u0438\u0435) \u0442\u0435\u0441\u0442\u043e\u0432\u0438 \u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b\u0438, \u043a\u043e\u0438\u0442\u043e, \u043e\u0442 \u0433\u043b\u0435\u0434\u043d\u0430 \u0442\u043e\u0447\u043a\u0430 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435, \u0441\u0430 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u0438, \u043d\u043e \u0441\u0430 \u0441 \u0435\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u0430 \u0434\u043e\u0446\u0438\u043c\u043e\u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0430 \u0441\u0442\u043e\u0439\u043d\u043e\u0441\u0442. \u0413\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u044a\u0442 \u043d\u0430 \u0442\u0435\u0441\u0442\u043e\u0432\u0435 \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u0430 \u0441\u043b\u0435\u0434\u043d\u0438\u0442\u0435 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0438.<br \/>1. \u0411\u0430\u0437\u0430 \u043e\u0442 \u0434\u0430\u043d\u043d\u0438 \u0441 \u0442\u0435\u0441\u0442\u043e\u0432\u0438 \u0437\u0430\u0434\u0430\u0447\u0438.<br \/>2. \u041c\u043e\u0434\u0443\u043b, \u0441 \u043f\u043e\u043c\u043e\u0449\u0442\u0430 \u043d\u0430 \u043a\u043e\u0439\u0442\u043e:<br \/>2.1. \u0443\u0447\u0438\u0442\u0435\u043b\u044f\u0442 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f \u043a\u043b\u0430\u0441\u0430, \u0443\u0447\u0435\u0431\u043d\u0438\u044f \u043f\u0440\u0435\u0434\u043c\u0435\u0442, \u0442\u0435\u043c\u0430\u0442\u0430\/\u0442\u0435\u043c\u0438\u0442\u0435 \u043e\u0442 \u0443\u0447\u0435\u0431\u043d\u0430\u0442\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0430 \u0438 \u0441\u044a\u043e\u0442\u0432\u0435\u0442\u043d\u0438\u0442\u0435 \u0437\u0430\u0434\u0430\u0447\u0438, \u043f\u043e \u043a\u043e\u0438\u0442\u043e \u0449\u0435 \u0441\u0435 \u043f\u0440\u043e\u0432\u0435\u0436\u0434\u0430 \u0442\u0435\u0441\u0442\u043e\u0432\u043e\u0442\u043e \u0438\u0437\u043f\u0438\u0442\u0432\u0430\u043d\u0435; \u0437\u0430\u0434\u0430\u0432\u0430 \u0438 \u0431\u0440\u043e\u044f \u043d\u0430 \u0442\u0435\u0441\u0442\u043e\u0432\u0438\u0442\u0435 \u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b\u0438;<br \/>2.2. \u0441\u0438\u0441\u0442\u0435\u043c\u0430\u0442\u0430 \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0437\u0438\u0440\u0430\u043d\u043e \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0430 \u0438 \u0440\u0430\u0437\u043f\u0435\u0447\u0430\u0442\u0432\u0430 \u0442\u0435\u0441\u0442\u043e\u0432\u0438 \u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b\u0438 \u0441\u044a\u0441 \u0437\u0430\u0434\u0430\u0434\u0435\u043d\u0438\u0442\u0435 \u043e\u0442 \u0443\u0447\u0438\u0442\u0435\u043b\u044f \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438.<br \/>3. \u041c\u043e\u0434\u0443\u043b \u0437\u0430 \u0430\u043a\u0442\u0443\u0430\u043b\u0438\u0437\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0431\u0430\u0437\u0430\u0442\u0430 \u0434\u0430\u043d\u043d\u0438 \u0441 \u0442\u0435\u0441\u0442\u043e\u0432\u0438 \u0437\u0430\u0434\u0430\u0447\u0438.<br \/>Keywords: test generator; test examination; databases; secondary education; methodology of teaching; electronic education<\/p>\n<p>\u00a0<\/p>\n<p><strong>TEST GENERATOR<\/strong><\/p>\n<p><strong>Abstract.<\/strong> The article describes a prototype of a computer system for preparation of paper-delivered test materials for evaluation of knowledge, skills and competence of students in classroom curriculum-based education. By using the system the teacher can quickly prepare and print multiple test sheets which are different from the students\u2019 viewpoint but assess one and the same knowledge or skill. The test generator integrates the following components:<br \/>1. Database with test problems.<br \/>2. Software module for printing in which:<br \/>\u2013 The teacher enters the amount of test materials;<br \/>\u2013 The teacher enters the subject, type, complexity and other parameters of the test problems;<br \/>\u2013 The system automatically generates and prints the test materials with the defined criteria.<br \/>3. Software module for database management.<\/p>\n<p>Dr. Angel Angelov, Assoc. Prof.; Mr. Vesselin Dzivev, PhD student<br \/>Faculty of Mathematics and Informatics<br \/>Sofia University <br \/>5, James Bourchier Blvd.<br \/>1164 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=\"art03\"><\/a>\u041b\u041e\u0413\u0410\u0420\u0418\u0422\u041c\u0418\u0427\u041d\u0418 \u0418 \u0422\u0420\u0418\u0413\u041e\u041d\u041e\u041c\u0415\u0422\u0420\u0418\u0427\u041d\u0418 \u0424\u0423\u041d\u041a\u0426\u0418\u0418\u00a0\u0412 \u0422\u0420\u0410\u041d\u0421\u0426\u0415\u041d\u0414\u0415\u041d\u0422\u041d\u0418 \u0423\u0420\u0410\u0412\u041d\u0415\u041d\u0418\u042f (II \u0427\u0410\u0421\u0422)<\/strong><\/p>\n<p>Diana Stefanova<\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> \u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u043f\u0440\u043e\u0434\u044a\u043b\u0436\u0435\u043d\u0438\u0435 \u043d\u0430 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u043e\u0442 \u0441\u044a\u0449\u0438\u044f \u0430\u0432\u0442\u043e\u0440 \u0432 \u0431\u0440\u043e\u0439 1\/2017 \u0433. \u043d\u0430 \u0441\u043f. \u201e\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\u201c, \u043f\u043e\u0441\u0432\u0435\u0442\u0435\u043d\u0430 \u043d\u0430 \u0442\u0440\u0430\u043d\u0441\u0446\u0435\u043d\u0434\u0435\u043d\u0442\u043d\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f, \u043a\u0430\u0442\u043e \u0441\u0435\u0433\u0430 \u0432\u043c\u0435\u0441\u0442\u043e \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438 \u043e\u0442 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u043d\u0438 \u0438 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430\u0442 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438 \u043e\u0442 \u043b\u043e\u0433\u0430\u0440\u0438\u0442\u043c\u0438\u0447\u043d\u0438 \u0438 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u041f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u0438 \u0441\u0430 \u043f\u043e\u0434\u0445\u043e\u0434\u0438 \u0437\u0430 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435\u0442\u043e \u0438\u043c. <br \/><em>Keywords:<\/em> transcendental equations; logarithmic equations; trigonometric equations; problem solving<\/p>\n<p>\u00a0<\/p>\n<p><strong>LOGARITHMIC AND TRIGONOMETRIC FUNCTIONS\u00a0IN TRANSCENDENTAL EQUATIONS (PART II)<\/strong><\/p>\n<p><strong>Abstract.<\/strong> The paper is a continuation of the paper by the same author in issue 1\/2017 of \u201cMathematics and Informatics\u201d journal, dedicated to transcendental equations and combinations of logarithmic and trigonometric functions which are considered instead of combinations of exponential and trigonometric functions. Approaches for their solutions are proposed.<\/p>\n<p>\u00a0<\/p>\n<p>Ms. Diana Stefanova, PhD<br \/>Teacher in Mathematics<br \/>116, Tsar Ivan Asen II Str.<br \/>4230 Asenovgrad, 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\"><\/a>\u041f\u0420\u0418\u041b\u041e\u0416\u0415\u041d\u0418\u0415 \u041d\u0410 \u0412\u0420\u042a\u0417\u041a\u0410\u0422\u0410 \u041c\u0415\u0416\u0414\u0423 \u0421\u0420\u0415\u0414\u041d\u041e \u0410\u0420\u0418\u0422\u041c\u0415\u0422\u0418\u0427\u041d\u041e\u00a0\u0418 \u0421\u0420\u0415\u0414\u041d\u041e \u0413\u0415\u041e\u041c\u0415\u0422\u0420\u0418\u0427\u041d\u041e \u0417\u0410 \u0420\u0410\u0426\u0418\u041e\u041d\u0410\u041b\u041d\u041e \u0414\u041e\u041a\u0410\u0417\u0412\u0410\u041d\u0415 \u041d\u0410 \u041d\u042f\u041a\u041e\u0418 \u041d\u0415\u0420\u0410\u0412\u0415\u041d\u0421\u0422\u0412\u0410<\/strong><\/p>\n<p>\u0420\u0430\u0434\u0430\u043d \u041c\u0438\u0440\u044f\u043d\u043e\u0432, \u0419\u043e\u0440\u0434\u0430\u043d \u041f\u0435\u0442\u043a\u043e\u0432<br \/>University of Economics \u2013 Varna<\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442 \u0437\u0430 \u0434\u043e\u043a\u0430\u0437\u0432\u0430\u043d\u0435 \u043d\u0430 \u043d\u044f\u043a\u043e\u0438 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430, \u043a\u0430\u0442\u043e \u0441\u0435 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u0442\u043e \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u043c\u0435\u0436\u0434\u0443 \u0441\u0440\u0435\u0434\u043d\u043e \u0430\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u0447\u043d\u043e \u0438 \u0441\u0440\u0435\u0434\u043d\u043e \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e \u0437\u0430 \u043f\u043e\u0434\u0445\u043e\u0434\u044f\u0449\u043e \u043f\u043e\u0434\u0431\u0440\u0430\u043da \u0440\u0435\u0434\u0438\u0446a \u043e\u0442 \u0447\u0438\u0441\u043b\u0430. \u041f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u0438 \u0441\u0430 \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043d\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438\u0442\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u0438 \u0447\u0440\u0435\u0437 \u0430\u043b\u0442\u0435\u0440\u043d\u0430\u0442\u0438\u0432\u043d\u0438 \u043f\u043e\u0434\u0445\u043e\u0434\u0438 \u2013 \u043c\u0435\u0442\u043e\u0434 \u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u0442\u0430 \u0438\u043d\u0434\u0443\u043a\u0446\u0438\u044f \u0438\u043b\u0438 \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0435 \u043d\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043f\u0440\u0438 \u043a\u043e\u0435\u0442\u043e \u0447\u0438\u0442\u0430\u0442\u0435\u043b\u044f\u0442 \u043c\u043e\u0436\u0435 \u0434\u0430 \u0441\u0440\u0430\u0432\u043d\u0438 \u0442\u044f\u0445\u043d\u0430\u0442\u0430 \u0442\u0440\u0443\u0434\u043e\u0435\u043c\u043a\u043e\u0441\u0442 \u0438 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u043d\u043e\u0441\u0442.<br \/><em>Keywords:<\/em> inequalities; mathematical induction; arithmetic mean; geometric mean; methodology<\/p>\n<p>\u00a0<\/p>\n<p><strong>AN APPLICATION OF THE RELATION BETWEEN ARITHMETIC MEAN AND GEOMETRIC MEAN FOR RATIONAL PROVING SOME INEQUALITIES<\/strong><\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> In the present paper an idea for proving particular inequalities is revealed using the well-known relation between arithmetic mean and geometric mean. Methodologically the proposed inequalities are also solved in different ways by using alternative approaches \u2013 by mathematical induction or by exploring functions so that the level of difficulty and rationality of different solutions may be easily compared.<\/p>\n<p>\u00a0<\/p>\n<p>Dr. Radan Miryanov, Assist. Prof.; Dr. Jordan Petkov, Assist. Prof. <br \/>University of Economics \u2013 Varna<br \/>77, \u201cKniaz Boris I\u201d Blvd.<br \/>9002 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=\"art05\"><\/a>\u041e\u041f\u0420\u0415\u0414\u0415\u041b\u042f\u041d\u0415 \u0411\u0420\u041e\u042f \u041d\u0410 \u041a\u041e\u0420\u0415\u041d\u0418\u0422\u0415 \u041d\u0410 \u0415\u0414\u0418\u041d \u041a\u041b\u0410\u0421 \u041f\u0410\u0420\u0410\u041c\u0415\u0422\u0420\u0418\u0427\u041d\u0418 \u0410\u041b\u0413\u0415\u0411\u0420\u0418\u0427\u041d\u0418 \u0423\u0420\u0410\u0412\u041d\u0415\u041d\u0418\u042f \u041e\u0422 \u0422\u0420\u0415\u0422\u0410 \u0421\u0422\u0415\u041f\u0415\u041d<\/strong><\/p>\n<p>\u00a0<\/p>\n<p>Rosen Nikolaev, Tanka Milkova<br \/>University of Economics \u2013 Varna<\/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 \u043c\u0435\u0442\u043e\u0434\u0438\u043a\u0430 \u0437\u0430 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u043d\u0435 \u0431\u0440\u043e\u044f \u043d\u0430 \u043a\u043e\u0440\u0435\u043d\u0438\u0442\u0435 \u043d\u0430 \u0435\u0434\u0438\u043d \u043a\u043b\u0430\u0441 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043e\u0442 \u0442\u0440\u0435\u0442\u0430 \u0441\u0442\u0435\u043f\u0435\u043d \u0441 \u0440\u0435\u0430\u043b\u0435\u043d \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u044a\u0440, \u043f\u0440\u0438 \u043a\u043e\u0438\u0442\u043e \u0435\u0434\u0438\u043d \u043e\u0442 \u043a\u043e\u0440\u0435\u043d\u0438\u0442\u0435 \u043c\u043e\u0436\u0435 \u0434\u0430 \u0441\u0435 \u043d\u0430\u043c\u0435\u0440\u0438 \u043d\u0435\u043f\u043e\u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0435\u043d\u043e. \u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d \u0435 \u0438 \u043f\u043e-\u043e\u0431\u0449 \u043f\u043e\u0434\u0445\u043e\u0434 \u0437\u0430 \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0435 \u043d\u0430 \u043a\u0443\u0431\u0438\u0447\u043d\u0438 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f, \u043a\u043e\u0439\u0442\u043e \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0438 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a\u0438 \u043d\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<br \/><em>Keywords:<\/em> parametric equation; cubic function; methodology<\/p>\n<p>\u00a0<\/p>\n<p><strong>DETERMINING THE NUMBER OF THE ROOTS OF A CLASS OF THIRD ORDER PARAMETRIC ALGEBRAIC EQUATIONS<\/strong><\/p>\n<p><strong>Abstract.<\/strong> The article is devoted to \u0430 methodology of determining the number of the roots of a class of cubic algebraic equations with real parameters in which one of the roots can be determined directly. A more general approach is presented too using derivatives and graphical representations of functions.<\/p>\n<p>\u00a0<\/p>\n<p>Dr. Rosen Nikolaev, Assoc. Prof.; Dr. Tanka Milkova, Assoc. Prof. <br \/>University of Economics \u2013 Varna<br \/>77, \u201cKniaz Boris I\u201d Blvd.<br \/>9002 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=\"art06\"><\/a>INTERESTING PROOFS OF SOME ALGEBRAIC INEQUALITIES<\/strong><\/p>\n<p>\u0160efket Arslanagi\u0107, Faruk Zejnulahi<br \/>University of Sarajevo &#8211; Bosnia and Herzegovina<\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> The paper considers interesting proofs of two algebraic inequalities.<br \/><em>Keywords:<\/em> inequality; radical; generalisation<\/p>\n<p>\u00a0<\/p>\n<p>Prof. Dr. \u0160efket Arslanagi\u0107; Mag. Faruk Zejnulahi, Assist. Prof.<br \/>Faculty of Mathematics and Natural Sciences<br \/>University of Sarajevo<br \/>Sarajevo, Bosnia and Herzegovina<\/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\"><\/a>PROBLEMS ON THE BROCARD CIRCLE<\/strong><\/p>\n<p>1)Sava Grozdev, 2)Hiroshi Okumura,3)Deko Dekov <br \/>1)University of Finance, Business and Entrepreneurship \u2013 Sofia <br \/>2), 3) Independent researcher<\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> We present problems for students about the Brocard circle. The problems are discovered by the computer program \u201cDiscoverer\u201d, created by the authors.<br \/><em>Keywords:<\/em> Brocard circle; Euclidean geometry; triangle geometry; computer discovered mathematics; \u201cDiscoverer\u201d<\/p>\n<p>\u00a0<\/p>\n<p>Prof. Sava Grozdev, DSc.<\/p>\n<p>University of Finance, Business and Entrepreneurship <br \/>1, Gusla Str.<br \/>1618 So\ufb01a, Bulgaria<\/p>\n<p>Prof. Hiroshi Okumura, PhD<br \/>Maebashi Gunma<br \/>371-0123 Japan<\/p>\n<p>Dr. Deko Dekov, Assoc. Prof.<br \/>81, Zahari Knjazheski Str.<br \/>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=\"art08\"><\/a>\u041d\u042f\u041a\u041e\u041b\u041a\u041e \u041a\u041e\u041d\u0421\u0422\u0420\u0423\u041a\u0426\u0418\u0418,\u00a0\u041f\u041e\u0420\u041e\u0414\u0415\u041d\u0418 \u041e\u0422 \u041f\u0420\u0418\u041d\u0426\u0418\u041f\u0410 \u0417\u0410 \u0414\u0423\u0410\u041b\u041d\u041e\u0421\u0422<\/strong><\/p>\n<p>\u00a0<\/p>\n<p><span style=\"font-size: 12.16px;\">1) Sava Grozdev, 2) Veselin Nenkov<\/span><\/p>\n<p>1)University of Finance, Business Entrepreneurship \u2013 Sofia, Bulgaria<br \/>2)\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 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u0435\u043d \u0430\u043d\u043e\u043d\u0441 \u0437\u0430 \u043d\u044f\u043a\u043e\u043b\u043a\u043e \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0446\u0438\u0438, \u043f\u043e\u0440\u043e\u0434\u0435\u043d\u0438 \u043e\u0442 \u043f\u0440\u0438\u043d\u0446\u0438\u043f\u0430 \u0437\u0430 \u0434\u0443\u0430\u043b\u043d\u043e\u0441\u0442 \u0438 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u0442\u0430 \u043d\u0430 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440. \u0414\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u0430\u0442\u0430 \u0449\u0435 \u0431\u044a\u0434\u0430\u0442 \u0438\u0437\u043b\u043e\u0436\u0435\u043d\u0438 \u0432 \u0441\u043b\u0435\u0434\u0432\u0430\u0449\u0430 \u043f\u0443\u0431\u043b\u0438\u043a\u0430\u0446\u0438\u044f.<br \/><em>Keywords:<\/em> triangle; centroid; Dezargues\u2019 theorem; \u0441ircum curve; Euler curve; Euler line<\/p>\n<p>\u00a0<\/p>\n<p><strong>SOME CONSTRUCTIONS, GENERATED BY THE DUALITY PRINCIPLE<\/strong><\/p>\n<p><strong>Abstract.<\/strong> The paper announces some geometric constructions, generated by the duality principle and obtained by means of a computer. The proofs will be presented in a further publication.<\/p>\n<p>Prof. Sava Grozdev, DSc.<br \/>University of Finance, Business and Entrepreneurship<br \/>1, Gusla Str.<br \/>1618 Sofia, Bulgaria<\/p>\n<p>Dr. Veselin Nenkov, Assoc. Prof.<br \/>Technical College, Lovech<br \/>31, Sajko Saev Str.<br \/>5500 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=\"art09\"><\/a>\u041f\u0420\u0418\u041b\u041e\u0416\u0415\u041d\u0418\u0415 \u041d\u0410 \u041b\u0418\u041d\u0415\u0419\u041d\u0410\u0422\u0410 \u0410\u041b\u0413\u0415\u0411\u0420\u0410 \u0412 \u0418\u041a\u041e\u041d\u041e\u041c\u0418\u041a\u0410\u0422\u0410<\/strong><\/p>\n<p>\u00a0<\/p>\n<p>\u0412\u0435\u043b\u0438\u043a\u0430 \u041a\u0443\u043d\u0435\u0432\u0430, \u0417\u0430\u0445\u0430\u0440\u0438\u043d\u043a\u0430 \u0410\u043d\u0433\u0435\u043b\u043e\u0432\u0430<br \/>Agricultural University \u2013 Plovdiv (Bulgaria)<\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> \u0412 \u0441\u0442\u0430\u0442\u0438\u044f \u0441\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438 \u043e\u0441\u043d\u043e\u0432\u043d\u0438 \u043f\u043e\u043d\u044f\u0442\u0438\u044f \u043e\u0442 \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u0442\u0430 \u0430\u043b\u0433\u0435\u0431\u0440\u0430 \u0441 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0432 \u0438\u043a\u043e\u043d\u043e\u043c\u0438\u043a\u0430\u0442\u0430. \u0426\u0435\u043b\u0442\u0430 \u0435 \u0434\u0430 \u0441\u0435 \u043f\u0440\u043e\u0432\u043e\u043a\u0438\u0440\u0430\u0442 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0438\u0442\u0435 \u0432 \u0442\u044a\u0440\u0441\u0435\u043d\u0435 \u043d\u0430 \u043f\u0440\u0438\u043b\u043e\u0436\u043d\u0438\u044f \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440 \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u043d\u0438\u0442\u0435 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u043f\u043e\u043d\u044f\u0442\u0438\u044f \u0438 \u0434\u0430 \u0431\u044a\u0434\u0430\u0442 \u0443\u043b\u0435\u0441\u043d\u0435\u043d\u0438 \u043f\u0440\u0438 \u0438\u0437\u0443\u0447\u0430\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u0438 \u043f\u0440\u0438\u043b\u043e\u0436\u043d\u0438 \u0434\u0438\u0441\u0446\u0438\u043f\u043b\u0438\u043d\u0438, \u043a\u044a\u0434\u0435\u0442\u043e \u0441\u0430 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u0438 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0437\u043d\u0430\u043d\u0438\u044f \u0438 \u0443\u043c\u0435\u043d\u0438\u044f. \u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d \u0435 \u0435\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u0440\u0435\u043d \u043f\u0440\u0438\u043c\u0435\u0440 \u043d\u0430 \u043c\u043e\u0434\u0435\u043b\u0430 \u043d\u0430 \u041b\u0435\u043e\u043d\u0442\u0438\u0435\u0432, \u043a\u043e\u0439\u0442\u043e \u0432 \u043e\u0431\u0449\u0438\u044f \u0441\u043b\u0443\u0447\u0430\u0439 \u043e\u043f\u0438\u0441\u0432\u0430 \u0432\u0440\u044a\u0437\u043a\u0438\u0442\u0435 \u043c\u0435\u0436\u0434\u0443 \u0438\u043a\u043e\u043d\u043e\u043c\u0438\u0447\u0435\u0441\u043a\u0438\u0442\u0435 \u043e\u0442\u0440\u0430\u0441\u043b\u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u0442\u0430 \u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0438 \u043b\u0438\u043d\u0435\u0439\u043d\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f.<br \/><em>Keywords:<\/em> matrix; determinant; inverse matrix; matrix equation; Leontiev model<\/p>\n<p>\u00a0<\/p>\n<p><strong>APPLICATION OF LINEAR ALGEBRA IN ECONOMICS<\/strong><\/p>\n<p><strong>Abstract.<\/strong> Basic concepts of Linear algebra are presented in the present note with application in Economics. The aim is to provoke students in searching the applied character of basic mathematical notions and facilitate them in studying various applied disciplines where certain mathematical knowledge and skills are needed. An elementary example of the Leontiev model is presented, which in the general case describes relations between economic branches by means of systems of linear algebraic equations.<\/p>\n<p>Dr. Velika Kuneva, Assoc. Prof.; Ms. Zaharinka Angelova, student<br \/>Faculty of Economic<br \/>Agricultural University <br \/>12, Mendeleev Blvd.<br \/>4000 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=\"art10\"><\/a>\u0421\u041a\u041e\u0420\u041e\u0421\u0422\u0422\u0410 \u041d\u0410 \u0421\u0412\u0415\u0422\u041b\u0418\u041d\u0410\u0422\u0410<\/strong><\/p>\n<p>1) Sava Grozdev, 2) Veselin Nenkov<br \/>1)University of Finance, Business Entrepreneurship \u2013 Sofia, Bulgaria<br \/>2)\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 \u043f\u043e\u0432\u043e\u0434 \u0433\u043e\u0434\u0438\u0448\u043d\u0438\u043d\u0430\u0442\u0430 \u043e\u0442 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u043d\u0435\u0442\u043e \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u0442\u0430 \u043d\u0430 \u0441\u0432\u0435\u0442\u043b\u0438\u043d\u0430\u0442\u0430 \u0441\u0430 \u043e\u0442\u0431\u0435\u043b\u044f\u0437\u0430\u043d\u0438 \u043d\u044f\u043a\u043e\u0438 \u0444\u0430\u043a\u0442\u0438 \u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430.<br \/><em>Keywords:<\/em> light; speed; second; meter; nanometer<\/p>\n<p>\u00a0<\/p>\n<p><strong>THE SPEED OF LIGHT<\/strong><\/p>\n<p><strong>Abstract.<\/strong> Some facts and properties are considered in the paper on occasion of the anniversary of the speed of light measurement.<\/p>\n<p>Prof. Sava Grozdev, DSc.<br \/>University of Finance, Business and Entrepreneurship<br \/>1, Gusla Str.<br \/>1618 Sofia, Bulgaria<\/p>\n<p>Dr. Veselin Nenkov, Assoc. Prof. <br \/>Technical College Lovech<br \/>31, Sajko Saev Str.<br \/>5500 Lovech, Bulgaria<\/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>\n<p style=\"text-align: right;\">\u00a0<\/p>","protected":false},"excerpt":{"rendered":"<p>CONTENTS \/ \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\u0418\u0417\u0430 \u0434\u043d\u0435\u0432\u043d\u0438\u044f \u0440\u0435\u0434 \u0432 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u0442\u043e [For the Agenda in the Education] \/ \u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432 \/ Sava Grozdev &#8211; \u0441\u0442\u0440.\u00a0335\u00a0 \u00a0 \u0413\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 \u043d\u0430 \u0442\u0435\u0441\u0442\u043e\u0432\u0435 [Test Generator] \/ \u0410\u043d\u0433\u0435\u043b \u0410\u043d\u0433\u0435\u043b\u043e\u0432, \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u0414\u0437\u0438\u0432\u0435\u0432 \/ Angel Angelov, Vesselin Dzivev &#8211; \u0441\u0442\u0440.\u00a0344\u00a0 \u00a0 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\u041b\u043e\u0433\u0430\u0440\u0438\u0442\u043c\u0438\u0447\u043d\u0438 \u0438 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 [&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":[3486],"tags":[],"yoast_head":"<!-- This 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\u0433\u043e\u0434\u0438\u043d\u0430 LX, 2017 - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"CONTENTS \/ \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\u0418\u0417\u0430 \u0434\u043d\u0435\u0432\u043d\u0438\u044f \u0440\u0435\u0434 \u0432 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u0442\u043e [For the Agenda in the Education] \/ \u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432 \/ Sava Grozdev &#8211; \u0441\u0442\u0440.\u00a0335\u00a0 \u00a0 \u0413\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 \u043d\u0430 \u0442\u0435\u0441\u0442\u043e\u0432\u0435 [Test Generator] \/ \u0410\u043d\u0433\u0435\u043b \u0410\u043d\u0433\u0435\u043b\u043e\u0432, \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u0414\u0437\u0438\u0432\u0435\u0432 \/ Angel Angelov, Vesselin Dzivev &#8211; \u0441\u0442\u0440.\u00a0344\u00a0 \u00a0 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\u041b\u043e\u0433\u0430\u0440\u0438\u0442\u043c\u0438\u0447\u043d\u0438 \u0438 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/foreignlanguages.azbuki.bg\/en\/matematics\/matharticles2016-2\/4-lxx-2017\/\" \/>\n<meta property=\"og:site_name\" content=\"\u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/Azbuki55\/\" \/>\n<meta property=\"article:published_time\" content=\"2017-08-31T11:25:07+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2019-06-24T14:33:14+00:00\" \/>\n<meta property=\"og:image\" 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