{"id":40372,"date":"2015-10-04T21:59:00","date_gmt":"2015-10-04T18:59:00","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles\/mathinfocontent052015\/"},"modified":"2019-06-24T17:33:14","modified_gmt":"2019-06-24T14:33:14","slug":"mathinfocontent052015","status":"publish","type":"post","link":"https:\/\/newspaper.azbuki.bg\/en\/matematics\/matharticles\/mathinfocontent052015\/","title":{"rendered":"Mathematics and Informatics, Number 5\/2015, Volume 58"},"content":{"rendered":"<p><strong><a name=\"top\"><br \/> <\/a>CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 <\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>EDUCATIONAL TECHNOLOGY \/ <\/strong><strong>EDUCATIONAL TECHNOLOGIES<\/strong><\/p>\n<p><a href=\"#art01\">\u041e\u0442 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u043a\u044a\u043c \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0438 \u0438\u0433\u0440\u0438 [From Mathematical to Computer Games] <\/a>\/ <br \/>\u041f\u0430\u0432\u0435\u043b \u0410\u0437\u044a\u043b\u043e\u0432 \/ Pavel Azalov &#8211; 455<\/p>\n<a href=\"https:\/\/newspaper.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a>\n<p>&nbsp;<\/p>\n<p><a href=\"#art02\">\u0427\u0435\u0442\u0438\u0440\u0438\u0447\u043b\u0435\u043d\u043d\u0430\u0442\u0430 \u0440\u0435\u043b\u0430\u0446\u0438\u044f \u201e\u041e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 \u2013 \u041f\u0440\u043e\u0446\u0435\u0434\u0443\u0440\u0438 \u2013 \u0414\u0435\u0439\u043d\u043e\u0441\u0442\u0438 \u2013 <br \/>\u0414\u0435\u0439\u0441\u0442\u0432\u0438\u044f\u201c \u0432 \u0441\u0438\u0441\u0442\u0435\u043c\u0430\u0442\u0430 \u201eO\u043f\u043f\u0440\u043e\u0434\u0435\u0439\u201c \u0438 \u043f\u0440\u0438\u043d\u043e\u0441\u044a\u0442 \u045d \u0437\u0430 \u0435\u0444\u0435\u043a\u0442\u0438\u0432\u043d\u043e \u0438\u0437\u043f\u044a\u043b\u043d\u0435\u043d\u0438\u0435 \u043d\u0430 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438\u0442\u0435 \u043f\u0440\u043e\u0446\u0435\u0441\u0438 \u0432 \u0435\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u0438\u0442\u0435 \u0434\u043e\u043a\u0443\u043c\u0435\u043d\u0442\u0438<br \/> [The Four-member Relation \u201cOperations-Procedures-Activities-Actions\u201d in the \u201cOpprodey\u201d System <br \/>And its Contribution to the Effective Execution of Information Processes in to Electronic Documents] <\/a>\/ <br \/>\u0420\u0438\u0434\u0432\u0430\u043d \u0418\u0441\u0443\u0444\u043e\u0432 \/ Ridvan Isufov &#8211; 483<\/p>\n<a href=\"https:\/\/newspaper.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a>\n<p>&nbsp;<\/p>\n<p><strong>EDUCATIONAL RESEARCH \/ <\/strong><strong>\u041d\u0410\u0423\u0427\u041d\u041e\u2013\u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0418 \u0421\u0422\u0410\u0422\u0418\u0418<\/strong><\/p>\n<p><a href=\"#art03\">\u0421\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u0438 \u0438 \u0441\u043f\u0435\u0446\u0438\u0444\u0438\u043a\u0430\u0446\u0438\u0438 \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u0442\u0430 \u043d\u0430 \u0435\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u043e\u0442\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 <br \/>[Standards and Specifications in the e-Learning Field] <\/a>\/ <br \/>\u041c\u0438\u043b\u0435\u043d \u041f\u0435\u0442\u0440\u043e\u0432, \u041a\u0430\u043c\u0435\u043b\u0438\u044f \u0419\u043e\u0442\u043e\u0432\u0441\u043a\u0430 \/ Milen Petrov, Kamelia Yotovska &#8211; 497<\/p>\n<a href=\"https:\/\/newspaper.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a>\n<p>&nbsp;<\/p>\n<p><a href=\"#art04\">Computer Discovered Mathematics: Antipedal Corner Products <\/a>\/ <br \/>Sava Grozdev, Deko Dekov &#8211; 513<\/p>\n<a href=\"https:\/\/newspaper.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a>\n<p>&nbsp;<\/p>\n<p><a href=\"#art05\">\u041f\u044a\u043b\u043d\u043e \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435 \u043d\u0430 \u0442\u0435\u043e\u0440\u0435\u043c\u0430\u0442\u0430 \u043d\u0430 \u0413\u0440\u0438\u0444\u0438\u0442\u0441 \u0441 \u043a\u043e\u043d\u0438\u0447\u043d\u0438 \u0441\u0435\u0447\u0435\u043d\u0438\u044f<br \/> [Full Genarization of The Griffits Theorem with Conics] <\/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; 520<\/p>\n<a href=\"https:\/\/newspaper.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a>\n<p>&nbsp;<\/p>\n<p><a href=\"#art06\">\u0413\u0435\u043d\u0435\u0437\u0438\u0441 \u0438 \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u043d\u0430 T\u0435\u043e\u0440\u0438\u044f\u0442\u0430 \u043d\u0430 \u0440\u0430\u0432\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0442\u043e \u0440\u0430\u0437\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 <br \/>[Genesis and Development of the Theory of Uniform Distribution]<\/a> \/ <br \/>\u0421\u0438\u043b\u0432\u0438\u044f \u0411\u0430\u0439\u0447\u0435\u0432\u0430, \u0412\u0430\u0441\u0438\u043b \u0413\u0440\u043e\u0437\u0434\u0430\u043d\u043e\u0432 \/ Sylviya Baycheva, Vassil Grozdanov -539<\/p>\n<a href=\"https:\/\/newspaper.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a>\n<p>&nbsp;<\/p>\n<p><strong>CONTEST PROBLEMS \/\u041a\u041e\u041d\u041a\u0423\u0420\u0421\u041d\u0418 \u0417\u0410\u0414\u0410\u0427\u0418<\/strong><\/p>\n<p>\u041a\u043e\u043d\u043a\u0443\u0440\u0441\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u0431\u0440\u043e\u044f [Contest Problems of the Issue] &#8211; 549<\/p>\n<a href=\"https:\/\/newspaper.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a>\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 4, 2015 <br \/>[Solutions of the Contest Problems from issue 4, 2015] &#8211; 550<\/p>\n<a href=\"https:\/\/newspaper.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a>\n<p>&nbsp;<\/p>\n<p><strong>READ IN THE LATEST ISSUES OF \u201eAZ BUKI\u201c JOURNALS \/ <br \/>\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; 553<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>GUIDE FOR AUTHORS \/ \u0423\u041a\u0410\u0417\u0410\u041d\u0418\u0415 \u0417\u0410 \u0410\u0412\u0422\u041e\u0420\u0418\u0422\u0415 &#8211; 555<\/strong><\/p>\n<hr \/>\n<p><strong><a name=\"art01\">&nbsp;<\/a><strong>\u041e\u0422 \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u0427\u0415\u0421\u041a\u0418 \u041a\u042a\u041c \u041a\u042a\u041c \u041a\u041e\u041c\u041f\u042e\u0422\u042a\u0420\u041d\u0418 \u0418\u0413\u0420\u0418<\/strong><\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Pavel Azalov<\/strong><\/p>\n<p>\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<\/p>\n<p><strong>Abstract.<\/strong> \u0415\u0434\u043d\u043e \u043e\u0442 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u044f\u0442\u0430 \u043d\u0430 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0438\u0442\u0435 \u0438\u0433\u0440\u0438 \u0435 \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u0442\u0430 \u043d\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u0442\u043e. \u0422\u043e\u0437\u0438 \u0432\u0438\u0434 \u0438\u0433\u0440\u0438 \u0441\u0435 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430 \u043a\u0430\u043a\u0442\u043e \u043f\u0440\u0438 \u0443\u0441\u0432\u043e\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u043d\u043e\u0432\u0438 \u0437\u043d\u0430\u043d\u0438\u044f, \u0442\u0430\u043a\u0430 \u0438 \u043f\u0440\u0438\u0438\u0437\u0433\u0440\u0430\u0436\u0434\u0430\u043d\u0435 \u043d\u0430 \u0443\u043c\u0435\u043d\u0438\u044f \u0437\u0430 \u0432\u0437\u0435\u043c\u0430\u043d\u0435 \u043d\u0430 \u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438 \u043e\u0431\u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0432 \u043d\u0435\u043f\u043e\u0437\u043d\u0430\u0442\u0430\u043e\u0431\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0430. \u0421\u0430\u043c\u043e\u0442\u043e \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0432\u0430\u043d\u0435 \u043d\u0430 \u043d\u0435\u0441\u043b\u043e\u0436\u043d\u0438 \u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438 \u0438\u0433\u0440\u0438 \u0435 \u0441\u044a\u0449\u043e \u0441 \u043e\u0433\u0440\u043e\u043c\u0435\u043d\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u0435\u043d \u0435\u0444\u0435\u043a\u0442. \u0422\u043e\u0432\u0430 \u0435 \u0438 \u0430\u043a\u0446\u0435\u043d\u0442\u044a\u0442 \u043d\u0430 \u0442\u0430\u0437\u0438 \u0441\u0442\u0430\u0442\u0438\u044f.\u0422\u0440\u044a\u0433\u0432\u0430\u0439\u043a\u0438 \u043e\u0442 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430 \u0437\u0430\u0434\u0430\u0447\u0430, \u043e\u043f\u0438\u0441\u0430\u043d\u0430 \u043a\u0430\u0442\u043e \u0438\u0433\u0440\u0430, \u0432 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d \u043c\u043e\u0434\u0435\u043b \u0437\u0430 \u0438\u0437\u0433\u0440\u0430\u0436\u0434\u0430\u043d\u0435 \u043d\u0430 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0438 \u0438\u0433\u0440\u0438 \u0432\u044a\u0440\u0445\u0443 \u0433\u0440\u0438\u0434.\u0418\u0437\u0433\u0440\u0430\u0434\u0435\u043d\u043e \u0435 \u044f\u0434\u0440\u043e \u043e\u0442 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u0438\u0442\u0435 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u0438 \u043a\u043b\u0430\u0441\u043e\u0432\u0435, \u0441 \u043a\u043e\u0438\u0442\u043e \u0441\u0435 \u043c\u043e\u0434\u0435\u043b\u0438\u0440\u0430\u0442 \u0441\u0440\u0435\u0434\u0430\u0442\u0430 \u0437\u0430 \u0438\u0433\u0440\u0430 (\u0433\u0440\u0438\u0434), \u0443\u0447\u0430\u0441\u0442\u043d\u0438\u0446\u0438\u0442\u0435 \u0432 \u0438\u0433\u0440\u0430\u0442\u0430 \u0438 \u0441\u0430\u043c\u0430\u0442\u0430 \u0438\u0433\u0440\u0430, \u043a\u043e\u044f\u0442\u043e \u0433\u0438 \u043e\u0431\u0435\u0434\u0438\u043d\u044f\u0432\u0430 \u0432 \u0435\u0434\u043d\u043e\u0446\u044f\u043b\u043e. \u041d\u0430 \u0431\u0430\u0437\u0430\u0442\u0430 \u043d\u0430 \u0434\u0432\u0435 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u0438 \u0438\u0433\u0440\u0438, \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u0438\u0440\u0430\u043d\u0438 \u043e\u0442 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u0438\u0442\u0435 \u043a\u043b\u0430\u0441\u043e\u0432\u0435, \u0441\u0435\u043f\u043e\u043a\u0430\u0437\u0432\u0430 \u043d\u0430\u0447\u0438\u043d\u044a\u0442, \u043f\u043e \u043a\u043e\u0439\u0442\u043e \u043c\u043e\u0433\u0430\u0442 \u0434\u0430 \u0441\u0435 \u0441\u044a\u0437\u0434\u0430\u0434\u0430\u0442 \u043d\u043e\u0432\u0438 \u0438\u0433\u0440\u0438 \u0432\u044a\u0440\u0445\u0443 \u0433\u0440\u0438\u0434.\u0412\u0441\u044f\u043a\u0430 \u0438\u0433\u0440\u0430 \u0438\u043c\u0430 \u0441\u043f\u0435\u0446\u0438\u0444\u0438\u0447\u043d\u0430 \u0438\u043d\u0438\u0446\u0438\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f \u043d\u0430 \u0433\u0440\u0438\u0434\u0430, \u043f\u0440\u0430\u0432\u0438\u043b\u0430 \u0437\u0430 \u201e\u043f\u0440\u0438\u0434\u0432\u0438\u0436\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0444\u0438\u0433\u0443\u0440\u0438\u0442\u0435\u201c, \u043a\u0440\u0438\u0442\u0435\u0440\u0438\u0439 \u0437\u0430 \u0437\u0430\u0432\u044a\u0440\u0448\u0432\u0430\u043d\u0435 \u043d\u0430 \u0438\u0433\u0440\u0430\u0442\u0430 \u0438 \u043e\u0431\u044f\u0432\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u043f\u043e\u0431\u0435\u0434\u0438\u0442\u0435\u043b\u044f.\u0412\u0441\u0435\u043a\u0438 \u0435\u0434\u0438\u043d \u043e\u0442 \u0442\u0435\u0437\u0438 \u0435\u043b\u0435\u043c\u0435\u043d\u0442\u0438 \u043d\u0430 \u0438\u0433\u0440\u0430\u0442\u0430 \u0435 \u0438\u043b\u044e\u0441\u0442\u0440\u0438\u0440\u0430\u043d \u0447\u0440\u0435\u0437 \u0444\u0443\u043d\u043a\u0446\u0438\u0438\u0442\u0435, \u0441 \u043a\u043e\u0438\u0442\u043e \u0441\u0435\u0440\u0435\u0430\u043b\u0438\u0437\u0438\u0440\u0430\u0442 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0438\u0442\u0435 \u043d\u0430 \u0434\u0432\u0435 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u0438 \u0438\u0433\u0440\u0438.\u0424\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u0430\u043d\u043e \u0435 \u0438 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e \u043e\u0442 \u0438\u0433\u0440\u0438, \u043a\u043e\u0438\u0442\u043e \u043c\u043e\u0433\u0430\u0442 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u043e \u0434\u0430 \u0441\u0435 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u044f\u0442\u043d\u0430 \u0431\u0430\u0437\u0430\u0442\u0430 \u043d\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438\u044f \u043c\u043e\u0434\u0435\u043b. \u041d\u044f\u043a\u043e\u0438 \u043e\u0442 \u0442\u0435\u0437\u0438 \u0438\u0433\u0440\u0438 \u0438\u043c\u0430\u0442 \u0438\u0437\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u0441\u043a\u0438 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440 \u0438 \u043c\u043e\u0433\u0430\u0442 \u0434\u0430 \u0431\u044a\u0434\u0430\u0442 \u0432 \u043e\u0441\u043d\u043e\u0432\u0430\u0442\u0430 \u043d\u0430 \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u043d\u0438 \u0438 \u043d\u0435\u0442\u0440\u0438\u0432\u0438\u0430\u043b\u043d\u0438 \u043f\u0440\u043e\u0435\u043a\u0442\u0438.<\/p>\n<p>Keywords: computer games, matematical games, games on grid<\/p>\n<p>&nbsp;<\/p>\n<p><strong>FROM MATHEMATICAL TO COMPUTER GAMES<\/strong><\/p>\n<p><strong>Abstract.<\/strong> Educational games are used not only for acquisition of new factualknowledge but also for developing logical thinking and decision making in mostlyuncommon virtual environment. The creation of such games has also its own educationalmerits and this aspect is the key accent of this paper.Leading from a specific mathematical problem, redefined as a game, the paper laysout a model for building a set of computer games on grid. This model is presented bydeveloping a set of program classes. They are used for designing the grid and the playersof a game.The examples considered in this paper are based on two specific games that usethe program classes described above. Each game has a specific grid initialization anda corresponding configuration of the participating players\/figures. The rules of howplayers \u201emove on the grid\u201c should also be determined in advance together with thecriteria for determining when of the end of the game is reached and who the winner is,if any.A set of sample computer games illustrates the ideas described in the text. Usingthe model in consideration as a foundation, the paper shares ideas for developing futurecomputer games on grid. Some of these games have possible research value and couldbe explored as interesting and in some cases challenging projects.<\/p>\n<p align=\"right\">&nbsp;<\/p>\n<p align=\"right\"><strong>Dr. Pavel Azalov, Assoc. Prof.<\/strong><\/p>\n<p align=\"right\">Pennsylvania State University<\/p>\n<p align=\"right\">Hazleton campus, U.S.A.<\/p>\n<hr \/>\n<p>&nbsp;<\/p>\n<p><strong><a name=\"art02\">&nbsp;<\/a><strong> \u041e\u041f\u0415\u0420\u0410\u0426\u0418\u0418 \u2013 \u041f\u0420\u041e\u0426\u0415\u0414\u0423\u0420\u0418 \u2013 \u0414\u0415\u0419\u041d\u041e\u0421\u0422\u0418 \u2013\u0414\u0415\u0419\u0421\u0422\u0412\u0418\u042f\u201c \u0412 \u0421\u0418\u0421\u0422\u0415\u041c\u0410\u0422\u0410 \u201e\u041e\u041f\u041f\u0420\u041e\u0414\u0415\u0419\u201c <br \/>\u0418 \u041f\u0420\u0418\u041d\u041e\u0421\u042a\u0422 \u040d \u0417\u0410 \u0415\u0424\u0415\u041a\u0422\u0418\u0412\u041d\u041e \u0418\u0417\u041f\u042a\u041b\u041d\u0415\u041d\u0418\u0415\u041d\u0410 \u0418\u041d\u0424\u041e\u0420\u041c\u0410\u0426\u0418\u041e\u041d\u041d\u0418\u0422\u0415 \u041f\u0420\u041e\u0426\u0415\u0421\u0418 \u0412\u0415\u041b\u0415\u041a\u0422\u0420\u041e\u041d\u041d\u0418\u0422\u0415 \u0414\u041e\u041a\u0423\u041c\u0415\u041d\u0422\u0418<\/strong><\/strong><\/p>\n<p align=\"right\">&nbsp;<\/p>\n<p align=\"right\"><strong>\u0420\u0438\u0434\u0432\u0430\u043d \u0418\u0441\u0443\u0444\u043e\u0432<\/strong><\/p>\n<p align=\"right\">Sofia University<\/p>\n<p align=\"right\">&nbsp;<\/p>\n<p><strong>Abstract.<\/strong> \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430 \u043c\u043e\u0434\u0435\u043b \u0437\u0430 \u0435\u0444\u0435\u043a\u0442\u0438\u0432\u043d\u043e \u0438\u0437\u043f\u044a\u043b\u043d\u0435\u043d\u0438\u0435 \u043d\u0430 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u043f\u0440\u043e\u0446\u0435\u0441\u0438 \u043f\u0440\u0438 \u0441\u044a\u0437\u0434\u0430\u0432\u0430\u043d\u0435\u0442\u043e \u0438 \u043e\u0431\u0440\u0430\u0431\u043e\u0442\u043a\u0430\u0442\u0430 \u043d\u0430 \u0435\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u0438 \u0434\u043e\u043a\u0443\u043c\u0435\u043d\u0442\u0438.<\/p>\n<p>Keywords: operation, procedure, activity, action, information process, electronicdocument<\/p>\n<p>&nbsp;<\/p>\n<p><strong>THE FOUR-MEMBER RELATION \u201cOPERATIONS-PROCEDURESACTIVITIES ACTIONS\u201d IN THE \u201cOPPRODEY\u201d SYSTEM ANDITS CONTRIBUTION TO THE EFFECTIVE EXECUTION <br \/>OF INFORMATION PROCESSES IN TO ELECTRONIC DOCUMENTS<\/strong><\/p>\n<p align=\"center\">&nbsp;<\/p>\n<p><strong>Abstract.<\/strong> The article presents a model for effective execution of information processes related to electronic document creation and processing.<\/p>\n<p>&nbsp;<\/p>\n<p>Keywords: operation, procedure, activity, action, information process, electronic document<\/p>\n<p align=\"right\"><strong>Dr. Ridvan Isufov, Assist. Prof.<\/strong><\/p>\n<p align=\"right\">Faculty of Mathematics and Informatics<\/p>\n<p align=\"right\">Sofia University<\/p>\n<p align=\"right\">5, James Bourchier blvd.<\/p>\n<p align=\"right\">1164 Sofia, Bulgaria<\/p>\n<hr \/>\n<p align=\"right\"><strong><strong><a name=\"art03\">&nbsp;<\/a>\u0421\u0422\u0410\u041d\u0414\u0410\u0420\u0422\u0418 \u0418 \u0421\u041f\u0415\u0426\u0418\u0424\u0418\u041a\u0410\u0426\u0418\u0418 \u0412 \u041e\u0411\u041b\u0410\u0421\u0422\u0422\u0410 \u041d\u0410 \u0415\u041b\u0415\u041a\u0422\u0420\u041e\u041d\u041d\u041e\u0422\u041e \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415<\/strong><\/strong><\/p>\n<p align=\"right\"><strong>\u041c\u0438\u043b\u0435\u043d \u041f\u0435\u0442\u0440\u043e\u0432, \u041a\u0430\u043c\u0435\u043b\u0438\u044f \u0419\u043e\u0442\u043e\u0432\u0441\u043a\u0430<\/strong><\/p>\n<p align=\"right\">Sofia University<\/p>\n<p align=\"right\">&nbsp;<\/p>\n<p><strong>Abstract.<\/strong> \u0413\u043e\u043b\u044f\u043c\u043e\u0442\u043e \u0440\u0430\u0437\u043d\u043e\u043e\u0431\u0440\u0430\u0437\u0438\u0435 \u043e\u0442 \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u0438 \u0438 \u0441\u043f\u0435\u0446\u0438\u0444\u0438\u043a\u0430\u0446\u0438\u0438, \u043a\u043e\u0438\u0442\u043e \u0441\u0435 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0432\u0430\u0442 \u043e\u0442 \u043c\u043d\u043e\u0433\u043e \u043d\u0430 \u0431\u0440\u043e\u0439 \u043e\u0440\u0433\u0430\u043d\u0438\u0437\u0430\u0446\u0438\u0438 \u0438 \u043a\u043e\u043d\u0441\u043e\u0440\u0446\u0438\u0443\u043c\u0438, \u043f\u043e\u043a\u0440\u0438\u0432\u0430\u0442 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u0438 \u0430\u0441\u043f\u0435\u043a\u0442\u0438 \u043d\u0430 \u043f\u0440\u043e\u0446\u0435\u0441\u0430 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435. \u041d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0441\u0442\u0430\u0442\u0438\u044f \u0435 \u043e\u043f\u0438\u0442 \u0437\u0430 \u0430\u043d\u0430\u043b\u0438\u0437 \u0438 \u0438\u043d\u0442\u0435\u0440\u043f\u0440\u0435\u0442\u0430\u0446\u0438\u044f \u043d\u0430 \u043b\u0438\u0442\u0435\u0440\u0430\u0442\u0443\u0440\u043d\u0438 \u0438\u0437\u0442\u043e\u0447\u043d\u0438\u0446\u0438 \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u0442\u0430 \u043d\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u0438\u0442\u0435 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u0437\u0430 \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u0438 \u0438 \u0441\u043f\u0435\u0446\u0438\u0444\u0438\u043a\u0430\u0446\u0438\u0438 \u0437\u0430 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435\u043d\u0438 \u043a\u0443\u0440\u0441\u043e\u0432\u0435 \u0437\u0430 \u0435\u043b\u0435\u043a\u0440\u043e\u043d\u043d\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435.<\/p>\n<p align=\"right\">Keywords: e-learning standards, e-learning specifications, ISO<\/p>\n<p align=\"right\">&nbsp;<\/p>\n<p align=\"center\"><strong>STANDARDS AND SPECIFICATIONS IN THE E-LEARNING FIELD<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract.<\/strong> There are a variety of standards and specifications, which have been developed by many organizations and consortia. Thus, various aspects of the learning process are covered. The article is an attempt to analyze and interpret some references in the field of the educational technology standards and specifications for quality training e-courses.<\/p>\n<p align=\"right\">&nbsp;<\/p>\n<p align=\"right\"><strong>Dr. Milen Petrov, Assoc. Prof.<\/strong><\/p>\n<p align=\"right\">Department of Software Technologies<\/p>\n<p align=\"right\">Faculty of Mathematics and Informatics<\/p>\n<p align=\"right\">Sofia University<\/p>\n<p align=\"right\">1, James Bourchier Blvd.<\/p>\n<p align=\"right\">1164 Sofia, Bulgaria<\/p>\n<p align=\"right\">&nbsp;<\/p>\n<p align=\"right\"><strong>Dr. Kamelia Yotovska, Assist. Prof.<\/strong><\/p>\n<p align=\"right\">Department of Biology Education<\/p>\n<p align=\"right\">Faculty of Biology<\/p>\n<p align=\"right\">Sofia University<\/p>\n<p align=\"right\">1164 Sofia<\/p>\n<p align=\"right\">8, Dragan Tsankov Blvd.<\/p>\n<hr \/>\n<p align=\"right\"><strong><strong><a name=\"art04\">&nbsp;<\/a>COMPUTER DISCOVERED MATHEMATICS: ANTIPEDAL CORNER PRODUCTS<\/strong><\/strong><\/p>\n<p align=\"right\">&nbsp;<\/p>\n<p align=\"right\"><strong><sup>1<\/sup>Sava Grozdev, Deko Dekov<\/strong><\/p>\n<p align=\"right\"><sup>1<\/sup>University of Finance, Business and Entrepreneurship<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract.<\/strong> By using the computer program \u201cDiscoverer\u201d, we propose theorems about antipedal corner products.<\/p>\n<p>Keywords: antipedal corner product, triangle geometry, remarkable point, computerdiscovered mathematics, Discoverer.<\/p>\n<p align=\"right\">&nbsp;<\/p>\n<p align=\"right\"><strong>Prof. Sava Grozdev, DSc<\/strong><\/p>\n<p align=\"right\">University of Finance, Business and Entrepreneurship<\/p>\n<p align=\"right\">1, Gusla Street<\/p>\n<p align=\"right\">1618 Sofia, Bulgaria<\/p>\n<p align=\"right\">&nbsp;<\/p>\n<p align=\"right\">Dr. Deko Dekov, Assoc. Prof.<\/p>\n<p align=\"right\">81, Zahari Knjazheski Street<\/p>\n<p align=\"right\">6000 Stara Zagora, Bulgaria<\/p>\n<hr \/>\n<p align=\"right\"><strong><strong><a name=\"art05\">&nbsp;<\/a>\u041f\u042a\u041b\u041d\u041e \u041e\u0411\u041e\u0411\u0429\u0415\u041d\u0418\u0415 \u041d\u0410 \u0422\u0415\u041e\u0420\u0415\u041c\u0410\u0422\u0410 \u041d\u0410 \u0413\u0420\u0418\u0424\u0418\u0422\u0421 \u0421 \u041a\u041e\u041d\u0418\u0427\u041d\u0418 \u0421\u0415\u0427\u0415\u041d\u0418\u042f<\/strong><\/strong><\/p>\n<p align=\"right\"><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<\/strong><\/p>\n<p align=\"right\"><sup>1<\/sup>VUZF University<\/p>\n<p align=\"right\"><sup>2<\/sup>\u0422\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438 \u043a\u043e\u043b\u0435\u0436 \u2013 \u041b\u043e\u0432\u0435\u0447<\/p>\n<p>\u0420\u0435\u0437\u044e\u043c\u0435. \u0412 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0441\u0442\u0430\u0442\u0438\u044f \u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u043e \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435 \u043d\u0430 \u0437\u0430\u0431\u0435\u043b\u0435\u0436\u0438\u0442\u0435\u043b\u043d\u0430\u0442\u0430 \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u043d\u0430 \u0413\u0440\u0438\u0444\u0438\u0442\u0441 \u043e\u0442 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f\u0442\u0430 \u043d\u0430 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430. \u0422\u043e\u0432\u0430 \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435 \u0441\u044a\u0434\u044a\u0440\u0436\u0430 \u0441\u043f\u0435\u0446\u0438\u0430\u043b\u043d\u043e\u0442\u043e \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435 \u043d\u0430 \u0442\u0435\u043e\u0440\u0435\u043c\u0430\u0442\u0430 \u043d\u0430 \u0413\u0440\u0438\u0444\u0438\u0442\u0441, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043e \u043e\u0442 \u0430\u0432\u0442\u043e\u0440\u0438\u0442\u0435 \u0432 (Grozdev &amp; Nenkov, 2015).<\/p>\n<p>Keywords: triangle, conic, pedal circle, pedal curve, Euler curve.<\/p>\n<p align=\"center\">&nbsp;<\/p>\n<p align=\"center\"><strong>FULL GENARIZATION OF THE GRIFFITS THEOREM WITH CONICS<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract.<\/strong> The present paper considers a generalization of the remarkable Griffits theorem from the geometry of triangle. This generalization contains the special one, obtained by the authors in (Grozdev &amp; Nenkov, 2015).<\/p>\n<p align=\"right\">&nbsp;<\/p>\n<p align=\"right\"><strong>Prof. Sava Grozdev, DSc<\/strong><\/p>\n<p align=\"right\">University of Finance, Business and Entrepreneurship<\/p>\n<p align=\"right\">1, Gusla Str.<\/p>\n<p align=\"right\">1618 Sofia, Bulgaria<\/p>\n<p align=\"right\">&nbsp;<\/p>\n<p align=\"right\">Dr. Veselin Nenkov, Assoc. Prof.<\/p>\n<p align=\"right\">Technical College Lovech<\/p>\n<p align=\"right\">31, Sajko Saev Str.<\/p>\n<p align=\"right\">Lovech, Bulgaria<\/p>\n<hr \/>\n<p align=\"right\"><strong><a name=\"art06\">&nbsp;<\/a>\u0413\u0415\u041d\u0415\u0417\u0418\u0421 \u0418 \u0420\u0410\u0417\u0412\u0418\u0422\u0418\u0415 \u041d\u0410 \u0422\u0415\u041e\u0420\u0418\u042f\u0422\u0410 \u041d\u0410 \u0420\u0410\u0412\u041d\u041e\u041c\u0415\u0420\u041d\u041e\u0422\u041e \u0420\u0410\u0417\u041f\u0420\u0415\u0414\u0415\u041b\u0415\u041d\u0418\u0415<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>\u0421\u0438\u043b\u0432\u0438\u044f \u0411\u0430\u0439\u0447\u0435\u0432\u0430, \u0412\u0430\u0441\u0438\u043b \u0413\u0440\u043e\u0437\u0434\u0430\u043d\u043e\u0432<\/strong><\/p>\n<p>South-West University \u201cNeofit Rilski\u201d<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract.<\/strong> \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0438 \u043f\u043e\u0441\u0442\u0430\u0432\u044f\u043c\u0435 \u0437\u0430 \u0446\u0435\u043b \u0434\u0430 \u043d\u0430\u043f\u0440\u0430\u0432\u0438\u043c \u043a\u0440\u0430\u0442\u044a\u043a \u0438\u0441\u0442\u043e\u0440\u0438\u0447\u0435\u0441\u043a\u0438 \u043f\u0440\u0435\u0433\u043b\u0435\u0434 \u043d\u0430 \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0435\u0442\u043e \u043d\u0430 \u0442\u0435\u043e\u0440\u0438\u044f\u0442\u0430 \u043d\u0430 \u0440\u0430\u0432\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0442\u043e \u0440\u0430\u0437\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043d\u0430 \u0440\u0435\u0434\u0438\u0446\u0438. \u0429\u0435 \u0437\u0430\u0441\u0435\u0433\u043d\u0435\u043c \u0441\u0430\u043c\u043e \u043d\u044f\u043a\u043e\u0438 \u0430\u0441\u043f\u0435\u043a\u0442\u0438 \u043d\u0430 \u0442\u0430\u0437\u0438 \u0442\u0435\u043e\u0440\u0438\u044f, \u043a\u0430\u0442\u043e \u0449\u0435 \u043f\u0440\u043e\u0441\u043b\u0435\u0434\u0438\u043c \u0438 \u0430\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u0430\u043c\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u0438 \u0437\u0430 \u0433\u0435\u043d\u0435\u0437\u0438\u0441\u0430 \u0438 \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0435\u0442\u043e \u043d\u0430 \u0441\u044a\u043e\u0442\u0432\u0435\u0442\u043d\u0438\u0442\u0435 \u043f\u043e\u043d\u044f\u0442\u0438\u044f \u0438 \u0442\u0432\u044a\u0440\u0434\u0435\u043d\u0438\u044f.<\/p>\n<p>Keywords: Uniform Distribution Theory, Uniform Distribution of Sequences, Discrepancy, Diaphony.<\/p>\n<p>&nbsp;<\/p>\n<p align=\"center\"><strong>GENESIS AND DEVELOPMENT OF THE THEORY OF UNIFORM DISTRIBUTION<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract.<\/strong> The aim of the paper is to propose a brief historical overview of the development of the theory of the uniform distribution of sequences. We will discuss only some aspects of the theory, tracing and analyzing specific examples of the genesis and the development of corresponding concepts and statements.<\/p>\n<p align=\"right\">&nbsp;<\/p>\n<p align=\"right\"><strong>Mrs. Sylviya Baycheva, PhD Student<\/strong><\/p>\n<p align=\"right\">South-West University<\/p>\n<p align=\"right\">66, Ivan Michailov Str.<\/p>\n<p align=\"right\">2700 Blagoevgrad, Bulgaria<\/p>\n<p align=\"right\">&nbsp;<\/p>\n<p align=\"right\"><strong>Dr. Vassil Grozdanov, Assoc. Prof.<\/strong><\/p>\n<p align=\"right\">South-West University<\/p>\n<p align=\"right\">66, Ivan Michailov Str.<\/p>\n<p align=\"right\">2700 Blagoevgrad, Bulgaria<\/p>\n<p align=\"right\">&nbsp;<\/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>CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 &nbsp; EDUCATIONAL TECHNOLOGY \/ \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u0422\u0415\u041b\u041d\u0418 \u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0418\u0418 \u041e\u0442 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u043a\u044a\u043c \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0438 \u0438\u0433\u0440\u0438 [From Mathematical to Computer Games] \/ \u041f\u0430\u0432\u0435\u043b \u0410\u0437\u044a\u043b\u043e\u0432 \/ Pavel Azalov &#8211; 455 &nbsp; &nbsp; \u0427\u0435\u0442\u0438\u0440\u0438\u0447\u043b\u0435\u043d\u043d\u0430\u0442\u0430 \u0440\u0435\u043b\u0430\u0446\u0438\u044f \u201e\u041e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 \u2013 \u041f\u0440\u043e\u0446\u0435\u0434\u0443\u0440\u0438 \u2013 \u0414\u0435\u0439\u043d\u043e\u0441\u0442\u0438 \u2013 \u0414\u0435\u0439\u0441\u0442\u0432\u0438\u044f\u201c \u0432 \u0441\u0438\u0441\u0442\u0435\u043c\u0430\u0442\u0430 \u201eO\u043f\u043f\u0440\u043e\u0434\u0435\u0439\u201c \u0438 \u043f\u0440\u0438\u043d\u043e\u0441\u044a\u0442 \u045d \u0437\u0430 \u0435\u0444\u0435\u043a\u0442\u0438\u0432\u043d\u043e \u0438\u0437\u043f\u044a\u043b\u043d\u0435\u043d\u0438\u0435 \u043d\u0430 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438\u0442\u0435 \u043f\u0440\u043e\u0446\u0435\u0441\u0438 \u0432 \u0435\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u0438\u0442\u0435 \u0434\u043e\u043a\u0443\u043c\u0435\u043d\u0442\u0438 [The Four-member [&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 5, \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\/en\/matematics\/matharticles\/mathinfocontent052015\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" 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455 &nbsp; &nbsp; \u0427\u0435\u0442\u0438\u0440\u0438\u0447\u043b\u0435\u043d\u043d\u0430\u0442\u0430 \u0440\u0435\u043b\u0430\u0446\u0438\u044f \u201e\u041e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 \u2013 \u041f\u0440\u043e\u0446\u0435\u0434\u0443\u0440\u0438 \u2013 \u0414\u0435\u0439\u043d\u043e\u0441\u0442\u0438 \u2013 \u0414\u0435\u0439\u0441\u0442\u0432\u0438\u044f\u201c \u0432 \u0441\u0438\u0441\u0442\u0435\u043c\u0430\u0442\u0430 \u201eO\u043f\u043f\u0440\u043e\u0434\u0435\u0439\u201c \u0438 \u043f\u0440\u0438\u043d\u043e\u0441\u044a\u0442 \u045d \u0437\u0430 \u0435\u0444\u0435\u043a\u0442\u0438\u0432\u043d\u043e \u0438\u0437\u043f\u044a\u043b\u043d\u0435\u043d\u0438\u0435 \u043d\u0430 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438\u0442\u0435 \u043f\u0440\u043e\u0446\u0435\u0441\u0438 \u0432 \u0435\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u0438\u0442\u0435 \u0434\u043e\u043a\u0443\u043c\u0435\u043d\u0442\u0438 [The Four-member 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