{"id":41154,"date":"2016-10-28T10:34:12","date_gmt":"2016-10-28T07:34:12","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles\/5-lix-2016\/"},"modified":"2019-06-18T21:58:29","modified_gmt":"2019-06-18T18:58:29","slug":"5-lix-2016","status":"publish","type":"post","link":"https:\/\/bel.azbuki.bg\/en\/matematics\/matharticles\/5-lix-2016\/","title":{"rendered":"Mathematics and Informatics, Number 5\/2016, Volume 59"},"content":{"rendered":"

<\/a>CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415<\/strong><\/p>\n

 <\/p>\n

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><\/p>\n

\u0411\u0430\u0437\u0438\u0442\u0435 \u0434\u0430\u043d\u043d\u0438 \u043a\u0430\u0442\u043e \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u043e \u0437\u0430 \u043f\u043e-\u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435\u043d\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043f\u043e \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 <\/a>
[Databases as Means for More Qualitative Training in Information Technologies] <\/a>
\/ \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u0414\u0437\u0438\u0432\u0435\u0432 \/ Vesselin Dzivev
\"icon\" Open the full text<\/a><\/p>\n

 <\/p>\n

\u0415xcel \u0432 \u043f\u043e\u043c\u043e\u0449 \u043f\u0440\u0438 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u043d\u044f\u043a\u043e\u0438 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u043d\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f <\/a>
[Using \u0415xcel for Solving Some Exponential Equations] <\/a>
\/ \u0414\u0438\u0430\u043d\u0430 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432\u0430, \u041f\u043b\u0430\u043c\u0435\u043d \u041f\u0435\u043d\u0435\u0432 \/ Diana Stefanova, Plamen Penev
\"icon\" Open the full text<\/a><\/p>\n

 <\/p>\n

An Improvement of the Gerretsen’s Inequality for Non-obtuse Triangles <\/a>
\/ Šefket Arslanagi\u0107
\"icon\" Open the full text<\/a><\/p>\n

 <\/p>\n

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><\/p>\n

Three Inequalities for the Altitudes of a Triangle <\/a>
\/ Šefket Arslanagi\u0107
\"icon\" Open the full text<\/a><\/p>\n

 <\/p>\n

Computer Discovered Mathematics: Orthology Centers of the Euler Triangles <\/a>
\/ Sava Grozdev, Deko Dekov
\"icon\" Open the full text<\/a><\/p>\n

 <\/p>\n

Forecasting of Time-Series for Financial Markets <\/a>
\/ Reinhard Magenreuter
\"icon\" Open the full text<\/a><\/p>\n

 <\/p>\n

Neural Networks <\/a>
\/ Reinhard Magenreuter
\"icon\" Open the full text<\/a>         <\/p>\n

 <\/p>\n

\u0410\u043a\u0430\u0434\u0435\u043c\u0438\u0447\u043d\u0430\u0442\u0430 \u043b\u0435\u043a\u0446\u0438\u044f – \u0442\u0440\u0430\u0434\u0438\u0446\u0438\u043e\u043d\u043d\u0430 \u0444\u043e\u0440\u043c\u0430 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u0432\u044a\u0432 \u0432\u0443\u0437 \u0441 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u0437\u0430 \u0438\u043d\u043e\u0432\u0430\u0446\u0438\u043e\u043d\u043d\u043e \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u043d\u0430 \u043f\u043e\u0437\u043d\u0430\u0432\u0430\u0442\u0435\u043b\u043d\u0438\u044f \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b <\/a>
[The Academic Lecture – a Traditional Form of Instruction in Higher Education with Possibilities for Innovative Development of Learning Potential] <\/a>
\/ \u0415\u043b\u0435\u043d\u0430 \u0420\u0430\u0434\u043e\u0432\u0430\u043d\u043e\u0432\u0430 \/  Elena Radovanova
\"icon\" Open the full text<\/a><\/p>\n

 <\/p>\n

CONTEST PROBLEMS \/ \u041a\u041e\u041d\u041a\u0423\u0420\u0421\u041d\u0418 \u0417\u0410\u0414\u0410\u0427\u0418<\/strong><\/p>\n

\u041a\u043e\u043d\u043a\u0443\u0440\u0441\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438  \u043d\u0430 \u0431\u0440\u043e\u044f
[Contest Problems of this Issue]<\/p>\n

\u0420\u0435\u0448\u0435\u043d\u0438\u044f \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438\u0442\u0435 \u043e\u0442 \u0431\u0440\u043e\u0439 6, 2015 
[Solutions of the Contest Problems from Issue 6, 2015]
\"icon\" Open the full text<\/a><\/p>\n

  <\/p>\n

READ IN THE LATEST ISSUES OF „AZBUKI“ JOURNALS <\/strong>
\/ \u0412 \u041d\u041e\u0412\u0418\u0422\u0415 \u0411\u0420\u041e\u0415\u0412\u0415 \u041d\u0410 \u0421\u041f\u0418\u0421\u0410\u041d\u0418\u042f\u0422\u0410 \u041d\u0410 \u0418\u0417\u0414\u0410\u0422\u0415\u041b\u0421\u0422\u0412\u041e „\u0410\u0417\u0411\u0423\u041a\u0418“ \u0427\u0415\u0422\u0415\u0422\u0415<\/strong><\/p>\n

 <\/p>\n

GUIDE FOR AUTHORS \/ \u0423\u041a\u0410\u0417\u0410\u041d\u0418\u042f \u0417\u0410 \u0410\u0412\u0422\u041e\u0420\u0418\u0422\u0415<\/strong><\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

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<\/a>\u0411\u0410\u0417\u0418\u0422\u0415 \u0414\u0410\u041d\u041d\u0418 \u041a\u0410\u0422\u041e \u0421\u0420\u0415\u0414\u0421\u0422\u0412\u041e \u0417\u0410 \u041f\u041e-\u041a\u0410\u0427\u0415\u0421\u0422\u0412\u0415\u041d\u041e \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415 \u041f\u041e \u0418\u041d\u0424\u041e\u0420\u041c\u0410\u0426\u0418\u041e\u041d\u041d\u0418 \u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0418\u0418<\/strong><\/p>\n

\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u0414\u0437\u0438\u0432\u0435\u0432
\u0421\u043e\u0444\u0438\u0439\u0441\u043a\u0438 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 „\u0421\u0432. \u041a\u043b\u0438\u043c\u0435\u043d\u0442 \u041e\u0445\u0440\u0438\u0434\u0441\u043a\u0438“<\/p>\n

\u0420\u0435\u0437\u044e\u043c\u0435. \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u043e\u043f\u0438\u0441\u0432\u0430\u0442 \u043d\u043e\u0432\u0438 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u0437\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e „\u0418\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438“ \u0441 \u043f\u0440\u0435\u043e\u0431\u043b\u0430\u0434\u0430\u0432\u0430\u0449\u043e \u0438\u0437\u0443\u0447\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0431\u0430\u0437\u0438 \u043e\u0442 \u0434\u0430\u043d\u043d\u0438. \u041f\u0440\u0438 \u043f\u0440\u0438\u043b\u0430\u0433\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0442\u043e\u0437\u0438 \u0432\u0438\u0434 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u0441\u0435 \u0430\u043a\u0446\u0435\u043d\u0442\u0438\u0440\u0430 \u0432\u044a\u0440\u0445\u0443 \u043e\u0441\u043c\u0438\u0441\u043b\u044f\u043d\u0435\u0442\u043e \u043d\u0430 \u0434\u0430\u043d\u043d\u0438\u0442\u0435, \u0442\u044f\u0445\u043d\u043e\u0442\u043e \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0432\u0430\u043d\u0435 \u0432 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u044f \u0438 \u0437\u043d\u0430\u043d\u0438\u044f. \u041e\u043f\u0438\u0441\u0430\u043d\u0438 \u0441\u0430 \u043e\u0441\u043e\u0431\u0435\u043d\u043e\u0441\u0442\u0438\u0442\u0435 \u0432 \u043c\u0435\u0442\u043e\u0434\u0438\u043a\u0430\u0442\u0430 \u043f\u0440\u0438 \u043f\u0440\u0438\u043b\u0430\u0433\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0442\u043e\u0437\u0438 \u043f\u043e\u0434\u0445\u043e\u0434 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e.
Keywords: computer systems and technologies, databases, secondary education, methodology of teaching, electronic education<\/p>\n

 <\/p>\n

DATABASES AS MEANS FOR MORE QUALITATIVE TRAINING IN INFORMATION TECHNOLOGIES<\/strong><\/p>\n

Abstract. The article describes new opportunities for training in “Information Technologies” predominantly studying databases. In applying this type of training it focuses on understanding the data, the transformation into information and knowledge. The peculiarities of the methodology are described  in applying this approach to training.<\/p>\n

Mr. Vesselin Dzivev, PhD student
Faculty of Mathematics and Informatics
Sofia University<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

<\/a>\u0415XCEL \u0412 \u041f\u041e\u041c\u041e\u0429 \u041f\u0420\u0418 \u0420\u0415\u0428\u0410\u0412\u0410\u041d\u0415 \u041d\u0410 \u041d\u042f\u041a\u041e\u0418 \u041f\u041e\u041a\u0410\u0417\u0410\u0422\u0415\u041b\u041d\u0418 \u0423\u0420\u0410\u0412\u041d\u0415\u041d\u0418\u042f<\/strong><\/p>\n

\u0414\u0438\u0430\u043d\u0430 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432\u0430, \u041f\u043b\u0430\u043c\u0435\u043d \u041f\u0435\u043d\u0435\u0432<\/p>\n

\u0420\u0435\u0437\u044e\u043c\u0435. \u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430 \u0432\u043a\u043b\u044e\u0447\u0432\u0430\u043d\u0435 \u043d\u0430 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u043d\u0430 \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0430\u043b\u043d\u0430\u0442\u0430 \u0441\u0440\u0435\u0434\u0430 \u043d\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0430\u0442\u0430 Excel \u0437\u0430 \u0440\u0430\u0437\u043d\u043e\u043e\u0431\u0440\u0430\u0437\u044f\u0432\u0430\u043d\u0435 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u043d\u044f\u043a\u043e\u0438 \u0433\u0440\u0443\u043f\u0438 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u043d\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043e\u0442 \u0443\u0447\u0435\u043d\u0438\u0446\u0438 \u0432 \u0441\u0440\u0435\u0434\u043d\u043e\u0442\u043e \u0443\u0447\u0438\u043b\u0438\u0449\u0435
Keywords: problem solving, indicative equation, number, table, macros<\/p>\n

 <\/p>\n

\u0415XCEL HELPS IN SOLVING SOME EXPONENTIAL EQUATIONS<\/strong><\/p>\n

Abstract. The paper proposes to include possibilities of the experimental environment of the program Excel in varying the problem solving of some groups exponential equations by secondary students.<\/p>\n

Dr. Diana Stefanova
Teacher in Mathematics<\/p>\n

Mr. Plamen Penev
Teacher in Informatics<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

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<\/a>AN IMPROVEMENT OF THE GERRETSEN’S INEQUALITY FOR NON-OBTUSE TRIANGLES<\/strong><\/p>\n

Šefket Arslanagi\u0107
University of Sarajevo<\/p>\n

Abstract. The inequality \"\" is proved in the paper as a generalization of the Gerretsen’s inequality \"\" for non-obtuse triangles.
Keywords:  non-obtuse triangle, inequality, g\u0435neralization<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

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<\/a>THREE INEQUALITIES FOR THE ALTITUDES OF A TRIANGLE<\/strong><\/p>\n

Šefket Arslanagi\u0107
University of Sarajevo<\/p>\n

Abstract. The following three inequalities are considered in the paper \"\", \"\" , \"\" Arrangements of inequalities are considered too.
Keywords: triangle, altitude, inequality, generalization, arrangement<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

<\/a>COMPUTER DISCOVERED MATHEMATICS: ORTHOLOGY CENTERS OF THE EULER TRIANGLES<\/strong><\/p>\n

Sava Grozdev, Deko Dekov
University of Finance, Business and Entrepreneurship<\/p>\n

Abstract. The paper studies the orthologic triangles of the Euler triangles and their orthology centers. The results are discovered by the computer program “Discoverer”.
Keywords: Euler triangles, orthologic triangles, orthology center, computer-generated mathematics, Discoverer.<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

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<\/a>FORECASTING OF TIME-SERIES FOR FINANCIAL MARKETS<\/strong><\/p>\n

Reinhard Magenreuter
University of Finance, Business and Entrepreneurship<\/p>\n

Abstract. One of the four backbones to analyze time-series in general and forecast time-series for financial markets, particularly, is the Chaos-Theory. The four backbones are: Chaos-theory, Fuzzy logic, Neural networks and Genetic algorithms. Although each method itself is a powerful analytic tool, the present paper suggests to combine them to a hybrid analytic and analysis tool, where all methods interact and result in promising outcomes.
Keywords: market, chaos, synergetics, forecasting<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

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<\/a>NEURAL NETWORKS<\/strong><\/p>\n

Reinhard Magenreuter
University of Finance, Business and Entrepreneurship               <\/p>\n

Abstract. There are four backbones to analyze time-series in general and forecast time-series for financial markets: Chaos-theory, Fuzzy logic, Neural networks and Genetic algorithms. The first one is considered in (Magenreuter, 2016), while the present paper is dedicated to the third backbone including an example with promising outcomes in financial markts.
Keywords: perceptron, sigmoid, neural network, financial market, time-series, forecasting<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

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<\/a>\u0410\u041a\u0410\u0414\u0415\u041c\u0418\u0427\u041d\u0410\u0422\u0410 \u041b\u0415\u041a\u0426\u0418\u042f – \u0422\u0420\u0410\u0414\u0418\u0426\u0418\u041e\u041d\u041d\u0410 \u0424\u041e\u0420\u041c\u0410 \u041d\u0410 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415 \u0412\u042a\u0412 \u0412\u0423\u0417 \u0421 \u0412\u042a\u0417\u041c\u041e\u0416\u041d\u041e\u0421\u0422\u0418 \u0417\u0410 \u0418\u041d\u041e\u0412\u0410\u0426\u0418\u041e\u041d\u041d\u041e \u0420\u0410\u0417\u0412\u0418\u0422\u0418\u0415 \u041d\u0410 \u041f\u041e\u0417\u041d\u0410\u0412\u0410\u0422\u0415\u041b\u041d\u0418\u042f \u041f\u041e\u0422\u0415\u041d\u0426\u0418\u0410\u041b<\/strong><\/p>\n

\u0415\u043b\u0435\u043d\u0430 \u0420\u0430\u0434\u043e\u0432\u0430\u043d\u043e\u0432\u0430
\u0422\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 – \u0421\u043e\u0444\u0438\u044f<\/p>\n

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Keywords: education, lecture, learning, innovation system<\/p>\n

 <\/p>\n

THE ACADEMIC LECTURE – A TRADITIONAL FORM OF INSTRUCTION IN HIGHER EDUCATION WITH POSSIBILITIES FOR INNOVATIVE DEVELOPMENT OF LEARNING POTENTIAL<\/strong><\/p>\n

Abstract. The article structures and systematizes knowledge rationally, which adaptively correlates the managing and self-managing activity of learners. The contemporary requirements for intensification today impose developing learning potential to the highest degree. In line with these requirements, there is a need to offer possibilities for developing the lecture as a basic form of instruction within the University.<\/p>\n

Ms. Elena Radovanova, Assist. Prof.
Faculty of Mathematics and Informatics
Technical University<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>","protected":false},"excerpt":{"rendered":"

CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415   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 \u0411\u0430\u0437\u0438\u0442\u0435 \u0434\u0430\u043d\u043d\u0438 \u043a\u0430\u0442\u043e \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u043e \u0437\u0430 \u043f\u043e-\u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435\u043d\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043f\u043e \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 [Databases as Means for More Qualitative Training in Information Technologies] \/ \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u0414\u0437\u0438\u0432\u0435\u0432 \/ Vesselin Dzivev \u041e\u0442\u0432\u043e\u0440\u0438 \u043f\u044a\u043b\u043d\u0438\u044f \u0442\u0435\u043a\u0441\u0442   \u0415xcel \u0432 \u043f\u043e\u043c\u043e\u0449 \u043f\u0440\u0438 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u043d\u044f\u043a\u043e\u0438 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u043d\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f [Using \u0415xcel for Solving Some Exponential Equations] \/ \u0414\u0438\u0430\u043d\u0430 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432\u0430, […]<\/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":"\n"\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430", \u043a\u043d\u0438\u0436\u043a\u0430 5, \u0433\u043e\u0434\u0438\u043d\u0430 LIX, 2016 - \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:\/\/vocedu.azbuki.bg\/matematics\/matharticles\/5-lix-2016\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\""\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430", \u043a\u043d\u0438\u0436\u043a\u0430 5, \u0433\u043e\u0434\u0438\u043d\u0430 LIX, 2016 - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415   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 \u0411\u0430\u0437\u0438\u0442\u0435 \u0434\u0430\u043d\u043d\u0438 \u043a\u0430\u0442\u043e \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u043e \u0437\u0430 \u043f\u043e-\u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435\u043d\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043f\u043e \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 [Databases as Means for More Qualitative Training in Information Technologies] \/ \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u0414\u0437\u0438\u0432\u0435\u0432 \/ Vesselin Dzivev \u041e\u0442\u0432\u043e\u0440\u0438 \u043f\u044a\u043b\u043d\u0438\u044f \u0442\u0435\u043a\u0441\u0442   \u0415xcel \u0432 \u043f\u043e\u043c\u043e\u0449 \u043f\u0440\u0438 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u043d\u044f\u043a\u043e\u0438 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u043d\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f [Using \u0415xcel for Solving Some Exponential Equations] \/ \u0414\u0438\u0430\u043d\u0430 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432\u0430, […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/vocedu.azbuki.bg\/matematics\/matharticles\/5-lix-2016\/\" \/>\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=\"2016-10-28T07:34:12+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2019-06-18T18:58:29+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/matematics\/matharticles\/5-lix-2016\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/matematics\/matharticles\/5-lix-2016\/\"},\"author\":{\"name\":\"\",\"@id\":\"\"},\"headline\":\"„\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430“, \u043a\u043d\u0438\u0436\u043a\u0430 5, \u0433\u043e\u0434\u0438\u043d\u0430 LIX, 2016\",\"datePublished\":\"2016-10-28T07:34:12+00:00\",\"dateModified\":\"2019-06-18T18:58:29+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/matematics\/matharticles\/5-lix-2016\/\"},\"wordCount\":1003,\"publisher\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#organization\"},\"articleSection\":[\"\u0421\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435 \u043d\u0430 \u0441\u043f. \\\"\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\\\"\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/matematics\/matharticles\/5-lix-2016\/\",\"url\":\"https:\/\/vocedu.azbuki.bg\/matematics\/matharticles\/5-lix-2016\/\",\"name\":\"\\\"\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\\\", \u043a\u043d\u0438\u0436\u043a\u0430 5, \u0433\u043e\u0434\u0438\u043d\u0430 LIX, 2016 - 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