Application of Mathematical Methods for Constructing a Two-Factor Economic Model

Приложение на математически методи за конструиране на двуфакторен икономически модел

Author(s): Rosen Nikolaev,Tanka Milkova,Radan Miryanov / Language(s): Bulgarian / Publication Year: 0

Keywords: Mathematical Methods; Two-factor economic model

In the field of economic science and its manifestations, there is almost no creation of scientific knowledge without the participation of fundamental knowledge in mathematics. A number of branches of mathematics such as linear algebra, analytical geometry, financial mathematics, differential and integral calculus, probability theory, statistics, game theory, mass service theory, stock theory, risk theory and many others are widely used. The aim of this paper is to investigate a two-factor model by applying knowledge of differential calculus of two variables and the method of least squares.

Mathematical Methods for Unique (Unconditional) Solutions of Additive Factor Analysis of Changes of Volume Output Values (Product) with Two Factors in Economy

Математически методи за еднозначни (неусловни) решения на адитивни факторни анализи на промените на обемни резултативни величини (продукции) с два фактора в икономиката

Author(s): Emil Hristov / Language(s): Bulgarian / Publication Year: 0

Keywords: Mathematical methods; Factor analysis

The one-valued (unconditional) solutions of additive factor quantities with two factors in the economy are presented. The elementary factor dependence of the production of an individual commodity with the product of two factors was used, where is the price of the commodity (intensive factor), is its natural quantity (extensive factor). For the solution of the additive factor analysis, a simple geometric method is proposed with two rectangles, the areas of which represent the volumes and production of the commodity. The bases of the two rectangles represent the values of the extensive factor and , and the heights of the rectangles represent the values of the intensive factor from the base and reporting periods. True and accurate effects are obtained by multiplying each factor change (the difference between the factor's reporting and base value) by the lesser of the other factor's value from the base or reporting period. The smaller values are determined simply and easily with the suggested elementary but strict mathematical criteria, which are the inequalities between the reported and the base value of each factor. The single-valued solution and elementary mathematical criteria are summarized by the discrete odd function of the mathematical signum. With it, all additive factor analyzes from all areas of life are solved unequivocally.

Inverse Function and Inverse Trigonometric Functions

Обратна функция и обратни тригонометрични функции

Author(s): Sava Grozdev,Veselin Nenkov,Tatiana Madjarova / Language(s): Bulgarian / Publication Year: 0

Keywords: Inverse function; Inverse trigonometric functions

The concept of inverse function is one of the most difficult for students to understand. On the other hand, the introduction of inverse trigonometric functions further complicates the understanding of inverse functions. Therefore, here we have tried to show one way of introducing the concept of an inverse function. At the same time, special attention was paid to obtaining the inverse trigonometric functions.

Methodological Aspect of the Problem of Continuity of School and University Mathematical Education

Методологический аспект проблемы преемственности школьного и вузовского математического образования

Author(s): Maria Shabanova,Larisa Udovenko / Language(s): Russian / Publication Year: 0

Keywords: Mathematical education at the university; Тhe problem of continuity; Мethodological aspect;

The unresolved problem of continuity of school and university mathematical education is one of the reasons for the expulsion of students from the first courses of those areas of training that provide for the continuation of mathematical education. The complexity of solving this problem is related to its complex nature: the difference in the requirements for the level of mathematics of graduates of secondary schools and university students, the rupture of meaningful links between school and university mathematics courses, the change in the form of the organization of the educational process. The article highlights and reveals another aspect of this problem – the methodological one. The authors present the theoretical foundations and an example of creating methodological conditions that facilitate the student's transition from one form of educational cognition to another.

On Experimental Study of Non-Euclidean Geometries within Training Teachers

Об экспериментальном изучении неевклидовых геометрий в процессе подготовки учителей

Author(s): Alexander Yastrebov / Language(s): Russian / Publication Year: 0

Keywords: Dynamic geometry system; Experimental study; Instrument; Lobachevskian geometry; Model by Cayley–Klein

A set of computer instruments, created by the author within dynamic geometry system GeoGebra, is described. Some special methods of using these instruments are proposed. The instruments help students to create dynamic drawings within the model by Cayley–Klein for discovering some theorems of Lobachevskian geometry.

Study on the Availability of a Commercial Network of Retail Fuel Outlets in Bulgaria

Изследване на осигуреността с търговска мрежа от обекти за продажба на дребно на горива в България

Author(s): Michal Stoyanov / Language(s): Bulgarian / Publication Year: 0

Keywords: Retail trade network; Commercial outlets; Sale of fuels; Fossil fuels

The research objective of this work is to keep track of the availability of fuel retail outlets to the Bulgarian population between 2013 and 2022. In parallel, the evolution of the number of registered passenger cars in the country, which should be provided with an appropriate level of fuel retail outlets, is traced. A disproportionate change in the growth of the car fleet is noted, compared to the distribution of fuel retail outlets. The prospects for development in the direction determined by the gradual massification of electric vehicles and the deployment of the infrastructure of alternative charging stations in the country are examined.

A Practical Problem in Analytic Geometry

Една практическа задача по аналитична геометрия

Author(s): Jordan Petkov,Radan Miryanov / Language(s): Bulgarian / Publication Year: 0

Keywords: Interior point; Triangle; Analytical geometry; Computer graphics

The report presents a possible application of the knowledge provided by the fundamental mathematical discipline “Linear Algebra and Analytic Geometry” in solving an informatics problem, more precisely, a Computer Graphics problem. In addition, the given task provides a good opportunity to exercise the theoretical statements related to vectors and an equation of a line in the plane.

Advantages and Disadvantages of Beta and Sigma Convergence Analysis in the Study of Structural Convergence of Economies

Предимства и недостатъци на бета и сигма конвергентния анализ при изследване на структурната конвергенция на икономиките

Author(s): Silvia Gospodinova / Language(s): Bulgarian / Publication Year: 0

Keywords: Structural convergence; β&σ convergent analysis

Through β and σ convergence analysis, the real convergence in the economies of the European Union can be traced. For this purpose, the main criteria for convergence policies are sought and shown, as well as their results, as this is important for the efficiency and competitiveness of these economies. The task of this type of analysis is to trace the extent to which convergent policies create trends and change policies in individual countries, because sometimes countries take decisions that differ from the single policy of the European Community. When carrying out this type of analysis, it is necessary to know the advantages and disadvantages of each of the methods and indicators for analysis and to assess in the specific situation which is more reliable.

“Lost Generation” in Bulgaria – Development and Forecast

„Загубеното поколение“ в България –изменение и прогноза

Author(s): Vanya Stoyanova / Language(s): Bulgarian / Publication Year: 0

Keywords: Lost generation; NEET; Adaptive exponential smoothing

The report looks at the “lost generation” – those who are not employed and not in education – as a potential opportunity to increase the labor force. The development of this social group for the period 2018 – 2024 is under consideration. A forecast is made using an adaptive exponential smoothing model.

The Oil Price and the External Bulgaria's Trade in the Context of Fundamental Economic Research

Цената на петрола и външната търговия на България в контекста на фундаменталните икономически изследвания

Author(s): Lyubomir Lyubenov / Language(s): Bulgarian / Publication Year: 0

Keywords: Elasticity; Energy resourses; Foreign trade; Oil; Regression

The objective of this report is to assess the impact of oil price dynamics on Bulgaria's foreign trade using elasticity theory and one-factor linear regression. This involves the use of specific methods that require fundamental knowledge and research experience. Bulgaria's foreign trade was found to be inelastic in general with respect to oil prices. This was explained by the particularities of the period studied, the type of data and the method used. The study provides a good basis for a more in-depth study using the Almon model. Bulgaria's imports of energy resources and crude oil are mainly determined by the oil price. This makes it a significant factor for our economy and suggests that it is determined by factors external to the EU.

Applying Dynamic Time Warping to Analyze Shape Similarities in Time Series Data

Приложение на динамичното времево изкривяване за анализ на сходството във формата на времеви редове

Author(s): Slaveya Zhelyazkova / Language(s): Bulgarian / Publication Year: 0

Keywords: Dynamic time warping; Cluster analysis; dtwclust; Real house price indices

The paper explores the potential of dynamic time warping (DTW) to detect shape-based similarities in time series data and assesses its effectiveness for cluster analysis using the "dtwclust" package in R. Theoretical considerations are demonstrated with an empirical analysis of real house price indices for 46 countries, utilizing OECD data spanning 2010–2023. Results indicate that employing DTW significantly influences clustering outcomes, as it enables the detection of shape similarities in time series, even in cases of temporal shifts and asynchronous patterns. This may lead to the identification of fewer clusters compared to standard clustering approaches. Furthermore, the choice of distance measure—Euclidean versus Manhattan—affects the clustering structure, with validity indices suggesting that DTW using Manhattan distance achieves better-defined, more distinct clusters. Comparative analysis with conventional hierarchical clustering highlights consistencies when similar distance metrics are applied.

From Theoretical Knowledge to Practical Application: Financial Literacy in The Bulgarian School

От теоретични знания до практическо приложение: финансовата грамотност в българското училище

Author(s): Manya Maneva / Language(s): Bulgarian / Publication Year: 0

Keywords: Literacy; Numeracy; Financial literacy; PISA

Financial literacy is essential for preparing students to manage their personal finances responsibly and to develop skills that are useful throughout life. The purpose of this article is to demonstrate how financial education can be integrated into the teaching of mathematics, which is a basic science. Early financial education prepares students for the realities of working life, including paying taxes and making investments. This integration of financial education into mathematics not only increases students' financial literacy, but also strengthens their analytical skills, which are essential for successful personal finance management.

Application of the Mathematical Optimization Model in the Various Sectors of the Economy

Възможности за прилагане на модела на математическото оптимиране в различните сектори на икономиката

Author(s): Julieta MIhaylova / Language(s): Bulgarian / Publication Year: 0

Keywords: Mathematical Optimization; Economics; Economic Sectors

One of the popular definitions of economics as a science is that it studies human behaviour as a relationship between objectives and scarce resources which have alternative uses. This paper proposes that the suitable formal method for such a research is mathematical optimization. Examples from different sectors of the economy are considered. It may be concluded that mathematical optimization is fundamental to economic theory.

Creating Linear Models of Economic Processes: Modelling Fuel Consumption

Създаване на линейни модели на икономически процеси: Моделиране на разхода на гориво

Author(s): Julieta MIhaylova / Language(s): Bulgarian / Publication Year: 0

Keywords: System of Linear Equations; Аpproximation Мethod; Fuel Consumption

Mathematics is a fundamental discipline in higher education. It is essential that students are motivated and that their interest in the material is stimulated so that they can acquire the basic knowledge they need as fully as possible. In this paper, it is argued that presenting the material through practical examples that have applicable solutions would lead to increased student interest.

Methods for Assessing the Risk of an Investment Project Built on a Photovoltaic System

Методи за оценка на риска на инвестиционен проект за изгражданe на фотоволтаична система

Author(s): Imrel Nizam / Language(s): Bulgarian / Publication Year: 0

Keywords: Risk; Investment projects; Returnability

The report examines risk and the management of risk factors in investment projects, with a focus on constructing a photovoltaic system for electricity generation in Bulgaria. The assessment of investment risk is crucial due to the high uncertainty and the scale of capital investments. The project includes identifying risk factors, quantitative measurement, planning management measures, and monitoring the execution of risk-related activities. Various approaches to risk measurement are introduced, including statistical methods such as variance analysis, which allow for assessing deviations in returns and forecasting future income. The report also explains specific risks associated with photovoltaic projects, such as technological risk (equipment and system selection), risks from weather conditions and the nature of solar radiation, financial risks from fluctuations in component prices, and business risk from market fluctuations. To minimize adverse effects, strategies such as monitoring, pre-negotiation with suppliers, and planning emergency actions are suggested.

HUMAN CAPITAL: YOU CAN'T GO, YOU CAN'T STAY. MIGRATION AND MIGRATION ATTITUDES OF BELARUSIANS THROUGH THE PRISM OF SOCIOLOGY

ЧЕЛОВЕЧЕСКИЙ КАПИТАЛ: УЕХАТЬ НЕЛЬЗЯ ОСТАТЬСЯ МИГРАЦИЯ И МИГРАЦИОННЫЕ НАСТРОЕНИЯ БЕЛОРУСОВ ЧЕРЕЗ ПРИЗМУ СОЦИОЛОГИИ

Author(s): Elena Artemenko,Andrei Yeliseyeu,Vladimir Dunaev / Language(s): Belarusian

This study continues the cycle of BISS works "Human capital as a factor of competitiveness and modernization" and is based on the results of a national survey (December 2012 - January 2013), commissioned by the Belarusian Institute of Strategic Studies. Based on the data we received (it should be noted that the topic of migration was secondary in the questionnaire), as well as the available results of other public opinion studies on the topic of migration, BISS offers several preliminary conclusions.

HUMAN CAPITAL: VENTURE PROJECTS IN BELARUS

ЧЕЛОВЕЧЕСКИЙ КАПИТАЛ: ВЕНЧУРНЫЕ ПРОЕКТЫ В БЕЛАРУСИ

Author(s): Olga Malashenkova / Language(s): Bosnian

This study is part of the BISS project "Human Capital in Belarus: Sources of Competitiveness and Modernization". In this article, based on the comparison of world experience and Belarusian practice of implementing venture projects, analysis of normative legal acts of Belarus, as well as other conditions of activity of the venture industry; problems are identified and the development of venture investments in the country is assessed, proposals are formulated to eliminate some of the specified barriers.

HUMAN CAPITAL: THE CURRENT STATE OF THE SCIENTIFIC AND INNOVATIVE COMPLEX AND THE SPECIFICITY OF DECISION-MAKING IN THE INNOVATION POLICY

ЧЕЛОВЕЧЕСКИЙ КАПИТАЛ: АКТУАЛЬНОЕ СОСТОЯНИЕ НАУЧНО-ИННОВАЦИОННОГО КОМПЛЕКСА И СПЕЦИФИКА ПРИНЯТИЯ РЕШЕНИЯ В ИННОВАЦИОННОЙ ПОЛИТИКЕ

Author(s): Andrey Shuman / Language(s): Belarusian

This study is part of the BISS project "Human Capital in Belarus: Sources of Competitiveness and Modernization". The purpose of the work is to determine the current state of the scientific and innovative complex and to reveal the specifics of decision-making in the innovative policy of the Republic of Belarus. Based on the works of the "Human capital" cycle, BISS plans to prepare direct proposals to the government that will contribute to improving the state of the scientific and innovative potential of Belarus.

THE SHADOW ECONOMY OF BELARUS IN A REGIONAL PERSPECTIVE

ТЕНЕВАЯ ЭКОНОМИКА БЕЛАРУСИ В РЕГИОНАЛЬНОЙ ПЕРСПЕКТИВЕ

Author(s): Alexei Pikulik,Elena Artemenko / Language(s): Belarusian

Keywords: shadow economy in Belarus; corrupotion;

The study is devoted to the analysis of the public perception of the shadow economy and the assessment of citizens' involvement in shadow activities. The purpose of the work is to demonstrate and analyze the results of representative opinion polls conducted in May-June 2015 simultaneously in Belarus, Lithuania, Latvia, Estonia, Poland and Sweden. BISS acted as a member of the research consortium, which was organized and worked under the leadership of the Lithuanian Free Market Institute of Lithuania (LLRI). The study uses a "narrow" interpretation of the term "shadow economy", which includes the market production of exclusively legal goods and services that are deliberately hidden from state authorities. The uniqueness of this study is both in the wide regional coverage (six countries at the same time) and in the unification of the analysis methodology. The surveys were conducted by the research company SprinterResearch using the CAWI (ComputerAssistedWebInterview) method. The total sample consisted of 6,035 respondents, the sample for Belarus — 1,002 (18-75 years old, structured by gender, age and type of settlements).

REFORM. ALTERNATIVE VIEW: CIVIL SOCIETY AND POLITICAL OPPOSITION HAVE A PARTICULAR ATTITUDE TO REFORMS IN BELARUS

РЕФОРУМ. АЛЬТЕРНАТИВНЫЙ ВЗГЛЯД: У ГРАЖДАНСКОГО ОБЩЕСТВА И ПОЛИТИЧЕСКОЙ ОППОЗИЦИИ ОСОБОЕ ОТНОШЕНИЕ К РЕФОРМАМ В БЕЛАРУСИ

Author(s): Elena Artemenko / Language(s): Russian

In the countries of Eastern and Central Europe, the third sector played an important role in the transformation processes: as an aggregator of public interests and their lobbyist, as a source of expertise and a partner in promoting the idea of reform. In Belarus, due to state restrictions and dependence on foreign aid, the third sector has been in a rather vulnerable position for a long time and has limited influence on the situation in the country. In the conditions when the dialogue with the West is established by the Belarusian authorities without the need to attract mediators in the form of representatives of civil society or the political opposition, the third sector risks falling out of the process of transformation of Belarusian institutions. The study of the attitude of civil society and political opposition to reforms in the country allows us to assess their potential role in reformation and the opportunity to join the transformation process, if such an opportunity presents itself. As part of the "REFORUM" project, BISS conducted a survey of the opinions of representatives of public organizations and the political opposition, the subject of which was the attitude of civil society to reforms in Belarus. It makes it possible to assess the change in attitudes towards reforms during 2014-2015, as well as to compare the results with the survey among representatives of other groups: the population as a whole, officials and entrepreneurs