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This study demonstrates the high capabilities of data mining and the random forest (RF) machine learning technique for processing experimental data in the field of laser equipment and technology and extracting significant information from these. The subject of study is the copper bromide vapor laser, used as a brightness amplifier and as an active medium in active optical systems actively developed in recent years. Published data from 465 experiments on this type of laser are statistically examined. RF regression models are built to predict the output power as a basic laser characteristic. The dependence of the output power on the input electric power, the pulse repetition frequency, the pressure of the additional gases in the discharge, and other operating and geometric parameters of the laser is determined. The models fit up to 98% of the experimentally measured laser output power data.

Preserving the air quality in urban areas is crucial for the health of the population as well as for the environment. The availability of large volumes of measurement data on the concentrations of air pollutants enables their analysis and modelling to establish trends and dependencies in order to forecast and prevent future pollution. This study proposes a new approach for modelling air pollutants data using the powerful machine learning method Random Forest (RF) and Auto-Regressive Integrated Moving Average (ARIMA) methodology. Initially, a RF model of the pollutant is built and analysed in relation to the meteorological variables. This model is then corrected through subsequent modelling of its residuals using the univariate ARIMA. The approach is demonstrated for hourly data on seven air pollutants (O3, NOx, NO, NO2, CO, SO2, PM10) in the town of Dimitrovgrad, Bulgaria over 9 years and 3 months. Six meteorological and three time variables are used as predictors. High-performance models are obtained explaining the data with R2 = 90%-98%.

The process of learning and acquiring mathematics by students is inextricably linked with the need to measure the achieved level of their knowledge and skills at each stage of education. The aim of the study is to propose a methodological approach for evaluating students’ mathematics competencies in engineering degrees, developed in accordance with the results of the European Erasmus+ project Rules_Math. A competency assessment model is presented that includes three main components: multiple-choice test, tasks to solve and a small practical project on a topic from the curriculum for first-year students. The multiple-choice test aims to assess students' understanding of the basic notions, concepts, and methods in the field. Solving problems should measure the level of knowledge and skills acquired. The practical project could evaluate the students’ ability to apply what has been learned to solve practice-oriented tasks. It is recommended to use mathematical software. The approach is demonstrated with a specific example of assessing mathematical competencies for solving non-linear equations of a single variable. Answers and solutions are also provided. The presented methodology can be used by professors and tutors in higher education institutions to update the assessment of students' competencies in mathematics.

Copper and copper-compound vapor lasers are most powerful in the visible spectrum with output power over 100 W. They offer unique properties including a laser beam with high coherence and convergence and high average output powers with relatively small dimensions. Recently, these lasers, and in particular the copper bromide (CuBr) laser, have been widely used as radiation sources and vapor brightness amplifiers in a new type of laser active optical systems, designed for the visual monitoring and control of fast processes shielded by intense background lighting. However, new problems arise with the development of such optical systems, related to the laser technology and the optimization of their operating parameters. Important operating characteristics of copper lasers include the input electric power and the gas temperature of the discharge. The upper limit of the laser power that can be supplied to the gas discharge is studied herein by considering the permissible thermal population thresholds of the lower level of the λ = 510.6 nm laser line. The application of enhanced analytical models based on a steady-state heat conduction equation and computer simulations enables the development of a methodology to determine the maximum possible electric power that can be supplied to the gas discharge, taking into account its radial distribution across the tube cross-section. This methodology is then applied to the case of an actual small-bore CuBr laser used as a brightness amplifier.

The aim of this study is to evaluate students&rsquo, achievements in mathematics using three machine learning regression methods: classification and regression trees (CART), CART ensembles and bagging (CART-EB) and multivariate adaptive regression splines (MARS). A novel ensemble methodology is proposed based on the combination of CART and CART-EB models in a new ensemble to regress the actual data using MARS. Results of a final exam test, control and home assignments, and other learning activities to assess students&rsquo, knowledge and competencies in applied mathematics are examined. The exam test combines problems on elements of mathematical analysis, statistics and a small practical project. The project is the new competence-oriented element, which requires students to formulate problems themselves, to choose different solutions and to use or not use specialized software. Initially, empirical data are statistically modeled using six CART and six CART-EB competing models. The models achieve a goodness-of-fit up to 96% to actual data. The impact of the examined factors on the students&rsquo, success at the final exam is determined. Using the best of these models and proposed novel ensemble procedure, final MARS models are built that outperform the other models for predicting the achievements of students in applied mathematics.

The subject of investigation is a new high-powered strontium bromide (He– $$\hbox {SrBr}_{2})$$ vapor laser emitting in the infrared spectrum. The aim of the study is to investigate the possibilities for optimizing the thermal mode of the laser by enhancing its operating characteristics. Based on a previous analytical self-consistent model of the authors, a model of the device temperature profile is presented under the conditions of forced convection. The model consists of quasi-stationary heat transfer equation with appropriate set of boundary conditions to investigate the influence of the cooling processes in the laser tube with transverse external air cooling. An assessment is performed of the nature of the main physical processes accompanying the distribution of heat energy from the center of the tube and its interaction with the ambient environment under forced convection. Through simulations, it has been found that when air flow rate changes, the operating temperature can vary widely within 100 K. It is also illustrated how to increase the supplied electric power while maintaining the maximum working temperature at the center of the laser tube. The model allows for detailed examination of the thermal processes, it does not require temperature measurements, and it can be used for different geometric dimensions of the laser tube, values of the supplied electric power, coefficients of thermal conductivity of the structural materials, and other operational and design parameters. The developed model is applicable to a wide range of metal vapor lasers, and other closely related ones.

Due to their unique radiation properties, metal vapor lasers find a variety of applications, including being used as a high- brightness amplifier in new active optical systems. This type of systems has been actively developed in recent years and is applied for visual control of fast processes in screening the background illuminations. A computer model is built and applied to an existing laser source allowing to determine the radial distribution of gas temperature in the cross section of the laser tube. Computations are performed using a preset qualitative type radial distribution of the electric power supplied to the gas discharge. The influence of the electric power supplied to the gas discharge and the wall temperature on the thermal resistance of the gas discharge was evaluated by means of computer simulations. The proposed methodology allows the planning of experiments and developing new laser sources with improved output characteristics.

The problem of atmospheric air pollution is of great concern to human health, the clean environment and the climate, and is an actual topic in environmental research. The major pollutants of air are PM10, PM2.5, SO2, ozone (O3) and more. For each geographical region, there are specific sources of pollution, as well as conditions for the containment of harmful emissions into the air for longer periods of time. Bulgaria is a member state of the European Union in which low air quality is permanently reported, against the statutory limits in European legislation. Significant exceedances of regulatory limits have been measured for many of the major air pollutants. This paper focuses on the application and comparison of two machine learning methods - Boosted trees and regularized regression to investigate the influence of meteorological, atmospheric and other factors on air quality based on empirical data. Hybrid type models have also been built and tested. The modeling process uses daily average ground level ozone (O3) and PM10 emissions data in the city of Ruse, Bulgaria, measured at licensed automated stations, under the control of the European Environment Agency in Bulgaria. As a result, validated models with high statistical goodness-of-fit indicators such as coefficient of determination, root mean square error, etc. The best selected models show very good agreement with the measured data in the order of 80-90%. Short-term forecasts for future pollution have been made. There is a slight preference for hybrid boosted trees and regularized regression models over those generated by individual methods.

This study explores hourly data for 9 air pollutants and 6 meteorological variables in Dimitrovgrad, Bulgaria for a period of one year. Factor analysis is applied for the classification of the variables. A grouping of pollutants and meteorological hazard is established in 7 artificial factors, which allows the explanation of relationships between variables and mutual sources of air pollution. As one of the key problematic air pollutant, PM10 is identified with an average value over the year of 58.7 micrograms per cubic meter. Using SARIMA method from the Box-Jenkins methodology with seasonal parameter s = 24 hours, models of PM10 with transfer functions are constructed and analyzed. For realistic forecasting of PM10 values at future times, it is necessary to know the data of both the meteorological variables and air pollutants that are precursors of PM10, on which its concentrations depend. For this purpose, SARIMA is applied in two successive steps. First, models are developed to forecast each precursor depending on the weather variables. In a second step, the obtained forecasted precursor and meteorological data are used to model and forecast PM10. The constructed models explain the considered data set with 68% to 86% and RMSE = 0.133. The forecast of PM10 pollution is calculated for 168 hours after the period with data not used in the modeling process.

The further development of a unified approach for competence-based teaching and learning of mathematics is an important step towards creating European standards, including assessment standards. A necessary stage when solving this ambitious problems is the performance of an in-depth analysis of the current state in various European countries. The article considers some issues in this regard, related to the competence of first-year university students in the context of acquiring competences for mathematical modeling of level one. As an example, the topic of data modeling using cluster analysis and software is presented and analyzed. The results of a survey among students are presented.

The team that has developed this project is part of a consortium of several European institutions that have joined with a common goal: to help the current engineering teaching-learning system, so that to make possible a competencies-based assessment. Moreover advocacy and networking will be part of the consortium activities during the whole project. RULES_MATH acronym corresponds to ‘New rules for assessing mathematical competencies’, and that is exactly what we propose: to work with the mathematical competencies, specifically try to incorporate them into the assessment process. We focus on science and engineering degrees, since in all these studies several Mathematics courses are part of their curriculum, mainly in the first couple of years. In this paper we present one of our first activities that we want to achieve under the project: the selection of several tools and rules that will make possible an assessment and evaluation according to our high education common European space. These ideas are part of the objectives of promoting and institutionalizing good teaching practices and the enhancement of teaching materials. Other goals are to improve the dissemination of academic activities to the business world, administrations and society in general.

Providing young people with key competences to help them adapt to the rapidly changing interconnected world is a key part of the European Union's strategies for delivering job growth and sustainable development. The article discusses the issue of developing, expanding and enriching the set of mathematical competences in learners by using specialized mathematical software. It presents the experience of the authors of a particular course in Software Systems in Mathematics in the context of the integration of computer-based and competence-based teaching and learning in mathematics as well as some special assessment methods.

A family of copper bromide metal vapor lasers used as brightness amplifiers in recently developed optical systems is considered. One of the main problems of this area is to investigate the basic amplification characteristics of the laser medium. In this study, a simplified mathematical model is developed based on the one-dimensional stationary equation for determining the electron temperature of the discharge. The proposed model allows to calculate the radial distribution of the electron temperature of the discharge by taking into account the radial distribution of the supplied electric power. Computer simulations are run to investigate the dependence of electron energy as a function of the electrical power supplied to the gas discharge tube. The natural limits of this process are specified.

Despite the existing public and government measures for monitoring and control of air quality in Bulgaria, in many regions, including typical and most numerous small towns, air quality is not satisfactory. In this paper, factor analysis and Box–Jenkins methodology are applied to examine concentrations of primary air pollutants such as NO, NO2, NOx, PM10, SO2 and ground level O3 in the town of Blagoevgrad, Bulgaria within a 1 year period from 1st September 2011 to 31st August 2012, based on hourly measurements. By using factor analysis with PCA and Promax rotation, a high multicollinearity between the six pollutants has been detected. The pollutants were grouped in three factors and the degree of contribution of the factors to the overall pollution was determined. This was interpreted as the presence of common sources of pollution. The main part of the study involves the performance of time series analysis and the development of univariate stochastic seasonal autoregressive integrated moving average (ARIMA) models with recording on a hourly basis as seasonality. The study also incorporates the Yeo–Johnson power transformation for variance stabilizing of the data and model selection by using Bayersian information criterion. The obtained SARIMA models demonstrated very good fitting performance with regard to the observed air pollutants and short-term predictions for 72 h ahead, in particular in the case of ozone and particulate matter PM10. The presented statistical approaches allow the building of non-complex models, effective for short-term air pollution forecasting and useful for advance warning purposes in urban areas.

Fine particulate matter (PM10) air pollution is a serious problem affecting the health of the population in many Bulgarian cities. As an example, the object of this study is the pollution with PM10 of the town of Pleven, Northern Bulgaria. The measured concentrations of this air pollutant for this city consistently exceeded the permissible limits set by European and national legislation. Based on data for the last 6 years (2011-2016), the analysis shows that this applies both to the daily limit of 50 micrograms per cubic meter and the allowable number of daily concentration exceedances to 35 per year. Also, the average annual concentration of PM10 exceeded the prescribed norm of no more than 40 micrograms per cubic meter. The aim of this work is to build high performance mathematical models for effective prediction and forecasting the level of PM10 pollution. The study was conducted with the powerful flexible data mining technique Classification and Regression Trees (CART). The values of PM10 were fitted with respect to meteorological data such as maximum and minimum air temperature, relative humidity, wind speed and direction and others, as well as with time and autoregressive variables. As a result the obtained CART models demonstrate high predictive ability and fit the actual data with up to 80%. The best models were applied for forecasting the level pollution for 3 to 7 days ahead. An interpretation of the modeling results is presented.

Due to advancement in computing technology researchers are focusing onto novel predictive models and techniques for improving the design and performance of the devices. This study examines a recently developed high-powered SrBr 2 laser excited in a nanosecond pulse longitudinal He–SrBr 2 discharge. Based on the accumulated experiment data, a new approach is proposed for determining the relationship between laser output power and basic laser characteristics: geometric design, supplied electric power, helium pressure, etc. Piece-wise linear and nonlinear statistical models have been built with the help of the flexible predictive MARS technique. It is shown that the best nonlinear MARS model containing second degree terms provides the best description of the examined data, demonstrating a coefficient of determination of over 99%. The resulting theoretical models are used to estimate and predict the experiment as well as to analyze the local behavior of the relationships between laser output power and input laser characteristics. The second order model is applied to the design and optimization of the laser in order to enhance laser generation.

There is significant practical interest in the determining of the thermal parameters of metal vapor and metal vapor halide lasers. This study develops a self-consistent analytical model determining the radial temperature profile of a high-powered strontium bromide (SrBr2) vapor laser, emitting in the infrared spectrum. The model is built under the assumption of arbitrary distribution of power density for the internal heat source without any given specific experiment measurements. It makes it possible to evaluate the nature of the main physical processes of the transfer of heat from the center of the tube to its interaction with the ambient environment. An exact solution of a heat conduction equation with first- and second-order boundary conditions is applied for the active laser medium. New boundary conditions are proposed, including third and fourth order ones, taking into account the various heat transfer processes through the layers of the gas discharge tube. Structural materials, the thermal conductivity of the helium layer between the ceramic and quartz tubes, the transmittance of heat in the outer quartz tube and suitable boundary conditions for the thermal insulation and the ambient environment are taken into consideration. The model is applied to calculate the temperature distribution within the laser tube of an existing high-powered SrBr2 laser in the case of natural convection. Very good fit is achieved with the experiment. The model is applicable for preliminary evaluation of the temperature profile of both existing and new metal vapor and other similar laser devices.

The dependence of the output power of CuBr lasers (operating at wavelengths of 510.6 and 578.2 nm) on ten input physical parameters has been statistically analysed based on a large amount of experimental data accumulated for these lasers. Regression models have been built using the flexible nonparametric method of multivariate adaptive regression splines (MARS) to describe both linear and nonlinear local dependences. These models cover more than 97% initial data with an error comparable with the experimental error; they are applied to estimate and predict the output powers of both existing and future lasers. The advantage of the models constructed for estimating laser parameters over the standard parametric methods of multivariate factor and regression analysis is demonstrated.

The subject of investigation is a SrBr2 laser generating at a wavelength λ = 6.45 µm. This type of laser gen- eration is finding ever wider application in medicine when working with soft and bone tissue providing rapid subsequent recovery. Of all laser sources generating at this wavelength, the new SrBr2 laser is gaining ever more ground due to its ad- vantages and is therefore of commercial interest. With the goal of developing new, higher-powered SrBr2 lasers, in this paper, the so-called phenomenological modeling has been used for the first time for this type of laser. An estimation of the degree of influence of 7 independent input laser quantities on laser output power has been performed using factor and regression analysis. A methodology has been developed with the help of which a series of new SrBr2 lasers with higher output power than existing ones has been predicted. Problems related to the planning of the experiment have been partially solved - car- rying out of filtering and extremal experiment.

When designing and modeling metal vapor and metal halide vapor lasers, the radial distribution of the gas temperature is found by solving the steady-state heat conduction equation for the internal tube at mixed boundary conditions. The volume power density is usually taken as a constant and the unknown value for the temperature of the inner wall is substituted by the measured temperature of the outer wall of the composite laser tube. In this paper, these inaccuracies are overcome. A general solution of the steady-state heat conduction problem has been suggested for an arbitrary volume power density. In order to determine the temperature of the inner wall, a complete model of the radial heat flow has been constructed. The resulting model has been applied in order to evaluate the gas temperature of a new high-powered strontium laser at different qualitative distributions of volume power density. The results have been compared with the known simple models. The presented model could be used on its own for existing and future lasers or as part of other types of theoretical or computer models.

Two different predictive modelling approaches – classical SARIMA time series methodology and the new Generalised PathSeeker (GPS) regularised regression method, supported by stochastic gradient boosting trees, RuleLearner and other data mining techniques - are used to examine the concentration of particulate matter PM10 in the town of Kardzhali, Bulgaria. Empirical models are developed to simulate and forecast pollution levels based on hourly PM10 data from 1 January 2011 to 28 February 2014 in dependence on six meteorological variables. The constructed models have been used for 5-days-ahead hourly forecasts, compared to actual data from 1 to 5 March 2014. The obtained SARIMA and GPS models fit very well to historical data with coefficients of determination R2 = 90% and 82% and root mean square error RMSE = 0.114 and 0.151, respectively. In forecasting, the GPS models outperform SARIMA approach. This could be explained by the preliminary classification provided by the data mining techniques and cross-validation procedure.

An analytic model is proposed to calculate the buffer-gas temperature in the discharge-tube cross section of the copper bromide vapour laser. The model is the generalisation of the previous models developed by the authors. Assuming that the volume electric power is arbitrary distributed over the tube radius, the general solution of the quasi-stationary heat conduction equation with the boundary conditions of the first and second kinds is presented. Application of the model is considered by the example of a copper bromide vapour laser emitting at 510.6 and 578.2 nm at different specific radial distributions of the volume power. The obtained results are compared with the temperature profiles known to date. Application of this model to molecular lasers is also discussed.

In order to model the output laser power of a copper bromide laser with wavelengths of 510.6 and 578.2 nm we have applied two regression techniques—multiple linear regression and multivariate adaptive regression splines. The models have been constructed on the basis of PCA factors for historical data. The influence of first- and second-order interactions between predictors has been taken into account. The models are easily interpreted and have good prediction power, which is established from the results of their validation. The comparison of the derived models shows that these based on multivariate adaptive regression splines have an advantage over the others. The obtained results allow for the clarification of relationships between laser generation and the observed laser input variables, for better determining their influence on laser generation, in order to improve the experimental setup and laser production technology. They can be useful for evaluation of known experiments as well as for prediction of future experiments. The developed modeling methodology is also applicable for a wide range of similar laser devices—metal vapor lasers and gas lasers.

A new analytic model is proposed for calculating the temperature profile of gas in the transverse section of the discharge tube of copper bromide lasers emitting at 510.6 and 578.2 nm. The model is described by the quasi-stationary heat conduction equation with the boundary conditions of the third and fourth kinds taking into account the alternating volume electric power along the tube radius. The exact solution of the problem is obtained. The model was used to calculate the temperature profiles of the discharge in the case of natural and forced convection cooling. The obtained results are compared with previously known temperature distributions. The improved model proposed in the paper can be used to analyse existing lasers and develop new lasers.

A statistical classification analysis of parameters of a CuBr laser emitting at 510.6 and 578.2 nm is performed for the first time based on numerous experimental data. The ten basic parameters affecting the laser output power are investigated by using the multidimensional cluster analysis. Classification tables and dendrograms for these parameters are presented. The obtained results are consistent with our previous study of laser parameters based on the multidimensional factor and regression analysis and supplement it. Some experiment-planning tasks are solved.

A new approach for improving the efficiency of a copper bromide vapour laser with wavelengths of 510.6 and 578.2 nm is implemented. Multi-factor and regression analyses of a large amount of experimental data have outlined the parameters with highest impact on the laser efficiency. They are electric input power, inside diameter of the rings, distance between the electrodes, inside diameter of the laser tube, hydrogen pressure and electric input power per unit length. The results obtained allow discovery of the internal structure of dependences among parameters, to better account for the physical processes that influence efficiency, to improve the planning of further experiments and laser production technology.

To improve the planning of experiments, the statistical analysis of a large amount of experimental data obtained for a copper bromide laser emitting at 510.6 nm and 578.2 nm was performed. Various statistical methods such as factor analysis, method of principal components, multiple regression and others were applied for studying the influence of the ten basic input laser parameters on the output laser power. It was found that the most important parameters are the inside diameter of the laser tube, the diameter of internal rings, the length of the active area and the input electrical power.

Based on the two-dimensional heat conduction equation solved under boundary conditions of the third and fourth kind, a new approach is proposed for determining the gas temperature in the cross section of a copper bromide laser. Temperature profiles in the cases of the natural and forced convection are obtained taking into account the basic laser parameters such as the laser design, the input electric power, etc. In particular, computer simulations for the case of forced convection are performed in order to increase the input electric power at a fixed maximum discharge temperature.

Fine particulate matter PM2.5 and PM10 air pollutants are a serious problem in many urban areas affecting both the health of the population and the environment as a whole. The availability of large data arrays for the levels of these pollutants makes it possible to perform statistical analysis, to obtain relevant information, and to find patterns within the data. Research in this field is particularly topical for a number of Bulgarian cities, European country, where in recent years regulatory air pollution health limits are constantly being exceeded. This paper examines average daily data for air pollution with PM2.5 and PM10, collected by 3 monitoring stations in the cities of Plovdiv and Asenovgrad between 2011 and 2016. The goal is to find and analyze actual relationships in data time series, to build adequate mathematical models, and to develop short-term forecasts. Modeling is carried out by stochastic univariate and multivariate time series analysis, based on Box-Jenkins methodology. The best models...

A Generalized PathSeeker Regularized Regression (GPSRR), based on data mining approach, is applied for statistical modeling and prediction of output power of copper bromide vapor lasers. The aim is on the basis of available experimental data to construct appropriate predictive models of the output power of the lasers depending on 10 operating laser characteristics in order to direct future experiments and designing new laser devices with increased output power. In particular, the influence on model performance and predictive ability of several data transformations, used to improve the normality of the distribution of the dependent variable is investigated. As a main result, numerous combined models, built by GPSRR with data mining techniques are obtained and their adequacy is established by cross-validation. It is found that the best combined models demonstrate up to 98-99% of fitting the experimental data. The combined models with the proposed preliminary transformations improve the adequacy and predictive ability of GPSRR in the region of high values of the output power by up to 10%. This was established both for learn and test random samples, showing a perfect out-of-sample performance of this type of model approach. The models are applied for predicting of laser output power for new laser devices of the same type by up to 15%.

Variety of electron, ion and plasma technologies as well as gas discharge devices operate in fixed form of the discharge. The transition from weak to heavy current in radio-frequency low-current discharge leads to instabilities in physical processes and it is very critical for the normal functionality of the technology or device. In this paper by means of Townsend criterion the influence of the incoming electric power and voltage on this transition in a cross-section of the discharge is numerically simulated. The calculations show a possible change of applied designed power up to 32% without weak to heavy-current transition. It is also obtained that the rise in 40% of the pressure can change the critical breakdown power only up to 12%. These results are in agreement with the simple analytical one-dimensional models and experimental data.

In this paper there is proved a generalization of a theorem of Stein and Weiss concerning metric properties of the conjugate characteristic functions of given sets on the interval [0, 2π]. As an application for the Hilbert transform of a bounded function, the optimal correlation where the Favard's constant : is also established.

Subject of investigation is a new high-powered strontium bromide (SrBr2) vapor laser emitting in multiline region of wavelengths. The laser is an alternative to the atom strontium lasers and electron free lasers, especially at the line 6.45 μm which line is used in surgery for medical processing of biological tissues and bones with minimal damage. In this paper the experimental data from measurements of operational and output characteristics of the laser are statistically processed by means of cluster analysis and tree-based regression techniques. The aim is to extract the more important relationships and dependences from the available data which influence the increase of the overall laser efficiency. There are constructed and analyzed a set of cluster models. It is shown by using different cluster methods that the seven investigated operational characteristics (laser tube diameter, length, supplied electrical power, and others) and laser efficiency are combined in 2 clusters. By the built regression tree models using Classification and Regression Trees (CART) technique there are obtained dependences to predict the values of efficiency, and especially the maximum efficiency with over 95% accuracy.

Numerous time series methods are used in environmental sciences allowing the detailed investigation of air pollution processes. The goal of this study is to present the empirical analysis of various aspects of stochastic modeling and in particular the ARIMA/SARIMA methods. The subject of investigation is air pollution in the town of Kardzhali, Bulgaria with 2 problematic pollutants – sulfur dioxide (SO2) and particulate matter (PM10). Various SARIMA Transfer Function models are built taking into account meteorological factors, data transformations and the use of different horizons selected to predict future levels of concentrations of the pollutants.