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The monitoring and control of air quality in urban areas is important problem in many European countries. The main air pollutants are observed and a huge amount of data is collected during the last years. In Bulgaria, the air quality is surveyed by the official environmental agency and in many towns exceedances of harmful pollutants are detected. The aim of this study is to investigate the pollution from 9 air pollutants in the town of Dimitrovgrad, Bulgaria in the period of 5 years based on hourly data. Principal Component Analysis (PCA) is used to discover the patterns in the overall pollution and the contribution of the 9 pollutants. In addition the Generalized Path Seeker (GPS) regularized regression method is applied to find dependence of CO (carbon monoxide) with respect to other pollutants and 8 meteorological parameters. It is reported that the CO concentrations are in continuously repeated low level quantities very harmful for human health.

This study examines the available experiment data for a copper bromide vapor laser (CuBr laser), emitting in the visible spectrum at 2 wavelengths—510.6 and 578.2 nm. Laser output power is estimated based on 10 independent input parameters. The CART method is used to build a binary regression tree of solutions with respect to output power. In the case of a linear model, an approximation of 98% has been achieved and 99% for the model of interactions between predictors up to the the second order with an relative error under 5%. The resulting CART tree takes into account which input quantities influence the formation of classification groups and in what manner. This makes it possible to estimate which ones are significant from an engineering point of view for the development and operation of the considered type of lasers, thus assisting in the design and improvement of laser technology.

Two types of predictive modeling techniques - seasonal autoregressive integrated moving average (SARIMA) and a new Generalized PathSeeker (GPS) Regularized Regression method have been used for modeling data related to ambient air quality. The models are built for the measured data for the primary air pollutant - particulate matter PM10 in the town of Shumen, Bulgaria. The time series analysis was carried out based on hourly data with respect to six meteorological variables during a period of one month. The constructed models have been used for short-term four-days-ahead forecasts. The obtained results demonstrate some advantages of the GPS method over seasonal ARIMA stochastic modeling and its applicability. This gives a new perspective for analyzing and preventing the possible pollution problems in urban areas.

New results of statistical modeling of data on laser efficiency of copper bromide lasers using the nonparametric method of multivariate adaptive regression splines (MARS). Linear and nonlinear models are built, based on original data of families of copper bromide lasers, developed in Laboratory of Metal Vapor Lasers of Institute of Solid State Physics of Bulgarian Academy of Sciences during the last 30 years. The obtained models are applied for estimating the values of laser efficiency, as well as for directing and predicting of future experimental studies in order to improve the laser performance.

Using the results for the time- and spatially-averaged electron temperature, which were previously obtained by the line-ratio method of optical emission spectroscopy for several metal halide vapour lasers excited in nanosecond pulsed longitudinal discharge and analytically solving steady-state heat conduction equation for electrons as well, radial distribution of electron temperature, i.e. spatially-resolved electron temperature, is obtained.

The urban air pollution is one of the main factors determining the ambient air quality, which affects on the human health and the environment. In this paper parametric time series models are obtained for studying the distribution over time of primary pollutants as sulphur and nitrogen oxides, particulate matter and a secondary pollutant ground level ozon in the town of Shumen, Bulgaria. The methods of factor analysis and ARIMA are used to carry out the time series analysis based on hourly average data in 2011 and first quarter of 2012. The constructed models are applied for a short-term air pollution forecasting. The results are estimated on the basis of national and European regulation indices. The sources of pollutants in the region and their harmful effects on human health are also discussed.

This paper examines experiment data for a Ne-CuBr UV copper ion laser excited by longitudinal pulsed discharge emitting in multiline regime. The flexible multivariate adaptive regression splines (MARSs) method has been used to develop nonparametric regression models describing the laser output power and service life of the devices. The models have been constructed as explicit functions of 9 basic input laser characteristics. The obtained models account for local nonlinearities of the relationships within the various multivariate subregions. The built best MARS models account for over 98% of data. The models are used to estimate the investigated output laser characteristics of existing UV lasers. The capabilities for using the models in predicting existing and future experiments have been demonstrated. Specific analyses have been presented comparing the models with actual experiments. The obtained results are applicable for guiding and planning the engineering experiment. The modeling methodology can be applied for a wide range of similar lasers and laser devices.

A numerical model for determining gas temperature distribution in the cross-section of the laser tube of a copper bromide (CuBr) laser is presented. The model is derived on the basis of quasistationary heat conduction equation subject to nonlinear boundary conditions. For the first time the real physical conditions, such as the temperature of the reservoirs and other design elements are taken into account. The obtained temperature profile allows finding out specific operating conditions when the laser generation fails to be effective due to the process of overheating. These results are applicable in research and engineering practice for improving the laser tube design and the overall device performance.

When analyzing experiment data, the main statistical procedure is finding relationships in the data and developing models to describe them. Modeling is a powerful means of estimation, simulation, and prediction of the experiment and an indispensable tool in practical engineering. This paper considers the use of the multivariate adaptive regression splines (MARS) method to describe local relationships in the experiment data for several types of metal vapor lasers. The investigated data has been collected from patented UV ion lasers developed at the Bulgarian Academy of Sciences in the last ten years. A short description of MARS is provided. Specific MARS models have been developed describing the efficiency of an ultraviolet ion copper bromide vapor laser dependent on the change of 9 main input physical laser characteristics. The models are of linear and nonlinear type. It has been established that the best statistical indices and model fit are those of nonlinear models which contain second order local term...

An improved theoretical model of the gas temperature profile in the cross-section of an ultraviolet copper ion excited copper bromide laser is developed. The model is based on the solution of the one-dimensional heat conduction equation subject to special nonlinear boundary conditions, describing the heat interaction between the laser tube and its surroundings. It takes into account the nonuniform distribution of the volume power density along with the radius of the laser tube. The problem is reduced to the boundary value problem of the first kind. An explicit solution of this model is obtained. The model is applied for the evaluation of the gas temperature profiles of the laser in the conditions of free and forced air-cooling. Comparison with other simple models assumed constant volume power density is made. In particular, a simple expression for calculating the average gas temperature is found.

A new statistical approach to predict the possible increase of the laser generation in copper bromide lasers is presented. The results are based on a big amount of experimental data with wavelengths 510.6 nm and 578.2 nm, obtained in Georgi Nadjakov Institute of Solid State Physics, Bulgarian Academy of Sciences. The data are treated by statistical methods, such as multivariable factor analysis and linear regression modeling. The approximate increase of the output laser power up to 18% is obtained by using six input working parameters. The proposed methodology is applied for prognosticate the experiment and further design of the laser tube.

On the basis of experimental data, the overall efficiency of the copper bromide laser is investigated by means of factor analysis, variances, and other methods. The relative influence of the main laser parameters: inner diameter of the laser tube, electrode separation distance, input electric power and others are estimated with respect to the factors. The obtained results can be applied for different types of optimization in order to improve the output laser characteristics.

Дисертационният труд е посветен на задачи от физиката на джозефсоновите контакти. Разгледани са различни аспекти, свързани с магнитните моменти в джозефсонов контакт. Получени са числени решения на математическите задачи, описващи динамиката на магнитния момент за наномагнит в близост до джозефсонов контакт, динамиката на магнитните моменти по пространствените координати на джозефсонов контакт и магнитната прецесия в джозефсонов контакт под влияние на външен ток. В процеса на числения анализ бе установено, че при работа с голяма стъпка по променливата „време“ системата става, в повечето случаи, нерешима. Промяната на някои физични параметри правят системата твърда. Решение на проблема бе намерен и приложен, използвайки неявния метод на Гаус-Лежандър. Прави се анализ на проявяването на различните стабилни състояния след инжектирането на външния ток. Получени са три стабилни състояния, за които е разработена програма, позволяваща по-обстоен анализ, в зависимост от променящите се стойности на физичните параметри. Приложени са аналитични методи от теорията на интегруемите модели за получаване на точни решения на някои гранични задачи, възникващи при дълги джозефсонови контакти, с цел подобряването на числените изследвания. Аналитичните решения са получени в стационарния случай, при нулев външен ток, на „двойното синус-Гордън“ уравнение с гранични условия на Нойман. The dissertation is dedicated to problems in the field of physics concerning Josephson junctions. Different aspects, related to the magnetic moments in a Josephson junction, have been considered. Numerical solutions of the mathematical problems, describing the dynamics of the magnetic moment for a nanomagnet near a Josephson junction, the dynamics of the magnetic moments in the spatial coordinates of a Josephson junction and the magnetic precession in a Josephson junction under the influence of an external current, have been acquired. During the process of numerical analysis, it was found that when working with a large step on the variable "time" the system becomes, in most cases, unsolvable. Changing some physical parameters make the system stiff. A solution to the problem was found and implemented using the implicit Gauss-Legender method. An analysis is made of the manifestation of the various steady states after the injection of the external current. Three stable states have been obtained, for which a program has been developed that allows a more detailed analysis, depending on the changing values of the physical parameters. Analytical methods from the theory of integrable models have been applied as to obtain exact solutions of some boundary value problems arising from long Josephson junctions, in order to improve numerical research. The analytical solutions were obtained in the stationary case, at zero external current, of the "double sine-Gordon" equation with Neumann.

Дисертационният труд разглежда ЛМП, усилватели на яркостта в оптични системи. Развити са аналитични модели за определяне на температурата на електроните и газовата температура на ЛМП. Развита е методика за определяне на максимално възможната подавана електрическа мощност в газовия разряд и максималната енергия на електроните от позициите на устойчивост на разряда. Данни от публикувани експерименти, през Факторен анализ и Множествена линейна регресия, дадоха емпирични модели: Класификация на основните лазерни характеристики в 3 фактора, описващ данните до 76%; Нелинеен полиномен модел от втора степен, основан на множествен регресионен анализ от общо 27 независими променливи и една константа, установи високо ниво на надеждност за около 93% от данните. Получените моделни стойности са сравнени с известни от литературата числени резултати от симулации за същите данни. Проведени са статистически анализи: непараметричен корелационен анализ на Спирмън за изучаване на взаимовръзките между 12 работни характеристики и изходната мощност; и дейта майнинг с машинно обучение регресионна техника Random forest (RF). Построени са регресионни модели на изходната мощност. Установена е степента на влияние на независимите величини върху стойностите на изходната мощност. Резултатите имат практическо приложение и потвърдителен характер на известни факти за ЛМП. Предложените подходи дават възможност за явно определяне на влиянието на отделните работни характеристики върху изходната мощност. The dissertation deals with MVL, brightness amplifiers in optical systems. Analytical models are developed to determine the temperature of the electrons and the gas temperature of MVL. Methodology is developed for determining the maximum possible electric power supplied in the gas discharge and the maximum energy of the electrons from the positions of discharge resistance. Data from published experiments, through Factor Analysis and Multiple Linear Regression, gave empirical models: Classification of basic laser characteristics into 3 factors, describing data up to 76%; A second-degree nonlinear polynomial model based on multiple regression analysis of a total of 27 independent variables and one constant found a high level of reliability for about 93% of the data. The obtained model values are compared with known numerical results from simulations for the same data. Statistical analyzes are performed: nonparametric Spearman correlation analysis to study the relationships between 12 performance characteristics and output power; and data mining with machine learning regression technique Random forest (RF). Regression models of the output power are built. The degree of influence of the independent quantities on the values of the output power is established. The results have practical application and confirmatory nature of facts about MVL. The proposed approaches make it possible to clearly determine the impact of individual performance characteristics on output power.

The main goal of this dissertation is to apply data mining with machine learning methods for statistical modeling and study of dependencies in empirical data from animal husbandry. The object of the study is the 305-day milk productivity of Holstein- Friesians cows raised on farms in Bulgaria.Using the CART method, regression trees were constructed on the dependence of 305-day milk yield on 12 linear traits and the farm as an environmental factor in -Holstein Friesians type cows from 4 farms on the territory of Bulgaria (n = 97). The main factors for greater milk yield are identified farm (growing conditions, health care, etc.) and some linear features. The models match the measured data up to R2 = 70%. Using the ensemble data mining method CART Ensembles and Bagging, the ranking variable for 305-day milk yield was modeled depending on 12 exterior features and the farm. The influence of all studied factors for explanation of milk yield was evaluated. The best models in this group explain the actual observations with R2 = 0.894 and accuracy RMSE = 816.01 kg. A comparison of the results obtained from the models was performed. The RF method was found to have the best predictive statistics, followed by CART Ensemble and Bagging and CART. All models were cross-validated and their residues were analyzed. The methods used work well with small samples and ordinary data type. Основната цел на настоящия дисертационен труд е да се приложат дейта майнинг с машинно обучение методи за статистическо моделиране и изследване на зависимости в емпирични данни от животновъдството. Обект на изследването е 305-дневната млечна продуктивност на крави от породата Холщайн-Фрезийска, отглеждани във ферми на територията на България.С помощта на метода CART са построени регресионни дървета на зависимостта на 305 дневната млечност от 12 линейни признаци и фермата като средови фактор при крави тип Фрезийска-Холщайн от 4 ферми на територията на България (n=97). Като основни фактори за по-голяма млечност са идентифицирани фермата (условия на средата на отглеждане, здравни грижи и други) и някои линейни признаци. Моделите достигат съвпадение с измерените данни до R2=70%.С приложение на ансамбловия дейта майнинг метод CART Ensembles and Bagging е проведено моделиране на ранговата променлива за 305-дневната млечност в зависимост от 12 екстериорни признаци и фермата. Оценено е влиянието на всички изследвани фактори за обяснение на млечността. Най-добрите модели от тази група обясняват реалните наблюдения с R2=0,894 и точност RMSE=816,01 кг. Проведено е сравнение на получените резултати от моделите. Установено е, че най-добри предсказващи статистики има методът RF, следван от CART Ensemble and Bagging и CART. Всички модели са кросвалидирани и е проведен анализ на остатъците им. Използваните методи работят добре и с малки извадки и ординален тип данни.