Application of the Classification and Regression Trees for Modeling the Laser Output Power of a Copper Bromide Vapor Laser

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

Modeling of Output Characteristics of a UV Cu+ Ne-CuBr Laser

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

Modeling of the Radial Heat Flow and Cooling Processes in a Deep Ultraviolet Cu

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

ON THE ASSESSMENT OF MATHEMATICAL COMPETENCIES FOR SOLVING NON-LINEAR EQUATIONS

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