Production economics forms a very important part of an enormous range of economic theory. Agricultural production is no exception. When evaluating the competitiveness of the multifunctional agriculture, it is necessary to use the measure of efficiency instead of productivity. The conception of the efficiency is explained and the methods for measurement are provided. The authors discuss the methods of Stochastic Frontier Approach (SFA), Free Disposal Hull (FDH) and Data Envelopment Analysis (DEA) that are particularly useful for multi-criterial evaluation of multifunctional processes. Those methods assign an efficiency score to each Decision Making Unit (DMU) based on how well it transforms a given set of inputs into outputs. Most studies have only focused on application of DEA method for assessment of the efficiency of agriculture farms. There is still a need on applications for sectors. This paper provides an examination of the applicability of DEA method to agriculture sectors efficiency measurement. By applying mathematical models, which are based on the DEA, the efficiency of agriculture in each EU country was evaluated.

Production economics forms a very important part of an enormous range of economic theory. Agricultural production is no exception. When evaluating the competitiveness of the multifunctional agriculture, it is necessary to use the measure of efficiency instead of productivity. The conception of the efficiency is explained and the methods for measurement are provided. The authors discuss the methods of Stochastic Frontier Approach (SFA), Free Disposal Hull (FDH) and Data Envelopment Analysis (DEA) that are particularly useful for multi-criterial evaluation of multifunctional processes. Those methods assign an efficiency score to each Decision Making Unit (DMU) based on how well it transforms a given set of inputs into outputs. Most studies have only focused on application of DEA method for assesment of the efficiency of agriculture farms. There is still a need on applications for sectors. This paper provides an examination of the applicability of DEA method to agriculture sectors efficiency measurement. By applying mathematical models, which are based on the DEA, the efficiency of agriculture in each EU country was evaluated.

Since 2014, there have been admission tests in mathematics for applicants to the Estonian University of Life Sciences for Geodesy, Land Management and Real Estate Planning; Civil Engineering; Hydraulic Engineering and Water Pollution Control; Engineering and Technetronics curricula. According to admission criteria, the test must be taken by students who have not passed the specific mathematics course state exam or when the score was less than 20 points. The admission test may also be taken by those who wish to improve their state exam score. In 2016, there were 126 such applicants of whom 63 took the test. In 2015, the numbers were 129 and 89 and in 2014 150 and 47 accordingly. The test was scored on scale of 100. The arithmetic average of the score was 30.6 points in 2016, 29.03 in 2015 and 18.84 in 2014. The test was considered to be passed with 1 point in 2014 and 20 points in 2015 and 2016. We analyzed test results and gave examples of problems which were solved exceptionally well or not at all.

Since 2014, there have been admission tests in mathematics for applicants to the Estonian University of Life Sciences for Geodesy, Land Management and Real Estate Planning; Civil Engineering; Hydraulic Engineering and Water Pollution Control; Engineering and Technetronics curricula. According to admission criteria, the test must be taken by students who have not passed the specific mathematics course state exam or when the score was less than 20 points. The admission test may also be taken by those who wish to improve their state exam score. In 2016, there were 126 such applicants of whom 63 took the test. In 2015, the numbers were 129 and 89 and in 2014 150 and 47 accordingly. The test was scored on scale of 100. The arithmetic average of the score was 30.6 points in 2016, 29.03 in 2015 and 18.84 in 2014. The test was considered to be passed with 1 point in 2014 and 20 points in 2015 and 2016. We analyzed test results and gave examples of problems which were solved exceptionally well or not at all.

Faba beans (Vicia faba L.) are an excellent protein source and should be more present in human diet, but due to their long cooking time, they are rarely used. So, in order to increase the accessibility of faba beans (Vicia faba L.), experiments were carried out to obtain new food products. Extrusion-cooking was chosen as the potential thermal cooking process and two different products were obtained. One was made exclusively from faba bean (Vicia faba L.) flour, while the second one was produced with a 50% addition of wheat flour to bean flour. Protein content, size, volume mass, pH and starch content for obtained products were analysed in order to characterise the products, as well as to see the differences from non-extruded faba beans (Vicia faba L.) and obtained samples. The experiments were carried out using faba beans (Vicia faba L.) obtained at Ltd. “Pure Horticultural Research Centre”. They were milled at Ltd. “Grauda spēks” and extruded with a twin screw extruder at Ltd. “Milzu”. The experiments showed that the extrusion process had decreased the protein content by 9%, but the starch content had risen by 13% with the addition of wheat flour. But, for sample, without added wheat flour differences were not significant. No significant size differences were observed in the obtained samples and pH values had no significant differences between extruded samples.

Faba beans (Vicia faba L.) are an excellent protein source and should be more present in human diet, but due to their long cooking time, they are rarely used. So, in order to increase the accessibility of faba beans (Vicia faba L.), experiments were carried out to obtain new food products. Extrusion-cooking was chosen as the potential thermal cooking process and two different products were obtained. One was made exclusively from faba bean (Vicia faba L.) flour, while the second one was produced with a 50% addition of wheat flour to bean flour. Protein content, size, volume mass, pH and starch content for obtained products were analysed in order to characterise the products, as well as to see the differences from non-extruded faba beans (Vicia faba L.) and obtained samples. The experiments were carried out using faba beans (Vicia faba L.) obtained at Ltd. “Pure Horticultural Research Centre”. They were milled at Ltd. “Grauda spēks” and extruded with a twin screw extruder at Ltd. “Milzu”. The experiments showed that the extrusion process had decreased the protein content by 9%, but the starch content had risen by 13% with the addition of wheat flour. But, for sample, without added wheat flour differences were not significant. No significant size differences were observed in the obtained samples and pH values had no significant differences between extruded samples.

The goal of this research is to explore sentence structures expressed by parts of speech. Due to a small amount of data, a problem of sparse data has arisen, which was solved by recording the annotated sentences and considering a “framework” of a sentence made up from a verb and a noun, which was conditionally called a code. The code of a sentence is created by changing each word of a sentence by a symbol (letter or number) that encodes one or other property of that word as a constituent of the sentence. Zipf’s law describes sentences, encoded like that, rather well. If we ‘learn’ well to identify and analyze (annotate, translate, etc.) sentences of the simplest structure, we can automatically process quite a large part of text sentences. It is possible to identify at least 17% of sentences consisting of the simplest structure.

The goal of this research is to explore sentence structures expressed by parts of speech. Due to a small amount of data, a problem of sparse data has arisen, which was solved by recording the annotated sentences and considering a “framework” of a sentence made up from a verb and a noun, which was conditionally called a code. The code of a sentence is created by changing each word of a sentence by a symbol (letter or number) that encodes one or other property of that word as a constituent of the sentence. Zipf’s law describes sentences, encoded like that, rather well. If we ‘learn’ well to identify and analyze (annotate, translate, etc.) sentences of the simplest structure, we can automatically process quite a large part of text sentences. It is possible to identify at least 17% of sentences consisting of the simplest structure.

In this article, common test results over the years 2000 – 2016 are analysed. The test questions for new entrants were based on secondary school mathematics. The students took the test in the first lesson of the higher mathematics course. The test results were analysed by years, by tasks and by specialities, and their differences were found. The test results’ dependence on state-exams score was studied and other types of dependence were looked at. It was found that the test score has a strong correlation with a state-exam but with high school mathematics mark and with later higher mathematics course marks has very weak correlation. During these 16 years, the questions that have been the most difficult for students have not changed. The highest test scores were found among students who had chosen the most popular specialities (with the highest competition).

In this article, common test results over the years 2000 – 2016 are analysed. The test questions for new entrants were based on secondary school mathematics. The students took the test in the first lesson of the higher mathematics course. The test results were analysed by years, by tasks and by specialities, and their differences were found. The test results’ dependence on state-exams score was studied and other types of dependence were looked at. It was found that the test score has a strong correlation with a state-exam but with high school mathematics mark and with later higher mathematics course marks has very weak correlation. During these 16 years, the questions that have been the most difficult for students have not changed. The highest test scores were found among students who had chosen the most popular specialities (with the highest competition).

The kinetics of plasma nitriding of CoCr alloy below temperatures of nitrides formation and mechanisms of nitrogen penetration are analyzed by proposed kinetic modeling in this article. Proposed nitrogen diffusion model is based on the trapping – detrapping (TD) model and developed taking into account the effect of the concentration dependent diffusivity of nitrogen, nitrogen adsorption on the surface of alloy and surface swelling process. The model indicates the influence of chromium atoms to nitrogen atoms diffusivity. The model consists of time and depth dependent diffusion, which is described by a partial differential equation, and it is solved by using Crank – Nicolson finite difference method. By fitting of experimental nitrogen depth profiles, it is shown that nitrogen diffusion coefficient varies with nitrogen concentration according to Einstein-Smoluchowski relation. Nitrogen depth profiles in plasma nitrided medical grade CoCr alloy (ISO 5831 – 12) at T = 400 °C for 1, 4 and 20 hours calculated on the basis of this model are in good agreement with experimental nitrogen profiles. Furthermore, the swelling process is showed and analysed, derived the dependency of swelling rate on nitriding duration – the swelling rate is inversely proportional to the square root of nitriding duration. The obtained diffusion coefficient value and the swelling process rates satisfy the experimental data form Ref. The derived model explains physical processes during plasma nitriding and allows obtaining nitrogen depth profiles for any requisite nitriding duration.

The kinetics of plasma nitriding of CoCr alloy below temperatures of nitrides formation and mechanisms of nitrogen penetration are analyzed by proposed kinetic modeling in this article. Proposed nitrogen diffusion model is based on the trapping – detrapping (TD) model and developed taking into account the effect of the concentration dependent diffusivity of nitrogen, nitrogen adsorption on the surface of alloy and surface swelling process. The model indicates the influence of chromium atoms to nitrogen atoms diffusivity. The model consists of time and depth dependent diffusion, which is described by a partial differential equation, and it is solved by using Crank – Nicolson finite difference method. By fitting of experimental nitrogen depth profiles, it is shown that nitrogen diffusion coefficient varies with nitrogen concentration according to Einstein-Smoluchowski relation. Nitrogen depth profiles in plasma nitrided medical grade CoCr alloy (ISO 5831 – 12) at T = 400 °C for 1, 4 and 20 hours calculated on the basis of this model are in good agreement with experimental nitrogen profiles. Furthermore, the swelling process is showed and analyzed, derived the dependency of swelling rate on nitriding duration – the swelling rate is inversely proportional to the square root of nitriding duration. The obtained diffusion coefficient value and the swelling process rates satisfy the experimental data form Ref. The derived model explains physical processes during plasma nitriding and allows obtaining nitrogen depth profiles for any requisite nitriding duration.

The article deals with the problem of local mobility of peasants in Vilnius Governorate in the nineteenth century. To solve the problem, statistical-demographical data from the “Memory Books” permanently issued by the Tsarist Russian government was used. Pure demographic data brings little information, unless it is properly mathematically processed. Such processing leads to the discovering of new proportions concerning inhabitants, villages and farmsteads. Such proportions are related to the administrative territorial unit under investigation and show how many people reside in a farmstead and how many farmsteads are comprised in a village. In the course of time, numbers of villages and farmsteads change, and these numbers show the numbers of people taking part in local mobility of inhabitants. The higher are changes in villages and farmsteads, the higher is mobility of inhabitants.

The article deals with the problem of local mobility of peasants in Vilnius Governorate in the nineteenth century. To solve the problem, statistical-demographical data from the “Memory Books” permanently issued by the Tsarist Russian government was used. Pure demographic data brings little information, unless it is properly mathematically processed. Such processing leads to the discovering of new proportions concerning inhabitants, villages and farmsteads. Such proportions are related to the administrative territorial unit under investigation and show how many people reside in a farmstead and how many farmsteads are comprised in a village. In the course of time, numbers of villages and farmsteads change, and these numbers show the numbers of people taking part in local mobility of inhabitants. The higher are changes in villages and farmsteads, the higher is mobility of inhabitants.

An induction motor reliability survey at an egg processing plant shows that almost 50% of the total motor failures are fan induction motors. Visual investigations of the faulty fan motors show that the main cause of the induction motor failure is air gap eccentricity. In this study, experimental tests are performed on a 1.1kW three-phase induction motor to detect air gap eccentricity and overheating of the induction motor. Heating tests show that end shield housing temperature reaches 100°C with blocked air flow from the fan, which can reduce the lifespan of the bearing. Dimension measurements of the end shield housing show that the dimensions of both tested motors back-end shields are larger than ISO tolerance grade limit. It leads to a loose fit between the housing and bearing, causing air gap eccentricity. Also, both motor back end shield housing has an out-of-round condition leading to an unbalanced magnetic pull. To detect the air gap eccentricity caused by too loose of a fit between housing bore and bearing, current Park’s vector approach is used. To measure three phase current, Hall Effect current transducers, a digital oscilloscope is used and Matlab software to process the measurement data. Results show that Park’s vector approach can be used to detect the air gap eccentricity caused by too loose a fit between bearing and housing. Therefore, the Park’s vector approach can be used to diagnose air gap eccentricity and analyse the type of the air gap eccentricity.

An Induction motor reliability survey at an egg processing plant shows that almost 50% of the total motor failures are fan induction motors. Visual investigations of the faulty fan motors show that the main cause of the induction motor failure is air gap eccentricity. In this study, experimental tests are performed on a 1.1kW three-phase induction motor to detect air gap eccentricity and overheating of the induction motor. Heating tests show that end shield housing temperature reaches 100°C with blocked air flow from the fan, which can reduce the lifespan of the bearing. Dimension measurements of the end shield housing show that the dimensions of both tested motors back-end shields are larger than ISO tolerance grade limit. It leads to a loose fit between the housing and bearing, causing air gap eccentricity. Also, both motor back end shield housing has an out-of-round condition leading to an unbalanced magnetic pull. To detect the air gap eccentricity caused by too loose of a fit between housing bore and bearing, current Park’s vector approach is used. To measure three phase current, Hall Effect current transducers, a digital oscilloscope is used and Matlab software to process the measurement data. Results show that Park’s vector approach can be used to detect the air gap eccentricity caused by too loose a fit between bearing and housing. Therefore, the Park’s vector approach can be used to diagnose air gap eccentricity and analyse the type of the air gap eccentricity.