The decreasing number of the Lithuanian residents has strong impact on the educational system: the number of pupils is decreasing, the schools are getting closed. School is considered to be the provider of educational services, so it is necessary to search, how to preserve and attract clients – pupils. The growing competition induces search for distinctiveness among the schools. According to the theory of generations of William Strauss and Neil Howe, now we have to educate representatives of generation Z, who do not like violence, restrictions, want to be distinctive and are open to the world of technologies. The teacher faces the challenge when s/he wants to convey mathematical skills to these pupils. The profile teaching followed by training based on individual curricula provided more choices for the pupils. This freedom led to the dead-end of mathematical literacy and forced to return to a compulsory national final exam of Mathematics and to change the indexes for the persons entering studies of the first cycle and integrated studies. In the article, mathematics achievements and situation in schools in Lithuania as well as the measures taken to improve mathematical literacy in the country are described.

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 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 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.

In the food industry, there is always a demand for food products which are colourful, have an attractive appearance, and also have nutritional and health-enhancing properties to attract the attention of consumers. Synthetic pigments are widely used in the global market, however, they can cause many side effects such as hyperallergenicity, carcinogenicity and other toxicological problems. Recent studies have revealed that microorganisms are an abundant source of natural colours that allow the industrial production of safe, environmentally friendly biodegradable pigments. The aim of the work was to isolate pigmented microorganisms from environmental samples, select fermentation conditions, isolate pigments from microorganisms and check their antimicrobial activity. Pigments have been isolated from various sources such as soil, food waste, flour, etc. Growth parameters of pigment-producing microorganisms such as growth temperature, pH, and tryptone and NaCl concentration in the medium were optimised to evaluate pigment production. After fermentation, five types of pigments were isolated by cell lysis with an ultrasonic bath and solvent extraction. The antimicrobial activity of the extracted pigments was investigated. During the study, the optimal conditions for the growth of microorganisms were determined: temperature of 30 °C, pH of 7, concentration of 3% tryptone and 6% NaCl in the culture medium. Glycerol was found as an additional carbon source, which had a positive effect on pigments production. The results of the antibacterial effect of the extracted pigments showed that P. aeruginosa was the most sensitive to the effect of the pigments. The pink-red pigment showed the highest antimicrobial activity against the tested pathogenic bacteria.

The contemporary scientific and technical community claims that the new development paradigm will be based on the priority of the universal laws of nature, the principles of ecological economics and the widespread use of digital transformation. The analysis of the sustainable development strategy Latvia 2030 and the presented changes in the value of indicators showed that, it is quite difficult to put together a common unified picture of Latvia’s movement towards sustainable development. The main goal of the article is to present a new approach to the assessment of sustainable development and to monitoring system, using a system’s power changes analysis method. In the context of a Latvian sustainable development strategy, the authors presented the results of the formalisation of new approach to the sustainable development monitoring, using an invariant coordinate system in units of power (energy flow) in compare with calculated data in monetary terms. Calculations and the initial interpretation of the results of Latvia as well as of the five EU countries from the Baltic Sea region – Denmark, Sweden, Finland, Estonia and Lithuania – were carried out for the period 1990–2019. The presented indicators of sustainable development show that achieving the strategic goals of Latvia 2030 would be very difficult without any serious internal and external incentives. The results can provide a basis for creation of the development strategy both the country as a whole and each region separately.

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.

1991-2017 the Southeast coast of the Baltic Sea area, Lithuania, Latvia and Kaliningrad Region of the Russian coastal habitats was very intense, often chaotic variety of recreational facilities and areas of privatization and urbanization. These processes significantly influenced the character of the recreational landscape of Palanga, Jurmala and other resorts and coastal areas, as well as the expression of the urban structure and architecture of seaside towns, Ventspils, Liepaja, Giruliai, Melnragė, Karklė, Šventoji, Curonian Spit and other settlements. After a quarter of a century, some tendencies of the recreational environment and the evolution of the cultural landscape identity can be noticed. Recently, several projects for the improvement of recreational infrastructure and architectural environments have been implemented in Lithuania with the assistance of the European Union Structural Funds. Unfortunately, the results of the projects are not always positive. The planning of coastal settlements is often overlooked by good long-term planning experience. This article analyses the impact of changes in the quality of the Lithuanian recreational territorial system in the South-Eastern Baltic and the region’s recreational potential. Palanga resort areas dominated by architectural chaos and recreational quality of the environment tended to deteriorate; especially experts poorly assessed the central Basanavičiaus Street. The changes in cultural landscapes are influenced by a whole range of methodological and practical factors: insufficiently effective research and modelling methods, unjustified privatization of state property, huge flows of individual automobiles, and faults in the formation of recreational greenery. Based on the research of the recreational system of the coastal region of the long-term seaside, it can be concluded that in recent years the quality of the environment of many coastal zones of Lithuania has lost important qualitative components, deteriorated the quality of public spaces and increased urban and architectural chaos