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This article offers a comprehensive overview of the results obtained through numerical methods in solving the minimal surface equation, along with exploring the applications of minimal surfaces in science, technology, and architecture. The content is enriched with practical examples highlighting the diverse applications of minimal surfaces.

Nowadays, there is a lack of smart marine monitoring systems, which have possibilities to integrate multi-dimensional components for monitoring and predicting marine water quality and making decisions for their optimal operations with minimal human intervention. This research aims to extend the smart coastal marine monitoring by proposing a solar energy planning and control component. The proposed approach involves the adaptive neuro-fuzzy inference system (ANFIS) for the wireless buoys, working online during the whole year in the Baltic Sea near the Lithuanian coast. The usage of our proposed fuzzy solar energy planning and control components allows us to prolong the lifespan of batteries in buoys, so it has a positive impact on sustainable development. The novelty and advantage of the proposed approach lie in establishing the ANFIS-based model to predict and control solar energy in a buoy for different lighting and temperature conditions depending on the four year seasons and to make a decision to transfer the collected data. The energy planning and consumption system for the wireless sensor network of buoys is carefully evaluated, and its prototype is developed. The proposed approach can be practically used for environmental monitoring, providing stakeholders with relevant and timely information for sound decision-making about hydro-meteorological situations in coastal marine water.

Our research is devoted to development of information infrastructure for e-service semi-automatic provision by using distributed data warehouses (DWs) of water protection domain. Development of software for semi-automatic service provision is based on artificial planner and structure of goals adapted for specialized needs of end users. Such e-service preparation mechanism can work under the unified coherent framework for solving the environment protection problems by evaluation of the processes of water consumption and contamination. The possibilities of integration of distributed DWs of water management sector into web portal meeting the requirements of conceptual interoperability are presented. Design approach is based on development of decision support system (DSS) that is designed as multilayered system with multi–componential, interoperable structure of databases (DBs), which are under responsibility of different public administration institutions such as European Environment Information and Observation Network (EIONET) and national environment protection agencies. The infrastructure of EIONET is used for supporting and improving data and information flows. The Water resource management information system (WRMIS) became the kernel component of DSS. WRMIS prototype facilitates data flows between the institutions and gives access to data for relevant institutions and the public providing e-services using proposed DSS. The research investigations are made according to the requirements of European Union Water Framework Directive, Sustainable Development Strategy and ReportNet as the EIONET infrastructure for supporting and improving data and information flows. Additional means are integrated in the structures of DSS as knowledge representation techniques based on conceptual schemas, data flow diagrams, and decision-making rules. The on-line management techniques are based on assurance of interoperability by using Open Web Platform W3C standards for web service development, such as XML, SOAP, HTTP, etc.

The survey of the current status in ontological engineering is presented: notion, peculiarities, applications, design and evaluation of ontologies. The possibilities of using The Brain™, a personal desktop productivity tool, for visualisation of ontologies are outlined and compared with that of Hyperbolic ontology viewer of Ontobroker.

Rule-based systems are usually interpreted as a shallow expert systems realization tool. The paper analyses how the applicability of production rules can be extended using the proposed rule base structuring discipline. Its main constructions are rule grouping according to elementary aspects of investigation, and decomposition of actions. In addition, the rule cycle construction is used for discrete time simulation tasks. The proposed method is illustrated by 2 applications: the expert subsystem for a database, and the simulator of a water heater.

The paper deals with a simple model of the competition of two queuing systems, providing the same service. Each system may vary its service price and its service rate. The customers choose the system with less total service price, that depends on the waiting time and on the service price. The possibility for the existence of equilibrium is investigated. Simple cases are investigated analytically. It is shown that the Nash equilibrium exists in special cases only. A modification of the Stakelberg equilibrium is proposed as a model of competition with a prognosis. This prognosis helps form more stable prices and more stable strategies of competitors. The case of social economics is investigated, too. The dynamics of the competition of more realistic stochastic queuing systems is investigated by Monte Carlo simulation. The simulative analysis is realized by means of a rule-based simulation system.