Topic

1. THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING
                Basic principles of mathematical modelling. Direct and inverse problems of mathematical modelling. Universality of mathematical models. Analogy principle. Model hierarchy.
                Methodology of mathematical modelling. System analysis. Complex systems and decomposition. Static and dynamic models. Discrete and continuous. Deterministic and stochastic.
                Ordinary and partial differential equations. Theory and applications. Applied algebra and numerical analysis. Numerical methods and optimization methods. Variation methods. Approximation, stability, convergence.
                Probability theory and applied statistics. Stochastic processes. Combinatorics. Graph theory. Waiting line theory. Games theory. Statistical Theory of Expert Assessments.
                Theory of management, optimization and their applications. Statistical modelling and applications.
                New objects and methods of mathematical modelling. Fractals in mathematics. Dimensionality of self-similarity. Self-organisation and structure formation. Synergetics.
Software tools for mathematical modelling. Applied packages for engineering analysis. Mathematical modelling of future internet and development of future technologies for internet security. Mathematical models and intelligent information systems.
                Mathematical modelling in fundamental and applied physics, mechanics, chemistry and biology.

                2. MATHEMATICAL MODELLING OF TECHNOLOGICAL PROCESSES AND SYSTEMS
Technological processes as objects of automation. Approaches to construction of mathematical models. Main phases in analytical and experimental modelling. Mathematical methods of management.
Modelling of continuous and discrete processes and of complex production systems. Optimization. New methods and approaches.
Modelling of smart production technologies and systems. Modern machine building technologies – laser, plasma, ultrasound, radiation, optical, etc. Additive technologies and additive production. Digital production of optimal items made of metal, polymers, composites and ceramics.
                Virtual technologies and simulations. Information and computer technologies. Robotics. Artificial intellect. Radio electronics. Instrument making. Communication and navigation engineering and technologies. Mathematical modelling and supercomputing engineering.
               Modelling of materials, structures, systems - SMART technologies. Powder and plasma metallurgy. Materials science, physics, mechanics and chemistry of solid state. Composite materials and coatings. Strengthening technologies. Microtechnologies and micromechanical systems. Nanotechnologies, nanoelectronics, nanometrology, nanoequipment and nanoindustry.
                Modelling of environmentally benign technology. Waste treatment. Energy engineering and technologies. Solar and hydrogen power generation. Energy recuperation.
Ecological modelling. Modeling of forest ecosystems. Modelling of integrated infrastructure and urban development, environment and ecology, global changes and nature risks, water resources.
                Modelling in geology and geophysics. Extraction and processing of mineral raw materials. Mechanization, electrification and automation of mines.
                Modelling of new and advanced technologies for designing and management of processes in petroleum refining and petrochemistry, chemical, metallurgical, plastic and rubber, paper and pulp, textile, leather, pharmaceutical and etc. industries.
Mathematical models and intelligent information systems in transport problems. Security and sustainable development. Virtual simulations and optimization of logistics processes.

3. MATHEMATICAL MODELLING OF SOCIO-ECONOMIC PROCESSES  AND SYSTEMS
Socio-economic systems, methods for their study and modelling. Specific features of socio-economic processes modelling. Advantages and shortcomings of generally accepted approaches. Factors for the efficient modelling of processes. Up-to-date trends and computing complexes for modelling of socio-economic processes.               
Statistical and stochastic models. Neural networks. Situation modelling.
Software for modelling and management of business processes. Program languages, tools and technologies for modelling and management of business processes.
Mathematical models of business strategies and management strategies. Industrial management. Production engineering and management. Technological entrepreneurship and innovation. Organisational behaviour and leadership. Social and behavioural simulation. Project management.
Models of innovation management, of innovation products and intellectual property marketing.
Nonlinear processes, system analysis and applied synergetics. Synergetic, geopolitical and geo-economic models on the targeted development of competitiveness and finances.
Modelling of clouds services, data analysis and assessment. 3D production simulation. Remote control and maintenance of facilities.
Modelling of Smart Factory, industrial infrastructure , integrated production and industrial restructuring; Industrial internet infrastructure.
               Modelling of innovation and credit and taxation state policy as determining factor for the industry digitalisation development. Models on the effect of smart production technologies and systems on the financial sector and economic development. Global, regional and investment consequences. Investments in high tech sectors.
Mathematical models and social issues of production digitalisation. Models for concepts of human labour, employment, skills and strategies for the labour force development. Potential danger of unemployment. Digital competence. Matching the engineering and digital competences. E-training.

4. MATHEMATICAL MODELLING OF MEDICAL-BIOLOGICAL PROCESSES AND SYSTEMS
Specific features of modeling living systems. Methods and tools for mathematical modeling and computer science in theoretical biophysics, biology, medicine. the role of the models in the development of molecular and cell biology, systemic biology, physic-chemical biology, genetic and biomedical engineering, physiology, fundamental medicine.
Features of mathematical models of medical and biological systems: the presence of aftereffects in the dynamics of the describing system, the uncertainty (structured and unstructured) of the parameters of the mathematical model, the possible presence of random factors, the multicriteria of the tasks, often with conflicting criteria. Mathematical models of the dynamics of infectious diseases, the task of processing static and dynamic observations in real time.
Specific features of imitative modeling of biological processes and systems. Specialized languages for imitative modeling. Imitative modeling of nerve fibers conductivity.
Auto-oscillation processes in biological systems. Generalized model "predator - prey". Auto-oscillation in biochemical reactions. Fluctuation in photosynthetic processes.
Models for transport of substances through biomembranes. Diffusion. Cell membranes. Passive and active transport. Symport and antiport. Membrane exchangers.
Models of excitational environments. Membrane potential. Rest potential. Membrane patterns as electrical circuits.
Organism and principles of its management. Mechanisms of management - the impact of organ, body, population. Target function of control at cell level, organism, population. Evolutionary Optimality. Mathematical modeling of organisms.
Modeling of muscle impulses. Mathematical model of heart muscle. Modeling electrical and mechanical phenomena in the heart muscle. Modeling of the cardiac activity based on the theory of determined chaos. Modeling and simulation of the locomotor system and organs in the human body.
Mathematical models of diseases. Solution of diagnostic problems. Analysis of information flows in the medical care system. Synthesis of medical care systems.
Prospects in the development of the "virtual person". Artificial life and Virtual evolution. Computer modeling of the life forms.

4.1. SPECIAL MATHEMATICAL ISSUES, APPLICABLE IN THE PROBLEMS IN MODELING OF MEDICAL-BIOLOGICAL SYSTEMS
Mathematical approaches to the analysis of dynamic processes, based on the theory of image recognition, mathematical stability theory, statistical methods, computer technologies and decision making theory, methods for solving multicriteria problems.
The theory of differential-difference systems of delayed and neutral types. The direct Lyapunov method for analyzing stability and robust stability. Nonlinear systems and the area of asymptotic stability.
Systems with distributed parameters. Numerical methods for differential-difference systems and systems of partial differential equations: convergence, accuracy, stability, complexity. Discretization, accuracy estimation.
Control laws synthesis. Stabilization, adaptation of parameters, compensation of delays. Multi-agent systems and switching systems. Optimal control. New approaches to realizing control laws in real time.
Information systems and modern computer technologies. Features of application packages for medical diagnostics, planning and implementation of therapy, as well as further support of the patient.
Applications of graph theory in mathematical models of dynamical systems. Applications of graph theory in multidimensional dynamical equations systems of mathematical physics, including problems of identification of system parameters and stabilization of equilibrium states.

The official language of theInternational Scientific Conference “MATHMODEL” is English.

 

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