{"id":1658,"date":"2025-02-12T22:16:16","date_gmt":"2025-02-12T19:16:16","guid":{"rendered":"http:\/\/math.karazin.ua\/?page_id=1658"},"modified":"2025-02-12T22:16:16","modified_gmt":"2025-02-12T19:16:16","slug":"%d0%ba%d0%b0%d1%84%d0%b5%d0%b4%d1%80%d0%b0-%d0%bf%d1%80%d0%b8%d0%ba%d0%bb%d0%b0%d0%b4%d0%bd%d0%be%d1%97-%d0%bc%d0%b0%d1%82%d0%b5%d0%bc%d0%b0%d1%82%d0%b8%d0%ba%d0%b8","status":"publish","type":"page","link":"https:\/\/math.karazin.ua\/en\/scientific-directions\/%d0%ba%d0%b0%d1%84%d0%b5%d0%b4%d1%80%d0%b0-%d0%bf%d1%80%d0%b8%d0%ba%d0%bb%d0%b0%d0%b4%d0%bd%d0%be%d1%97-%d0%bc%d0%b0%d1%82%d0%b5%d0%bc%d0%b0%d1%82%d0%b8%d0%ba%d0%b8\/","title":{"rendered":"Department of Applied Mathematics"},"content":{"rendered":"<p><i>Mathematical control theory<\/i><\/p>\n<p>&nbsp;<\/p>\n<ul>\n<li>Mapping nonlinear controlled systems to linear ones<\/li>\n<li>Min-moment problem and solution of the time-optimal control problem<\/li>\n<li>\u041c\u0435\u0442\u043e\u0434 \u0444\u0443\u043d\u043a\u0446\u0456\u0457 \u043a\u0435\u0440\u043e\u0432\u0430\u043d\u043e\u0441\u0442\u0456<\/li>\n<li>Mapping trajectories of nonlinear controlled systems to trajectories of linear systems<\/li>\n<li>Controllability of linear systems with control constraints<\/li>\n<li>Algebraic methods for studying nonlinear controlled systems<\/li>\n<li>Homogeneous approximation, methods of its description and construction<\/li>\n<li>Nonlinear time-optimal control problem<\/li>\n<li>Nonlinear controlled systems, mapping of nonlinear systems<\/li>\n<li>Stabilization problem for nonlinear systems in the critical case<\/li>\n<li>Positional synthesis problem for essentially nonlinear systems<\/li>\n<li>Stabilization, finite-time stabilization, estimation of motion time<\/li>\n<li>Controllability of mechanical systems<\/li>\n<li>Uncertain systems. Synthesis problem for robust systems, robust control<\/li>\n<\/ul>\n<p><i>Mathematical biology<\/i><\/p>\n<ul>\n<li>Mathematical modeling in biology and medicine<\/li>\n<li>Mathematical modeling in ecology<\/li>\n<li>Optimization methods<\/li>\n<li>Biomechanics<\/li>\n<li>Mathematical modeling of liver regeneration processes<\/li>\n<li>Problem of finding optimal control strategies for liver regeneration processes<\/li>\n<\/ul>\n<p><i>Partial Differential Equations<\/i><\/p>\n<ul>\n<li>Control theory<\/li>\n<li>Qualitative properties of solutions<\/li>\n<li>Boundary value problems<\/li>\n<li>Nonlinear partial differential equations<\/li>\n<li>Qualitative theory of quasilinear parabolic equations<\/li>\n<\/ul>\n<p><i>Algebra<\/i><\/p>\n<ul>\n<li>Algebraic properties of implicit differential and difference equations over rings, including over the ring of integers and over the ring of polynomials<\/li>\n<li>Linear and nonlinear differential equations in modules over commutative rings<\/li>\n<li>Non-Archimedean topologies, p-adic numbers<\/li>\n<\/ul>\n<p><i>Hydrodynamics<\/i><\/p>\n<ul>\n<li>Wave motions, vortices<\/li>\n<li>Hydrodynamic theory of filtration<\/li>\n<\/ul>\n<p><i>Applied interval analysis<\/i><\/p>\n<ul>\n<li>Methods for solving interval equations<\/li>\n<li>Stability of interval matrices<\/li>\n<\/ul>\n<p><i>Data analytics\u00a0<\/i><\/p>\n<ul>\n<li>Data structures and models<\/li>\n<li>Databases, information systems<\/li>\n<li>Structural and semantic data analysis<\/li>\n<li>Volumetric and cross-domain knowledge<\/li>\n<\/ul>","protected":false},"excerpt":{"rendered":"<p>\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u0430 \u0442\u0435\u043e\u0440\u0456\u044f \u043a\u0435\u0440\u0443\u0432\u0430\u043d\u043d\u044f &nbsp; \u0412\u0456\u0434\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u043d\u044f \u043d\u0435\u043b\u0456\u043d\u0456\u0439\u043d\u0438\u0445 \u043a\u0435\u0440\u043e\u0432\u0430\u043d\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043c \u043d\u0430 \u043b\u0456\u043d\u0456\u0439\u043d\u0456 Min-\u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0430 \u043c\u043e\u043c\u0435\u043d\u0442\u0456\u0432 \u0456 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1645,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1658","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/math.karazin.ua\/en\/wp-json\/wp\/v2\/pages\/1658","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.karazin.ua\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/math.karazin.ua\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/math.karazin.ua\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/math.karazin.ua\/en\/wp-json\/wp\/v2\/comments?post=1658"}],"version-history":[{"count":1,"href":"https:\/\/math.karazin.ua\/en\/wp-json\/wp\/v2\/pages\/1658\/revisions"}],"predecessor-version":[{"id":1663,"href":"https:\/\/math.karazin.ua\/en\/wp-json\/wp\/v2\/pages\/1658\/revisions\/1663"}],"up":[{"embeddable":true,"href":"https:\/\/math.karazin.ua\/en\/wp-json\/wp\/v2\/pages\/1645"}],"wp:attachment":[{"href":"https:\/\/math.karazin.ua\/en\/wp-json\/wp\/v2\/media?parent=1658"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}