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Matematický ústav Akademie věd České republiky, v.v.i. |
Research at the Institute
Research in the Institute is concerned mainly with mathematical
analysis (differential equations, numerical analysis, functional
analysis, theory of functions, mathematical physics), probability
theory and mathematical statistics, mathematical logic, theoretical
computer science and graph theory, numerical algebra, topology (general
and algebraic), and theory of teaching mathematics. The Institute has
eight departments with research focused as follows:
- Department of Real and Probabilistic Analysis
- Theory of Perron-type non-absolutely convergent integrals, theory of
generalized differential equations, abstract integration theories,
boundary value problems. Theory of stochastic equations in particular
that of stochastic evolution equations. Development of multivariate and
non-parametric statistical methods and their
application in biology and in materials science, theory of random
closed sets
and their statistical testing (stereology).
- Department of Evolution Differential Equations
- General theory of evolution equations and qualitative properties of
their solutions, in particular: theory of integro-differential
equations of parabolic and
hyperbolic type (equations with memory), mathematical models in fluid
dynamics, Navier-Stokes equations, non-smooth and singular evolution
problems, nonlinear conservation laws, long time behavior of solutions
to
equations of hyperbolic and parabolic type with weak dissipation,
time-periodic processes, free boundary problems.
- Department of Qualitative Methods of Mathematical Analysis
- The investigation of the structure of function spaces and of
operators on these spaces. Application of the results to the solution
of boundary value problems. Bifurcation, stability and continuation of
solutions to variational inequalities and related problems,
applications to problems in mechanics and to reaction-diffusion systems
with (boundary or additional) conditions describing some regulation.
Existence of solutions of static contact problems with Coulomb friction
and dynamic contact problems formulated by the Signorini contact
condition. Application of boundary integral equation method to
mathematical physics.
- Department of Constructive Methods of Mathematical Analysis
- Mathematical and numerical analysis by means of the finite element
method of nonlinear physical phenomenons that are mathematically
described by partial differential equations and inequalities of
elliptic, parabolic or hyperbolic type.
- Department of Topology and Functional Analysis-
The operator theory in connection with the theory of Banach algebras
and the function theory. General topology, functional analysis, Boolean
algebras.
- Department of Mathematical Logic, Numerical Algebra and Graph Theory - Mathematical logic, set theory, proof complexity, computational complexity, on-line algorithms,
extremal combinatorial problems, theory of matrices, numerical algebra.
- Branch in Brno -
Algebraic topology, differential geometry, homological algebra,
homological physics. Global properties of linear differential equations
of higher order. Boundary value problems for functional differential
equations and their systems. Asymptotic behaviours of solutions of
differential equations. Partial differential equations of hyperbolic
type. Differential equations in the Banach spaces. Qualitative theory
of half-linear and quasi-linear differential/difference equations and
dynamic equations on time scales.
- Department of Didactics of Mathematics -
Problems of mathematics education of students aged 5-15 years.
For more information about the research in the Institute, see the yearbook of the Institute (.pdf, 850KB).
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