Conjugate Analysis, Harmonic Analysis, Classical and Global Analysis, Banach Spaces, Ordered Spaces, Universally Unbounded Spaces, Topology and Connections with Set Theory, Descriptive Set Theory and Combinatorics, Operator Theory, Non-Commutative Operator Algebras, EP Operators, Generalized Inverse Operators, Stability of Functional Equations, Analytic Inequalities, Applications of Analysis to Economic Problems, Nonlinear Analysis, Dominated Analysis, Nonlinear Monotone Operators, Nonlinear Stochastic Equations, Dominated Evolutionary Conclusions.
Research Areas
Today, the research activity of the Department’s members is significant, as recorded in the international database of mathematical works MathSciNet, with more than 450 articles in high-level scientific journals in recent years. The main areas of research activity of the Department are
Mathematical Analysis
Differential Equations
Linear and Nonlinear Problems, Solution Explosion Problems, Solution Stability, The Direct and Inverse Scattering Problems in Acoustic, Electromagnetic, Elastic, Thermoelastic Fields and Applications in Biomedical Engineering, Eigenvalue Problems, Dynamical Systems, Bifurcation Theory, Construction of Mathematical Models.
Numerical Analysis
Study and Construction of New Runge-Kutta & Runge-Kutta-Nystrom Methods for 1st & 2nd Order Differential Equations, and Methods with Interpolation Properties, Optimal Control in Ordinary & Partial Differential Equations, Existence and Optimization Conditions for Non-Convex Optimal Control Problems, Discretization with Runge-Kutta and Finite Element Methods, Error Estimates for Finite Element Methods in Evolutionary Problems and in Systems arising in Optimization Problems, Approximation Methods for Partial Differential Equations with Solutions with Low Regularity Assumptions.
Statistics and Probabilities
Reliability Analysis and System Reliability, Queuing Theory and Service Systems, Stochastic Calculus, Stochastic Differential Equations, Financial Models, Stochastic Processes, Time Series and Regression Analysis, Statistical Modeling, Statistical Quality Control, Statistical Methods of Classification & Statistical Diagnostic Medicine, Statistical Survival and Reliability Models, Statistical Methods for Locating Outliers, Model and Variable Selection, Optimal Statistical Data Partitions, Development of Non-Parametric Bayesian Statistical Methodology, MCMC Methods and Stochastic Optimization Algorithms.
Algebra
Numerical Fields of Matrices, Spectral Disturbances of Matrices, Pseudospectra of Polynomial Matrices and Stability of Systems, L-Property of Matrices, Analysis of Positive Matrices, Associative and Non-Associative Algebras, Grassmann Algebras, and Lie Superalgebras.
Topology
Low-Dimensional Topology, Node Theory, and Applications in Biology, Physics, and Chemistry.
Distinctive Mathematics and Theoretical Computer Science
Theory of Codes, Graphs, Graph Representation, Algorithms and Complexity, and Their Applications in Informatics.
Systems Theory and Optimal Control
Geometric Properties, Stability, Stabilization, Observers, Stochastic Control.
Geometry
Geometric Methods in Engineering, Algorithmic Geometry.