## Accredited Research Centers & Groups

## Accredited Research Centers by the Babeş-Bolyai University

### Research Center of Applied Analysis

**Supervisor: Dr. Radu Precup, Professor**

Our research concentrates on:

- Fixed point and variational methods for nonlinear equations and systems;
- Loewner theory and open problems of univalent functions;
- Nonlinear multicriteria optimization;
- The Poincare problem and periodic solutions for differential systems;
- Geometry of Banach spaces and generalized metric spaces;
- Nonlinear elliptic boundary value problems in Lipschitz domains and different spaces, using methods of potential theory and variational and topological techniques;
- Numerical and approximation methods for nonlinear equations;
- Analysis of some mathematical models from biology and medicine.

### Research Center of Algebras, Groups and Application

**Supervisor: Dr. Andrei Mărcuş, Professor**

**Research directions:** Category theory and Homological algebra, Universal algebras and multialgebras, Group graded rings, Hopf algebra actions,Abelian groups and Modules, Representations of finite groups and finite dimensional algebras, Applications of algebra in Coding theory

### Applied Computational Intelligence Research Center

**Supervisor: Dr. Horia F. Pop, Professor**

**Research directions:**Artificial Intelligence, Computational Intelligence, Machine Learning, Soft Computing, Real Applications

### Software Engineering Research Center

**Supervisor: Dr. Simona Motogna, Associate Professor**

- Program Analysis and Verification: formal mechanisms (such as Session Logic, K-framework) applied to specify and verify different program properties;
- Software Quality: studies related to evaluation and estimation of software quality factors in large applications and in different versions, and their relation to OO metrics;
- Model Driven Engineering: studies related to Executable Models and their specification language (fUML) and their impact on software development;
- Component Based Software Engineering: deals with developing software as a composition of various third party components. Our studies address problems such as: component selection, constraint based configuration of components and different optimizations.

**Research directions:** Program Analysis and Verification, Software Quality, Model Driven Engineering, Component Based Software Engineering

### Centre for the Study of Complexity

**Supervisor: Dr. Rodica Lung, Associate Professor**

## Research groups on Mathematics accredited by the faculty

### Analysis and Optimization Research Group

**Supervisor: Dr. Kassay Gábor, Professor**

### Geometry Research Group

**Supervisor: Dr. Dorin Andrica, Professor**

- The study of some problems involving the functional category of a pair of differentiable manifolds;
- To obtain some formulas of Rodrigues type for Lie groups of matrices with direct applications in geometric mechanics;
- The study of some properties in the generalized geometry;
- New approaches in the study of Blundon’s configurations.

### Complex Analysis Research Group

**Supervisor: Dr. Gabriela Kohr, Professor**

- Loewner chains and the Loewner differential equation in
**C**^{n}. Analytic and geometric approaches. - Modern applications of Loewner’s theory and control theory to study of univalent mappings with parametric representation on the unit ball in
**C**^{n}. - Variational methods in the study of extremal problems for univalent mappings on the unit ball in
**C**^{n}. - Approximation results for families of univalent mappings in
**C**^{n}. - Harmonic and pluriharmonic univalent mappings.
- Global injectivity results on finite and infinite dimensional complex Banach spaces.
- Applications of geometric function theory in the study of free boundary problems (Hele-Shaw flows).

**Research directions:** Complex analysis in one and higher dimensions, Geometric function theory, Loewner theory in **C**^{n}, Univalent mappings, Applications of complex analysis in fluid mechanics

### Nonlinear Operators and Differential Equations Research Group

**Supervisors: Dr. Radu Precup, Professor and Dr. Adrian Petruşel, Professor**

- Development of operator methods (Fixed Point Theory, Critical Point Theory, Coincidence Point Theory, Spectral Operator Theory) for equations and system of nonlinear equations;
- Applications of the operator methods for the study of various integral, differential and partial differential equations and systems;
- Poincare problem and periodic solutions for systems of differential equations;
- Banach spaces and generalized metric spaces geometry;
- Real-life applications.

The scientific activity of the research group takes into account institutional and personal international cooperation with researchers from Spain, France, Italy, Russia, Hungary, Serbia, China, Taiwan, Thailand, and so on. An important role of the research group scientific life is the research seminar on Nonlinear Operators and Differential Equations (NODE) which has activities every Thursday from 10.30 to 11.30, in room e, Mathematica building.

**Research directions:**

- Development of various operator methods for the study of different nonlinear equations and systems of equations, at least from the following perspectives: existence, uniqueness, qualitative properties of the solutions;
- Applications of the abstract operator methods to nonlinear integral, differential and partial differential equations;
- Modelling and simulation for real-life problems from economy, biology, medicine, etc.

### Numerical and Stochastic Analysis Research Group

**Supervisor: Dr. Octavian Agratini, Professor**

**Research directions:** Numerical methods, Approximation operators, Computer aided geometric design

### Mechanics and Astronomy Research Group

**Supervisor: Dr. Mirela Kohr, Professor**

- Nonlinear elliptic boundary value problems in fluid mechanics based on potential theory, variational methods, and topological methods.
- Boundary value problems on domains with low regularity in the n-dimensional Euclidean setting or compact Riemannian manifolds.
- Partial differential equations, boundary integral equations, integro-differential equations, and their applications in fluid mechanics.
- Pseudodifferential elliptic operators.
- Applications of complex analysis in fluid mechanics.
- Numerical analysis in fluid mechanics and heat and mass transfer theory.
- Dynamical systems in celestial mechanics and astrononmy.

**Research directions:** Potential theory, Fluid mechanics, Partial differential equations, Computational analysis, Celestial mechanics

### Simulation Modelling Control and Visualization Research Group

**Supervisor: Dr. Libál András, Associate Professor**

## Research groups on Computer Science accredited by the faculty

### Research group on Machine Learning

**Supervisor: Dr. Gabriela Czibula, Professor**

**Research directions:** Supervised, unsupervised and reinforcement learning, Hybrid and dynamic machine learning models, Relational association rule mining, Search-based software engineering, Applications of machine learning in various domains, like: software engineering, bioinformatics and computational biology, bioarchaeology, computer vision, natural language processing, social media, etc.

### Distributed Systems and Web Communication Research Group

**Supervisor: Dr. Rareş Boian, Associate Professor**

**Research directions:**Distributed Systems, Computer Networks, Web Communications and Optimization, Web Services Architectures, Cloud systems, Multimedia Streaming, Distributed Virtual Environments, Virtual Reality

### High Performance Interdisciplinary Applications Research Group

**Supervisor: Dr. Virginia Niculescu, Associate Professor**

**Research directions:** Distributed and parallel programming, Models optimization, Simulation and visualization, Image processing and virtual reality, Big Data Analytics, Numerical and statistical simulations

### Formal Concept Analysis Research Group

**Supervisor: Dr. Christian Săcărea, Associate Professor**

- Theory development: Triadic and temporal FCA (3FCA, TCA);
- Applications: weblog analysis, business intelligence, using VR and AR to visualize conceptual structures.

**Research directions:** Formal Concept Analysis and Applications