Research Center for Applied Mathematics in Engineering Sciences (RAMSES)
Keywords: 
divided differences, positive linear operators, special functions, meanvalue theorems, interpolation operators, asymptotic expansions, splines, and Bezier approximation
approximation theory, linear positive operators of Jackson type, orthogonal polynomials, quadrature formulas with high degree of exactness 
Presentation
 New methods and tools in Approximation Theory: obtaining high accurracy representations for the reminder in
approximation formulas; study of the topology of the set of unbounded divergence for approximation procedures.
 Application of MATHEMATICA’s aproximation subroutines: implementing the computation of the nonlinear
functions on low cost microcontrollers.
 High degree quadrature formulas: improving the current accuracy of quadrature formulas by using Laurent
orthogonal polynomials.
 New algorithms for energyminimizing curves and surfaces: obtaining the approximation error, convergence
rate, consistency and stability conditions.
Functional, Differential and Integral Equations:
 Functional Equations: Existence and representation of singlevalued and multivalued solutions. HyersUlam
stability of equations in algebraic and topological structures. Applications to the stability and perturbations of
Dynamical Systems.
 Differential and Integral Equations: Existence and uniqueness of solutions for Ordinary, Partial Differential and
Integral Equations using techniques of Fixed Point Theory. HyersUlam stability of Ordinary, Partial Differential
Equations and Integral Equations. HyersUlam stability of differential and integral operators. Monotone iterative
techniques: obtaining twosided approximations for fixed points and coupled fixed points of monotone and mixed
monotone operators in ordered metric spaces.
 MATLAB and MATHEMATICA
Infrastructures

Applications
Development of original solutions for modelling dynamic 3D environments.
 Development of numerical algorithms for stochastic programming problems arising from application fields such as robotics and energy systems.
Development of realtime perception systems for structured or unstructured 3D
environments, applied to driving assistance systems, autonomous robots, space
observation, or computer assisted medical diagnosis.
 Development of simulation and planning software modules with direct application in robotics and autonomous navigation.
 Development of state of the art solution using pattern recognition and machine learning for specific problems.
Image processing basics: Image processing algorithms and techniques, pattern recognition, machine learning, kernel methods with applications in different fields (computer vision, neuroscience, medical, speech recognition)
Numerical optimization algorithms, time stepping schemes for rigid body systems with applications to robotics, autonomous navigation and granular materials.

Contact
Str. G.Baritiu Nr. 25 G, 400027
ClujNapoca, jud. Cluj, România
Tel: +40 264 401261 +40 264 401539
Fax:
eMail: Mirc...@math.utcluj.ro
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