Faculty of Automation and Computer Science > Research > Mathematics > Research areas > Applied Mathematics

Applied Mathematics

Research team

Alexandru Ioan Mitrea, Nicolaie Lung, Mircea Ivan, Ioan Gavrea, Gheorghe Toader, Silvia Toader, Daniela Rosca, Radu Peter, Dorian Popa, Mircia Gurzau, Dalia Cimpean, Vasile Dincuta, Daniela Inoan, Adela Novac, Mircea Rusu, Daria Dumitras, Alina Santamarian, Eugenia Duca, Lucia Blaga, Teodor Potra, Ciresica Jalobeanu, Adela Capata 

Research fields

  • Approximation of functions, finite element method, quadrature formulas
  • Partial differential equations, numerical methods
  • Differential geometry of curves, deformable curves (snakes)
  • Calculus of Variations
  • Optimization
  • Image Processing
  • Medical Image Analysis

 

Recent research projects

 

“MoDef – Modelling using advanced methods and techniques based on the theory of deformable surfaces with applications in computer assisted surgery and other modelling procedures of anatomic structures”, national research grant funded by ANCS, CNMP-PC, no. D11-018/2007-2010

Alexandru Ioan Mitrea coordinator, Sergiu Nedevschi, Mircea Ivan, Nicolaie Lung, Gheorghe Toader, Dorian Popa, Daniela Inoan, Radu Peter, Mircia Gurzau, Dalia Cimpean, Delia Mitrea, Mircea Rus, Sorina Ciplea, Mihaela Manisor 

Project summary:

The theory of deformable models is an advanced and interdisciplinary scientific domain, which has appeared and developed in the last twenty years in connection

with practical problems of medicine, image processing and physics. The notions of deformable surface and deformable curve, commonly known as snakes, were

introduced by M.Kaas, A.Witkin and D.Terzopoulos in 1988. In time, this domain is characterized by a rapid development and proliferation : the anisotropic model (1988), the probabilistic model-Kalman snake (Terzopoulos, Szelinsky-1992), the model of deformable surfaces proposed by L.Cohen and I.Cohen (1992), the classical g-snake (Rougon and Preteux-1994), the adaptive oriented g-snakes (Rougon and Preteux-1998), the multiscale segmentation models (Sochen and others,1998), the active multiscale models (Bresson and others,2005). The applications in medical image analysis has a continuous expansion, especially concerning computerized medical images; we also remark, the application of the finite element method associated to cylindrical or spherical type surfaces in the segmentation of some anatomical structures.

 

The objectives of our project are the following:

- to realize a systematic and rigorous investigation of the deformable surfaces, from a mathematical point of view, including the energy-functional and the evolution equations of its associated surface

- to generate performing algorithms (iterative methods) in order to obtain the optimal surface (the minimum of the energy-functional)

- to characterize the stability and the convergence of the previous algorithms (including the approximation error)

- based on the previous mathematical results including performing algorithms, to generate a software component in the context of the partnership in order to implement the 3D computerized model of the abdominal wall; this component will  use the Visual C++ language of the environment DotNet and will simulate the movements of the abdominal wall in real time in the case of the patients with post-surgery hernia as well as after prosthetic procedures; at this level, some instruments of generating a context of virtual reality will be used

- to implement other assisting methods of the modelling procedures on anatomic structures, such as orthodontic prosthetic, as well as of an expert kernel for assisting surgery decisions and other similar procedures to build a knowledge base which will contain all the results obtained before surgery and that will be the reference element for the statistical analysis of the post surgery results.

 

“Multi-resolution analysis, numerical methods and reverse dynamics, integrated in software instruments for performance improving in the satellite tele-detection”, national research grant funded by  CNCSIS A-1582, (2007-2008).

Nicolaie Lung project manager, Mircea Ivan, Paulina Mitrea, Delia Mitrea, Daniela Inoan, Mircea Rus, Adela Novac, Alina Sintamarian.

“Advanced Methods and Alghorithms of Mathematics related to the Deformable Curves Theory with applications in Image Processing and Medicine”, national research grant funded by CNCSIS A- 1255, (2006-2008).

Alexandru Ioan Mitrea project manager, Nicolaie Lung, Mircea Ivan, Gheorghe Toader, Radu Peter,  Mircia Gurzau, Delia Mitrea, Dalia Cimpean, Vasile Dincuta.

Publications

A. Capata, “Existence results for Stampacchia and Minty type generalized variational inequality problems”, Annales of the T. Popoviciu Sminar of Functional Equations, Approximation and Convexity, 7, 2009, 13-31.

 

D. S. Cimpean, “Mathematical models applied in engineering”, Editura Digital Data Cluj, Cluj-Napoca, 2009.

 

D. S. Cimpean, I. Pop, D. Ingham, J. Merkin, “Fully developed mixed convection flow between inclined parallel plates filled  with a porous medium”, Transport in Porous Media International Journal, 77 (1), 2009, 87-102.

 

E. Duca, D. Duca, “Otimization problems  and approximated optimization problems”, Studia Universitatis Babes-Bolyai Mathematica, 54 (4), 2009, 49-62.

 

C. Marza, E. Duca, G. Iacob, “Technical applications of the curved surfaces intersections to the pipelineconections”, Acta Technica Napocensis Series: Applied Mathematics and Mecanics, Ia (52), 2009, 169-175.

 

B. Gavrea, “Some convergence results in rigid-body dynamics”, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2009, Rethymno, Greece, 18-22 September 2009, 1396-1399.

 

V. Boca, C. Gyenge, O. M. Gurzau, L. Olah, “Research regarding analitical and numerical determination of worm gear with parabolical profile”, Proceedings of the MTeM (Modern Technologies in Manufacturing), Technical University of Cluj Napoca, (Faculty of Machine Building, Department of Manufacturing Engeenering), 2009, 3-16.

 

V.-H. Ile, “Functii de tip logic cu aplicatii in mecanica structurilor”, Editura Mediamira, Cluj-Napoca, 2009.

 

V. Chifu, I. Salomie, R. Agota, V. Radoi, D. Inoan, “Web Service Composition Approach Based On a Graph of Service Cells”, Proceedings of the 2th Knowledge Engineering: Principles and Techniques Conference (KEPT2009), Babes-Bolyai University, Cluj-Napoca, 2009, 308-311.

 

A.I. Mitrea, S. Nedevschi, D.M. Ivan, D. Mitrea, O.M. Gurzau, N. Lung, D.Cimpean, “Modele deformabile 2D. Aplicatii”, Editura UT Press, Cluj-Napoca, 2009.

 

A.I. Mitrea, D.M. Ivan, D. Mitrea, D. Inoan, P. Mitrea, “Deformable variational models used in medical imaging”, Proceedings of the International Conference on Advancements of Medicine and Health Care Through Technology  (Meditech), IFMBE Proceedings Springer, vol. 26, 2009, 273-278.

 

I. Raşa, “A general block frequency test”, Automation Computers Applied Mathematics, 18 (1), 2009, 173-176.

 

D. Rosca, “Matematici discrete”, Editura Mediamira, Cluj-Napoca, 2009.

 

G. Plonka, S. Tenorth, D. Rosca, “Image approximation by a hybrid method based on the Easy Path Wavelet Transform”, Proceedings of the 43rd Asilomar Conference on Signals, Systems and Computers, Nov. 1-4, 2009, Pacific Grove, CA, pp. 442-446.

 

G. Plonka, D. Rosca, “Sparse representation of sperical data using the Easy Path Wavelet Transform”, Proceedings of the 8th International Conference on Sampling Theory and Applications, Marseille May 18-22, 2009, paper 89.

 

Gh. Toader, “The hierarchy of convexity and some classic inequqlities”, Journal of Mathematical Inequalities, 3 (3), 2009, 305-313.

Gh. Toader, S. Toader, “A hierarchy of logarithmic convexity of functions”, Annales of the Tiberiu Popoviciu Sminar of Functional Equations, Approximation and Convexity, 7, 2009, 147-154.

 

D. S. Cimpean, I. Pop, D. Ingham, J. Merkin, “Fully developed mixed convection flow between inclined parallel plates filled with a porous medium”, Transport in Porous Media International Journal, 10 (7), 2008 (online).

 

D. S. Cimpean, “Entropy analysis for a mixed convection flow in an inclined channel: downward case”, Automation Computers Applied Mathematics, 17 (3), 2008, 229-236.

 

D. S. Cimpean, N. Lungu, I. Pop, “A problem of entropy generation in a channel filled with a porous medium”, Creative Mathematics and Informatics, 17 (3),  2008, 357-362.

 

E. Duca, “Pareto solutions for a multiobjective optimization problem”, Automation Computers and Applied Mathematics, 17 (3), 2008, 253-261.

 

B. Gavrea, “Pointedness of the friction cone in rigid-body simulation”, Automation Computers and Applied Mathematics, 17 (3), 2008, 435-442.

 

O. M. Gurzau, D. Popa, “Mathematical models of the heat transfer in Tissues”, Automation Computers and Applied Mathematics, 17 (1), 2008, 88-93.

 

O. M.  Gurzau, D. Popa, S. Nedevschi, “An Approximation of the Freezing  Front in an Experiment in Vitro with two Cryoprobes”, Biosignal 2008, Brno , Univ.of Technology, IEEE, EMB, EURASIP, Abstract page 41, vol. 19, Extended paper on CD, ISSN 1211-412x, ISBN 978-80-214-3612-1

 

O. M. Gurzau, D. Popa, “Mathematical models of the heat transfer in tissues”, Automation Computer Science Applied Mathematics, 17 (1), 2008, 88-93. (ISSN 1221-347x)

 

V. Ile, “Logic type functions in the torsion problem of "L" shape cut bar”, Automation Computers and Applied Mathematics, 17 (3), 2008, 449-457.

 

A. I. Mitrea, “Matematici avansate”, Editura Mediamira, Cluj-Napoca, 2008.

 

A. I. Mitrea, D. Mitrea, “Discrete best approximation in the theory of deformable models”, Automation, Computers and Applied Mathematics, 17 (3), 2008, 351-359.

 

A. I. Mitrea, P. Mitrea, “Deformable Models: Software Implementation based on Mathematical Fundamentals”, Proceedings of IEEE Conference Automation, Quality and Testing, Robotics (AQTR 2008), UTCN, IPA, IEEE, TTTC, vol. 3, 2008, 378-383.

 

D. Moga, R. A. Munteanu, M. Dumitrean, M. Dobra, R. Moga,  “Wireless system for remote tilt measurement in monitoring and control applications”, Advances in Electrical and Computer Engineering, 8 (2), 2008, 32-36.

 

R. Moga, M. Munteanu, C. Rusu, D. Rafiroiu, G. Chindris, R. A. Munteanu, “A hierarchical implementation of medical data transmission”, 2008 IEEE International Conference on Automation, Quality and Testing, Robotics AQTR 2008 (Quality of Life and e-Health Section), ISBN 978-1-4244-2576-1,Cluj-Napoca, May 22-25, 2008, 77-80.

 

R. Moga, M. Munteanu, M. Olteanu, L. Vlădăreanu, R. A. Munteanu, A. Gal, “Electronic image processing in biometrics analysis through virtual instrumentation”, Computers and Simulation in Modern Science, Volume II, Selected papers from the WSEAS Conferences 2008,  ISI Proceedings, Published by WSEAS, ISSN 1790-2769, 322-327.

 

D. Rosca, “Piecewise constant wavelets on triangulations, obtained by 1-3 splitting”, International Journal on Wavelets, Multiresolution and information processing, 6 (2), 2008, 209-222.

 

J-P. Antoine, D. Rosca, “The wavelet transform on the two-sphere and related manifolds – A Review” (invited paper), Proceedings of SPIE, Optical and Digital Image Processing, vol. 7000 (2008), B-1-15

 

D. Rosca, J-P. Antoine, “Constructing orthogonal wavelet bases on the sphere”, 16th European Signal Processing Conference (EUSIPCO 2008), Lausanne, Switzerland, August 25-29, 2008, paper 1569102372.


A. I. Mitrea, “On the Diffusion Equation connected to the theory of Deformable Models”, Proceedings of the  International  Conference-Competitiveness and European Integration, Quantitative Economics Section, Cluj-Napoca, Romania, October 26-27, 2007, 182-187

 

U. Abel, M. Ivan, “A complete asymptotic expansion of power means”, Journal of Mathematical Analysis and Applications, 325(1), 2007, 554-559.

 

M. Ivan, “A note on the Hermite interpolation polynomial for rational functions”, Applied Numerical Mathematics,57(2), 2007, 230–233.

 

O. M. Gurzau, D. Popa, T. Marita, M. Lucan, “Mathematical and Experimental Models of the Heat Transfer in Tissues”,Automation Computers and Applied Mathematics. Scientific Journal, 2007, 67-72.

 

A. Mitrea, “Multi-resolution analysis, numerical methods and reverse dynamics, integrated in software instruments”, Proceedings of International IEEE-TTTC International Conference on Automation, Quality and Testing, Robotics AQTR 2006 (THETA 15), Cluj-Napoca, Romania, May 25-28, 2006, 475-479.

 

D. Cimpean, J. Merkin, I. Pop, D. Ingham, “On a Free Convection Problem Over a Vertical Flat Surface in a Porous Medium”, Transport in Porous Media International Journal, 64, 2006, 393-411.

 

A. I. Mitrea, D. Mitrea, “Calculus of variations in the theory of deformable models with applications to image processing”, Automation Computers and Applied Mathematics. Scientific Journal, 15(1), 2006, 57-62.

 

N. Lungu, Qualitative problems in the theory of differential equations, 2006, Digital Data Publisher.

 

G. Toader, J. Sandor, “Inequalities for general integral means”, Journal of Inequalities in Pure and Applied Mathematics, 7(1), 2006, art.13,

http://jipam.vu.edu.au/,

 

P. Mitrea, A. I. Mitrea, M. Anisiu, A. Imbroane, “Multi-resolution analysis, numerical methods and reverse dynamics, integrated in software instruments”, Proceedings of International IEEE-TTTC International Conference on Automation, Quality and Testing, Robotics AQTR 2006 (THETA 15), Cluj-Napoca, Romania, May 25-28, 2006, 475-479.

 

A. Crai, T. G. Potra,  H. Iancau, “Mathematical modeling of the flow of the composite materials with short fibres”, Proceedings of the Conference “Trends in Development of Machinery and Associated Technology” – TMT, Barcelona,Spain, September, 2006, 1179-1183

 

I. Gavrea, “About a result of Tiberiu Popoviciu”, in B.Bojanov (Ed.), Proceedings of the International Conference Constructive theory of functions, Varna, Bulgaria, 2005, 121-126.

 

A. Sintamarian, “Common fixed point structures for multivalued operators”, Scientiae Mathematicae Japonicae 63(1), 2006, 37-46.

 

A. Sintamarian, “Selections and common fixed points for some generalized multivalued contractions”, Demonstratio Mathematica, 39(3), 2006, 609-617.

 

L. Lupsa, L. Blaga, “A Special Type of the Min-efficient Solution of (CT) Problem”, Automation Computers and Applied Mathematics. Scientific Journal., 15(2), 2006, 193-201

 

L. Lupsa, L. Blaga, “Optimum points and integer unimodal functions”, Automation Computers and Applied Mathematics. Scientific Journal, 13(1), 2004, 21-30

 

S. Toader, G. Toader, “The moments of a generalization of Friedman’s distribution”, Stochastic Analysis and Applications, 3, 2003, 193-201.

 

I. A.  Rus, A.  Petrusel, A. Sintamarian, “Data dependence of the fixed point set of some multivalued weakly Picard operators”, Nonlinear Analysis Theory Methods & Applications, 2003, 1947-1959.