Faculty of Electrical Engineering and Computing, Department of Applied Mathematics

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Main research field

Mathematical analysis, Differential equations and dynamical systems, Mathematical modelling, Discrete mathematics, Algebra

Specific research areas

Fractal analysis of solutions of differential equations and trajectories of dynamical systems, estimation of integrals, sums and integral transforms, constructions of combinatorial designs, vertex op

Technology keywords

  • Algorithms and Complexity
  • Mathematical modelling
  • Statistical Analysis

Services offered

  • Teaching and Training
  • Diagnostics
  • Preparation of environmental or energy related studies

Market sectors

  • Oil & Gas Producers
  • Alternative Energy
  • Aerospace & Defense
  • Electronic & Electrical Equipment
  • Industrial Engineering
  • Health Care Equipment & Services
  • Pharmaceuticals & Biotechnology
  • Mobile Telecommunications
  • Electricity
  • Software & Computer Services
  • Technology Hardware & Equipment

Short summary (English)

1) Nonlinear Analysis of Differential Equations and Dynamical Systems research group is interested in fractal properties of solutions of differential equations and trajectories of dynamical systems. Connections between box dimensions of trajectories and the bifurcation have been discovered. Study of fractal oscillations includes Euler, Hartman-Wintner and Bessel equation, nonautonomous linear systems also. New type of zeta functions, and nonregularity of weak solutions of elliptic BVPs are studied from the fractal geometry point of view. 2) The interest of Combinatorial Designs group lies in constructing t-designs, discrete configurations with rigid structure and difference sets, block designs possessing a regular automorphism group. Methods include algebraic and computational tools. Partial classifications, with constraints like tactical decompositions, are carried out. Applications in coding theory connected with design theory are going to be studied. 3) The main interest of the research of the Mathematical Analysis group is estimation of integrals, sums and integral transforms. Some topics which are studied recently are: error bounds for quadrature rules, Euler and Montgomery type identities, Ostrowski’s inequality, Hilbert’s inequality and Euler-Maclaurin formula, complete monotonicity of digamma function, Bernoulli’s polynomials, asymptotic expansion of gamma function and quotient of gamma functions. Mathematical modelling is represented by applications in semiconductor modelling in the petroleum engineering (multiphase flows in porous media) and analysis of thin and composite structures, focusing on deriving and justifying the simplified models of thin structures. 4) Two topiscs are related to Lie algebra: fermionic realizations of affine Lie algebrtas and Hopf algebra structure of the Poincaré algebra.

Short summary (Croatian)

Grupa za Nelinearnu analizu diferencijalnih jednadžbi i dinamičke sustave se bavi fraktalnim svojstvima rješenja diferencijalnih jednadžbi i trajektorijama dinamičkih sustava. Otkrivena je veza između box dimenzije trajektorije i bifurkacije. Posebno je proučena Hopfova bifurkacija. Studija fraktalnih oscilacija uključuje Eulerove, Hartman-Wintnerove i Besselove jednadžbe kao i neautonomne linearne sustave. Novi tip zeta funkcija i neregularnost slabog rješenja eliptičkog BVP su analizirani s pozicije fraktalne geometrije. Interes grupe za Kombinatorni dizajn vezan je za konstrukcije t-dizajna, diskretnih konfiguracija sa čvrstom strukturom i diferencijskim skupovima te blok dizajnima s regularnom grupom automorfizama. Koriste se algebarske tehnike i rezultati rada računala. Dobivena je djelomična klasifikacija s uvjetima tipa taktične dekompozicije. Planira se rad na primjenama u teoriji kodiranja vezano uz teoriju dizajna. Glavno područje grupe za Matematičku analizu su ocjene integrala, suma i integralnih transformacija. U zadnje vrijeme su analizirane sljedeće teme: granice pogreške kvadratnog pravila, identiteti tipa Eulera i Montgomeryja, nejednakost Ostrowskog, Hilbertova nejednakost i Euler-Maclaurinova formula, potpuna monotonost digama funkcije, Bernoullijevi polinomi, asimptotsko proširenje gama funkcije i kvocijent gama funkcija. Matematičko modeliranje je zastupljeno primjenama u poluvodičkom modeliranju u naftnom inženjerstvu (višefazni tok u poroznom sredsvu) te analizi tankih i kompozitnih struktura s naglaskom na izvod i opravdanje pojednostavljenih modela s tankom strukturom. Dva istraživanja su vezana za Liejeve algebre: fermionske realizacije afinih Liejevih algebri te Hopfova struktura Poincaréove algebre.

Last update: 21.11.2014. 13:11:17

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