Research

• My main research interest is the interplay between abstract mathematical ideas and practical scientific and engineering problems, where mathematics contributes methods for solving problems and science and engineering provide the incentive and stimulation for further development and generalization of mathematical theories. Within this context, I have been studying the linear and nonlinear Boltzmann equations, Lie groups, Lie algebras and Calabi Yau spaces, dynamical systems and chaos, queueing models and time series and singular value decomposition. Results have been applied to rarefied gas dynamics, muon catalyzed fusion, high energy theoretical physics and superstring theory, reliability, performance and capacity of distributed information systems and blind deconvolution and multipath mitigation in communication systems and sustainable building design.

Publications

• E. Rusjan and P. F. Zweifel, Scattering Kernels for the Muon Diffusion Equation, Phys. Rev. A38 (1988) 1860.
• B. R. Greene, M. R. Plesser, E. Rusjan and X. Wang, Gauge Symmetry Breaking in Superconformal Orbifolds, Mod. Phys. Lett. A6 (1991) 591.
• A. Bojanczyk, J. LaRue, E. Rusjan and E. Vega, Multipath Detection, Proceedings of 4th Multinational Covert Passive Radar Conference (PCR-2005), 2005.
• B. Rusjan, E. Rusjan, Zeitkonstanten von Raumen schwerer Bauart nach VDI 2078 (Time Constants for Rooms with Heavy Walls Defined by VDI 2078), HLH 57, (2006), Nr. 5, 76-79.

Projects

• Singular value decomposition of circulant matrices in multipath mitigation.
• Finite fields and primitive polynomials in algebraic coding theory and communication.
• Data mining and search engine algorithms.
• Finite element modeling of thermal properties of buildings.

Presentations

• Partial Differential Equations, Integral Equations and Applications. (academia, Rome Labs, industry)
• Lie Groups, Lie Algebras and the Role of Symmetry in High Energy Physics. (academia)
• Singular Value Decomposition and DSP Applications. (academia, Rome Labs, industry)
• Modern Algebra and Algebraic Coding Theory. (academia, Rome Labs, high school)