(with M. J. Everitt, J. H. Samson, S. E. Savel'ev, A. M. Zagoskin, S. Heidel, J. C. Zúñiga-Anaya) Recursive simulation of quantum annealing, Journal of Physics A: Mathematical and Theoretical, Vol. 48 (2015) 415301.
The Dirichlet ring and unconditional bases in L2[0,2pi], Functional Analysis and Its Applications, Vol. 47, No. 3, pp. 227-232, 2013;
Translated from Funktsionalnyi Analiz i Ego Prilozheniya, Vol. 47, No. 3, pp. 75-81, 2013
Signals generated in memristive circuits, Nanoscale Systems: Mathematical Modeling, Theory and Applications ("NanoSystems MMTA"). Volume 1, pp. 48-57, ISSN (Online) 2299-3219, DOI: 10.2478/nsmmt-2012-0004, November 2012
A fast-transform basis with hysteretic features, IEEE Conference Proceedings: Electrical and Computer Engineering (CCECE), 2011 24th Canadian Conference on,
8-11 May 2011, pp.000253-000257, doi: 10.1109/CCECE.2011.6030449
Mesoscopic mechanics, Journal of Physics and Chemistry of Solids, Vol. 65/8-9 (2004), 1507-1515, Special issue: Inhomogeneous and strongly correlated materials and the study of matter at extreme conditions
Method of Enhancement of the Visual Display of Images and Other Visual Data Records, US Patent Number 7194143, issue date 3/20/07. The patent can be looked up here.
Qualitative Analysis of Quantum States and Observables, the Landau Seminar at the Department of Physics, University of Loughborough, Loughborough,
Leicestershire, England, 28 June, 2017
Harmonic Analysis of Quantum States and Observables, EMN Quantum 2017, Vienna, Austria, 18-22 June, 2017
Searching for a spread-spectrum approach to some inverse problems, 10th International Conference on Scientific Computing and Applications (ICSCA 2016), The Fields Institute, Toronto, Ontario, 6-10 June 2016
Towards Quantum Image Processing, Saskatoon mini-Symposium: Applications of Quantum Engineering to Magnetic Resonance Imaging, Saskatoon, Saskatchewan, 18-19 August 2014
Linear Operators for the Analysis of Nonlinear Systems, 11th World Congress of Computaitonal Mechanics, 5th European Conference on Computaitonal Mechanics, Barcelona, Spain, 20-25 July 2014
Applying simulated quantum dynamics, Canadian Applied and Industrial Mathematics Society 2014 Annual Meeting, Saskatoon, Saskatchewan, 22-26 June 2014
Emerging applications of simulated quantum dynamics, International Focus Workshop on Metamaterials and Quantum Criticality, Loughborough,
Leicestershire, UK, March 25, 2014
From nonlinear eigenvalue problems to fast transforms, number theoretic operators, and special quantum states, Faculty of Mathematics, Informatics and Mechanics,
University of Warsaw, Warsaw, Poland, November 21, 2013
Nonlinear oscillators and number theoretic quantum states, the Landau Seminar at the Department of Physics, University of Loughborough, Loughborough,
Leicestershire, England, October 30, 2013
Mathematical analogies between the eigenmodes of memristive nanosystems and some cryptography-specialized quantum states,
BIT's 3rd Annual World Congress of Nanoscience and Nanotechnology-2013, Xi'an, China, September 28, 2013
Mathematical Models of Complex Phenomena, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences,
Wuhan, China, September 24, 2013
Operators resulting from the Dirichlet series, 2012 Canadian Mathematical Society Summer Meeting,
Regina, Saskatchewan, June 2-4, 2012
Modelling with the Logistic Operator Equation, 3rd International Conference on Econophysics, Loughborough, England,
September 23-29, 2011
A Fast-Transform Basis with Hysteretic Features, 24th Canadian Conference on Electrical and Computer Engineering, Niagara Falls, Ontario,
May 8-11, 2011
Nonlinear eigenvalue problems with applications to quantum systems, 2010 Canadian Mathematical Society Winter Meeting,
Vancouver, British Columbia, December 4-6, 2010
(joint work with F. Sage), Numerical Quantum Chaos in Nonlocal Quantum Dynamics,
presented (by FS) at the 1st Meeting of the Canadian Prairie Theoretical Physics Network,
Lethbridge, August 25, 2010
Nonlinear quantum spectroscopy, OTAMP 2010,
Fifth International Conference on Operator Theory Analysis and Mathematical Physics, Bedlewo, Poland,
August 5 - 12, 2010
Nonlinear eigenvalue problems and quantum systems, Faculty of Mathematics, Informatics and Mechanics,
University of Warsaw, Warsaw, Poland, July 27, 2010
Quantum spectroscopy, nonlinear operator equations, etc.,
Fourth Annual Meeting of the Prairie Network for Research in
Mathematical Sciences, Manitoba, April 30-May 2, 2010
On the topological characteristic of the spectra of some composite quantum systems, 2009 Canadian Mathematical Society Winter Meeting,
Windsor, Ontario, December 5-7, 2009
On the noncommutative Schrödinger equation, Third Annual Meeting of the Prairie Network for Research in
Mathematical Sciences, Saskatchewan, April 29-May 1, 2009
On the Stationary Solutions of the Noncommutative Schrödinger Equation, The Sixth IMACS International Conference on:
Nonlinear Evolution Equations and Wave Phenomena, Georgia, USA, March 23-26, 2009
Exploiting the paradigm of quantum information in nanosystem modeling,
The Sixth International Conference on Computational Methods of Science and Engineering, ICCMSE 2008, Greece, Sept. 25-30, 2008
Izabela Vlahu, M.Sc., is working toward Ph.D. degree in Mathematics under joint supervision by Prof. Paul Babyn and APS. Izabela is interested in the mathematical methods for medical image and signal analysis.
Qi Guo is an M.Sc. student interested in mathematical models of complex systems
Students will be given an opportunity to conduct theoretical as well as experimental research in Pure and Applied Mathematics.
Students with an interest in scientific computation will be given access to a Compute Cluster equipped with the user-friendly
MATLAB parallel programming tools. Available directions of study:
The mathematical aspects of quantum systems and nanosystems
Differential-algebraic eigenvalue problems
Applications of Number Theory in signal processing
The research topics are applicable to the emerging field of Nanotechnology, but also
lead to new perspectives at some purely mathematical problems.
Students with an interest in the Quantum Theory, Nonlinear Differential Equations, or Analytic Number Theory may find the projects naturally appealing.