Associate Professor

• Teaching
• Research
• Recent Preprints
• Publications
• Patent
• Recent Invited Talks and Conference Presentations
• Current Graduate Students
• Projects Available for Prospective PhD and Master's Students
• Contact information

Current and Recent Teaching

• Math 436.3/818.3 Mathematical Modelling II (T2 2017-18)
  
• Math 124.3 Calculus II for Engineers (T2 2017-18)
  
• Math 436.3/818.3 Mathematical Modelling II (T2 2016-17)
  
• Math 366.3 Linear Algebra II (T1 2016-17)
  
• Math 336.3 Mathematical Modelling I (T1 2016-17)
  
• Math 124.3 Calculus II for Engineers (T2 2015-16)
  
• Math 366.3 Linear Algebra II (T1 2015-16)
  
• Math 123.3 Calculus I for Engineers (T1 2015-16)
  
• Math 438.3/838.3 Methods of Applied Mathematics (Methods of Applied Math II) (T2 2014-15)
  

Research

My professional interests include these topics:
• Quantum system theory, simulation, and modelling; complex systems; operator equations
  
• Harmonic analysis of signals; Riemann's zeta and the Broadband Redundancy; fast-transform bases; nonlinear oscillators
  
• Quantum technologies; Quantum Image Processing
  
• The broader potentialities or limitations of the nascent quantum technologies
  (see Zagoskin and Sowa, Can We See or Compute our Way out of Plato's Cave?, J Appl Computat Math 2014, 3:7,
  or: A. Sowa, The quantum sieve of Eratosthenes, Journal of Physical Mathematics 7:180)
  

  Some of my recent results are described (in telegraphese) in this note: A. Sowa, Qualitative Analysis of Quantum Signals, CMS Notes, Vol. 49, No. 5 / November 2017
  

Recent Preprints

• Encoding spatial data into quantum observables

Peer-Reviewed Publications

• Riemann's zeta function and the broadband structure of pure harmonics, The IMA Journal of Applied Mathematics (Oxford Academic), Vol. 82 (2017), 1238-1252
• On the Dirichlet matrix operators in sequence spaces, Applicationes Mathematicae (Institute of Mathematics, Polish Academy of Sciences), 44,2 (2017), pp. 185-196
• Image processing via simulated quantum dynamics, Random Operators and Stochastic Equations (De Gruyter), Vol. 25, No. 1 (2017), 27-39
• (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.
• Interacting Bose gas, the logistic law, and complex networks, Russian Journal of Mathematical Physics, Vol. 22, No 1 (2015), 98-111
• (with Y. Guo and G.-F. Zheng) Existence and Asymptotic Behavior of Solutions for Nonlinear Maxwell Equations Arising in Mesoscopic Electromagnetism, Journal of Nonlinear Analysis B: Real World Applications, 20C (2014), pp. 99-111, DOI: 10.1016/j.nonrwa.2014.05.002
• (with A. Shamloo) A numerically efficient approach to the modelling of double-Qdot channels, Nanoscale Systems: Mathematical Modeling, Theory and Applications ("NanoSystems MMTA"). Volume 2, pp. 145-156, ISSN (Online) 2299-3290, DOI: 10.2478/nsmmt-2013-0009, September 2013
• 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
• Factorizing matrices by Dirichlet multiplication, Linear Algebra and its Applications, Vol. 438, No. 5 (2013), 2385-2393
• On an eigenvalue problem with a reciprocal-linear term, Waves in Random and Complex Media, Vol. 22, No. 2 (2012), 186-206, doi: 10.1080/17455030.2011.636085
• Spectra of Nonlocally Bound Quantum Systems, Russian Journal of Mathematical Physics, Vol. 18, No.2 (2011), 227-241, doi:10.1134/S1061920811020117
• 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
• Evolving states in nonlocal type dynamics of composite systems, Journal of Geometry and Physics, Vol. 61 (2011), 26-36, doi:10.1016/j.geomphys.2010.09.006
• The Problem of Extrapolation of Quantum States, Advanced Studies in Theoretical Physics, Vol. 4, 2010, No. 12, 575 - 585
• Exploiting the Paradigm of Quantum Information in Nanosystem Modeling, AIP Conference Proceedings Vol. 1148 (August 2009), 233-236
• Stationary states in nonlocal type dynamics of composite systems, Journal of Geometry and Physics, Vol. 59 (2009), 1604-1612, doi:10.1016/j.geomphys.2009.07.015
• A model for nonlocal bonding in bipartite systems, Journal of Modern Optics, Vol. 56, Issue 12 (2009), 1363-1368
• Quantum entanglement in composite systems, Theoretical and Mathematical Physics, Vol. 159 (2009) 654-666
• Modeling a quantum Hall system via elliptic equations, Advances in Mathematical Physics, Vol. 2009, Article ID 514081, 9 pages
• Parametric models of the Hall effect in the strongly correlated regime, Waves in Random and Complex Media, Vol. 19, No. 1 (2009), 5-10
• Fractional Quantization of Hall Resistance as a Consequence of Mesoscopic Feedback, Russian Journal of Mathematical Physics, Vol. 15, No.1 (2008), 122-127
• Sensitivity to lattice structure in the mesoscopic-loop models of planar systems, Advanced Studies in Theoretical Physics, Vol. 1 (2007), 433-448
• Integrability in the mesoscopic dynamics, Journal of Geometry and Physics, Vol. 55, No.1 (2005), 1-18
• 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
• Novel nondiffusive flows with applications to image enhancement, International Journal of Computational and Numerical Analysis and Applications, Vol. 3, No. 3 (2003), 325-349
• The (fully) Nonlinear Maxwell Theory delineated, Journal of Geometry and Physics, Vol. 45, No. 1-2 (2003), 54-74
• Nonlinear Maxwell Theory and Electrons in Two Dimensions, Communications in Mathematical Physics, Vol. 226 (2002), 559-566
• (with R. R. Coifman) New methods of controlled total variation reduction for digital functions, SIAM Journal on Numerical Analysis, Vol. 39, No. 2 (2001), 480-498
• (with R. R. Coifman) Combining the calculus of variations and wavelets for image enhancement, Applied and Computational Harmonic Analysis, Vol. 9 (2000), 1-18
• On an equation arising from the geometry of Riemannian submersions, Journal fur die reine und angewandte Mathematik, Vol. 514 (1999), 1-8
• High Accuracy Multiwavelets with Short Supports, IEEE Transactions on Signal Processing, Vol. 46, No. 12 (1998), 3420-3422
• Magnetic Oscillations and Maxwell Theory, Physics Letters A, Vol. 228 (1997), 347-350

Patent

• 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.

Recent Invited Talks and Conference Presentations

• Deploying Harmonic Analysis in Quantum and Nano Engineering, The Fields Institute, Focus Program on Nanoscale Systems and Coupled Phenomena, Mathematical Analysis, Modelling, and Applications, Toronto, Ontario, 14 May 2018
• The Broadband Redundancy and Its Applications, the Landau Seminar at the Department of Physics, Loughborough University, Loughborough, Leicestershire, England, 19 October, 2017
• (A. Sowa, A. Zagoskin, and A. Balanov) A Nonlinear Master Equation Model for Quantum Metamaterials, The fourth AMMCS International Conference (AMMCS2017), Waterloo, Ontario, 20-25 August 2017
• (B-Z. Li, A. Sowa) Numerical Methods for Analysis and Representation of Quantum States Associated with Integral Transform, The fourth AMMCS International Conference (AMMCS2017), Waterloo, Ontario, 20-25 August 2017
• (S.A. Melli, A.P. Sowa, K.A. Wahid) Image Denoising via Redundant Quantum Channels, The fourth AMMCS International Conference (AMMCS2017), Waterloo, Ontario, 20-25 August 2017
• (Q. Guo, A. Sowa) Examples of Quantum-dynamical Nonlaws and Their Properties, The fourth AMMCS International Conference (AMMCS2017), Waterloo, Ontario, 20-25 August 2017
• Qualitative Analysis of Quantum States and Observables, the Landau Seminar at the Department of Physics, Loughborough University, 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, Loughborough University, 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
• (F. Sage, A. Sowa), 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

Current Graduate Students

• Congratulations to Izabela Vlahu who has successfully defended her PhD thesis "The Orthogonal Band Decomposition of the Finite Dirichlet Matrix and Its Applications" on 13 December 2017. Izabela's research work has been co-supervised by Prof. Paul Babyn (Department of Medical Imaging, U of S) and APS.
• Qi Guo is a M.Sc. student interested in mathematical models of complex systems

Projects Available for Prospective PhD and Master's Students

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.

Applications are welcome. For general information about the Graduate Program click here.

Contact Information

Mathematics and Statistics
University of Saskatchewan
106 Wiggins Road
Saskatoon, SK S7N 5E6 
CANADA

Phone: (306) 966-6114
Fax: (306) 966-6086
For E-mail address click here