## Professor Alexander Balinsky

### Overview

Telephone: +44(0)29 208 75528

Fax: +44(0)29 208 74199

Extension: 75528

Location: M/1.15

#### Research Group

Analysis and Differential Equations

#### Recent Significant Publications

**Balinsky A and Mohammad N**, “*Sparse Natural Image Statistics and their Applications to Colorization and Compression*”, IEEE 2010 International Conference on Image Processing, September 26-29, 2010, Hong Kong.

**Balinsky A, Balinsky H and Simske S**, "*On Helmholtz's principle for Document Processing*", 10th ACM Symposium on Document Engineering (DocEng2010), Manchester, UK, 21-24 September 2010.

**Balinsky A and Evans W D**, “*Some recent results on Hardy-type inequalities*”, Applied Mathematics & Information Sciences 4(2) (2010), 191–208.

**Balinsky A and Mohammad N**, “*Non-linear Filter Response Distributions of Natural Colour Images*”, CCIW 2009, Springer Lecture Notes in Computer Science 5646, 101-108, 2009.

**Balinsky A and Balinsky H**, “On *Semi-Supervised Learning and Sparsity*”, 2009 IEEE International Conference on Systems, Man, and Cybernetics, October 11-14, 2009, San Antonio, Texas, USA.

#### Teaching

MA0376 Mathematical Foundations of Internet Security

#### Administrative Duties

School IT Committee

WIMCS Research Chair in Mathematical Physics

### Publications

**Balinsky A and Mohammad N**, “*Sparse Natural Image Statistics and their Applications to Colorization and Compression*”, IEEE 2010 International Conference on Image Processing, September 26-29, 2010, Hong Kong.

**Balinsky A, Balinsky H and Simske S**, "*On Helmholtz's principle for Document Processing*", 10th ACM Symposium on Document Engineering (DocEng2010), Manchester, UK, 21-24 September 2010.

**Balinsky A and Evans W D**, “*Some recent results on Hardy-type inequalities*”, Applied Mathematics & Information Sciences 4(2) (2010), 191–208.

**Balinsky A and Mohammad N**, “*Non-linear Filter Response Distributions of Natural Colour Images*”, CCIW 2009, Springer Lecture Notes in Computer Science 5646, 101-108, 2009.

**Balinsky A and Balinsky H**, “On *Semi-Supervised Learning and Sparsity*”, 2009 IEEE International Conference on Systems, Man, and Cybernetics, October 11-14, 2009, San Antonio, Texas, USA.

**Balinsky A and Mohammad N**, “*Colorization of Natural Images via L1 Optimization*”, IEEE Workshop on Applications of Computer Vision (WACV) 2009 Snowbird, Utah, December 7-8,2009

**Balinsky A, Evans W D, Hundertmark D and Lewis R T**, On Inequalities of Hardy-Sobolev Type, *Banach J. Math. Anal*. 2 (2008), no. 2, 94-106.

**Balinsky A, Evans W D and Saito Y**, Dirac–Sobolev inequalities and estimates for the zero modes of massless Dirac operators, *J. Math. Phys. *49, (2008) (*10 pages*).

**Balinsky A and Balinsky H**, Affine invariant total variation models, *In Proc. of The 10th IASTED International Conference on Computer Graphics and Imaging *,February 13 – 15, 2008 , Innsbruck, Austria.

**Balinsky A and Ryan J**, Some Sharp $L^{2}$ Inequalities for Dirac Type Operators,* Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)*, December 2007.

**Balinsky A and Balinsky H**, Affine Invariant Total Variation Models, Research Disclosure, 2007, N. 519, ISSN 0374-4353.

**Balinsky A and Tyukov A***,* On localization of pseudo-relativistic energy*, Proc. Royal Society, Mathematical, physical and engineering sciences, *2006, vol. 462, no2067, pp. 897-912

**Balinsky A and Tyukov A***,* On Hardy type inequalities. Recent advances in differential equations and mathematical physics, 69--77,* Amer. Math. Soc.*, Providence, RI, 2006.

**Balinsky A, Laptev A and Sobolev A V**, Generalized Hardy inequality for the magnetic Dirichlet forms*, J. Statist. Phys.* 116 (2004), no. 1-4, 507--521.

**Balinsky A**, Hardy type inequalities for Aharonov-Bohm magnetic potentials with multiple singularities, *Math. Res. Lett.* 10 (2003), 1-8.

**Balinsky A and Evans W D**, Zero modes of Pauli and Weyl-Dirac operators. *Advances in differential equations and mathematical physics (Birmingham, AL, 2002), *1--9, Contemp. Math., 327*, **Amer. Math. Soc., Providence, RI,*2003.

**Balinsky A and Evans W D**, On the zero modes of Weyl-Dirac operators and their multiplicity, *Bull. London Math. Soc.* 34 (2002), no. 2,__ __236--242.

**Balinsky A and Evans W D**, On the spectral properties of the Brown-Ravenhall operator, *J. Comput. Appl. Math. *148 (2002), no. 1, 239—255.

**Books**

**Balinsky A and Evans W D**, "Spectral Analysis of Relativistic Operators", Imperial College Press and World Scientific, September 2010.