Research information Vedad Pašić

My research interests can be broadly described as analysis of partial differential equations and spectral analysis, as well as alternative theories of gravity, which was the theme of my PhD thesis New Vacuum Solutions for Quadratic Metric-affine Gravity.

My current research deals with the massless Dirac operator primarily.

Main research collaborators :

Dmitri Vassiliev : Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK

Elvis Baraković : Department of Mathematics, University of Tuzla, Bosnia and Herzegovina

Nermin Okičić : Department of Mathematics, University of Tuzla, Bosnia and Hercegovina

Enes Duvnjaković : Department of Mathematics, University of Tuzla, Bosnia and Hercegovina

Books

1. Nermin Okičić, Vedad Pašić : Elementi matematičke logike sa primjenom u računarskoj nauci (Elements of mathematical logic with applications in computer science), Off-set Tuzla (2015), Excerpt available

2. Vedad Pašić : Euklidska diferencijalna geometrija krivih i površi u tri dimenzije (Euclidean Geometry of Curves and Surfaces in Three Dimensions), Univerzitet u Tuzli (2016), Whole text available

Published articles

1. Differential equations with periodic coefficients, (jointly with N. Okičić), Zbornik radova 4, Filozofski Fakultet, Univerzitet u Tuzli (2002), Open access

2. Acting conditions of the superposition operator in Banach spaces of weighted functions with a discrete argument, (jointly with N. Okičić and F. Dedagić), Zbornik radova 4, Filozofski Fakultet, Univerzitet u Tuzli (2002), Open access

3. PP-waves with torsion and metric-affine gravity, (jointly with D. Vassiliev), Classical and Quantum Gravity 22 (19), 3961 (2005), ArXiV preprint available Published version (password protected due to copyright issues)

4. New Vacuum Solutions for Quadratic Metric-Affine Gravity - a Metric Affine Model for the Massless Neutrino?, Mathematica Balkanica New Series 24 (3-4), 329-340 (2010), Open access

5. A new representation of the field equations of quadratic metric-affine gravity, (jointly with E. Barakovic and N. Okicic), Advances in Mathematics: Scientific Journal 3 (1), 33-46 (2014), Open access

6. PP-waves with torsion: a metric-affine model for the massless neutrino, (jointly with E. Barakovic), General Relativity and Gravitation 46 (10), 1787 (2014), ArXiV preprint available Published version (password protected due to copyright issues)

7. A uniformly convergent difference scheme on a modified Shishkin mesh for the singularly perturbed reaction-diffusion boundary value problem, (jointly with E. Duvnjakovic, S. Karasuljic and H. Zarin), Journal of Modern Methods in Numerical Mathematics 6 (1), 28-43 (2015), Open access ArXiV preprint available

8. Continuity of modulus of noncompact convexity for minimalizable measures of noncompactness, (jointly with A. Rekic-Vukovic, N. Okicic and I. Arandjelovic), Functional Analysis, Approximation and Computation 7 (3), 39-46 (2015), Open access

9. Torsion Wave Solutions in Yang-Mielke Theory of Gravity, (jointly with E. Barakovic), Advances in High Energy Physics, Volume 2015, Article ID 239076, 7 pages, (2015), Open access ArXiV preprint available

I welcome research collaboration!

Conferences and seminars

0. Fractal Dimension, Mathematics Seminar Project, 2nd year undergraduate course (my first work with Dmitri Vassiliev, earned a 100%), School of Mathematical Sciences, University of Sussex, 1999. Transparencies available. Paper available.

1. Fraktalna dimenzija - koliko je vruća snjeĹžna pahuljica?, Matematički kolokvijum Odsjeka Matematika PMF-a Univerziteta u Tuzli, 2001. Transparencies available.

2. Quadratic metric-affine gravity - a new solution?, Bath Geometry Seminar, University of Bath, 27th May 2004.

3. PP-waves with torsion in metric-affine gravity, Bath Geometry Seminar, University of Bath, 1st March 2005.

4. PP-talasi sa torzijom u metrički-afinoj gravitaciji, Matematički kolokvijum Odsjeka Matematika PMF-a Univerziteta u Tuzli, 2005. Transparencies available.

5. Operator Theory and Spectral Analysis, London Mathematical Society Durham Symposium, 2nd - 12th August 2005.

6. Metrički-afin model za neutrino, Matematički kolokvijum Odsjeka Matematika PMF-a Univerziteta u Tuzli, 13th April 2006.

7. 42nd Karpacz Winter School of Theoretical Physics, Ladek Zdroj, Poland, 6-11th February 2006. (Website down, archived version here)

8. New Vacuum Solutions for Quadratic Metric-Affine Gravity, Marcel Grossmann Meeting on General Relativity, Berlin, 23-29th July 2006. Transparencies available.

9. Uvod u teleparalelizam i teleparalelna reprezentacija Weylove jednačine, Matematički kolokvijum Odsjeka Matematika PMF-a Univerziteta u Tuzli, 28th February 2008. Transparencies available.

10. New Vacuum Solutions for Quadratic Metric-Affine Gravity, University College London Seminar on General Relativity, 28th August 2008. Transparencies available. This is the longer version of the viva presentation I did a day earlier.
11. New Vacuum Solutions for Quadratic Metric-Affine Gravity, MASSEE International Congress on Mathematics MICOM 2009, Ohrid, Macedonia, 16-20th September 2009. Transparencies available. (Website down, archived version here)

12. SEE Doctoral Studies in Mathematical Sciences, 39th Spring Conference of the Union of Bulgarian Mathematicians, Albena, Bulgaria, 6-10th April 2010.

13. SEE Doctoral Studies in Mathematical Sciences, BH Matematički Skup, Tuzla Summer University, Tuzla, 7-9th July 2010. Transparencies available.

14. Nova vakumska rješenja kvadratne metrički afine gravitacije, Matematički kolokvij Sveučilište Josip Juraj Stossmayer, Osijek, Hrvatska, 2nd December 2010. Transparencies available.

15. New representation of the field equations - looking for a new vacuum solution for QMAG, MASSEE International Congress on Mathematics MICOM 2012, Sarajevo, BiH, 19th September 2012. Transparencies available.

16. Metric-affine vs Spectral Theoretic Characterisation of the Massless Dirac Operator, 2nd International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2013), Sarajevo, BiH, 26-29th August 2013.

17. Periodic and other ergodic problems, Isaac Newton Institute, Cambridge, 23-27th March 2015.

18. Purely Axial Torsion Waves - New Solutions of Metric-affine Gravity, BiH Matematički skup International University Sarajevo, 4th June 2015. Transparencies available.

19. Physical Interpretation of PP-waves With Axial Torsion, 14th Marcel Grossmann Meeting on General Relativity, Rome, 12-18th July 2015. Transparencies available.

20. Axial Torsion Waves in Metric-affine Gravity, 14th Marcel Grossmann Meeting on General Relativity, Rome, 12-18th July 2015. Transparencies available.

21. Gravitacijska interpretacija nekih torzijskih talasa i analitička reprezentacija Diracove jednačine, Naučni kolokvij, Odsjek za matematiku, Prirodno-matematički Fakultet Sarajevo, 22nd October 2016. Transparencies available.

Research projects

Head of project :

1. Alternativne teorije gravitacije i analiza generisanih sistema nelinearnih parcijalnih diferencijalnih jednačina (Alternative theories of gravity and analysis of generated systems of nonlinear partial differential equations). Cofinanced by the Ministry of education and Science of FBiH 2012-13.

2. Diracov operator bez mase u teorijama gravitacije i spektralnoj analizi (The massless Dirac operator in theories of gravity and spectral analysis). Cofinanced by the Ministry of education and Science of FBiH 2014.

3. Primjena diferencijalne geometrije u ispitivanju Diracovog operatora bez mase (Application of differential geometry in viewing the massless Dirac operator). Cofinanced by the Ministry of education and Science of FBiH 2015.

Project participant :

1. Nelinearni operatori u težinskim prostorima funkcija prirodnog argumenta i primjene (Nonlinear superposition operators in natural argument function spaces with applications). Cofinanced by the Ministry of education, science, culture and sport of the Tuzla Canton 2005.

2. Istraživanja u teoriji nelinearnih operatora s primjenom u teorijskoj fizici i rješavanju nekih operatorskih jednačina (Theory of nonlinear operators with applications in theoretical physics and solving some operator equations). Cofinanced by the Ministry of education and Science of FBiH 2008-2009.

Research profiles