**Kazem Ghanbari , Ph.D.**

Professor of Mathematics

Interests:

**Differential equations, Inverse problems, Matrix Linear Operators and relevant spectral theory**

**Email: ****kghanbari@sut.ac.ir****, kazemghanbari@yahoo.com**

**Phone:**** +984133459063 (Work)**

Fax: +984133444300

** **

**Education:**

**Postdoctoral fellow, University of Waterloo, Department of Applied Math. Ontario, Canada, 2001-2002 (Supervisor Prof. Graham Gladwell)**

**Ph.D. Mathematics, Carleton University, School of Mathematics, Ontario, Canada, 1997-2001 (Supervisor Prof. Angelo Mingarelli)**

**M.Sc. and B.Sc. Mathematics, Tabriz University, Department of Mathematics, Tabriz, Iran, 1988-1993 (Supervisor Prof. Ali Jodayree)**

** **

**Professional Membership:**

Iranian Mathematical Society

**Areas of Interests:**

**ODE, Inverse problems, Inverse Matrix Eigenvalue Problems, Matrix operators and spectral Theory**

**Language**:

**Persian, Azari ( mother tunge), English (second language)**

**Teaching Experience:**

**Linear Algebra for engineers, University of Waterloo, 2002**

**Applied Mathematics, Carleton University, 2001**

**ODE and PDE Graduate courses at Sahand University of Tech.**

Advanced Engineering Math. in graduate and undergraduate level

**Calculus and Linear Algebra**

**Applications of Lie Groups to ODE and PDE, Graduate courses at Sahand University of Tech. and Tabriz University**

**Graduate Students:**

**(Ph.D. Supervision)**

**1- Hossein, Kheiri, Ph.D., (Advisor) Inverse problem of the Sturm-Liouville equation in the non-classic case with one turning point of order 4m + 1 with turning points, Tabriz University, January 2005.**

**2- Farshad Rezvan, Ph.D., (Adviosr) Applications of Lie Symmetry Group Analysis for Some Specific Partial Differential Equations, Tabriz Unversity, July 2010.**

**3- Mohammad Shahryari, P.hD., ( Advisor) Inverse Sturm-Liouville problem with discontinuity conditions inside finite interval and uniqueness of potential function by using three spectra, July 2012**

**4- Mohammad Dehghan, P.hD., ( Advisor) Reconstructing the Potential function of the indefinite Sturm-Liouville Problem using infinite product forms, 2013**

**5- Hanif Mirzaei, Ph.D., (Supervisor) Eigenvalue problems of second and fourth order Sturm-Liouville equations and related inverse problem in discrete and continuous cases, Agust 2013.**

**6- Mahsa Rahimnavasi Moghaddam, Ph.D., (Supervisor) Study on Isospectral Matrix Flows and Inverse Eigenvalue Problems fo Pentadiagonal Matrices, February 2017.**

**7- Yousef Gholami, Ph.D., (supervisor) Applications of Mathematical Inequalities in Fractional Differential and Difference Equations, March 2017**

**8- Tahereh Haghi, Ph.D., (supervisor) In progress**

**9- Fatemeh Ghanbari, Ph.D., (supervisor) In progress**

**(M.Sc. Supervison)**

**1- R. Dehghani, Existence of positive solutions for nonlinear fractional differential equations 2007.**

**2- V. Babapour, Similar properties of eigenvector and eigenvalues in continuous and discrete Sturm-Liouville problems April 2007**

**3- B. Shekarbegi, Inequalities for eigenvalues of fixed membrane problem and clamped plate problem and generalizations May 2007**

**4- E. Khosravi, Inverse problems for matrix Sturm-Liouville equation on a finite interval July 2007**

**5- M. Rahimi, Inverse spectral problems for Sturm-Liouville equation with eigenparameter dependent boundary conditions, November 2007.**

**6- M. R. Shirmohammadi, Existence of positive solutions for ODE and nonlinear fractional differential equations December 200710**

**7- R. Bagheri, Isospectral vibrating systems Summer 2008.**

**8- Samaneh Shahi, Centrosymmetric Isospectral Flows, 2010**

**9- A. Faraji, Recovery of the m-function from spectral data for generalized Sturm - Liouville problems Jan. 2010**

**10- Hamed Mansouri, Nth-order fuzzy linear differential equations and its Applications, Jan. 2010**

**11- Khabat Menbari, Asymptotics of eigenvalues for regular Sturm-Liouville problems with eigenvalue parameter in the boundary condition, July 2010**

**12- Zahra Rashipour, Two inverse eigenvalue problems for a special kind of matrices, September 2010**

**13- Farzaneh Gilasi, Inner totally positive matrices, September 2010**

**14- Farzaneh Madadjoo, Structure - preserving dynamical systems, September 2010**

**15- Syamak Fakheri, Solutions to a quadratic inverse eigenvalue problem, January 2011**

**16- F. Parvizpour, Constructing Jacobi matrices with prescribed mixed eigendata, January 2011**

**17- Vali Palizban, Universal bounds for eigenvalues of the biharmonic operator, July 2011**

**18- Mostafa Fallahi, Inverse eigenvalue problems for Sturm-Liouville equations with spectral parameter contained in one of the boundary conditions, July 2011**

**19- Mohadeseh Najafi Emnani, Analysis of stability and bifurcation for a delayed logistic equation, August 2011**

**20- Adel Valipour, On Sturm-Liouville operators with discontinuity conditions inside an interval, August 2011**

**21- Yousef Gholami, Existence of multiple positive solutions for m-point fractional boundary value problem on an infinite interval, July 2012**

**22- Tahereh Haghi, Some results for fractional boundary value problem of differential inclusions, September 2012**

**23- Nahid Jamshidi, Positive solution of singular boundary value problem for nonlinear fractional differential equation with nonlinearity that changes sign, September 2012**

**24- Sahar Alipour, Matrix representation of Sturm-Liouville problems with finite spectrum, Agust 2013.**

**25- Amene Derakhshani, Sturm-Liouville problems with finite spectrum, Agust 2013**

**26- Fahimeh Zolfi, Self-Adjoint differential equations for classical orthogonal polynomials, Agust 2013**

27- Roya Alikhah, The isospectral sixth order Sturm-Liouville equations, September 2014

28- Fereshteh Mehrizad, Inverse eigenvalue problem for pentadiagonal matrices, September 2014

29- Samira Saremi, Reconstruction of a Rod using one spectrum and minimal mass condition, Oct. 2014

**30- Mansoor Shafeeinezhad, Reconstructing the cross-sectional area of an axially vibrating non-unoform Rod from one of its mode shapes, June. 2015**

31- Somayeh Navidfar, On an inverse problem foe two spectra of finite Jacobi matrices, September 2015

32- Mojde Arodian, Explicit expression for the matrix exponential function obtained by means of an algebraic convolution formula, September 2016

33- Sahar Eghlimi, Oscillation criteria for second-order nonlinear perturbed differential equation, September 2016

**34- Saed Taheri Beni, Monotone positive solutions for a class of second-order nonlinear differential equations, September 2017**

**35- Maryam Gholampour, Existence of positive solutions for the cantilever beam equation with fully nonlinear terms, September 2017**

**36- Mina Salahi, Applications of total positivity theory to 1D prescribed curvature problems, February 2018**

**References:**

**Professor Graham Gladwell, University of Waterloo, Ontario, Canada, ****graham@gladwell.com**

**Professor Angelo Mingarelli, Carleton University, Ontario, Canada, ****angelo@math.carleton.ca**

**Professor Ali Asghar Jodayree Akbarfam, University of Tabriz, ****akbarfam@yahoo.com**

**Awards and Distinctions:**

**Winner of Professor ****Mehdi Radjabalipour's Prize for the best Research in Linear Algebra and Applications, Ferdowsi Mashhad University, Feb. 26, 2014**

**Distinguished researcher award of the Faculty of Science 4 times, SUT, Tabriz, Iran**

**Winner of schoolarship from MCHE for Ph.D. Carleton, Canada, 1997-2001**

**Winner of post doctoral fellowship from University of Waterloo, Canada 2001-2002**

**Conference Presentations:**

**1. 25th Annual Iranian Mathematics Conference, Sharif University of Technology, March 28-31 1994.**

**2. 20th Annual Southeastern-Atlantic Regional Conference on Differential Equations, Virginia Tech, Blacksburg, Virginia, USA, 2000.**

**3. AMS Sectional Meeting 2001, Las Vegas, NV, USA, April 21-22, 2001.**

**4. International Conference on Dynamics of Continuous, Discrete and Impulsive Systems, London, Canada, July 27-31, 2001.**

**5. The Tenth ILAS Conference, ***challenges in matrix theory *Auburn Univrsity, USA, June 10-13, 2002.

**6. International Conference on Dynamics of Continuous, Discrete and Impulsive Systems, Guelph, Canada, May 15-18, 2003.**

**7. Properties of Totally Positive matrices, 15-th ***Seminar on Algebra *Guilan University, Rasht, Iran, July 19-20, 2003.

**8. Totally positive matrices with three spectrum in common, 16-th ***Seminar on Algebra*, November 17-19, 2004,Institute for Advanced Studies in Basic Sciences, Zanjan, Iran.

**9. Some classes of the Euler-Bernoulli beams having the same spectral, 6-th ***Seminar on Differential equations and Dynamical systems*, October 6-9, 2004, Institute for Advanced Studies in Basic Sciences, Zanjan, Iran.

**10. Isospectral beams, ***International conference on differential equations and applications in mathematical biology*, Malaspina University - College, Nanaimo, BC, Canada, July 18-23, 2004.

**11. Fractal geometry and Affine transformations, 6-th Seminar on Topology and Geometry, July 15-17, 2004, Azerbaijan Tarbiatmoalem University, Tabriz, Iran.**

**12. LU- Factorization of totally positive matrices and total positivity interval, 3-th Seminar on Linear Algebra and its Applications, December 28-29, 2004, Kerman, Iran.**

**13. Inverse problem of three term recurrence relation in limit circle case, 35-th ***Iranian Mathematics conference,** January *26-29, 2005, Ahvaz, Iran.

**14. A survey on inverse and generalized inverse eigenvalue problems for Jacobi matrices, ***International conference, dedicated to commemorating of 50-th anniversary of prominent mahtematician I.T.Mamedov*, May 11-13, 2005, National Academy of Sciences of Azerbaijan, Baku, Azerbaijan.

**15. Analogous properties of the Green’s functions for discrete and continuous Sturm-Liouville systems, 7***th seminar on differential equations and dynamical systems*, 9-11 November 2005, Tabriz University, Tabriz, Iran.

**16. On the total positivity, 13-th International Linear Algebra Society (ILAS) conference, Amsterdam, Netherlands ,18-21 July 2006.**

**17. Multi-Isospecteal Totally Positive Matrices, 37th Annual Iranian Mathematics Conference- Azarbaijan Tarbiat Moallem University, 2-5 Sep. 2006.**

**18. Triple positive solutions for boundary value problem of nonlinear fractional differentialequation, 37th Annual Iranian Mathematics Conference-Azarbaijan Tarbiat Moallem University, 2-5 Sep. 2006, (With Reza Dehghani).**

**19. Isospectral Centrosymmetric Flows Preserving Staircase Structures, 40th Iranian International Conference on Mathematics 17-20 August 2009, Sharif University of Technology,Tehran, Iran (with Samaneh Shahi)**

**20. Centrosymmetric Matrix Flows Maintaining The Initial Structure, International Conference on Mathematical Applications in Engineering (ICMAE 10), 3-5 August 2010, Kuala Lumpur, Malaysia**

**21. Inequalities for eigenvalues of a general clamped plate problem, The World Congress on Engineering 2009, London Imperial College, UK, 1-3 Jul. 2009.**

**22. RECONSTRUCTION OF A JACOBI MATRIX FROM MIXED EIGENDATA, 41th Iranian International Conference on Mathematics 12-15 September 2010, University of Urmia, Urmia, Iran (with Zahra Rashidpour)**

**23. INNER TOTALLY POSITIVE MATRICES WITH TWO SPECTRUM IN COMMON, 41th Iranian International Conference on Mathematics 12-15 September 2010, University of Urmia, (with F. Gilasi) **

**24. STABILITY AND HOPF BIFURCATION FOR A DELAYED LOGISTIC POPULATION MODEL,41th Iranian International Conference on Mathematics 12-15 September 2010, University of Urmia, Urmia, Iran (with Mohadeseh Najafi)**

**25. Reconstruction of Jacobi matrix with three spectra, 21st Algebra Seminar of Iran, 10-11 November 2010 Faculty of Mathematical Sciences, University of Tabriz (with Fardin Parvizpour)**

**26. Inverse eigenvalue problem for pentadiagonal matrices, 6-th Seminar in Linear Algebra and Applications, University of Arak, Jun 2011 (with Hanif Mirzaei)**

**27. Generalized inverse eigenvalue problem using mixed eigendata, 6-th Seminar in Linear Algebra and Applications, University of Arak, Jun 2011 (with Fardin Parvizpour)**

**28. Tau method for eigenvalues of Euler-Bernoulli equation, 42-th Iranian International Conference on Mathematics, August 2011 Univwersity of Rafsanjan (with Hanif Mirzaei)**

**29. Existence of sulotions for fractional differential equations by operator theory, June 2012, University of Mazandaran (with Tahereh Haghi)**

**30. Existence results of Positive solution for nonlinear fractional eigenvalue problem, 9-th Seminar on Differential Equations, 11-13 July 2012, Shahid Madani University of Azarbaijan (with Y. Gholami)**

**31. Existence results of positive solution for multi-point boundary value problem of nonlinear fractional differential equation, 9-th Seminar on Differential Equations, 11-13 July 2012, Shahid Madani University of Azarbaijan (with Y. Gholami)**

**32. Existence, multiplicity and nonexistence results of positive solutions for m-point nonlinear fractional differential equation on half axis, 43-th Iranian International Conference on Mathematics, August 2012, University of Tabriz (with Y. Gholami)**

**33. Existence of positive solutions for a system of fractional boundary value problems, 43-th Iranian International Conference on Mathematics, August 2012, University of Tabriz (with T. Haghi)**

34. Isospectral Matrix Flow Maintaining Total Positivity, KU Leuven, Belgium, 11-15 July, ILAS 2016 (with M. R. Moghaddam)

35. The pseudo spectral method for solving fractional differential algebraic equations, Th 6th Seminar on Numerical Analysis and its Applications, Maragheh University, 20-21 July 2016 (with F. Ghanbari and P. Mokhtari)

**Publications:**

**K. Ghanbari and A. Mingarelli, A Generalized Inverse Eigenvalue Problem for Symmetric Matrices ****Int. J. Appl. Math.*** 4, (2), (2000), 199-209*

**K. Ghanbari, m-functions and inverse generalized eigenvalue problem, ****Inverse problems, ****17 (2001) 211-217**

**K. Ghanbari, Explicit solution for infinite dimensional generalized eigenvalue problem, ****Int. J. Math. and MSc****. 26 (2001) 9, 513-523**

**K. Ghanbari and Graham Gladwell, Total positivity interval***,* **Linear Algebra and its Applications ***393(2004) 197-202*

**K. Ghanbari, On the Isospectral beams, ****Electronic Journal of Differential equations12*** (2005)57-64.*

**K. Ghanbari, Pentadiagonal oscillatory matrices with two spectrum in common,*** ***Positivity**** 10 (2006) No.4, 721-729.**

**K. Ghanbari, On the similarities of discrete and continuous Sturm-Liouville problems***,* **Electronic Journal of Differential Equations*** (2007) No. 172, pp.1-8.*

**K. Ghanbari and R.Dehghani, Triple positive solutions for boundary value problem of nonlinear fractional differential equation, ****Bulletin of the Iranian Mathematical Society ****, 33 (2007) No. 2, pp. 1-14**

**K. Ghanbari, A survey on inverse and generalized inverse eigenvalue problems for Jacobi matrices, ****Applied Mathematics and Computation***, 195 (2008) 335-3363.*

**K. Ghanbari and F. Rezvan, On the pricipal equations of Isospectral beams, ****Applied Mathematics E-Notes****, 11(2011) pp.255-260**

**R. Dehghani and K. Ghanbari , Positive Solution for a fractional Eigenvalue Problem, ****Dynamics of Continuous***,* *Discrete and impulsive systems series A: Mathematical Analysis 18 (2012) 177-185*

**K. Ghanbari and B. Shekarbeigi, Inequalities for eigenvalues of a general clamped plate problem, ****Canadian Mathematical Bulletin*** 55 (2012) No.1*

**K. Ghanbari and Y. Gholami, Existence and multiplicity of positive solutions for m-point non-linear fractional differential equations on the half line, ****Electronic Journal of Differential Equations****,*** vol. 2012 (2012) No. 238, pp. 1-15.*

**K. Ghanbari and F. Parvizpour, Generalized inverse eigenvalue problems with mixed eigendata, ****Linear Algebra and Applications***, 437(2012) pp. 2056-2063*

**K. Ghanbari and Y. Gholami, Existence and nonexistence results of positive solution for nonlinear fractional eigenvalue problem,****J. Fractional Calculus and Appl.*** (JFCA), 4(2013) No. 9, pp. 1-12*** **

**N. Nyamoradi, K. Ghanbari and T. Haghi, The existence of multiple solutions for multi-point boundary value problems, ****Journal of Advanced Research in Applied Mathematics***, (2013) pp. 1-13.*

**K. Ghanbari and H. Mirzaei, On the Isospectral Sixth Order Sturm-Liuoville Equation, ****Journal of Lie Theory***, Heldermann Verlag, Vol. 23 (2013) 921-935.*

**K. Ghanbari, H. Mirzaei and GML Gladwell, Reconstruction of a Rod using one spectrum and minimal mass condition, ****Inverse Problems in Science and Engineering****, Vol. 22 Issue 2(2014) , http://dx.doi.org/10.1080/17415977.2013.782543**

**K. Ghanbari, F. Parvizpour and H. Mirzaei, Constructing Jacobi matrices using mixed eigendata, ***Linear and Multilinear Algebra**, (2013) , *Volume 62, Issue 6, June 2014, pages 721-734

**K. Ghanbari, H. Mirzaei, Inverse eigenvalue problem for pentadiagonal matrices, ****Inverse Problems in Science and Engineering****, Vol. 22 Issue 4 (2014) , http://dx.doi.org/10.1080/17415977.2013.797412**

**K. Ghanbari, Isospectral matrix flows maintaining the initial structure, ****Advanced Studies in Contemporary Mathematics ****, Vol. 23 (2013) No.2, 315-322.**

**K. Ghanbari , Y. Gholami and H. Mirzaei, Existence and multiplicity results of positive solutions for boundary value problems of nonlinear fractional differential equation, ****Dynamics of Continuous***,* *Discrete and impulsive systems series A: Mathematical Analysis 20 (2013) 543-558*

**K. Ghanbari and Y. Gholami, Existence and multiplicity of positive solutions for a coupled system of perturbed nonlinear fractional differential equations,*** **Computational Methods for Differential Equations*, *Vol.1 (2013) No.1, 39-54*

**M. Moghaddam, H. Mirzaei and K. Ghanbari, On the generalized inverse eigenvalue problem of constructing symmetric pentadiagonal matrices from three mixed eigendata, to appear in,**** ****Linear and Multilinear Algebra****, Volume 63, Issue 6, June 2015, pages 1154-1166**

**H. Mirzaei and K. Ghanbari****, Matrix Representation of a Sixth order Sturm-Liouville Problem and related Inverse Problem with Finite Spectrum, ****Bulletin of the Iranian Mathematical Society,**** Volume & Issue: Volume 41, Issue 4, August and September 2015, Page 793-1059**

**K. Ghanbari and Y. Gholami, **** ****Lyapunov type inequalities for fractional Sturm-Liouville problems and fractional Hamiltonian systems and Applications****,**** ****J. Fractional Calculus and Appl****.**** (JFCA), (JFCA), Vol. 7(1)(2016) **

**Y. Gholami, and ****K. Ghanbari**, ** ****Exsistence and uniqueness of positive solutions for coupled systems of fractional Delta-difference boundary value problems, **** ****J. Fractional Calculus and Appl.**** (JFCA), Vol. 7(2)(2016) **

**Y. Gholami and ****K. Ghanbari , **** ****Existence of positive solutions for a coupled hybrid system of quadratic fractional integral equations, ***Azerbaijan* Journal of Mathematics** **** Vol. 6, No. 2, 2016**

**Y. Gholami and K. Ghanbari , **** ****On solvability of coupled hybrid system of quadratic fractional integral equations, ****Tamkang Journal of Mathematics,**** Vol. 47 No. 3 (****2016)**

**K. Ghanbari and Y. Gholami****, ** **New classes of Lyapunov type inequalities of fractional Delta-difference Sturm-Liouville problems with applications, to aprear in ****Bulletin of the Iranian Mathematical Society**

**, 2017**

**Y. Gholami and K. Ghanbari , **** ****Coupled systems of fractional nabla-difference boundary value problems, ***Differential Equations & Applications**, Volume 8, Number 4 (2016), 459-470*

Mahsa R. Moghaddam; Kazem Ghnbari; Angelo B. Mingarelli*, *Isospectral matrix flow maintaining staircase structure and total positivity of an initial matrix, **Linear Algebra and Applications**, **Vol. 517 (2017) 1345-147**

Y. Gholami and K. Ghanbari , ** Existence of positive solutions for coupled systems of half-linear boundary value problems involving Caputo fractional derivatives, ***Fractional Differential Calculus*, **Vol. 6 No.2 (2016) 249-265 **

**T. Haghi and K. Ghanbari , Positive solutions for discrete fractional initial value problem, to apear in ***Computational Methods for Differential Equations*, *Vol.4 No.4 (2016) **285-297*

**Y. Gholami and K. Ghanbari**** ****, Existence of positive solutions for coupled systems of half-linear boundary value problems involving Caputo fractional derivatives, ***Fractional Differential Calculus*, **Vol. 6 No.2 (2016) 249-265 **

**Yousef Gholami and Kazem Ghanbari****, Coupled systems of Caputo type fractional -difference boundary value problems at resonance, to appear in ***Transaction of **Razmadze Mathematical Institute***,**** Science Direct, 171 (2017) 332-349**
**Yousef Gholami and Kazem Ghanbari****, Comparative dynamics of fractional half-linear boundary value problems via Lyapunov inequalities, ***J. Fractional Calculus and Appl.**(JFCA), Vol. 8(2) (2017) *
**Yousef Gholami and Kazem Ghanbari****, New class of conformable derivatives and applications to differential impulsive systems, to appear in ***SeMa, Springer* 2017
**Kazem Ghanbari and Yousef Gholami****, Lyapunov type inequalities for fractional impulsive Hamiltonian systems, to appear in****, ***Dynamics of Continuous**,*** ***Discrete and impulsive systems series A: Mathematical Analysis*
**F. Ghanbari, K. Ghanbari and P. Mokhtari****, High-Order Legendre collocation method for fractional order linear semi explicit differential algebraic equations, to appear in ****ETNA****, 2018**
**F. Ghanbari, K. Ghanbari and P. Mokhtari****, Generalized Jacobi Galerkin method for nonlinear fractional differential algebraic equations, ***Comp. Appl. Math**., Vol. 37 (Issue4) (2018) pp. 5456-5475*

**
****Books: **

*1- Differential Equations and Linear Algebra,*** ****Sahand University of Technology Publisher, 1997 **

*2- Advanced Engineering Mathematics***, Sahand University of Technology Publisher, 2006**** **

*3- Theory and Problems in Differential Equations***, ****Frouzesh Publisher Ltd. 2011, (Coauthor Hanif Mirzaei)**

*4- Linear Algebra and its Applications***,**** ****Sahand University of Technology Publisher, 2012, ****(Coauthor Ahmad Sadeghi Yazdankhah)**

**5- Lie Groups Method in Ordinary Differential Equations**, **Jihad Daneshgahi Publisher (ISBA), 2014**