|
Journal papers:
1. M. Pourbagher, D.K. Salkuyeh, On the solution of a class of complex symmetric linear systems, Applied Mathematics Letters, 76 (2018) 14-20.
2. D.K. Salkuyeh, M. Rahimian, A modification of the generalized shift-splitting method for singular saddle point problems, Computers and Mathematics with Applications, 74 (2017) 2940-2949.
3. D. Hezari, V. Edalatpour, H. Feyzollahzadeh, D. K Salkuyeh, On the generalized deteriorated positive semi-definite and skew-Hermitian splitting preconditioner, J. Comput. Math., Accepted for Publication, July 2,2017.
4. M. Bastani, D.K. Salkuyeh, On the m-step two-parameter generalized Hermitian and skew-Hermitian splitting preconditioning
method, Afrika Matematika, 28 (2017) 999-1010.
5. F. P. A. Beik, D. Khojasteh Salkuyeh, A cyclic iterative approach and its modified version to solve coupled
Sylvester-transpose matrix equations,Linear and Multilinear Algebra, 65 (2017) 2406-2423.
6. V. Edalatpour, D. Hezari and D. Khojasteh Salkuyeh, A generalization of the Gauss-Seidel iteration method
for solving absolute value equations, Appl. Math. Comput. 293 (2017) 156-167.
7. D. Khojasteh Salkuyeh and M. Masoudi, A new relaxed HSS preconditioner for saddle point problems,
Numerical Algorithms, 74 (2017) 781–795.
8. D. Khojasteh Salkuyeh, M. Bastani, A new generalization of the HSS method for solving the continuous Sylvester equation,
Transactions of the Institute of Measurement and Control, 40 (2018) 303-317.
9. D. Khojasteh Salkuyeh, F. Panjeh Ali Beik, D. Hezari, A sequential two-stage method for solving generalized saddle
point problems, UPB Scientific Bulletin: Series A Applied Mathematics and Physics, 79 (2017) 131-140 .
10. D. Hezari, D. Khojasteh Salkuyeh, V. Edalatpour, A new iterative method for solving a class of complex symmetric system
of linear equations, Numerical Algorithms, 73 (2016) 927–955.
11. D. Khojasteh Salkuyeh, Stepsize Control for Cubic Spline Interpolation,International Journal of Applied and
Computational Mathematics, 3 (2017) 693–702.
12. D. Khojasteh Salkuyeh, A. Tavakoli, Interpolated variational iteration method for initial value problems,
Applied Mathematical Modeling, 40 (2016) 3979-3990.
13. F.P.A. Beik and D.K. Salkuyeh, An iterative algorithm for the best approximate $(P,Q)$-orthogonal symmetric and
skew-symmetric solution pair of coupled matrix equations, Transactions of the Institute of Measurement and Control, 39 (2017) 537–554.
14. D.K. Salkuyeh, M. Hasani and F.P.A Beik, On the Preconditioned AOR Iterative Method for Z-Matrices, Computational and Applied Mathematics, 36 (2017) pp 877–883.
15. V. Edalatpour, D. Hezari and D. Khojasteh Salkuyeh, Two efficient inexact algorithms for a class of large
sparse complex linear systems, Mediterranean Journal of Mathematics, 13 (2016) 2301–2318.
16. D. Hezari, V. Edalatpour and D. Khojasteh Salkuyeh, Preconditioned GSOR iterative method for a class of
complex symmetric system of linear equations, Numerical Linear Algebra with Applications, 2015 (22) 761-776.
17. D.K. Salkuyeh, M. Masoudi, D. Hezari, On the generalized shift-splitting preconditioner for saddle point problems,
Applied Mathematics Letters, 48 (2015) 55-61.
18. F.P.A. Beik and D.K. Salkuyeh, An iterative algorithm for the least squares solutions of matrix equations over symmetric
arrowhead matrices, Journal of Korean Mathematical Society, 52 (2015) 349—372.
19. N. Aghazadeh, D.K. Salkuyeh, M. Bastani, Two-parameter generalized Hermitian and skew-Hermitian splitting iteration method,
Interational Journal of Computer Mathematics, 93 (2016) 1119–1139.
20. N. Aghazadeh, M. Bastani, D. K. Salkuyeh, The generalized Hermitian and skew-Hermitian splitting iterative method
for image restoration, Applied Mathematical Modelling, 39 (2015) 6126-6138.
21. A. Golbabai, S.P.A Beik, D. K. Salkuyeh, A new approach for solving the first-order linear matrix differential equations,
Bulletin of Iranian Mathematical Society (BIMS), 42 (2016) 297-314.
22. V. Edalatpour, D. Hezari and D. K. Salkuyeh, Accelerated generalized SOR method for a class of complex systems of linear
equations, Mathematical Communications, 20 (2015) 37-52.
23. D.K. Salkuyeh, On the solution of a class of fuzzy system of linear equations, Sadhana, 40 (2015) 369-377.
24. F. P.A. Beik and D.K. Salkuyeh, Weighted versions of Gl-FOM and Gl-GMRES for solving general coupled linear matrix
equations, Computational Mathematics and Mathematical Physics, 55 (2015) 1606-1618.
25. D. K. Salkuyeh and Z. Hassanzadeh, A Newton two-stage waveform relaxation method for solving systems of nonlinear algebraic
equations, Mathematical Communications, 20 (2015) 1-15.
26. D. K. Salkuyeh, F. P. A. Beik, Minimum norm least-squares solution to general complex coupled linear matrix equations via
iteration, FILOMAT, 29 (2015) 1389-1407.
27. F. Toutounian, D. K. Salkuyeh, M. Mojarrab, LSMR iterative method for general coupled matrix equations,
Journal of Applied Mathematics, 8, 2014.
28. F.P.A. Beik, D.K. Salkuyeh, A finite iterative algorithm for Hermitian reflexive and skew-Hermitian solution groups of the
general coupled linear matrix equations, Journal of Applied Mathematics and Computing, 48 (2015) 129-155.
29. D. K. Salkuyeh, A. Rafiei, H. Roohani, ILU Preconditioning Based on the FAPINV Algorithm, Opuscula Mathematica, 35 (2014) 235–250.
30. D. K. Salkuyeh, V. Edalatpour, D. Hezari, Polynomial preconditioning for the GeneRank problem, Electronic Transactions
on Numerical Analysis (ETNA), 41 (2014) 179-189.
31. D. K. Salkuyeh, D. Hezari, V. Edalatpour, Generalized SOR iterative method for a class of complex symmetric linear
system of equations, International Journal of Computer Mathematics, 92 (2015) 802-815.
32. D. K. Salkuyeh, The Picard-HSS iteration method for absolute value equations, Optimization Letters, 8 (2014) 2191–2202. ISI)
33. Z. Hassanzadeh and D.K Salkuyeh, Two-stage waveform relaxation method for the initial value problems with non-constant
coefficients, Computational & Applied Mathematics, 33 (2014) 641–654.
34. M. Hassani, D. K. Salkuyeh, On a class of multi-level preconditioners for Z-matrices, Afrika Matematika, 26 (2015) 201-213.
35. D. K. Salkuyeh, F.P. A. Beik, On the gradient based algorithm for solving the general coupled matrix equations, Transactions
of the Institute of Measurement and Control, 36 (3) (2014) 375–381.
36. S. Erfani, A. Tavakoli, D.K. Salkuyeh, An efficient method to set up a Lanczos based preconditioner for discrete ill-posed
problems, Applied Mathematical Modelling, 37 (2013) 8742–8756.
37. M. Hasani, D.k. Salkuyeh, Improvements of Two Preconditioned AOR Iterative Methods for Z-Matrices, Bulletin of the Iranian
Mathematical Society (BIMS) , 40 (2014) 357-371.
38. F.P.A. Beik, D.K. Salkuyeh, M. Mohseni Moghadam, Gradient based iterative algorithm for solving the generalized coupled
Sylvester-transpose and conjugate matrix equations over reflexive (anti-reflexive) matrices, Transactions of the Institute of
Measurement and Control, 36 (2014) 99-110.
39. D.K. Salkuyeh, F.P.A. Beik, An iterative method to solve symmetric positive definite matrix equations,
Mathematical Reports 16 (2014) 271-283.
40. F. Panjeh Ali Beik and D.K. Salkuyeh, The coupled Sylvester-transpose matrix equations over generalized
centro-symmetric matrices, International Journal of Computer Mathematics, 90 (2013) 1546-1566 .
41. D. K. Salkuyeh, S. Shamsi, A. Sadeghi, An improved symmetric SOR iterative method for augmented systems,
Tamkang J. Mathematics, 43 (2012) 479-490.
42. D.K. Salkuyeh, M. Bastani, Solution of the Complex Modified Korteweg-de Vries Equation by the Projected Differential
Transform Method, Applied Mathematics and Computation, 219 (2013) 5105-5112 .
43. D.k. Salkuyeh, An Iterative Method for Symmetric Positive Semidefinite Linear System of Equations, Demonstratio
Mathematica, 47 (2014) 482-492.
44. F. Panjeh Ali Beik and D.K. Salkuyeh, On the global Krylov subspace methods for solving general coupled matrix equations,
Computers and Mathematics with Applications, 62 (2011) 4605-4613.
45. M. Bastani and D. K. Salkuyeh, A highly accurate method to solve Fisher"s equation, Pramana-Journal of Physics, 78 (2011)
335-346.
46. D. K. Salkuyeh and S. Shamsi, A Preconditioner for the SOR-like Method for the Augmented Systems, Chiang Mai Journal of
Science, 39 (2012) 191-199.
47. M. Bastani and D.K. Salkuyeh, Numerical studies of a non-local parabolic partial differential equations by spectral collocation
method with preconditioning, Computational Mathematics and Modeling, 24 (2013) 81-89.
48. D. K. Salkuyeh, A short note on the paper ``Convergence of the TAGE iterative method for the system arisen from the cubic
spline approximation for the solution of two-point BVPs with forcing function in integral form", by Mohanty, Jain and Dhall, Applied
Mathematical Modelling, 36 (2012) 168-172.
49. D. K. Salkuyeh and Y. Abdolalizadeh, On the Preconditioning of the AOR Iterative Methods for M-matrices, International
Journal of Applied Mathematics and Computation, 3 (2011) 87-94.
50. D. K. Salkuyeh and M. Bastani, Convergence of the variational iteration method for the cubic nonlinear Schrodinger equation,
Journal of Advanced Research in Scientific Computing, 3(2) 2011, 31-41.
51. D. K. Salkuyeh and S. Behnejad, Letter to the Editor regarding ``Modified Hermitian and skew-Hermitian splitting
methods for non-Hermitian positive-definite linear systems"" [Numer. Linear Algebra Appl. 14 (2007) 217-235]", Numerical
Linear Algebra with Applications, 19 (2012) 885-890.
52. D. K. Salkuyeh, On the solution of the fuzzy Sylvester equation, Soft Computing, 15 (2010) 953-961.
53. D. K. Salkuyeh, H. Roohani, Convergence of the Variational Iteration Method for the Telegraph Equation with Integral
Conditions, Numerical Methods for Partial Differential Equations, 27 (2011) 1442-1455.
54. D. K. Salkuyeh, A. Fahim, A New Iterative Refinement of the Solution of Ill-Conditioned Linear System of Equations,
International Journal of Computer Mathematics, 88 (5) (2011) 950 – 956.
55. D. K. Salkuyeh and H. Roohani, On the relation between the AINV and the FAPINV algorithms, International Journal of
Mathematics and Mathematical Sciences, Volume 2009, Article ID 179481, 6 pages Hindawi Publishing Corporation).
56. D. K. Salkuyeh, A Sparse Approximate Inverse Preconditioner for Nonsymmetric Positive Definite Matrices, Journal of
Applied Mathematics and Informatics, 28 (2010) 1131-1141.
57. D. K. Salkuyeh, On the semi-discretization of the Sivashinsky equation, International Journal of Applied Mathematics and
Computation, 2 (2009) 94-100.
58. H. Roohani and D. K. Salkuyeh, New General Solutions for the General Elliptic and Auxiliary Equations and Application to the
Coupled KdV Equation, International Journal of Computer Mathematics, 87 (12) (2010) 2760-2768.
59. D. K. Salkuyeh and F. Toutounian, Optimal Iterate of the Power and Inverse Iteration Methods, Applied Numerical
Mathematics, 59 (2009) 1537-1548.
60. D. K. Salkuyeh and F. Toutounian, A Sparse-Sparse Iteration for Computing a Sparse Incomplete Factorization of the Inverse
of an SPD Matrix, Applied Numerical Mathematics, 59 (2009) 1265-1273.
61. D. K. Salkuyeh, A preconditioner for the normal equations, Journal of Applied Mathematics and Informatics, 28 (2010) 687-
696.
62. D. K. Salkuyeh and M. Hasani, A note on the pin-pointing solution of ill-conditioned linear system of equations, International
Journal of Computer Mathematics, 87 (2010) 1395 – 1400.
63. D. K. Salkuyeh and F. Saadati Sharafeh, On the Numerical Solution of the Burgers’s Equation, International Journal of
Computer Mathematics, 86(2009) 1334-1344.
64. D. K. Salkuyeh, The relation between the FSAI and the AIB algorithms, IUST International Journal of engineering Science,
19 (2008) 45-48. (ISC)
65. D. K. Salkuyeh, On the Preconditioning of the Block Tridiagonal Linear System of Equations, Journal of Applied
Mathematics and Computing, 28 (2008) 133-146.
66. D. K. Salkuyeh, F. Toutounian and H. Shariat Yazdi, A procedure with stepsize control control for solving n one-dimensional
IVPs, Mathematics and Computers in Simulation, 79 (2008) 167-176 .
67. D. K. Salkuyeh, Convergence of the variational iteration method for solving linear systems of ODEs with constant coefficients,
Computers and Mathematics with Applications, 56 (2008) 2027-2033.
68. D. K. Salkuyeh, A family of Newton-type methods for solving nonlinear equations, International Journal of Computer
Mathematics, 84 (2007) 411-419.
69. D. K. Salkuyeh, Generalized Jacobi and the Gauss-Seidel Methods for Solving Linear System of Equations, Numerical
Mathematics: A journal of Chinese universities English Series, 16 (2007) 164-170.
70. S. Karimi, D. K. Salkuyeh and F. Toutounian, A preconditioner for the LSQR algorithm, Journal of Applied Mathematics and
Informatics, 26 (2008) 213 - 222.
71. D. K. Salkuyeh, S. Karimi and F. Toutounian, A parallel algorithm to approximate inverse factors of a matrix via sparse-sparse
iterations, Appl. Math. Comput., 81 (2006) 782-79.
72. K. Salkuyeh, Positive integer powers of the tridiagonal Toeplitz matrices, International Mathematical Forum, 22 (2006) 1061-
1065.
73. D. K. Salkuyeh, On the finite difference approximation to the convection-diffusion equation, Appl. Math. Comput., 179 (2006)
79-86.
74. D. K. Salkuyeh and F. Toutounian, Numerical accuracy of a certain class of iterative methods for solving linear systems, Appl.
Math. Comput., 176(2006) 727-738.
75. D. K. Salkuyeh, On the solution of a class of elliptic problems, International Mathematical Forum, 10 (2006)485-494
76. D. K. Salkuyeh, Comments on ”A three-term recurrence for tridiagonal sytems”, Appl. Math. Comput., 176 (2006) 442-444.
77. D. K. Salkuyeh, A new approach to compute sparse approximate inverse factors, Appl. Math. Comput., 174(2006)1110-1121.
78. D. K. Salkuyeh and F. Toutounian, New approaches for solving large sylvester equations,Appl. Math. Comput., 173 (2006) 9-18.
(Correction )
79. D. K. Salkuyeh, CG-type algorithms to solve symmetric matrix equations, Appl. Math. Comput., 172(2006) 985-999.
80. D. K. Salkuyeh and F. Toutounian, A comparison between GMRES and the global GMRES Methods for solving Matrix
Equations, Jour. of Inst. of Math. and Comp. Sci. (Math. Ser), 17 (2004) 191-195.
81. F. Toutounian, D. K. Salkuyeh and B. Asadi, Numerical implementation of the QMR algorithm by using discrete stochastic
arithmetic,Journal of Applied Mathematics and Computing, 17 (2005) 457-473.
82. D. K. Salkuyeh and F. Toutounian, A new approach to compute sparse approximate inverse of an SPD, IUST International
Journal of Engineering Science, 15 (2004) 97-95.
83. D. K. Salkuyeh and F. Toutounian, A block version algorithm to approximate inverse factors, Applied Mathematics and
Computation 162 (2005) 1499-1509.
84. D.K. Salkuyeh and F. Toutounian, BILUS: A Block Version of ILUS Factorization, Journal of Applied Mathematics and
Computing, 15 (2004) 299-312.
85. A. Kerayechian and D. K. Salkuyeh, On the existence, uniqueness and approximation of a class of elliptic problems,
International Journal of Applied Mathematics, 11 (2002) 49-60.
86. D. K. Salkuyeh, A new implementation of the AIB algorithm for computing the inverse factors of a matrix, Journal of Science
and Technology (University of Mohaghegh Ardabili), 3(2006) 33-43.
Conference papers:
1. D. Khojasteh Salkuyeh, On the parallel version of the BAIB algorithm, 37th Annual Iranian Mathematics Conference,Azarbaijan
University of Tarbiat Moallem,Tabriz, Iran.
2. D. Khojasteh Salkuyeh, A generalization of the SOR method for solving linear system of equations, The 1st national
conference of mathematics and its applications, Islamic Azad university of Lahijan, 5-6 March 2008.
3. K. Shayesteh, A. Heydari, D. K. Salkuyeh, M. Abdorrahmani and N. Barahmati, Modeling of three-way catalytic converters: Study
of heat transfer and chemical reactions, The 11th National Iranian Chemical Engineering Congress, 2007.
4. D. K. Salkuyeh, T. Salimi, A Preconditioner for the Normal Equations, 5 th seminar on Linear Algebra and its applications,
Babolsar, Mazandaran, 2009.
5. H. Roohani and D. Khojasteh Salkuyeh, On the preonditioning based upon the FFAPINV algorithm, The 23rd International
Conference of the Jangjeon Mathematical Society, February 8-10, 2010, Ahvaz-Iran.
6. D. K. Salkuyeh, S. Shamsi, Generalized SOR method for Solving System of Linear Equations,
41st Annual Iranian Conference of Mathematics, September 12-15, 2010, Urmia University, Urmia-Iran.
7. D. K. Salkuyeh and A. Azarnejad Hassankiadeh, Convergence of the Generalized AOR Method for $alpha$-Strictly Diagonally
Dominant Matrices, 1st Regional Seminar Mathematics Students, Azarbaijan University of Tarbiat Moallem, July 18-19, 2011.
8. D. K. Salkuyeh and A. Ramzani, Convergence of the BLAGE iterative method for the solution of perturbed 2D Poisson"s
equation, 1st Regional Seminar Mathematics Students, Azarbaijan University of Tarbiat Moallem, July 18-19, 2011.
9. D. Khojasteh Salkuyeh, A Review of the Preconditioning Techniques Based on the FAPINV Algorithm, The 42nd Annual Iranian
Mathematics Conference, 5-8 September 2011,Vali-e-Asr University of Rafsanjan, Iran (Invited speaker).
10. D. Khojasteh Salkuyeh and N. Babazadeh, Some results on the preconditioned AOR iterative methods, The 42nd Annual
Iranian Mathematics Conference, 5-8 September 2011,Vali-e-Asr University of Rafsanjan, Iran.
11. D. Khojasteh Salkuyeh, A Generalization of the 2D-DSPM for Solving Linear System of Equations, The fourth national
mathematics conference, Payameh Noor, September 25 and 26, Ardabil.
12. D. Khojasteh Salkuyeh and Y. Darabi, Hybrid methods to solve matrix equations, The fourth national mathematics
conference, Payameh Noor, September 25 and 26, Ardabil.
13. D. Khojasteh Salkuyeh, Z. Hassanzadeh, Two-stage waveform relaxation method for the initial value problems, 9th Seminar
on Differential Equations and Dynamical Systems, July 11-13, 2012 (Shahid Madani University of Azarbayejan).
14. F. Panjeh Ali Beik, D. K. Salkuyeh, A projection technique for reflexive (anti-reflexive) solution of the coupled linear matrix
equations, The 4th Conference on Numerical Analysis and its Applications Faculty of Khansar, Khansar, Iran, May 7-8,
2013 (18-19 Ordibehesht, 1392).
15. D. Khojasteh Salkuyeh, A preconditioner for symmetric M-matrices, The 44nd Annual
Iranian Mathematics Conference, Ferdowsi University of Mashhad, 27-30 August 2013 ( 5-8 Sharivar 1392)..
16. D. Khojasteh Salkuyeh, F. Panjeh Ali Beik, On the convergence of the gradient based iterative method, The 44nd Annual
Iranian Mathematics Conference, Ferdowsi University of Mashhad, 27-30 August 2013 ( 5-8 Sharivar 1392).
17. D. Khojasteh Salkuyeh, D. Hezari, V. Edalatpour, An iterative method for a class of complex symmetric linear system of
equations, 5th Iranian conference on applied mathematics, Buali-Sina University, Hamadan, September 2-4, 2013 (11-13 Shahrivar 1392).
18. D. Khojasteh Salkuyeh, D. Masoudi, D. Hezari, A preconditioner based on the shift-splitting method for generalized saddle point
problems, The 46th Annual Iranian Mathematics Conference, Yazuniversity, Yazd, 25-28 August 2015 ( 1-3 Sharivar 1394).
19. D. Khojasteh Salkuyeh, M. Rahimian and T. Salimi, On the generalized shift-splitting method for singular saddle
point problems, The 6th Seminar on Numerical Analysis and its Applications, University of Maragheh, 20-21 July 2016.
Research Projects:
At University of Mohaghegh Ardabili (UMA):
1) A new approach to compute sparse approximate inverse of a matrix.
2) On the finite difference approximation to the Convection-Diffusion equation.
3) Generalization of some stationary iterative methods for solving large sparse linear system of equations.
4) On the BAIB algorithm for computing the sparse approximate inverse factors of a matrix.
5) Approximate solution of the Sivashinsky equation by using its semi-discretization.
6) On the preconditioning of the block tridiagonal linear system of equations.
7) Optimal iterate of the power and inverse iteration methods.
8) ILU preconditioning based on the FAPINV algorithm.
9) Stepsize control for interpolating cubic spline functions.
10) On the solution of the fuzzy Sylvester equation.
11) A generalization of the AOR iterative method.
At University of Guilan:
1) On the convergence of the Richardson method for matrix equations.
Published Books:
1) Numerical Methods in Linear Algebra (in persian), 350 pages, Publisher: Amoozeshhayeh Bounyadi
Errata to Book
To buy the book please click HERE!
2) Iterative Methods for Linear System of Equations (In Persian), 213 Pages, Publisher: Mowj-Chaharom.
To buy the book please click HERE or contact to Mazdak-Book: 013-33362211
3) Numerical Linear Algebra (in Persian), 245 pages, Publisher: Guilan Academic Center for Education.
To buy the book contact to Mazdak-Book: 013-33362211
Supervised Thesis (M.Sc):
At University of Mohaghegh Ardabili (UMA):
At University of Guilan:
1) Sara Shahnazari Karbasaraei, The Drazin inverse and its applications, Defense date: January 17, 2015.
2) Reza Rokhfrooz, The HSS method for nonlinear equations, Defense date: Januar 27, 2015.
3) Maryam Abdolmaleki, On preconditioned iteration methods for complex linear systems, Defense date: September 12, 2015.
At present, Maryam Abdolmaleki is a PhD student at Persian Gulf University under supervision of Dr. Saeid Karimi.
4. Sayyedeh Elaheh Ghoreishi Amri, Preconditioned generalized AOR methods for generalized least-squares problem,
Defense date: September 22, 2015.
5. Ghazaleh Hajiahmadi Foumani, On iterative methods for solving linear complementarity problem, Defense date: December 2015.
6. Meisam Jancook, An algorithm for solving shifted skew-Symmetric linear system, Defense date: December 2015.
7. Saman Lotfi, Hermitian and skew-Hermitian splitting method for solving Sylvester equation, Defense date: March 2016.
My PhD students:
1. Mehdi Bastani, Images restoration by solving linear system of equations based on the HSS iterative method,
Azarbaijan Shahid Madani University, Dr. Naser Aghazadeh (Supervisor), D. Khojasteh Salkuyeh (Advisor),
2. Davod Hezari, SOR iterative method and its acceleration for solving complex symmetric system of linear equations, Defense date: January 2016.
3. Vahid Edalatpour, On the preconditioning of complex system of linear equations, Defense date June 2016.
4. Mohsen Masoudi, 2013, Some results on the preconditiong of the saddle point problems, Ongoing.
5. Maryam Rahimian, 2015, Ongoing.
6. Tahereh Salimi, 2015, Ongoing.
|
Academic Rank:
