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Allama Iqbal

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	News Updates



	Registration of Private Candidates for B.A./B.Sc. Annual Examination 2014
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	B.Ed. 2nd Annual Examination, 2012 & 1st Annual Examination, 2013
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	Revised Commencement date of B.Com. Part-I & II Annual Examinations 2013
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	Revised LL.B Part-I, II & III Annual Examinations 2013
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	Notice Board


	Will be updated soon.

Department of Mathematics

The Department of Mathematics is one of the oldest departments of the University of the Punjab. It was established in 1880s and has produced many brilliant graduates, some of whom have acquired eminence in Mathematics and allied fields like Mathematical and Theoretical Physics. For many years teaching in this department was conducted on inter-Collegiate basis whereby teachers from local colleges like Government College, F.C. College, Dyal Singh College, Islamia College Civil Lines and M.A.O. College, Lahore used to come and take the M.Sc. classes in the University premises. In 1956, the University took the important step of building up the department as an independent institution, two whole time teachers: one reader and one senior lecturer were appointed.
Since then the department has been growing in strength. Presently department conducts BS (4 years), M.Sc. (Morning/ Evening), M.S./ M.Phil. and Ph.D. programmes.

Chairman's Message
We are proud of the fact that the Department of Mathematics, one of the oldest Departments of the University of the Punjab, continues to impart quality education to deserving persons from all areas of Pakistan. The development of science requires mathematical knowledge. Mathematics is a basic science which can be applied to various social sciences. Hence, Mathematics is a discipline supporting other disciplines by providing theoretical knowledge and techniques. The Department of Mathematics has its educational goal of producing mathematicians who can contribute to the need of society.
Mathematics have become an integral part of modern research in all disciplines, and advanced technology in industry, government. The students who want to study more about Mathematics are encouraged. Our department plays a key role in undergraduate and post graduate teaching mission of the University. At the research level, we focus on different areas of Pure Mathematics, Applied Mathematics and Computational Mathematics.
I welcome the new entrants to this old seat of learning and hope that they will have a comfortable stay in the Department. I am sure that they will make every effort to benefit from the excellent Faculty and adequate facilities of the University. May God bless them with more knowledge and success in their life!

SYLLABUS FOR 4 YEAR BS MATHEMATICS
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SYLLABUS FOR M.Sc MATHEMATICS (MORNING/EVENING) PROGRAMME
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SYLLABUS OF M.PHIL/M.PHIL LEADING TO PH.D./ PH.D.
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Teaching Faculty

Administrative Staff

Programs

Journal

Publications/ Research / Books

Last Three Year Articles

Year: Upto June,

2012

Prof. Dr. Shahid S. Siddiqi & Dr. Ghazala Akram,; Solution of the Special Seventh order Boundary Value Problem by the optimal Homotopy Asymtotic Method, Archives Des Sciences, 65 (2), 2012

Prof. Dr. Shahid S. Siddiqi & Dr. Ghazala Akram,; Solution of Seventh order boundary value problem by Differential Transformation Method, World Applied Sciences Journal , 16 (11), 2012

Prof. Dr. Shahid S. Siddiqi,; A new Family of Binary 5 Point Apporximating Non-Stationary Subdivision Scheme, Archives Des Sciences, 65 (5), 2012

Prof. Dr. Shahid S. Siddiqi,; Ternary Three Point Non-Stationary Subdivion scheme, Research Journal of Applied Sciences, 4 (13), 2012

Prof. Dr. Shahid S. Siddiqi & Dr. Ghazala Akram,; Symmetric Ternary interpolating C1 Subdivision scheme , International Mathematical Fourm, 7 (46), 2012

Prof. Dr. Shahid S. Siddiqi & Dr. Ghazala Akram,; Solution of Fourth Order Obstacle problems using Quintic B-Splines, Applied Mathematical Sciences , 6 (94), 2012

Prof. Dr. Shahid S. Siddiqi & Dr. Ghazala Akram,; Soultion of Seventh Order Boundary Value Problems by Variational Iteration Technique, Applied Mathematical Sciences , 6 (94), 2012

Prof. Dr. Shahid S. Siddiqi & Dr. Ghazala Akram,; Soultion of Delay Differential Equations Using Nonic Spline Collocation Methods, International Mathematical Fourm, 7 (46), 2012

Prof. Dr. Shahid S. Siddiqi,; A new method of Coner Cutting subdivion scheme, Applied Mathematical Sciences , 6 (99), 2012

10-

Prof. Dr. Muhammad Sharif ,; Quantum Correction for ABGB Black Hole, Astrophysics and Space Science , 337, 2012

11-

Prof. Dr. Muhammad Sharif ,; Phantom Energy Accretion by Stringy Charged Black Hole, Chinese Physics Letters, 29, 2012

12-

Prof. Dr. Muhammad Sharif ,; Interacting Modified Holographic Dark Energy in Kaluza Klein Universe, Astrophysics and Space Science , 337, 2012

13-

Prof. Dr. Muhammad Sharif ,; Newtonian and Post Newtonian Expansion free fluid eveolution in F® Gravity, Astrophysics and Space Science , 337, 2012

14-

Prof. Dr. Muhammad Sharif ,; Anisotropic Universe Model in Bransdicke Theory, European Physical Journal C, 72, 2012

15-

Prof. Dr. Muhammad Sharif ,; Effects of elecromagnetic Field on the dynamical Instability of cylindrical Collapse, Journal of Cosmology and Astroparticle Physics, 2, 2012

16-

Prof. Dr. Muhammad Sharif ,; Modified Holographic Dark Energy in Non-flat Kaluza Klein Universe with Varying G, European Physical Journal C, 72, 2012

17-

Prof. Dr. Muhammad Sharif ,; Non Commutative Correction to Thin Shell collapse in Reissner Nordstrom Geometry, Journal of Physical Society of Japan, 81, 2012

18-

Prof. Dr. Muhammad Sharif ,; Phantom Energy Accetion by a Class of Black holes, Journal of Physics: Conference , 354, 2012

19-

Prof. Dr. Muhammad Sharif ,; Dynamics of Spherically Symmetric Gravtitational Collapse in f ® theory, Journal of Physics: Conference , 354, 2012

20-

Prof. Dr. Muhammad Sharif ,; themodynamics in f (R,T) Theory of Gravity , Journal of Cosmology and Astroparticle Physics, 3, 2012

21-

Prof. Dr. Muhammad Sharif ,; Dynamics of a Magnetized Bianchi VI_0 Universe with anisotropic Fluid, Astrophysics and Space Science , 339, 2012

22-

Prof. Dr. Muhammad Sharif ,; Effects of Electromagnetic Field ont eh Dynamical Instability of Expansion free Gravitiational Collapse, General Relativity and gravitation , 44, 2012

23-

Prof. Dr. Muhammad Sharif ,; Shearfree Spherically Symmetric Fluid Models, Chinese Physics Letters, 29, 2012

24-

Prof. Dr. Muhammad Sharif ,; Black Hole Evaporation in a Nonocommutative Charged Vaidya Model, Journal of Experimental and Theoretical Physics, 114, 2012

25-

Prof. Dr. Muhammad Sharif ,; ERRATUM: Thermodynamics in F(R,T) Theory of Gravity, Journal of Cosmology and Astroparticle Physics, 5, 2012

26-

Prof. Dr. Muhammad Sharif ,; Fermion stunellign from Charged Acceleration and Rotating Black Holes with NUT parameter, European Physical Journal C, 72, 2012

27-

Prof. Dr. Muhammad Sharif ,; Gravitational Dust Collapse with Cosmological Constant , World Applied Sciences Journal , 16, 2012

28-

Prof. Dr. Muhammad Sharif ,; Isothermal plasma wave properties of the schwarzschild de-sitter black hole in a veselago medium, Astrophysics and Space Science , 340, 2012

29-

Prof. Dr. Muhammad Sharif ,; Statefinder Diagnostic for Dark Energy Models in Bianchi I universe, International Journal of Modern Physics D, 21, 2012

30-

Prof. Dr. Muhammad Sharif ,; Effects of Electromagnetic field on engergy Density inhomogeneity in Self Gravitatinf fluids, General Relativity and gravitation , 44, 2012

31-

Prof. Dr. Muhammad Sharif ,; Energy content of colliding plane waves using approximate noether symmetries, Brazilian Journal of Physics, 42, 2012

32-

Prof. Dr. Muhammad Sharif ,; Dynamics of Magnetized Bulk Viscous Strings in Brans Dicke Gravity, International Journal of Modern Physics D, 21, 2012

33-

Prof. Dr. Malik Zawwar Hussain,; Shape preserving curve interpolation , International Journal of Computer Mathematics, 89 (1), 2012

34-

Prof. Dr. Malik Zawwar Hussain,; Shape Preserving Positive and convex data visulization using rational bi-cubic functions, Pakistan Journal of Statistics and Operation Research, 8 (1), 2012

35-

Prof. Dr. Malik Zawwar Hussain,; Positive preserving scattered data interpolation scheme using the side vertex method , Applied Mathematical and Computation, 218, 2012

36-

Prof. Dr. Malik Zawwar Hussain,; C1 Monotone Cubic Hermite Interpolation, Applied Mathematics Lectures, 25, 2012

37-

Prof. Dr. Malik Zawwar Hussain,; Monotone Data Visulization using Rational Funcations, World Applied Sciences Journal , 16 (11), 2012

38-

Dr. Muhammad Aslam Malik,; Action of the Mobious Group M = (x,y: X2 =y2 =1) on certain real Quadratic Fields, Punjab University Journal of mathematics , 44, 2012

39-

Dr. Muhammad Aslam Malik,; Certain H-Subsets of Q (M)/Q under the action of H = (x, y: x2=y4=1), Pakistan Journal of Science., 64 (1), 2012

40-

Dr. Muhammad Aslam Malik,; The Graph 2-1 is an induced subgraph of Johson Graphs, International Contemporary Mathematical Sciences, 07 (08), 2012

41-

Dr. Muhammad Aslam Malik,; Some Results on induced sub Graphs of Johson Graphs , International Forum, 07 (09), 2012

42-

H.M. Kalid Mahmood & Dr. Muhammad Aslam Malik,; An Account of Congruences Mod Pk using Halley's Method, World Applied Sciences Journal , 16 (11), 2012

43-

Dr. Muhammad Aslam Malik,; A Classification of the Real Quadratic irration numbers $/Frace {a+\sqrt {n} {c} $ of $ Q (/sqrt {N} $ w.R.T modulo $3 r$, International Mathematical Fourm, 07 (39), 2012

Year:

2011

Prof. Dr. Muhammad Sharif,; The Psudo-Newtonian Force and Potential of the Stringy Black Holes, Romanian Journal of Physics, 56, 2011

Prof. Dr. Muhammad Sharif,; Kaluza-Klein Cosmology with Modified Holographic Dark Energy, General Relativity and Gravitation, 43, 2011

Prof. Dr. Muhammad Sharif,; Dispersion Modes of Hot Plasma for Schwarzschild de-Sitter Horizon in a Veselago Medium , Canadian Journal of Physics, 89, 2011

Prof. Dr. Muhammad Sharif,; Thermodynamics of Bardeen Black Hole in Noncommutative Space, Canadian Journal of Physics, 89, 2011

Prof. Dr. Muhammad Sharif,; Expansionfree Fluid Evolution and Skripkin Model in f(R) Theory, International Journal of Modern Physics D, 20, 2011

Prof. Dr. Muhammad Sharif,; K-essence Models and Cosmic Acceleration in Generalized Teleparellel Gravity, Physica Scripta, 84, 2011

Prof. Dr. Muhammad Sharif,; Anisotropic Dark Energy and Generalized Second Law of Thermodynamics, Physica Scripta, 84, 2011

Prof. Dr. Muhammad Sharif ,; Cylinder with Charged Anisotropic Source, Canadian Journal of Physics, 89, 2011

Prof. Dr. Malik Zawwar Hussain ,; Shape Preserving surface for the Visualization of Positive and Convex Data Using Rational Bi-Quadratic Splines,, International Journal of Computer Application, 27, 2011

10-

Prof. Dr. Malik Zawwar Hussain ,; Rational Bi-Cubic Functions Preserving 3D Positive Data , IEEE 8th International Conference Computer Graphics, Imaging and Visualization, ISI Proceeding, , 2011

11-

Prof. Dr. Malik Zawwar Hussain,; Shape Preserving Rational Cubic Spline for Positive and Convex Data, Egyptian Informatics Journals, Elsevier , 12, 2011

12-

Prof. Dr. Malik Zawwar Hussain,; Shape Preserving Constrained Data Visualization Using Rational Functions , Journal of Prime in Mathematic, 7, 2011

13-

Prof. Dr. Malik Zawwar Hussain,; Detecting Corner for 3D Objects, International Journal of Computer Vision and Image Processing, IGI Global Dissemination Knowledge, 1, 2011

14-

Prof. Dr. Malik Zawwar Hussain,; Shape Preserving Surface Data Visualization Using Rational Bi-Cubic Functions, Journal of Numerical Mathematics, 19, 2011

15-

Dr. Muhammad Aslam Malik ,; Intuitionistic Fuzzy BCI-Positive Implicate Ideas in BCI-algebras, , International Mathematical Forum, 6, 2011

16-

Dr. Muhammad Aslam Malik ,; Some Results on Intuitionistic Fuzzy BCI-(Positive Implicative, Implicative, Commutative) Ideas in BCI-Algebras, International Mathematical Forum, 6, 2011

17-

Dr. Ghazala Akram ,; Solution of Fifth Order Boundary Value Problems in Reproducing Kernel Space, Middel East Journal of Scientific, 10, 2011

Year:

2010

Prof. Dr. Shahid S. Siddiqi,; Approximating Time Evolution Related to Ginzburg-Landau Functionals via Sobolov Gradient Methods in a Finite-Element Setting Nauman Raza, Sultan Sial and Shahid S. Siddiqi, Journal of Computational Physics, Vol. 229, 2010

Prof. Dr. Shahid S. Siddiqi,; Modified form of Binary and Ternary 3-point Subdivision Schemes Shahid S. Siddiqi and Kashif Rehan, Applied Mathematics and Computation, Vol. 216, 2010

Prof. Dr. Shahid S. Siddiqi,; Improved binary four point subdivision scheme and new corner cutting scheme, Computers and Mathematics with Applications, Vol. 59, 2010

Prof. Dr. Shahid S. Siddiqi Dr. Ghazala Akram,; End Conditions for Interpolatory Nonic Splines, South East Asian Bulletin of Mathematics, Vol. 34, 2010

Prof. Dr. Shahid S. Siddiqi Dr. Ghazala Akram,; A Ternary 3-Point Scheme for Curve Designing, International Journal of Computer Mathematics, Vol. 87, 2010

Prof. Dr. Muhammad Sharif,; Energy Contents of Some Non-Vacum Spacetimes in Teleparallel Gravity:, Astrophys. Space Sci., 325, 2010

Prof. Dr. Muhammad Sharif,; Hot Plasma Waves in Schwarzschild Magnetosphere: M. Sharif and A. Rafique, Astrophys. Space Sci., 325, 2010

Prof. Dr. Muhammad Sharif,; Energy Contents of Gravitational Waves in Teleparallel Gravity, Mod. Phys. Lett., A25, 2010

Prof. Dr. Muhammad Sharif,; Effects of Electromagnetic Field on Five Dimensional Gravitational Collapse, J. Korean Phys. Society, 56, 2010

10-

Prof. Dr. Muhammad Sharif,; Plane Symmetric Solutions in f(R) Gravity, Mod. Phys. Lett., A25, 2010

11-

Prof. Dr. Muhammad Sharif,; Gravitational Charged Perfect Fluid Collapse in Friedmann Universe Models: M.Sharif and G. Abbas, Astrophys. Space Sci., 327, 2010

12-

Prof. Dr. Muhammad Sharif,; Energy Distribution in f(R) Gravity, Gen. Relativ. Grav., 42, 2010

13-

Prof. Dr. Muhammad Sharif,; Kinematic Self- Similar Solutions of Locally Rotationally Symmetric Spacetimes, Brazillian J. Physics, 40, 2010

14-

Prof. Dr. Muhammad Sharif,; Dynamics of Viscous Dissipative Plane Symmetric Gravitational Collapse, Gen. Relativ. Grav, 42, 2010

15-

Prof. Dr. Muhammad Sharif,; Quantum Corrections for a Bardeen Regular Black Hole, J. Korean Physical Society, 57, 2010

16-

Prof. Dr. Muhammad Sharif,; Effects of Electromagnetic Field on the Dynamics of Bianchi type VI_0 Universe with Anisotropic Dark Energy, Int. J. Mod Phys., D19, 2010

17-

Prof. Dr. Muhammad Sharif,; Non-Vacuum Bianchi Types I and V In f(R) Gravity, Gen. Relativ. Grav., 42, 2010

18-

Prof. Dr. Muhammad Sharif,; Kinematic Slef-Similar Heat Conducting and Charge Solutions, Chinese J. Phys., 48, 2010

19-

Prof. Dr. Muhammad Sharif,; Re-scaling of Energy in the Stringly Charged Black Hole Solutions using Approximate Symmetries, Canadian J. Phys, 88, 2010

20-

Prof. Dr. Muhammad Sharif,; Energy Contents of a Class of Regular Black Hole Solutions in Teleparallel Gravity, Mod. Phys. Lett., A25, 2010

21-

Prof. Dr. Muhammad Sharif,; Effect of (R) Dark Energy in Dissipative Anisotropic Collapsing Fluid, Mod. Phy. Lett., A25, 2010

22-

Prof. Dr. Muhammad Sharif,; Cold Plasma Wave Analysis in Magneto-Rotational Fluids, Astrophys. Space Sci., 330, 2010

23-

Prof. Dr. Muhammad Sharif,; Dynamics of Bianchi I Universe with Magnetized Anisotropic Dark Energy, Astrophys. Space Sci., 330, 2010

24-

Dr. Malik Zawwar Hussain,; C1 Positive Scattered Data Interpolation, Computers and Mathematics with Applications, 59, 2010

25-

Dr. Malik Zawwar Hussain,; Smooth Polynomial Approximation of Spiral Arcs, Cripps, Journal of Computation and Applied Mathematics, 233, 2010

26-

Dr. Malik Zawwar Hussain,; Positive Data Modeling Using Spline Function, Applied Mathematics and Computation, 216, 2010

27-

Dr. Malik Zawwar Hussain,; Scientific Data Visualization with Shape Preserving C1 Rational Cubic Interpolation,, European Journal of Pure and Applied Mathematics, 3(2), 2010

28-

Dr. Malik Zawwar Hussain,; Visualization of Monotone Data by Rational Bi-Cubic Interpolation, Transaction on Computational Science, VIII, LNCS 6260, 2010

29-

Dr. Malik Zawwar Hussain,; C1 Monotone Scattered Data Interpolation, Transaction on Computational Science, VIII, LNCS 6260, 2010

30-

Dr. Muhammad Aslam Malik,; Finite GS-quasigroups, Quasigroups and Related Systems, 18, 2010

31-

Dr. Muhammad Aslam Malik,; Symmetric Jenertion of the Rudvralis Group, Journal of London Mathematical Society, (2) 82, 2010

32-

Dr. Muhammad Aslam Malik,; Real Quadratic Irrational numbers and Modular Group Action, South East Asian Bulletin of Mathematics, , 2010

PUBLICATIONS: Articles: • Siddiqi, S. S. and Akram, G.,(2008) Quintic Spline Solutions of Fourth Order Boundary-Value Problems, International Journal of Numerical Analysis and Modeling, Canada, 5 (1):101-111 • Siddiqi, S. S. Akram, G. and Elahi, A. (2008), Quartic Spline Solution of Linear Fifth Order Boundary Value Problems Applied Mathematics and Computation, 196: 214-220. • Siddiqi, S. S. and Akram, G. (2008), Septic Spline Solutions of Sixth Order Boundary-Value Problems Journal of Computational and Applied Mathematics, 215: 288– 301. • Siddiqi, S. S. and Ahmad, N. (2008) A new 5-point Approximating subdivision scheme International Journal of Computer Mathematics, 85 (1): 65–72. • Siddiqi, S. S., and Akram, G.(2008) S olution of Twelfth Order Boundary Value Problems using Non Polynomial spline Technique, Applied Mathematics and Computation , 199 (2[1]):559–571. • Siddiqi, S. S. and Ahmad, N. (2008) A C 6 Approximating Subdivision Scheme Applied Mathematics Letters, 21 (7): 722–728. • Siddiqi, S. S. and Akram, G. , (2008) Quintic Spline Solutions of Fourth Order Boundary-Value Problems International Journal of Numerical Analysis and Modeling, Canada, 5 (1): 101-111. • Siddiqi, S. S. and Akram, G. and Elahi, A. (2008)., Quartic Spline Solution of Linear Fifth Order Boundary Value Problems Applied Mathematics and Computation, 196 :214-220. • Siddiqi, S. S. and Akram, G. (2008), Septic Spline Solutions of Sixth Order Boundary-Value Problems Journal of Computational and Applied Mathematics, 215: 288– 301. • Siddiqi, S. S., and Akram, G. (2008) S olution of Twelfth Order Boundary Value Problems using Non Polynomial spline Technique Applied Mathematics and Computation , 199 (2[1]): 559–571. • Sharif, M. (2007) Perturbed Self-Similar Massless Scalar Field in Spherically Symmetric Spaceimes Int. J. Mod. Phys. A (Singapore) 22 :4695-4708. • Sharif, M. and Sheikh, U. (2007) Isothermal Plasma Waves in a Gravitomagnetic Planar Analogue Class. Quantum Grav . (UK) 24 :5495-5514. • Sharif, M. and Ahmad, Z. (2007) Addendum: Gravitational Perfect Fluid Collapse with Cosmological Constant Mod. Phys. Lett. A (Singapore) 22 :2947-2948. • Sharif, M. (2007) Energy-Momentum Distribution of the Wyel-Lewis-Papapetrou and the Levi-Civita Metrics Braz. J. Phys. (Brazil) 37 :1292-1300. • Sharif, M. and Tehseen, N. (2007) Conformal Ricci and Matter Collineations for Anisotopic Fluid Chinese J. Phys. (China) 45 :592-605. • Sharif, M. and Sheikh, U. (2007) Effects of Schwarzschild Black Hole Horizon on Isothermal Plasma Wave Dispersion Gen. Relativ. Gav. (Germany) 39 :2095-2124. • Sharif, M. and Sheikh U. (2008) Effects of Schwarzschild Geometry on Isothermal Plasma Wave Dispersion J. Korean Physical Society (S. Korea) 52 :152-159. • Sharif, M. and Ahmad, Z. (2008) Plane Symmetric Gravitational Collapse, Int. J. Mod. Phys. A (Singapore) 23 :181-188. • Sharif, M. and Nazir, K. (2008) Energy-Momentum Problem of Bell-Szekeres Metric in General Relativity and Teleparallel Gavity Braz. J. Phys. (Brazil) 38 :156-166. • Sharif, M. and Sheikh U. (2008) Complex Wave Numbers in the Vicinity of the Schwarzschild Event Horizon, Int. J. Mod. Phys. A (Singapore) 23 :1417-1433. • Sharif, M. and Amir, M. (2008) Teleparallel Killing Vectors of the Einstein Universe Mod. Phys. Lett. A (Singapore) 23 :963-969. • Sharif, M. and Amir, M. (2008) Teleparallel Energy-Momentum Distribution of Spatially Homogeneous Rotating Spacetimes Int. J. Theor. Phys. (USA) 47 :1742-1750. • Sharif, M. and Ahmad, Z. (2008) Five Dimensional Perfect Fluid Collapse with Cosmological Constant J . Korean Physical Society (S. Korea) 52 :98-985. • Sharif, M. and Ahmad, Z. (2008) Higher Dimensional Perfect Fluid Collapse with Cosmological Constant Acta Physica Polonica B (Poland) 39 :1337-1347. • Sharif, M. and Nazir, K. (2008) Energy-Momentum Distribution of Gravitational Waves Commun. Theor. Phys. (China) 50 :664-668. • Hussain, M. & Hussain, M. Z. (2008), Convexity preserving rational bicubic interpolation, Computer Graphics and CAD/CAM , 2 (1-6):14-24. • Hussain, M. Z. & Sarfraz, M. (2008) Positivist-preserving interpolation of positive data by rational cubic, Journal of Computation and Applied Mathematics , 218 :(2) 446-458. • Husssain, M. Z. & Sarfraz, M. (2008), Monotone piecewise rational cubic interpolation, International Journal of Computer Mathematics, Doi: 10.1080/00207160701595145. • Hussain, M. Z. & Hussain, M. (2008), Convex Surface Interpolation, Lecture Notes in Computer Science 4975: 475-482. • Hussain, M. Z., Hussain, M. and Samreen, S. (2008), Visualization of shaped data by rational quartic spline interpolation, International Journal of Applied Mathematics & Statistics , 13 :34-46. • Hussain, M. Z., Sarfraz, M. & Hussain, M. (2008), visualization of constrained data by rational cubics, European Journal of Scientific Research, 31 (1):212-228. • Hussain, M.Z., Maria Hussain, & Tahira, S. S. (2008), Visualization of constrained data by rational cubics, European Journal of Scientific Research, 31 (1):319-327 • Siddiqi, S.S. and Akram, G. (2008) Quintic Spline Solutions of Fourth Order Boundary-Value Problems International Journal of Numerical Analysis and Modeling, Canada, 5 (1):101-111. • Siddiqi, S. S. Akram, G. and Elahi, A. (2008) Quartic Spline Solution of Linear Fifth Order Boundary Value Problems Shahid S. Siddiqi, Ghazala Akram and Arfa Elahi Applied Mathematics and Computation, 196:214-220. • Siddiqi, S. S. and Akram, G. (2008) Septic Spline Solutions of Sixth Order Boundary-Value Problems Journal of Computational and Applied Mathematics, 215: 288– 301. • S.S. Siddiqi and Akram, G. (2008) S olution of Twelfth Order Boundary Value Problems using Non Polynomial spline Technique Applied Mathematics and Computation , 199 (2[1]):559–571.

BOOKS:

JOURNALS: • Punjab University Journal of Mathematics