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Prof. Dr. Ghulam Mustafa
  • Prof. Dr. Ghulam Mustafa

  • Professor
    Post-Doc 2
  • ghulam.mustafa@iub.edu.pk

Profile Summary

Prof. Dr. Ghulam Mustafa is currently serving as the Dean of the Faculty of Physical and Mathematical Sciences at The Islamia University of Bahawalpur (IUB), Pakistan. He served for eight years as Chairperson of the Department of Mathematics at IUB.

He earned his Ph.D. in Mathematics in 2004 from the University of Science and Technology of China (USTC), P.R. China, under the Cultural Exchange Scholarship Program. He obtained his M.Sc. and M.Phil. degrees from Bahauddin Zakariya University, Multan, and completed his B.Sc. from The Islamia University of Bahawalpur at Dera Nawab College, Ahmadpur East.

In 2010, he visited the School of Mathematical Sciences, USTC, to conduct collaborative research under the “Pakistan Program for Collaborative Research – Foreign Visit of a Local Faculty Member.” In 2011, he completed a postdoctoral fellowship at Durham University, UK, funded by the Association of Commonwealth Universities. From 2013 to 2014, he was a visiting fellow at USTC, sponsored by the Chinese Academy of Sciences.

Prof. Dr. Mustafa has been a Professor of Mathematics since 2016. He has organized numerous national and international conferences, webinars, and Mathematical Olympiads. He has also presented his research at various national and international academic events.

He has completed two research projects funded by the Higher Education Commission (HEC) of Pakistan under the National Research Program for Universities (NRPU)and theStart-up Research Grant Program (SRGP). He has also supervised three students under the Science Talent Farming Scheme (STFS), sponsored by the Pakistan Science Foundation (PSF).

He has served—and continues to serve—as a chairman or member of various important university bodies, including the Senate, Finance and Planning Committee, Academic Council, Advanced Studies and Research Board, Affiliation Committee, Appeal Committee, Board of Studies, and the Board for the Management of Group Insurance Funds.

He is the author of several books, including:

·        Subdivision: Its Applications in Solid Modeling and Signal Compression(VDM Verlag, 2010)

·        Memories and Achievements of the Department of Mathematics, The Islamia University of Bahawalpur, Pakistan (1979–2021)(IUB Press)

·        The 20 Years Journey of the Computer-Aided Geometric Design Research Group Pakistan

Throughout his academic career, he has published more than 146 research papers and successfully supervised 14 Ph.D. and 97 M.Phil. scholars. He serves as an editor, associate editor, guest editor, and reviewer for several reputed journals and regularly reviews M.Phil. and Ph.D. theses from various universities. His research interests include geometric modeling, subdivision schemes, applied approximation theory, the numerical solution of differential equations, picture fuzzy graph, fuzzy set and decision-making.

Qualifications

DegreeBoard/UniversityYear of Passing
Post-Doc 2University of Science and Technology of China2014-05-08
Post-Doc 1Durham University UK2012-03-31
PhD MathematicsUniversity of Science and Technology of China2004-07-10
M.Phil MathematicsBahauddin Zakariya University, Multan1996-01-01
MSc Mathematics Bahauddin Zakariya University, Multan1993-01-01
BScIslamia University, Bahawalpur1991-01-01
FSc Pre-EnggBoard of Intermediate and Secondary Education, Bahawalpur1989-01-01
SSCBoard of Intermediate and Secondary Education, Bahawalpur1987-01-01

Experience

Professor on TTSThe Islamia University of Bahawalpur
ProfessorThe Islamia University of Bahawalpur
Associate ProfessorThe Islamia University of Bahawalpur
Assistant ProfessorThe Islamia University of Bahawalpur
LecturerThe Islamia University of Bahawalpur

Publications

Spherical fuzzy Bezier curve approximation for efficient lane-changing trajectories under uncertain data
A family of non-uniform, non-symmetric higher-arity interpolatory schemes with function-based mask design for enhanced smoothness and localized support
Insights into engineering shapes through curve and surface modeling with the 4-point quaternary subdivision scheme
Investigation of Chaotic Finance with Renewable Energy Effects Using Sustainable Fractional Approach
On Characterizations of Molecular Descriptors and Entropies for Oxytocin and Cholic Acid Chemical Networks
Numerical simulation of fourth-order Volterra partial integro-differential equations using subdivision and trapezoidal rules
Bifurcation and control of xanthomonas infectious disease spread in banana plants under hypersensitive response
Fractal curve generation through a general binary 6-point interpolating subdivision scheme with dual shape control parameters
Bounding the distance between the kth control mesh and the limit surface of Li's subdivision
Analysis and dynamics of cholera epidemic system in society via fractal-fractional operator
Innovative Numerical Method for Solving Heat Conduction Using Subdivision Collocation
Complex Pythagorean Parameterized Fuzzy Sets and their Applications to Countering Digital Crime and Digital Terrorism and Supply Chain Management Problem
An integrated outranking approach for selecting the best waste water treatment process with spherical fuzzy rough numbers
An extended Mittag Leffler function in terms of extended Wright complex hypergeometric function
A hybrid family of non-uniform ternary schemes with mixed symmetry for approximating shapes
A generalized fractional integral transform for solutions of fractional Burger’s equation
The generalized algorithm for fractional continuity of polynomial splines
Smooth transition and Gibbs oscillation minimization in a 7-point subdivision scheme with shape-control parameters for high smoothness
Study on symptomatic and asymptomatic transmissions of COVID-19 including flip bifurcation
Generation of fractal curves using new binary 8-point interpolatory subdivision scheme
QSPR analysis for physio-chemical properties of new potential antimalarial compounds involving topological indices
Chromatic polynomial of a picture fuzzy graph with application in traffic light control
Quantum thermodynamics of the charged AdS black hole with nonlinear electrodynamics field
Dynamical analysis of soliton structure for the nonlinear third-order Klein-Fock-Gordon equation under explicit approach
Thermal properties of Simpson--Visser Minkowski core regular black holes solution in Verlinde's emergent gravity
Innovative fractional integral transform for the solution of well known partial differential equations
Unified framework for curve modeling by family of quaternary schemes and its analysis
Unified framework of stationary and non-stationary subdivision schemes for curve modeling
The generalized classes of linear symmetric subdivision schemes free from Gibbs oscillations and artifacts in the fitting of data
An efficient computational approach for computing subdivision depth of non-stationary binary subdivision schemes
Modeling of curves by a design-control approximating refinement scheme
A study on the class of non-symmetric 3-point relaxed quaternary subdivision schemes
A convolution-based computational technique for subdivision depth of Doo-Sabin subdivision surface
Variations in 2D and 3D models by a new family of subdivision schemes and algorithms for its analysis
An effective approach to solve fractional partial differential equations based on hybrid B-spline
The family of multiparameter quaternary subdivision schemes
A family of integer-point ternary parametric subdivision schemes
Subdivision collocation method for one dimensional Bratu's problem
Recursive process for constructing the refinement rules of new combined subdivision schemes and its extended form
A divided differences based medium to analyze smoothness of the binary bivariate refinement schemes
A refinement schemes based unified algorithm for a class of nth order differential equations with a set of constraints
A new paradigm to design a class of combined ternary subdivision schemes
Construction and analysis of unified 4-point interpolating non-stationary subdivision surfaces
Unified framework of approximating and interpolatory subdivision schemes for construction of class of binary subdivision schemes
A shape-preserving variant of Lane-Riesenfeld algorithm
A new computational approach to estimate the subdivision depth of n-ary subdivision scheme
A new approach to increase the flexibility of curves and surfaces produced by 4-point ternary subdivision scheme
A 6-point subdivision scheme and its applications for the solution of 2nd order nonlinear singularly perturbed boundary value problems
The inequalities for the analysis of a class of ternary refinement schemes
The numerical solution of fourth order nonlinear singularly perturbed boundary value problems via 10-point subdivision scheme based numerical algorithm
Statistical analysis of subdivision schemes in terms of probability distribution
A subdivision based approach for singularly perturbed boundary value problems
A class of refinement schemes with two shape control parameters
A computational method for subdivision depth of ternary schemes
A novel numerical algorithm to estimate the subdivision depth of binary subdivision schemes
A family of 2n-point approximating subdivision schemes based on least squares method
A family of binary approximating subdivision schemes based on Binomial distribution
Families of non-linear subdivision schemes for scattered data fitting and their non-tensor product extensions
Generalized family of approximating schemes based on Newton interpolating polynomials and its error analysis
Semi-analytical solutions of multilayer flow of viscous fluids in a channel
A family of high continuity subdivision schemes based on probability distribution
Ridge regression based subdivision schemes for noisy data
Univariate approximating schemes and their non-tensor product generalization
A new paradigm for increasing the continuity of subdivision schemes
Fractal generation by 7-point binary approximating subdivision scheme
A family of univariate ternary subdivision schemes with 5 parameters
A family of 6-point n-ary interpolating subdivision schemes
Family of a-ary univariate subdivision schemes generated by Laurent polynomial
A class of shape preserving 5-point n-ary approximating schemes
Stationary and non-stationary univariate subdivision schemes
The (2n+1)\textsuperscript{2}-point scheme based on bivariate quartic polynomial
Generalization of binary tensor product schemes depends upon four parameters
Families of univariate and bivariate subdivision schemes originated from quartic B-spline
A numerical approach based on Bernstein polynomial for solving Volterra-Fredholm integral equations
A family of 2n-point ternary non-stationary interpolating subdivision scheme
Statistical and geometrical way of model selection for a family of subdivision schemes
The (2n)\textsuperscript{2}-point scheme based on bivariate cubic polynomial
3n-point quaternary shape preserving subdivision schemes
A subdivision collocation method for solving two point boundary value problems of order three
Family of a-point b-ary subdivision schemes with bell-shaped mask
A numerical approach based on subdivision schemes solving nonlinear fourth order boundary value problems
Construction and analysis of binary subdivision schemes for curves and surfaces originated from Chaikin points
Unification of the lambda-point a-ary subdivision scheme
An alternative method for constructing subdivision algorithm
A 10-point approximating subdivision scheme based on least squares technique
Wide-ranging families of subdivision schemes for fitting data
Engineering images designed by fractal subdivision scheme
A subdivision based iterative collocation algorithm for nonlinear third order boundary value problems
A new class of binary approximating subdivision schemes
Subdivision depth for triangular surfaces
Subdivision schemes based collocation algorithms for solution of fourth order boundary value problems
A new class of odd-point ternary non-stationary approximating schemes
A family of 4-point odd-ary non-stationary subdivision scheme
?1-regression based subdivision schemes for noisy data
Complete analysis of 3-point binary subdivision scheme
MHD stagnation slip flow over an unsteady stretching surface in porous medium
Numerical solution of two point boundary value problems by interpolating subdivision schemes
Binary univariate dual and primal subdivision schemes
Generalized and unified families of interpolating subdivision schemes
A six-point variant on the Lane-Riesenfeld algorithm
Estimating error bounds for G. Li et al.'s subdivision scheme
A generalized non-stationary 4-point b-ary approximating scheme
A new class of odd-point ternary non-stationary schemes
Numerical algorithm for analysis of n-ary subdivision schemes
Four-point n-ary interpolating subdivision schemes
A new non-tensor product C\textsuperscript{1} subdivision scheme for regular quad meshes
A family of 4-point n-ary interpolating scheme reproducing conics
The 4-point a-ary approximating subdivision scheme
A subdivision-regularization framework for preventing overfitting of data by a model
Construction and application of 3-point tensor product scheme
The mask of odd points n-ary interpolating subdivision scheme
A new 5-point ternary interpolating subdivision scheme and its differentiability
The family of even-point ternary approximating schemes
Unification and application of 3-point approximating subdivision schemes of varying arity
(2n-1)-point ternary approximating and interpolating subdivision schemes
The odd-point ternary approximating schemes
Subdivision depth computation for tensor product n-ary volumetric models
A unified three point approximating subdivision scheme
A generalized proof of the smoothness of 6-point interpolating scheme
A new 6-point ternary interpolating subdivision scheme and its differentiability
The mask of (2b+4)-point n-ary subdivision scheme
Subdivision depth computation for n-ary subdivision curves/surfaces
A random coincidence point theorem for multifunction
A new 4-point C\textsuperscript{3} quaternary approximating subdivision scheme
Error bounds for sqrt(3) subdivision surfaces
Estimating error bounds for quaternary subdivision schemes
The m-point approximating subdivision scheme
Ternary 6-point interpolating subdivision scheme
Estimating error bounds of Bajaj’s solid models and their control hexahedral meshes
Estimating error bounds for non-stationary binary subdivision curves/surfaces
Estimating error bounds for ternary subdivision curves/surfaces
Estimating error bounds for tensor product binary subdivision volumetric model
Estimating error bounds for binary subdivision curves/surfaces
Random fixed point theorems for contractive type multifunctions
Some random coincidence and random fixed point theorems for hybrid contractions
A subdivision scheme for volumetric model
A new solid subdivision scheme
Ternary wavelets and their applications to signal compression
A double-sequence random iteration process for random fixed points of contractive type random operators
An explicit pseudo-spectral scheme for Korteweg-de Vries Burgers equation
Some random coincidence point theorems
The Fourier pseudospectral method with restraint operator for Burgers equation
A three level pseudo-spectral method for vorticity equation
Random coincidence point theorems for generalized contractive type random multivalued operators on polish spaces
Random coincidence point theorems for Kannan type random multivalued operators on polish spaces
Random coincidence points of random multivalued operators on polish spaces

Projects

Supervisor/Mentorship of the research project for STFS (Science Talent Farming Scheme)

2020-06 - 2024-12

Associated With: PSF (Pakistan Science Foundation)

Show project

a)The research project for STFS (Science Talent Farming Scheme), for young students Phase-I (Component-I) 6th Batch, sponsored by PSF (Pakistan Science Foundation). Student name: Danial Hussain Shah (No. PSF/STFS/238/2022-23, dated 19-01-2024), Research report title: “Applications of Pascal’s triangle in CAGD and Graph Theory”b)The research project for STFS (Science Talent Farming Scheme), for young students Phase-I (Component-I) 5th Batch, sponsored by PSF (Pakistan Science Foundation). Stu-dent name: Hira Sardar (No. PSF/STFS/135/2019-20, dated 22-11-2021), Research re-port title: “Investigation of cubic B-spline for modeling of curves”c)The research project for STFS (Science Talent Farming Scheme), for young students Phase-I (Component-I)4th Batch, sponsored by PSF (Pakistan Science Foundation). Stu-dent name: Kashaf Aslam (PSF/STFS/135/2017-18, dated 15-06-2020), Research report title: “Investigation of Chaikin's corner cutting scheme for modeling of curves”

Generation of mask of univariate and bivariate non-stationary subdivision schemes and their analysis

2017-05 - 2018-04

Associated With: HEC (Higher Education Commission, Pakistan)

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This project focuses on creating and analyzing non-stationary subdivision schemes for curves and surfaces. We developed specialized masks to build high-quality models that stay smooth during the refinement process. A major highlight is the "application-first" focus, as these schemes are designed to handle noisy data and maintain natural shapes. By using tools like non-stationary interpolating methods, we can generate precise 3D structures and even complex fractal patterns. Overall, this research provides a flexible way to pick the best mathematical model for any specific design task.

Generation of mask, analysis, model selection and assessment for (n+1)-point m-ary univariate and bivariate subdivision schemes

2014-04 - 2017-03

Associated With: HEC (Higher Education Commission, Pakistan)

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This project improves Computer-Aided Geometric Design (CAGD) by creating new ways to model smooth objects. It focuses on (n+1)-point m-ary schemes for both curves and surfaces. We built these models using probability tools and Laurent polynomials to ensure they stay smooth and continuous. A major highlight is the "application-first" focus. We used ridge regression so the models can handle messy or noisy data from real-world scans. The project also ensures "shape-preserving" results, meaning the final design won't have accidental bumps or wobbles. Finally, we introduced new ways to pick the best model for any specific job. These techniques help designers build complex 3D structures using advanced cubic and quartic math.

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