Welcome to my homepage. I am Prof. Jayantha Lanel, a Professor in Mathematics, University of Sri Jayewardenepura (USJ). I joined the Department of Mathematics at USJ in 2010.
In the wide realm of mathematics, I have developed a particular interest in numerical analysis, this is the area in which I have done some research work for my master's degree at Sri Jayewardenepura University.
I completed my Ph.D. thesis titled Complex Root Isolation under the supervision of Professor Charles Cheng and graduated from Oakland University in Rochester, Michigan in 2009. In my thesis, for a given square-free polynomial p, compute the exact number of zeros of p in a rectangle R when there is a zero of p on the boundary of R.
My core research interests lie in Computer Algebra (symbolic mathematics), a relatively young area of Mathematics that provides plenty of tools to many scientific areas, such as engineering and physics.
After completing my doctorate, I decided to expand my research interest by working on some problems in Graph Theory and Its Applications one of the extensive and popular branch of mathematics, which has been applied to many problems in mathematics, computer science, and other scientific areas. At present, I am involved in many graduate/undergraduate research in this field as well as other fields such as Optimization, Deep Learning, etc.
Research Students
Ph.D. Graduates:
- B. A. K. Welihinda (Thesis Title: Analysis of the exultancy of Hamiltonian cycles in Cayley graphs of groups of special orders and its applications to public-key cryptography) in 2022.
- D.G.N.D. Jayarathna (Thesis Title: Modelling and Simulation of Cost Benefit Transportation System: Planning for a Warehouse Vendors System) in 2022.
Ph. D. Candidates:
- G. K. H. Thondilege, Mathematical Approach for Improved Image Preprocessing Techniques.
- T. A. H. Dilpriya, Enhancing Investment Strategies through Machine Learning Techniques, from Oct. 2022 onwards.
- Kavishka Rajapaksha, Analysis of Dynamic Nature of Multiplex Networks using Graph Theory, from March. 2024 onwards.
M.Phil. Graduates:
- H.K. Abeynanda (Thesis Title: Distributed Optimization of Limited Communication Net-works) in 2022.
M.Phil. Candidates:
- Chinthaka Wijerathne, A Study of Moore Graphs and Degree Diameter Problem to Construct a New General Upper Bound for the Order of Graphs, 2021 onwards.
- D.C. Gunawardhana, Applications of Topological Indices in Drug Design in terms of Quantitative Structure-Property Relationships/ Quantitative Structure Activity Relationships, from Oct. 2023 onwards.
M.Sc. Candidates:
- ...
M.Sc. Graduates:
- P.H.H.P.N. De Silva (M.Sc. in Industrial Mathematics, USJ), Optimum Plant Mix Selection for Urban Home Gardens in Sri Lanka), 2022
- Chiloma Subasinghe (M.Sc. in Industrial Mathematics, USJ), An Efficient Automated Timetable for Distance Education of the Open University of Sri Lanka, 2019
- P.W.C.E. Pathirana (M.Sc. in Industrial Mathematics, USJ), Developing a New Paper Structure For The GCE (O/L) Mathematics Paper Using Graph Theory, 2019
- M.G.R.U.K. Ferdinandes (M.Sc. in Financial Mathematics, University of Colombo), A Queuing Model to Optimize the Performance of Surgical Units, 2017
- M.T.M. Perera (M.Sc. in Financial Mathematics, University of Moratuwa),A Model to Optimize University Course Timetable Using Graph Coloring and Integer Linear Programming, 2016
- G.K.H. Thondilege (M.Sc. in Industrial Mathematics, USJ), Possibilities of Sharing Multi Species in a Cage Based on Their Food Preference Using Graph Coloring Technique, 2015
- D.M.K.N. Seneviratna (M.Sc. in Industrial Mathematics, USJ), Traveling Tourist Problem for Selected Destinations in Sri Lanka, 2011
Recent Publications
- Cryptographic Protocols using Semidirect Products of Finite Groups
- A Study on Distributed Optimization over Large-Scale Networked Systems
- Survey on Ten Years of Multi-Depot Vehicle Routing Problems: Mathematical Models, Solution Methods and Real-Life Applications
- A Study on Distributed Optimization over Large-Scale Networked Systems
- A Survey of Public-key Cryptography over Non-abelian Groups
- A third order convergent method for solving nonlinear equations
- An Efficient Automated Timetable for Distance Education of the Open University of Sri Lanka
- Five years of multi-depot vehicle routing problems
- A third order convergent method for solving nonlinear equations
- A Study on Graph Theory Properties of Constellations
- A Use of Graph Theory Properties of Constellations in Stellar Colonization
- HAMILTONIAN CYCLES IN CAYLEY GRAPHS OF SEMIDIRECT PRODUCTS OF FINITE GROUPS
- A Study on Graph Theory Properties of On-line Social Networks
- An Efficient Automated Timetable for Distance Education of the Open University of Sri Lanka
- Developing a New Paper Structure For The GCE (O/L) Mathematics Paper Using Graph Theory
- A Study on Graph Theory Properties of Constellations
- A Use of Graph Theory Properties of Constellations in Stellar Colonization
- HAMILTONIAN CYCLES IN CAYLEY GRAPHS OF SEMIDIRECT PRODUCTS OF FINITE GROUPS
- Identifying the Optimum Path and the Positions of the Bends in PVC and DI Pipes in Underground Water Lines.
- A Model To Reduce Traffic Congestion In Colombo City