Welcome to my homepage. I am Dr. Jayantha Lanel, a Senior Lecturer in Mathematics, University of Sri Jayewardenepura (USJ). I joined the Department of Mathematics at USJ in 2010. In addition, I am an academic counselor for Mathematics of Faculty of Applied Sciences.

In the wide realm of mathematics, I have developed a special interest in numerical analysis, this is the area in which I have done some research work for my master degree at Sri Jayewardenapura University.

I completed my Ph.D. thesis titled *Complex Root Isolation *under the supervision of Professor Charles Cheng and graduated from the Oakland University in Rochester, Michigan in 2009. In my thesis, for a given square-free polynomial *p, *compute 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/Computational Discrete Mathematics 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 involving in many graduate/undergraduate research in this field.

## Research Students

**Ph. D. Candidates:**

- B. A. K. Welihinda (Title: Analysis of the exultancy of Hamiltonian cycles in Cayley graphs of groups of special orders and its applications to public-key cryptography).
- D.G.N.D. Jayarathna (Title: Modelling and Simulation of Cost Benefit Transportation System: Planning for a Warehouse Vendors System).

**M.Phil. Candidates:**

- Chinthaka Wijerathne (Title: A Study of Moore Graphs and Degree Diameter Problem to Construct a New General Upper Bound for the Order of Graphs).
- H.K. Abeynanda (Title: Distributed Optimization of Limited Communication Net-works)

**M.Sc. Candidates:**

- P.H.H.P.N. De Silva (Title: Optimum Plant Mix Selection for Urban Home Gardens in Sri Lanka).

**M.Sc. Graduates:**

- 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
- P.D.A.G.D. De Almeida (M.Sc. in Industrial Mathematics, USJ),Data Model and Algorithms for Rates Base Route Planning with Rail Way Transportation Networks in USA, 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