# Research

My research activity can be described as Parallel and Mobile Computation for Scientific Problems. Some personal contributions can be summarised as follows.

** Computational Methods for Cancer Modelling: **

- Investigation of the Fister-Paneta equations with new results concerning the tumour grouth.
- Some modelling methods for cancer prediction based on the Gompertz and Fister-Paneta.
- 3D Visualisation framework for cancer tumours.
- 3D Models and animations for cancer.
- Models and simulations for cancer gene therapy.

**Loop Scheduling Methods for Parallel Computation **

- Efficient loop scheduling based on workload balance.
- An O(log p) Algorithm for Feedback Guided Dynamic Loop Scheduling method.
- Theoretical analysis of the Feedback Guided Dynamic Loop Scheduling method.
- Several convergence cases of the Feedback Guided Dynamic Loop Scheduling method.
- Applications of the Feedback Guided Dynamic Loop Scheduling method to scientific computing.

**Mobile Computing **

- MMPI - A Bluetooth based library for MPI computation across mobile piconets.
- A Framework for Bluetooth Gaming and Cooperative Mobile Graphics.
- Several algorithms to generate Fractals on Mobile devices.
- Educational mobile games with applications to m-learning.

**Image Processing **

- A new method for Image Sharpening based on the Smarandache inverse function.
- A theoretical study of Prime Number Fractals.
- Several classes of Prime Number Fractals both in 2D and 3D.
- Parallel algorithms for Fractal Image Compression.

**Computational Number Theory**

- Some algorithms (sequential and concurrent) for the Smarandache function.
- A primality study of some Smarandache sequences. !!! I found two interesting prime numbers, 12345678910987654321 and 1234567891010987654321 (they might have been known before) when I did this study. !!!
- Initiate the study of the average of the Smarandache function and prove that this average is less than O(n). Luca [2000] proved that the average is O(n/log(n)).
- Initiate the study of the harmonic series of the main Number Theory functions and proved:
- - The divergence of the series \sum_{n>0}{\frac{1}{S^2(n)}} (a ten year conjecture).
- - The divergence of the Erdos harmonic series in the general case.
- - The Euler harmonic series has the same convergence as the classical harmonic series. (the simplest and nicest result of mine).

**My Erdos Number is 3 **(P.Erdos(0)->R.Brent(1)->L.T.Yang(2)->S.Tabirca(3))