Transition from steady to chaos for the onset of Benard convection in porous medium was analyzed. The governing equation is reduced to ordinary differential equation and solved using built in MATLAB ODE45. The transition from steady to chaos take over from a limit cycle followed by homoclinic explosion.

A question of interest in the demografic and actuarial fields is the estimation of the complete sets of q(x)-values when the data are given in age groups. This study presents two techniques of expanding an abridged life table to a complete ones. The two expansion techniques used in the study are King's Osculatory Interpolation and Heligman-Pollard model. This work evaluated and compared the performance of King's Osculatory Interpolation and Heligman-Pollard model. For that purpose, empirical data sets on abridged life tables for Malaysian populations for the period of 1991, 1995 and 1999 for both gender were collected. Then each of the expanding techniques considered was applied to these abridged data sets. The complete sets of q(x)-values obtained from these two techniques were then used to produce the estimated abridged ones. These results were then compared with the actual values published in the abridged tables.

There are many researches showing that the life expectancy for most countries is increasing. Since the life expectancy at a particular age tends to increase over time for male and female, the mortality risk tends to be smaller over time. Therefore it is expected that pensioners tend to live longer and thereby cause increase in pension liabilities to the government. Countries are looking for solutions to decrease the effect of increased longevity on pension costs. The most common changes are to equalize the retirement age for male and female and to rise the retirement age. Therefore, we studied the longevity factor for the government pensioner in Malaysia at age 55, 56, 57, 58, 59 and 60 years respectively. Since the pensions are paid for the rest of the pensioner's life in the event of his death and also to his spouse and child if any in the form of a derivative pension, the longevity factor for pensioner, spouse and child will be formulated and estimated separately. To formulate and estimate these factors, the theory of annuities and the Pension Law of Malaysia need to be studied.

In the event of death of any government employee, their monthly pension will be given to their widow and their child. The government will stop paying that pension when the widow died and when the widow chooses to remarry. However, in 1st January 2002, the remarriage clause has been removed from the regulations. This would allow all widows who remarried to receive pension as usual. In view of this, there are possibilities that those widows who are still young might remarried. If many of the widows choose to remarry, it will be a burden to the government as it would increase the pension liabilities. However, we do not know how many of the widow will remarry. In view of this, the purpose of the study is to assess the impact to pension liabilities of government pension schemes on individual life due to removal clause of the remarriage by determining the pension factor and to assess to what extent the pension liabilities of government pension schemes would be affected.