Influence analysis of foamed asphalt mixture gradation based on mechanical properties
In order to determine the influence and rules of the gradation of foamed asphalt on the mechanical properties, three typical gradations of foamed asphalt including the continuous gradation AC-20, the discontinuous gradation SMA-20 and the skeleton embedded crowded structure FAC-20 were taken for dry and wet splitting strength test, besides the mechanical properties of asphalt mixture under different gradations were systematically researched. The gradation composition fluctuation of four key sieve pores consisting of 0.075 mm, 0.3 mm, 1.18 mm and 4.75 mm affecting the mechanical properties of the foamed asphalt mixture gradation were systematically researched. The experimental results showed that foamed asphalt mixture was not suited for the stable discontinuous gradation; the Wittgen stable recommended gradation of foamed asphalt had better mechanical properties; the passing rate of sieve pore size bellow 0.075mm was the key factor affecting the gradation properties of the foamed asphalt mixture, and the rate between five percent and twelve point five percent had better mechanical properties foamed asphalt mixture; the smaller sieve pore size was, the influence of the fluctuation of the passing rate on the mechanical properties of gradation was greater; among others
Foamed bitumen stabilised sandstone aggregates
Roads form a key element for the expansion of economy and development of a country. As with most countries, Brunei Darussalam has been facing a rapid development to meet the economic growth that requires an efficient road network. Therefore, the scarcity of conventional road aggregates in Brunei Darussalam means that the country has a strong dependence on imported aggregates from overseas to construct quality roads. Further restrictions on local road specifications make it almost impossible to include low quality granular materials. The study reported in this thesis was undertaken on the basis that the dependence on overseas resources is not a viable long- term solution. The research task has been, therefore, to ascertain the quality of local sandstones for road construction and then to propose means to upgrade their performance quality for optimum utilisation in cost effective applications. This study focused on the road base layer since that is where most aggregate is used. 
The approach used for this study was to identify the common rock in Brunei Darussalam and review the candidate treatment methods. A weighted matrix for these candidate treatment methods was constructed to determine the overall ranking with selected key criteria on the basis of the local climatic condition, construction preferences and traditions. From the reviews, Foamed bitumen was selected as a feasible treatment method that can improve the sandstone characteristics under local conditions. 
Three curing conditions were adopted in this study, simulating extreme field conditions in Brunei Darussalam, to characterise the mechanical properties of foamed bitumen stabilised sandstone mixtures, termed 'foam mix'. The following tests were conducted:
Mahler functions and transcendence
Transcendence theory of mahler functions of one variable.- Transcendence theory of mahler functions of several variables.- Algebraic independence of mahler functions and their values.- Applications of elimination theory.- Regular sequences and mahler functions.