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This paper studied the behaviour of the solution for an almost square crack, Ω, in the plane elasticity. The problem of sliding the resulting shear forces can be formulated as a hypersingular integral equation over a considered domain, Ω. The sharp corner of the square is rounded up such that the stress singularity is kept uniform form along the entire crack contour. The equation is then transformed into a similar hypersingular integral equation over a circular disc, D, using conformal mapping. The transformed hypersingular integral equation is afterward reduced to a system of linear algebraic equations using Galerkin method. The system of linear equations is solved numerically for the unknown coefficients, which later will be used in determining the stress intensity factors, maximum stress intensity and energy release rate. Comparison with the existing asymptotic solutions show a good agreement.

The fourth order Lucas sequence is a linear recurrence relation related to quartic polynomial and based on Lucas function. This sequence had been used to develop the LUC 4,6 cryptosystem. As we know, the efficiency is one of the crucial parts of the cryptosystem and it is depended on computation time for Lucas sequence which is used to develop the process encryption and decryption in the LUC 4.6 cryptosystem. In this paper, a method will be proposed to decrease the computation time for fourth order Lucas sequence. This method omits some terms of the sequence to decrease the computation time. Thus, if the LUC 4,6 cryptosystem is using this method to compute the plaintexts and cipher texts, then the computation time had been decreased.

Fire hazard is a common threat in longhouses in Sarawak. Among things that are crucial in fire prevention is the evacuation route, in which highly dependent on house construction and layout. This study aims to observe the evolution of the Iban longhouse architectural design and materials used to build the longhouse. The qualitative analysis method was applied through 2D photo analysis as well as on-site visual observation and measurement. Construction materials used have been surveyed to determine its combustibility. It has been noted that longhouses have evolved over the years, from traditional to semi-traditional and modern longhouses design. The changes include the layout design and construction materials of the longhouses. Traditional and semi-traditional longhouses are often built using wooden materials that are highly flammable, while modern longhouses are made from concrete materials. The types of construction materials contribute to fire severity. It can be concluded that the longhouse architectural design, along with its construction materials, plays an essential role in the understanding of fire hazard, which will serve as fundamental on the longhouse fire reduction.

This research proposes a three-point block method for solving Duffing type higher order ordinary differential equations (ODEs) which is also commonly referred as the Duffing oscillator. The research conducted implements a variable order step size technique for approximating the exact solution for the Duffing Oscillator. The proposed algorithm will be tested against various Duffing oscillators and numerical approximation will be compared with current viable methods. The accuracy and efficiency of the proposed method will be illustrated in the numerical results.