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In module variety, Riedtmann and Zwara have shown that geometric degeneration by orbit closure is equivalent to algebraic degeneration by exact sequence. In this paper, we define the U-algebraic degeneration by the notion U-exact sequence introduced by Davvas and Parnian-Gramaleky, and we give its relation with geometric degeneration. Moreover, we also explain its relation with virtual and homomorphism...
In this paper we study centroids and derivations of associative algebras. Using a classification result of associative algebras, we describe the centroids and derivations of low-dimensional associative algebras. We review some properties of the centroids in the light of associative algebras and use these properties to categorize the algebras into having small and not small centroids. We also give...
A new Runge-Kutta method, with phase-fitted and amplification-fitted is constructed for solving first-order ordinary differential equations with periodic solutions. This new method is based on the Runge-Kutta 3/8 Rule with fourth algebraic order. In the numerical results the new method is compared with the existing method; which show that the new method is more efficient.
Oscillating motion of Oldroyd-B flow in a capillary tube at a triangular sine and cosine pressure waveform is considered. An analytical solution of velocity field is obtained for an oscillating laminar flow, which can be used to determine the existence of trapezoidal waveform effect on the flow. When both triangular sine and cosine components are dominate, the oscillating flow can result in significant...
Numbers parts-whole relationship is mainly represented by number bonds in the Malaysian year one mathematics textbooks. Seldom tasks are given to encourage students to create their own representations. The purpose of this study was to investigate how year one students represent and solve word problems based on numbers parts-whole relationship. On this account a cross sectional survey was conducted...
An extended 2-point one-step block method formula with order four is formulated for solving stiff initial value problem. The method is similar to Runge-Kutta method which has a self-starting formula. The approximation solutions at two points will be computed simultaneously by integrating the coefficients over the closest point in the block. The accuracy and the stability properties of the method will...
Application of the quadrature-difference method for solving Fredholm integro-differential equations (FIDEs) is presented in this paper. The FIDEs will be discretized by using the combinations of Simpsons quadrature rule with finite difference. The method converts the FIDEs to a matrix equation which corresponds to a system of linear algebraic equations. The formulation and the implementation of the...
Unmanned Ground Vehicle (UGV) is a vehicle that operates while in contact with the ground with no human existence on board. The number of research involving autonomous UGV is increasing widely. It can be used for many applications where it might be risky to be handled by human. Mobile Guard UGV-Truck Surveillance (MG-TruckS) is a UGV that used to help security guard to monitor the residential area...
In this paper, a variable step size and variable order strategy ( VSVO) used in the block method is developed for solving directly the second order two-point boundary value problems (BVPs). The variable step size and variable order strategy managed to reduce the total step and assure the accuracy of the method. The proposed block method can compute the solutions at two points simultaneously and adapted...
Credit risk theory for valuation corporate bond is usually expressed as zero coupon bond. In real bond trading, the most common form of debt is coupon bond. This paper developed model of multiperiods coupon bond with classical approach as default time rule. It means that default occurs when the firm cannot fulfill its payment obligation at coupon date and/or at the maturity date. Some assumptions...
This paper presents 4-point 1-step block method (4LBVP) to solve the linear 2nd order boundary value problem (BVP) with Dirichlet boundary condition. 4LBVP will solve the linear 2nd order BVP with Dirichlet boundary condition directly without the need to reduce it first into the system of 1st order equations. 4LBVP will produce several numerical solutions simultaneously in one step. The formulation...
By making use of the generalised derivative operator, a new class of analytic functions is investigated. An upper bound of second Hankel determinant for functions belonging to this class is studied.
This paper will implement the use of two-point block method in the form of predictor-corrector Adams-Moulton to solve first order neutral delay differential equations (NDDES) of pantograph type. This two-point block method will compute the numerical solution at two points simultaneously. This method will approximate the solutions using constant step size. The delay solutions for the unknown function...
The numerical solution of neutral delay differential equation (NDDE) with variable step size implementation in multistep block method is addressed in this paper. The strategy of variable step size was actually from the idea in adapting the step size control mechanism in the block method that allows each block to have different step size ratios as it moves in the interval. Special attention is paid...
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