Academic Journal of Applied Mathematical Sciences
Online ISSN: 2415-2188
Print ISSN: 2415-5225
Print ISSN: 2415-5225
Quarterly Published (4 Issues Per Year)
Volume 8 Number 2 April 2022
Stable Numerical Differentiation Algorithms Based on the Fourier Transform in Frequency Domain
Authors: Yanling He ; Huilin Xu ; Xiaoyan Xiang
A class of stable numerical differential algorithms is constructed based on the Fourier transform. The instability of the numerical differentiation problem is overcome by modifying the integral “kernel” in the frequency domain. The convergence of the approximate derivatives is ensured based on some reasonable assumptions of the modified “kernel” function. The a-posteriori choice strategy of the regularization parameter is considered. Moreover, the convergence analysis and error estimate of the approximate derivatives are also given.
Rotation Equation of a Point in Air and its Solution
Authors: Tian-Quan Yun
Operator ∇ inner products on both sides of Combination of Boyles’ law and Chares law (“B-C law” in short), we got the “Wind Speed Equation of a Point in Air” (“Wind Speed Equation” in short). It suits for describing straight-line motion, and It states that mu ̇ is in proportion to ∇•T. Operator ∇ outer products on both sides of “Wind Speed Equation” (where T is replaced by T), we get the “Rotation Equation of a Point in Air” (“Rotation Equation” in short). It is a vector partial differential equation (PDE), suits for describing circular motion. It states that (mu ̇ ) is in proportion to T. Its solution is found by the method of separating variables. The existence of vector T is proved by the existence of rotation in the atmosphere and the solution of the “Rotation Equation”. It reveals that the vector form of B-C law holds in rotating air. Examples of up-side-down vertical rotation and horizontal rotation are given.
Linear Programming on Bread Production Using Uncertainty Approach
Authors: Adamu Wakili
Linear programming is applied to bread production and the raw materials for the research were collected from the bakery industry in Lokoja which were clearly identified. The paper took into account three types of bread with estimated profits and the problem was formulated from the collected data. The formulated problem was parameterized into parametric linear programming and run using the developed algorithm of linear programming The result obtained indicates that profit is made at d different values of the parameter,t, leaving the company the choice of any profit it wants to get.