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Academic Journal of Applied Mathematical Sciences

Online ISSN: 2415-2188
Print ISSN: 2415-5225

Quarterly Published (4 Issues Per Year)


Volume 7 Number 2 April 2021

1-D Optimum Path Problem and Its Application

Authors: Tian-Quan Yun
Pages: 137-142
DOI: doi.org/10.32861/ajams.72.137.142
The 1-D optimum path problem with two end-points fixed or one end-point fixed, the other end-point variable reduces to vector integral equations of Fredhom / Volterra type and is hard to solve. Translating it to scalar components equations would be an easier way of solving it. Here, the solution of the optimum path problem is recommended by connecting it with the Principle of minimum Energy Release (PMER). A lot of optimum path problems with path function E=cu2, where E is the released energy, u is the velocity, c is constant, can be solved by PMER, e.g., the Great Earthquake, the denotation of a nuclear weapon, the strategy of sports games. The one end-point fixed, the other end-point variable is studied for wing moving. High lights: The pulse-mode of nuclear denotation releasing energy is the same as Earthquake, Yun [1], shows that the derivative of wind velocity with respect to time in proportion to the derivative of temperature with respect to the track. Which conforms with the weather forecast in winter that strong wind companies with low temperature for cold wave coming, and also suits for the motion of mushroom cloud [2].

A Proposed Model for Improving Job Performance in the Technical and Vocational Training Corporation in Saudi Arabia: Based on Combining Six Sigma Methods and Structural Equation Modeling

Authors: Mohammed Naji Al-Ghamdi ; Ezz H. Abdelfattah ; Farouq Alam ; Ahmed Ezz
Pages: 129-136
DOI: doi.org/10.32861/ajams.72.129.136
The Six Sigma methodology has become a frequently used term in discussions regarding quality management and it is considered to be an important management philosophy, which supports organizations in their efforts to obtain satisfied customers. In this study, we proposed Six Sigma methodology to improve the Job Performance in the Technical and Vocational Training Corporation (TVTC) in Saudi Arabia. We focus on three dimensions in our study; first: preparations for the application of the Six Sigma methodology in TVTC, second: the application requirements of Six Sigma methodology, and third: the application of the Six Sigma methods affects Improve Job performance in TVTC. Since the neural of Six Sigma methodology depends on the mediator statistical analysis, we suggest using the Structural Equation Modeling (SEM) to test the proposed Six Sigma model in TVTC. From SEM results, we find that the Six Sigma preparations have a significant effect on the application requirements and that the application requirements have a significant effect on the Job performance in TVTC. Based on that, we recommend using the Six Sigma methodology in TVTC to improve the performance of these corporations.

Approaches for Solving Fully Fuzzy Rough Multi-Objective Nonlinear Programming Problems

Authors: E. Ammar ; A. Al-Asfar
Pages: 113-128
DOI: doi.org/10.32861/ajams.72.113.128
Practical nonlinear programming problem often encounters uncertainty and indecision due to various factors that cannot be controlled. To overcome these limitations, fully fuzzy rough approaches are applied to such a problem. In this paper, an effective two approaches are proposed to solve fully fuzzy rough multi-objective nonlinear programming problems (FFRMONLP) where all the variables and parameters are fuzzy rough triangular numbers.  The first, based on a slice sum technique, a fully fuzzy rough multi-objective nonlinear problem has turned into five equivalent multi-objective nonlinear programming (FFMONLP) problems.  The second proposed method for solving FFRMONLP problems is α-cut approach, where the triangular fuzzy rough variables and parameters of the FFRMONLP problem are converted into rough interval variables and parameters by α-level cut, moreover the rough MONLP problem turns into four MONLP problems. Furthermore, the weighted sum method is used in both proposed approaches to convert multi-objective nonlinear problems into an equivalent nonlinear programming problem. Finally, the effectiveness of the proposed procedure is demonstrated by numerical examples.

Bayesian Methods and Maximum Likelihood Estimations of Exponential Censored Time Distribution with Cure Fraction

Authors: Dr. Al Omari Mohammed Ahmed
Pages: 106-112
DOI: doi.org/10.32861/ajams.72.106.112
This paper is focused on estimating the parameter of Exponential distribution under right-censored data with cure fraction. The maximum likelihood estimation and Bayesian approach were used. The Bayesian method is implemented using gamma, Jeffreys, and extension of Jeffreys priors with two loss functions, which are; squared error loss function and Linear Exponential Loss Function (LINEX). The methods of the Bayesian approach are compared to maximum likelihood counterparts and the comparisons are made with respect to the Mean Square Error (MSE) to determine the best for estimating the parameter of Exponential distribution under right-censored data with cure fraction. The results show that the Bayesian with gamma prior under LINEX loss function is a better estimation of the parameter of Exponential distribution with cure fraction based on right-censored data.

Teaching and Learning Mathematical Philosophy Through Infinity

Authors: Mr. Lam Kai Shun
Pages: 94-105
DOI: doi.org/10.32861/ajams.72.94.105
Lam [1], explained how mathematics is not only a technical subject but also a cultural one. As such, mathematical proofs and definitions, instead of simply numerical calculations, are essential for students when learning the subject. Hence, there must be a change in Hong Kong’s local teachers’ pedagogies. This author suggests three alternative way to teach mathematical philosophy through infinity. These alternatives are as follows: 1. Teach the concept of a limit in formalism through story telling, 2. Use geometry to intuitively learn infinity through constructivism, and 3. Implement schematic stages for proof by contradiction. Simultaneously, teachers should also be aware of the difficulties among students in understanding different abstract concepts. These challenges include the following: 1.
Struggles with the concept of a limit, 2.Mistakes in intuitively computing infinity, and 3. Challenges in handling the method of proof by contradiction. Adopting these alternative approaches, can provide the necessary support to pupils trying to comprehend the above mentioned difficult mathematical ideas and ultimately transform students’ beliefs [2]. One can analyze these changed beliefs against the background of con-ceptual change. According to Davis [3], “this change implies conceiving of teaching as facili-tating, rather than managing learning and changing roles from the sage on the stage to a guide on the side”. As a result, Hong Kong’s academic results in mathematics should hopefully improve.

A Simplified Novel Technique for Solving Linear Programming Problems with Triangular Fuzzy Variables via Interval Linear Programming Problems

Authors: Ladji Kané ; Lassina Diabaté ; Daouda Diawara ; Moussa Konaté ; Souleymane Kané
Pages: 82-93
DOI: doi.org/10.32861/ajams.72.82.93
This study proposes a novel technique for solving Linear Programming Problems with triangular fuzzy variables. A modified version of the well-known simplex method and the Existing Method for Solving Interval Linear Programming problems are used for solving linear programming problems with triangular fuzzy variables. Furthermore, for illustration, some numerical examples and one real problem are used to demonstrate the correctness and usefulness of the proposed method. The proposed algorithm is flexible, easy, and reasonable.

Half Step Numerical Method for Solution of Second Order Initial Value Problems

Authors: Adeniran Adebayo O. ; Edaogbogun Kikelomo
Pages: 77-81
DOI: doi.org/10.32861/ajams.72.77.81
This paper presents a half step numerical method for solving directly general second order initial value problems. The scheme is developed via collocation and interpolation technique invoked on power series polynomial. The proposed method is consistent, zero stable, order four and three. This method can estimate the approximate solution at both step and off step points simultaneously by using variable step size. Numerical results are given to show the efficiency of the proposed scheme over some existing schemes of same and higher order.

Introduction of New Spiral Formulas from ROTASE Model and Application to Natural Spiral Objects

Authors: Hongjun Pan
Pages: 66-76
DOI: doi.org/10.32861/ajams.72.66.76
A new set of spiral formulas is introduced as a new member of the spiral formulas’ family, people with interest in mathematics and natural spirals may use the new spiral formulas to simulate natural spiral objects or generate their own spirals. The new formulas are derived from a proposed new hypothesis called Rotating Two Arm Sprinkler Emission model (ROTASE) for the formation of spiral galaxies. In this paper, the derivation of the new spiral formulas is illustrated with boats moving across a circular river from central round island. The formulas have only one parameter and one variable, the parameter can change with time in any format, the morphology of the spiral is decided by the behavior of the parameter. 4 real spiral galaxies are precisely simulated shown as examples. It is demonstrated in this paper that the new spiral formulas can be also applied to simulate Earth natural objects such as plants, animals and hurricanes which have spiral patterns. The result shows that the new formulas seem more universal spiral formulas which can produce various different spirals patterns, can be applied to architecture, artworks and industry design. The new spiral formulas will be a new addition to the family of current mathematic spiral formulas.