AMERICAN RESEARCH JOURNAL OF MATHEMATICS

5

Authors: William W.S. Chen

In the present paper, we used two different algorithms to solve some partial differential equations, where these equations originated from the well-known two parameters of lognormal distributions. The first approach that we adopted was the classical method which involved solving a triply of partial differential equations. The second approach that we used was the well-known Darboux Theorem. As we expected the two results were identical.

6

Authors: Isa Muslu,AvytAsanov,SedatYanik

TheLinear Fredholm-Stieltjes Integral Equation of the Second Kind (LFSIESK) is of wide spread use in many fields of engineering and applied mathematics. The quadrature methods are remarkable among the variety of numerical solutions to this equation.The aim of this paper is to find an approximation solution of the LFSIESK using the quadrature method the Generalized Simpson’s Method (GSM). Numerical example is presented at the end to show the efficiency and accuracy of the presented work. The software Maple 18 is used for the computations.

13

Authors: Ayiego, E . M,Mang’are P. A,Ngome, C. K,Mandilah, L.

Perennial poor performance in Mathematics at National examinations has elicited concern by the Government of Kenya. This dismal performance was attributed to broad curriculum, lack of facilities, inadequate staffing, poor pedagogical approaches and lack of hands on activities. Mathematics, which is crucial in Kenya's realization of vision 2030, hampers its achievement. Studies have shown that interventions so far adopted had yielded negligible impact. The acronym ASEI stands for Activity, Students, Experiment, Improvisation whereas PDSI stands for Plan, Do, See and Improve, hence the ASEI-PDSI movement. Therefore, there was need to establish the extent of practice and implementation of ASEI-PDSI pedagogical approach in Vihiga County. This work established the preparedness of Stakeholders in their roles to implement the ASEI-PDSI movement; and the extent of practice of this approach. The data was collected using questionnaires and interview schedules; with principals, Heads of Mathematics department, teachers and Education officers as the respondents. The data was analysed statistically. The study ascertained the practice of PDSI approach, rated at 4.332 on a 5-point Likert scale, impacting positively on performance and attitude. There were improved teaching methodologies, improvisation of resources, and use of lesson rationale in Mathematics. It was noted that 95.89 % of the teachers employed the ASEI approach. Also, 67.12 % and 10.96 % of the teachers improvised teaching and learning aids in the absence of the conventional ones mostly and always respectively. Teachers engaged students in varied activities in class and at home. However, 27.40 % rarely improvised since 35.71% of the teachers were new in the profession or experienced burn out syndrome due to overstaying in a station or missed critical SMASSE (strengthening of mathematics and science in secondary education) cycles. The study showed that 97.26 % of the teachers had schemes of work, affirming the importance of the tool for planning in any teaching and learning setup. The schemes of work were always used by 45.83 % and mostly used by 40.28 % of the sample respondents. However, 12.50 % used them rarely. These results need to inform stakeholders on effectiveness of the SMASSE in-service education training and make a follow up with a view of strengthening the Programme.

6

Authors: Svetlana Mustafina,Rustam Ikramov

Chemical transformations typically occur according to multiphase schemes. Changes in theconcentrations of the starting materials and intermediates with time are not always described with increasing ordecreasing functions. A detailed study of a complex process kinetics showed that at the presence of feedback far from equilibrium there may occur vibrational modes - periodic increase or decrease in the concentration of one of the components in time. In a numerical study of oscillating reactions there appears a problem in solving a rigid system of typical differential equations. The purpose of this study is to develop an algorithm and a program to solve the direct kinetic problem and to investigate multi component chemical systems with complex nonlinear dynamics.

8

Authors: Mustafina S,Vaytiev V

The paper shows a technique of researching of the direct kinetic problem sensitivity to the variation of the kinetic parameters within a given range. This technique is based on use of the computing device of the interval analysis. The direct problem solution in the conditions of kinetic parameters uncertainty was received by the interval method of the solution of a Cauchy problem for differential equations system. This interval method was adapted to the problems of chemical kinetics. The interval characteristics received during this method application were used for research of reagents and products concentration sensitivity in relation to kinetic parameters of mathematical model of industrially important reaction

8

Authors: Nuri CELIK

Control charts are one of the most common techniques that have been used to observe and control the process deviations in the industry. The easiest and the most prevalent method of control charts is the Shewhart Scontrol chart. This method is based on the normal distribution assumption. However, there are a lot of inferences in literature that non-normal distributions are much more common than the normal distribution. When thenormality assumption is not satisfied robust methods are preferred. In this paper, we determine some approaches by using robust scale estimators instead of simple standard deviation in order to apply S-control charts.Furthermore the performances of these different scale estimators are compared by Monte Carlo simulation study.Numerical examples are given at the end of the paper