American Research Journal of Mathematics

Paul T E Cusack

Here we consider the Hodge’s Conjecture that expresses when a projective manifold coincides with a sum of algebraic cycles. More generally, 

N. Saidulu1, A. Venkata Lakshmi2

The present paper is devoted to describing the boundary layer flow of a non-Newtonian Casson fluid accompanied by heat transfer towards a porous exponentially stretching sheet with velocity slip and thermal slip conditions in the presence of thermal radiation, suction/blowing, viscous dissipation and heat source/ sink effects. The governing partial differential equations are reduced to a set of non-linear ordinary differential equations by using suitable similarity transformations and solved numerically by an implicit finite difference scheme known as the Keller box method. In the present work the effects of the non-dimensional governing parameters on velocity and temperature profiles have been discussed and presented graphically. As well as for the local skin-friction coefficient and the local Nusselt numbers exhibited and examined. It is found that the temperature is increasing to higher value when the Casson parameter increases but reverse is true for the velocity distribution. Finally, the velocity and temperature 

Nuri CELIK1

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 the normality 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

Tchavdar T. Marinov1Brandon Bailey

An algorithm to investigate numerically the solitary wave-like solutionsof Boussinesq differential equation is constructed. The bifurcation problem is re-formulated as an inverse problem for coefficient identification, introducing a newparameter. Such a way the nontrivial solution is separated from the trivial one.The Method of Variational Imbedding (MVI) is used for solving the inverse prob-lem. As illustration of the approach a Mathematica code with the finite differencescheme is prepared and the numerical results, including verification of the scheme,connection between the solution and the coefficients, and capability of Mathematica to paralelize the algorithm are presented

Mintu Lal Saha1Saurabh Manro2

In this paper, we have established some common fixed point theorems for a pair of faintly compatible mappings by removing the containments and weakening the continuity conditions from the results due to Bisht and Shahzad [2]. We have used a weaker notion of reciprocal continuity and thereby obtaining a proper generalization of these results.

Vinod Mishra1Dimple Rani

There are enormous occasions when the methods for finding solutions of integral and integrodifferential equations lead to failure because of difficulty in inverting Laplace transform by standard technique. Numerically inverting Laplace transform is cost effective in comparison to rather complicated technique of complex analysis. In the process of numerical inversion, an odd cosine series which is ultimately based on Chebyshev polynomial has been used. The adequacy of method is illustrated through numerical examples of convolution type linear Volterra integral equations of second kind which include weakly singular Abel's integral equation and Volterra integro-differential equation.

Mustafina S1Vaytiev 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 tothe 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.

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.

1 Mustafina S2 Grigoryev I

Based on the method of particle swarm algorithm is developed in parallel global extremum search. C language for parallel programming in the system implements a method of particle swarm to the global minimization of functions. The algorithm been tested on a spherical function and Rastrigin function.

 1 Ayiego, E . M.3 Mang’are P. A.2,Ngome, C. K3  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.