Asian Research Journal of Mathematics

Let (G, ∗) be a group and X any set, an action of a group G on X, denoted as G×X → X, (g, x) 7→ g.x, assigns to each element in G a transformation of X that is compatible with the group structure of G. If G has a subgroup H then there is a transitive group action of G on the set (G/H) of the right co-sets of H by right multiplication. A representation of a group G on a vector space V carries the dimension of the vector space. Now, given a field F and a finite group G, there is a bijective correspondence between the representations of G on the finitedimensional F-vector spaces and finitely generated FG-modules. We use the FG -modules to construct linear ternary codes and combinatorial designs from the permutation representations of the group L₃(4). We investigate the properties and parameters of these codes and designs.

We further obtain the lattice structures of the sub-modules and compare these ternary codes with the binary codes constructed from the same group.

In this paper, we introduce the Hyperbolic Jacobsthal numbers and we present recurrence relations, Binet's formulas, generating functions and the summation formulas for these numbers. Moreover, we investgate Lorentzian inner product for the hyperbolic Jacobsthal vectors.

The equivalent linearization method introduced by Caughey is a powerful tool for analyzing random oscillations. The method is also easy to apply for deterministic oscillations. However, with strong nonlinear systems, the error of this method is usually quite large and even not acceptable. In conjunction with a weighted averaging, the equivalent linearization method has shown more accuracy than the classical one in which the conventional averaging value is used. Combining advantages of the classical equivalent linearization method and accuracy of the weighted averaging, the proposed method has shown that it is a useful tool for analyzing nonlinear oscillations including strong nonlinear systems. In this paper, the proposed method is applied to analyze a nonlinear Duffing – harmonic oscillator. The present results are compared with the results obtained by using other analytical methods, exact results and numerical results.

The article presents an extension of the Gompertz-Makeham distribution using the Lomax generator of probability distributions. This generalization of the Gompertz-Makeham distribution provides a more skewed and flexible compound model called Lomax Gompertz-Makeham distribution. The paper derives and discusses some Mathematical and Statistical properties of the new distribution. The unknown parameters of the new model are estimated via the method of maximum likelihood estimation. In conclusion, the new distribution is applied to two real life datasets together with two other related models to check its flexibility or performance and the results indicate that the proposed extension is more flexible compared to the other two distributions considered in the paper based on the two datasets used.

Aims/ Objectives: To investigate the influence of a model parameter on the convergence of two finite difference schemes designed for a convection-diffusion-reaction equation governing the pressure-driven flow of a Newtonian fluid in a rectangular channel.
Methodology: By assuming a uni-directional and incompressible channel flow with an exponentially time-varying suction velocity, we formulate a variable-coefficient convectiondiffusion- reaction problem. In the spirit of the method of manufactured solutions, we first obtain a benchmark analytic solution via perturbation technique. This leads to a modified problem which is exactly satisfied by the benchmark solution. Then, we formulate central and backward difference schemes for the modified problem. Consistency and convergence results are obtained in detail. We show, theoretically, that the central scheme is convergent only for values of a model parameter up to an upper bound, while the backward scheme remains convergent for all values of the parameter. An estimate of this upper bound, as a function of the mesh size, is derived. We then conducted numerical experiments to verify the theoretical results.
Results: Numerical results showed that no numerical oscillations were observed for values of the model parameter less than the theoretically derived bound.
Conclusion: We therefore conclude that the theoretical bound is a safe value to guarantee non-oscillatory solutions of the central scheme.

The chief object of this work present a new and simple condensation method of finding determinants of large matrices and solving large linear systems.

In this paper, we investigate the claimed optimality of a new method – Revised Distribution (RDI) Method – for finding optimal solution of balanced and unbalanced transportation models directly and compare the RDI method with other such methods. A large set of problems have been tested by RDI and other methods, and the results were compared with the Modified distribution (MODI) method – an optimal method. We found that the mostly the results of RDI are not optimal. For reference to prove our observations, we have added three example transportation problems here in this work and compared their results with MODI method to show that the RDI method like the direct exponential approach (DEA) method is not optimal method; but it is just an initial basic feasible solution (IBFS) for transportation problems.

Currently, the hostel life is so necessary for the students. During their higher studies, the students face a lot of problems of accommodation. After the solution of accommodation, the students face the issues in the hostels regarding their provided services. The data of students’ feedback is gathered from the Director MIS, MUET, Jamshoro by taking the sample of 60 students from each boy’s hostel. For analysis, we use the tool Statistical Package for Social Sciences (SPSS V.16). This study revealed the analysis of two services, water supply and first aid in the seven boy’s hostels of MUET, Jamshoro. The null hypothesis is accepted for all hostels except Rashidi, Hyder Bux Jatoi and Shah Abdul Latif. These results determined the strong relationship between the services water supply and first aid. From this study, we suggest to authorities of the university management to provide the necessary betterment regarding the water supply and first aid facilities in Rashidi, Hyder Bux Jatoi and Shah Abdul Latif hostels.

This study investigated the applicability of a class of instructional models based on constructivism in improving the achievement of senior secondary students in solid geometry using the quasi-experimental design. Two constructivist-based instructional models used were Teaching for Understanding (TfU) and Metacognitive Instructional (MCI) models. The exploration area was the Emohua Local Government Area (LGA) of Rivers State, Nigeria. An aggregate of 86 Senior Secondary Class I (SSC1) students took an interest in the investigation. To evaluate the achievement of the students in solid geometry, the researchers structured, approved and utilised an achievement test in solid geometry which contained 50 multiple-choice questions.  The reliability of the test was determined using KR-21 to get an index of 0.84. This research work was guided by two research questions and two null hypotheses separately. The mean, standard deviation, box-plots and Analysis of Covariance (ANCOVA) were used for data analysis. The findings showed that the class of instructional models based on constructivism significantly enhanced the learning of solid geometry amongst the SSC1 students. The MCI model was less effective than the TfU model in improving the learning of the students. Sex had no significant influence on the solid geometry achievement of SSC1 students irrespective of the instructional model used. The exploration suggested among others that solid geometry ought to be instructed by the educators of arithmetic using the instructional models based on constructivism.

The term corruption refers to the process that involves the abuse of a public trust or office for some private benet. Corruption becomes a threat to national development and growth especially when there is no political will to fight it. Prevention and disengagement initiatives are part of EACC strategies used to fight corruption. Prevention strategies aim to stop or discourage citizens from engaging in corruption. Disengagement strategies attempt to reform corrupt individuals and to reclaim the stolen resources back to the public kitty. We describe prevention and disengagement strategies mathematically using an epidemiological compartment model. The prevention and disengagement strategies are modeled using model parameters. The population at risk of adopting corrupt ideology was divided into three compartments: S(t) is the susceptible class, C(t) is the Corrupted class, and M(t) is the corrupt political/sympathersizer class. The model exhibits a threshold dynamics characterised by the basic reproduction number R0. When R₀ < 1 the system has a unique equilibrium point that is asymptotically stable. For R₀ > 1, the system has additional equilibrium point known as endemic, which is globally asymptotically stable. These results are established by applying lyapunov functions and the LaSalles invariance principle. Based on our model we assess strategies to counter corruption vice.

Fitting nonlinear models is not a single-step procedure but it involved a process that requires careful examination of each individual step. Depending on the objective and the application domain, different priorities are set when fitting nonlinear models; these include obtaining acceptable parameter estimates and a good model fit while meeting standard assumptions of statistical models. We propose steps in fitting nonlinear models in this research work. Two reciprocal power regression models were considered with a non-linear data set. Then, the following steps are considered (i) fit the models to the data collected using iterative steps, (ii) to develop a linear model to estimate the parameter β₁ and β₂ when the initial value (or growth rate β₃) lies between -1.0 ≤ β₃ ≤1.0 ); using the transform models of the reciprocal power regression model (iii) to find the “best” model between the two models using R², AIC and BIC. The results show Model B is better than Model A, using the model selection criteria.

The magnetic hydrodynamic free convective flow past an infinite stretching porous sheet at constant density for electrically conducting fluid with viscous dissipation was numerically studied. The study revolved around an unsteady two-dimensional free convective laminar flow through a porous medium with the interaction of magnetic area standard to the stream. The graphs represented the effects of material parameters on the temperature and velocity profiles across the fluid boundary layer. The solutions of partial differential equations obtained numerically using an implicit finite difference method for various values of (nu), numbers (0.5 to 0.7) at a constant thermal conductivity (kappa=0.1). The velocity and temperature of MHD flow increased with an increase in viscous dissipation and vice versa.