Abstract: Publication date: Sep 2019 Source:Mathematics and Statistics Volume 7 Number 4 Norazaliza Mohd Jamil The material of pipelines transporting water is usually polymers. Chlorine as oxidant agent is added into the water system to prevent the spread of some disease. However, exposure to a chlorinated environment could lead to polymer pipe degradation and crack formation which ultimately reaches a complete failure for the pipes. To save labor, time and operating cost for predicting a failure time for a polymer pipe, we focus on its modeling and simulation. A current kinetic model for the corrosion process of polymers due to the action of chlorine is extensively analyzed from the mathematical point of view. By using the nondimensionalization method, the number of parameters in the original governing equations of the kinetic model has been reduced. Then, the dimensionless set of differential equations is numerically solved by the Runge Kutta method. There are two sets of simulations which are low chlorine concentration and high chlorine concentration, and we captured some essential characteristics for both types. This approach enables us to obtain better predictive capabilities, hence increasing our understanding of the corrosion process. PubDate: Sep 2019

Abstract: Publication date: Sep 2019 Source:Mathematics and Statistics Volume 7 Number 4 Reem Allogmany Fudziah Ismail and Zarina Bibi Ibrahim In this paper, we present an implicit two-point block method for solving directly the general second order ordinary differential equations (ODEs). The method incorporates the first and second derivatives of f(x; y; y'), which are the third and fourth derivatives of the solution. The method is derived using Hermite Interpolating Polynomial as the basic function. A performance comparison of the two-point block method is compared in term of accuracy to several existing methods, which have order almost equal or higher than that of the new method. Numerical results interpret the accuracy and efficacy of the new method. Application of the new method is discussed. PubDate: Sep 2019

Abstract: Publication date: Sep 2019 Source:Mathematics and Statistics Volume 7 Number 4 A. Artykbaev and B. M. Sultanov The linear transformation of the plane is considered, whose matrix belongs to the Heisenberg group. The transformation matrix is neither symmetric nor orthogonal. But the determinant is one. The class of the second-order curves is studied, which is obtained from each other by the transformation under consideration. The invariant values of curves of this class are proved. In particular, the conservation of the product of semi-axes of curves in this class is proved, as well as the equality of the areas for the ellipses of the class under consideration. The obtained invariants of the second order curves are applied to curves of the second order, which is the indicatrix of the surface. Conclusion: a theorem is obtained which proves the invariance of the total curvature of a surface in a Euclidean space of the class under consideration is a transformation, which is a deformation. PubDate: Sep 2019

Abstract: Publication date: Sep 2019 Source:Mathematics and Statistics Volume 7 Number 4 Abdussakir The concept of the topological index of a graph is increasingly diverse because researchers continue to introduce new concepts of topological indices. Researches on the topological indices of a graph which initially only examines graphs related to chemical structures begin to examine graphs in general. On the other hand, the concept of graphs obtained from an algebraic structure is also increasingly being introduced. Thus, studying the topological indices of a graph obtained from an algebraic structure such as a group is very interesting to do. One concept of graph obtained from a group is subgroup graph introduced by Anderson et al in 2012 and there is no research on the topology index of the subgroup graph of the symmetric group until now. This article examines several topological indices of the subgroup graphs of the symmetric group for trivial normal subgroups. This article focuses on determining the formulae of various Zagreb indices such as first and second Zagreb indices and co-indices, reduced second Zagreb index and first and second multiplicatively Zagreb indices and several eccentricity-based topological indices such as first and second Zagreb eccentricity indices, eccentric connectivity, connective eccentricity, eccentric distance sum and adjacent eccentric distance sum indices of these graphs. PubDate: Sep 2019

Abstract: Publication date: Sep 2019 Source:Mathematics and Statistics Volume 7 Number 4 Lucy Twumwaah Afriyie Bashiru I. I. Saeed and Abukari Alhassan Statistical surveys are conducted to estimate population parameters where there are reasons restricting the use of the total population. In practice, there are two different survey strategies (i.e. simple and complex survey designs) to be implemented and the choice of a strategy depends on several factors including the characteristics of the population, the nature of the research questions, etc. However, when the complex survey design is used, standard statistical methods that do not take into account the complex nature of the survey design may lead to inaccurate estimates. In Ghana, living standard surveys are conducted using complex survey design involving stratifications, clustering and estimation of survey weights. In this study, bootstrap resampling methods are used to explore the effect of complex survey design in the analysis of child labour prevalence rate. The relative efficiency of the complex survey design approach was determined by using design effect (deff). Data from the Ghana Living Standard Survey Round 6 (GLSS 6) conducted by the Ghana Statistical Service in 2012 was used for the analysis and the target population was children aged 5–17 years. The results from the simulation study shows that relative efficient estimates are obtained when the complex survey design characteristics are considered in the analysis. Thus, ignoring the characteristics of complex survey design could lead to unrealistic estimates. PubDate: Sep 2019

Abstract: Publication date: May 2019 Source:Mathematics and Statistics Volume 7 Number 2 Swasti Maharani Toto Nusantara Abdur Rahman As'ari and Abdul Qohar Critical thinking is a skill needed for education. Critical thinking has two main components i.e. ability and critical thinking disposition. The purpose of this research is to describe the disposition of critical thinking of mathematics education students especially analyticity and systematicity component when solving non-routine problem (the problem that is not logical and incomplete). This research is a qualitative descriptive study. The stages in this study are first, students are given three non-routine questions. The second stage, the researchers observed directly and recorded the subject when working on the problem. Third, interviewing the subject related to non-routine problem resolution. Fourth, concluded by describing the disposition of critical thinking of mathematics teacher candidate students, especially analyticity and systematicity components. The results showed that the disposition of critical thinking of first-year college students in mathematics education major is still low. They have not analyzed the problems and answers well and have not written the answers in order and lack of focus when solving non-routine problems. They not yet have a high sense about the irregularities of the problem. It is highly recommended for further research that there is a need for advanced development to improve the disposition of critical thinking students. PubDate: May 2019

Abstract: Publication date: May 2019 Source:Mathematics and Statistics Volume 7 Number 2 Beshimov R. B. and Zhuraev R. M. In this paper, we study some topological properties of connected topological groups. From a logical point of view, the concept of a topological group arises as a simple combination of the concepts of a group and a topological space. In the same set G, operations multiplication and topological closure are specified simultaneously. PubDate: May 2019

Abstract: Publication date: May 2019 Source:Mathematics and Statistics Volume 7 Number 2 Ivy Barley Gabriel Asare Okyere Henry Man’tieebe Kpamma James Baah Achamfour David Kweku and Godfred Zaachi Economic trade amongst the various West African economies can either lead to mutual gains or losses. It is therefore important to assess the extent to which dependence amongst these countries can have on their economies. The linear correlation coefficient is normally used as a measure of dependence between random variables. However, there are some limitations when used for economic variables like the stock market; as they do not follow the elliptical distribution. Copulas, however are scale-free methods of constructing dependence structures amongst the stock markets, even in cases of data perturbations. The aim of this study is to assess the impact of data perturbations on the copula models. The maximum likelihood estimation method was the parameter estimation method used for the Archimedean copulas. The Clayton, Joe, Frank and Gumbel copulas were estimated. The Gumbel copula was the most robust copula in all the cases of data perturbations. PubDate: May 2019

Abstract: Publication date: May 2019 Source:Mathematics and Statistics Volume 7 Number 2 Ruggero Ferro An analogy with how life would be evolving in a town where one is moving in, may help us to understand what could be meant by discovery, insight and invention in mathematics. The relevant key common features of these two environments (life in an another town and mathematics) are: 1) the involved mental abilities to deal with the situation, 2) the realization that anything observed is contingent, 3) the discovery of the motivations of what has been done and of their influence up to the present via insight, 4) the need to understand the motivations and the manners of realization of what was done to continue the development, 5) the continuous evolution of needs and requirements that opens new problems that demand insight and invention for their solutions, 6) not every solution meets the goals and requirements with the same short range and long range convenience, thus a preventive evaluation is convenient according to criteria to be established, though a conclusive evaluation can be done only afterward. What observed will justify the support of a dynamic attitude toward mathematics and the refusal of the one claiming that everything can't be but the way it is, according to a priori mental evidence which is unduly assumed. PubDate: May 2019

Abstract: Publication date: Mar 2019 Source:Mathematics and Statistics Volume 7 Number 1 Young Whan Lee and Gwang Hui Kim In 2001, Maksa and P´ales [12] introduced a new type’s stability: hyperstability for a class of linear functional equation. Riedel and Sahoo [14] have generalized a functional equation associated with the distance between the probability distributions, which is . Elfen etc. [7] obtained the solution of the functional equation on semigroup G. The aim of this paper is to investigate the hyperstability and the Hyers-Ulam stability for the above Logarithm-type functional equation considered by Elfen, etc. Namely, if f is an approximative equation related to the above equation, then it is a solution of this equation which exists within " bound of a given approximative function f. PubDate: Mar 2019

Abstract: Publication date: Mar 2019 Source:Mathematics and Statistics Volume 7 Number 1 Ana Vivas-Barber and Sunmi Lee Influenza infection shows a wide range of severity and it is well known that a significant proportion of individuals is asymptomatic or experience mild infections. Also, It is widely accepted that influenza transmission dynamics depends on age distributions. An integro-partial differential system is considered for influenza transmission dynamics, which includes the standard Susceptible-Infected-Recovered (SIR) classes with a quarantine (Q) class and an asymptomatic class (A). In this work, we extend the previous model to an integro-partial differential model by including age-structure. We establish the existence of an endemic steady state distribution and its explicit expression. Then, an analytic expression for the basic reproduction number is obtained. Furthermore, we prove the local and global stability of the disease-free equilibrium. Some numerical simulations of the basic reproduction number have been carried out using age-dependent influenza parameter values. This study can provide effective interventions and implementing age-dependent countermeasures. PubDate: Mar 2019

Abstract: Publication date: Mar 2019 Source:Mathematics and Statistics Volume 7 Number 1 Barbara Abraham-Shrauner Exact traveling (solitary) wave solutions of nonlinear partial differential equations (NLPDEs) are analyzed for third-order nonlinear evolution equations. These equations have indeterminant homogenous balance and therefore cannot be solved by the Power Index Method (PIM). Some evolution equations are linearizable where solutions are transferred from those of a linear PDE. For other evolution equations transforming to a NLPDE which has a homogenous balance gives rise to possible solutions by the PIM. The solutions for evolution equations that are not linearizable are developed here. PubDate: Mar 2019

Abstract: Publication date: Mar 2019 Source:Mathematics and Statistics Volume 7 Number 1 Cem Onat and Mahmut Daskin Excess air coefficient (λ) is the most important parameter characterizing the combustion efficiency. Conventional measurement of λ is practiced by way of the flue analyze device with high market priced. Estimating of the λ from flame images is crucial in perspective of the combustion control because of decreasing structural dead time of the combustion process. Beside, estimation systems can be used continuously in a closed loop control system, unlike conventional analyzers. This paper represents a basic λ prediction system with a neural network for small scale nut coal burner equipped with a CCD camera. The proposed estimation system has two inputs. First input is stack gas temperature simply measuring from the flue. To choose the second input, eleven different matrix parameters have been evaluated together with flue gas temperature values and performed by matrix-based multiple linear regression analysis. As a result of these analyses, it has been seen that the trace of image matrix obtained from the flame image provides higher accuracy than the other matrix parameters. This instantaneous trace value of image source matrix is then filtered from high frequency dynamics by means of a low pass filter. Experimental data of the inputs and λ are synchronously matched by a neural network. Trained algorithm has reached R=0.984 in terms of accuracy. It is seen from the result that proposed estimating system using flame image with assistance of the stack gas temperature can be preferred in combustion control systems. PubDate: Mar 2019

Abstract: Publication date: Jul 2019 Source:Mathematics and Statistics Volume 7 Number 3 Aloev R. D. Eshkuvatov Z. K. Khudoyberganov M. U. and Nematova D. E. In the paper, we propose a systematic approach to design and investigate the adequacy of the computational models for a mixed dissipative boundary value problem posed for the symmetric t-hyperbolic systems. We consider a two-dimensional linear hyperbolic system with variable coefficients and with the lower order term in dissipative boundary conditions. We construct the difference splitting scheme for the numerical calculation of stable solutions for this system. A discrete analogue of the Lyapunov's function is constructed for the numerical verification of stability of solutions for the considered problem. A priori estimate is obtained for the discrete analogue of the Lyapunov's function. This estimate allows us to assert the exponential stability of the numerical solution. A theorem on the exponential stability of the solution of the boundary value problem for linear hyperbolic system and on stability of difference splitting scheme in the Sobolev spaces was proved. These stability theorems give us the opportunity to prove the convergence of the numerical solution. PubDate: Jul 2019

Abstract: Publication date: Jul 2019 Source:Mathematics and Statistics Volume 7 Number 3 Renz Jimwel S. Mina and Jerico B. Bacani Numerous researches have been devoted in finding the solutions , in the set of non-negative integers, of Diophantine equations of type (1), where the values p and q are fixed. In this paper, we also deal with a more generalized form, that is, equations of type (2), where n is a positive integer. We will present results that will guarantee the non-existence of solutions of such Diophantine equations in the set of positive integers. We will use the concepts of the Legendre symbol and Jacobi symbol, which were also used in the study of other types of Diophantine equations. Here, we assume that one of the exponents is odd. With these results, the problem of solving Diophantine equations of this type will become relatively easier as compared to the previous works of several authors. Moreover, we can extend the results by considering the Diophantine equations (3) in the set of positive integers. PubDate: Jul 2019

Abstract: Publication date: Jul 2019 Source:Mathematics and Statistics Volume 7 Number 3 Nurulkamal Masseran Lai Hoi Yee Muhammad Aslam Mohd Safari and Kamarulzaman Ibrahim Poverty is an important issue that needs to be addressed by all countries. Poverty is related to a group of people earning a low income (lower-tail of the income distribution). In Malaysia, low-income earners are classified as the B40 group. This study aims to describe the behavior of the low-income distribution using the power law model. For this purpose, an inverse Pareto model was applied for describing the lower tail data of Malaysian household income. A robust and efficient estimator, called the probability integral transform statistic estimator, was utilized for estimating the shape parameter of the inverse Pareto distribution. Based on the fitted inverse Pareto model, not all households in the B40 group complied with the power law behavior. However, the power law was able to provide a good description for the group of B40 that was below the poverty line. Based on the inverse Pareto model, the parametric Lorenz curve and the Gini index were derived to provide a robust measure of the income inequality of poor households in Malaysia. PubDate: Jul 2019

Abstract: Publication date: Jul 2019 Source:Mathematics and Statistics Volume 7 Number 3 Xin Yi Kh'ng Su Yean Teh and Hock Lye Koh Low-lying atoll islands that depend heavily on fresh groundwater for survival are particularly vulnerable to sea level rise (SLR), which calls for appropriate climate action SDG 13. As the sea level rises, the associated increase in surface seawater inundation and subsurface saltwater intrusion will reduce the availability of fresh groundwater due to permanent salinization of groundwater with corresponding thinning of freshwater lens. This paper provides scientific insights on how freshwater lens in atoll islands respond to SLR. Simulations on saturated-unsaturated variable-density groundwater flow with salt transport are performed by the groundwater flow and solute transport model SUTRA (Saturated-Unsaturated Transport) developed by the U.S. Geological Survey. Model simulations and statistical analyses suggest that freshwater lens thickness depends mainly on groundwater recharge rate, island size and aquifer hydraulic conductivity. The impact of various geo-hydrologic parameters on fresh groundwater sustainability is then analyzed to explore feasibility of increasing groundwater recharge through rainwater harvesting, as a mitigation measure. The implication to the achievement of sustainable clean water and sanitation for all (SDG 6) is also discussed. PubDate: Jul 2019

Abstract: Publication date: Jul 2019 Source:Mathematics and Statistics Volume 7 Number 3 Shahryar Sorooshian and Yasaman Parsia Multi Attribute Decision Making (MADM) is an asset to provide solutions for our todays' complex issues and problems. The fact of the matter is that the main source of information in many MADMs is a panel of experts. However, in some cases, there is a possibility of lack of knowledge by the panel to rank or weight one or a few particular criterion/criteria for the decision making. Therefore, the decision maker needs an altered source of information to complete the decision making process. Hence, WSM (Weighted Sum Method) by means of the most popular MADM techniques is selected; and as a prior aim of this article, a modified version of the WSM is proposed as a solution for multiple criteria decision makers by way of a solution for the cases when there is a need for another source of information to rank or weight the particular criterion/criteria. The modified WSM is presented in five stages. The validity, through feasibility, of the modified WSM is tested and verified in a numerical example. Additionally, following this article, future researches could use the same approach for modification of other MADMs to deal with two or more sources of information. PubDate: Jul 2019