Abstract: Publication date: Sep 2019 Source:Mathematics and Statistics Volume 7 Number 4A Afif Shihabuddin Norhaslinda Ali and Mohd Bakri Adam Air pollution index (API) is a common tool used to describe the air quality in the environment. High level of API indicates the greater level of air pollution which will gives bad impact on human health. Statistical model for high level of API is important for the purpose of forecasting the level of API so that the public can be warned. In this study, extremes of API are modelled using Generalized Pareto Distribution (GPD). Since the values of API are determined by the value of five pollutants namely sulphur dioxide, nitrogen dioxide, carbon monoxide, ozone and suspended particulate matter, data on API exhibit non-stationarity. Standard method for modelling the non-stationary extremes using GPD is by fixing the high constant threshold and incorporating the covariate model in the GPD parameters for data above the threshold to account for the non-stationarity. However, high constant threshold value might be high enough on certain covariate for GPD approximation to be a valid model for extreme values, but not on the other covariates which leads to the violation of the asymptotic basis of GPD model. New method for the threshold selection in non-stationary extremes modelling using regression tree is proposed to the API data. Regression tree is used to partition the API data into a stationary group with similar covariate condition. Then, a high threshold value can be applied within a group. Study shows that model for extremes of API using tree-based threshold gives a good fit and provides an alternative to the model based on standard method. PubDate: Sep 2019

Abstract: Publication date: Sep 2019 Source:Mathematics and Statistics Volume 7 Number 4A Norin Rahayu Shamsuddin and Nor Idayu Mahat Clustering with heterogeneous variables in a dataset is no doubt a challenging process owing to different scales in a data. The paper introduced a SimMultiCorrData package in R to generate the artificial dataset for clustering. The construction of artificial dataset with various distribution helps to mimic the scenario of nature of real datasets. Our experiments shows that the clusterability of a dataset are influenced by various factors such as overlapping clusters, noise, sub-cluster, and unbalance objects within the clusters. PubDate: Sep 2019

Abstract: Publication date: Sep 2019 Source:Mathematics and Statistics Volume 7 Number 4A F. Z. Che Rose M. T. Ismail and N. A. K. Rosili The existence of outliers in financial time series may affect the estimation of economic indicators. Detection of outliers in structural time series framework by using indicator saturation approach has become our main interest in this study. The reference model used is local level model. We apply Monte Carlo simulations to assess the performance of impulse indicator saturation for detecting additive outliers in the reference model. It is found that the significance level, α = 0.001 (tiny) outperformed the other target size in detecting various size of additive outliers. Further, we apply the impulse indicator saturation to detection of outliers in FTSE Bursa Malaysia Emas (FBMEMAS) index. We discover that there were 14 outliers identified corresponding to several economic and financial events. PubDate: Sep 2019

Abstract: Publication date: Sep 2019 Source:Mathematics and Statistics Volume 7 Number 4A Ling, A. S. C. Darmesah, G. Chong, K. P. and Ho, C. M. The losses caused by cocoa black pod disease around the world exceeded $400 million due to inaccurate forecasting of cocoa black pod disease incidence which leads to inappropriate spraying timing. The weekly cocoa black pod disease incidence is affected by external factors, such as climatic variables. In order to overcome this inaccuracy of spraying timing, the forecasting disease incidence should consider the influencing external factors such as temperature, rainfall and relative humidity. The objective of this study is to develop a Autoregressive Integrated Moving Average with external variables (ARIMAX) model which tries to account the effects due to the climatic influencing factors, to forecast the weekly cocoa black pod disease incidence. With respect to performance measures, it is found that the proposed ARIMAX model improves the traditional Autoregressive Integrated Moving Average (ARIMA) model. The results of this forecasting can provide benefits especially for the development of decision support system in determine the right timing of action to be taken in controlling the cocoa black pod disease. PubDate: Sep 2019

Abstract: Publication date: Sep 2019 Source:Mathematics and Statistics Volume 7 Number 4A Nurazlina Abdul Rashid Wan Siti Esah Che Hussain Abd Razak Ahmad and Fatihah Norazami Abdullah Classification methods are fundamental techniques designed to find mathematical models that are able to recognize the membership of each object to its proper class on the basis of a set of measurements. The issue of classifying objects into groups when variables in an experiment are large will cause the misclassification problems. This study explores the approaches for tackling the classification problem of a large number of independent variables using parametric method namely PLS-DA and PCA+LDA. Data are generated using data simulator; Azure Machine Learning (AML) studio through custom R module. The performance analysis of the PLS-DA was conducted and compared with PCA+LDA model using different number of variables (p) and different sample sizes (n). The performance of PLS-DA and PCA+LDA has been evaluated based on minimum misclassification rate. The results demonstrated that PLS-DA performed better than the PCA+LDA for large sample size. PLS-DA can be considered to have a good and reliable technique to be used when dealing with large datasets for classification task. PubDate: Sep 2019

Abstract: Publication date: Sep 2019 Source:Mathematics and Statistics Volume 7 Number 4A Noor Hidayah Mohd Zaki Aqilah Nadirah Saliman Nur Atikah Abdullah Nur Su Ain Abu Hussain and Norani Amit A queuing system is a process to measure the efficiency of a model by underlying the concepts of queue models: arrival and service time distributions, queue disciplines and queue behaviour. The main aim of this study is to compare the behaviour of a queuing system at check-in counters using the Queuing Theory Model and Fuzzy Queuing Model. The Queuing Theory Model gives performance measures of a single value while the Fuzzy Queuing Model has a range of values. The Dong, Shah and Wong (DSW) algorithm is used to define the membership function of performance measures in the Fuzzy Queuing Model. Based on the observation, the problem often occurs when customers are required to wait in the queue for a long time, thus indicating that the service systems are inefficient. Data including the variables were collected, such as arrival time in the queue (server) and service time. Results show that the performance measures of the Queuing Theory Model lie in the range of the computed performance measures of the Fuzzy Queuing Model. Hence, the results obtained from the Fuzzy Queuing Model are consistent to measure the queuing performance of an airline company in order to solve the problem in waiting line and will improve the quality of services provided by airline company. PubDate: Sep 2019

Abstract: Publication date: Sep 2019 Source:Mathematics and Statistics Volume 7 Number 4A Zakiah I. Kalantan and Faten Alrewely Mixture distributions have received considerable attention in life applications. This paper presents a finite Laplace mixture model with two components. We discuss the model properties and derive the parameters estimations using the method of moments and maximum likelihood estimation. We study the relationship between the parameters and the shape of the proposed distribution. The simulation study discusses the effectiveness of parameters estimations of Laplace mixture distribution. PubDate: Sep 2019

Abstract: Publication date: Sep 2019 Source:Mathematics and Statistics Volume 7 Number 4A Hafizah Bahaludin Mimi Hafizah Abdullah Lam Weng Siew and Lam Weng Hoe In recent years, there has been a growing interest in financial network. The financial network helps to visualize the complex relationship between stocks traded in the market. This paper investigates the stock market network in Bursa Malaysia during the 2008 global financial crisis. The financial network is based on the top hundred companies listed on Bursa Malaysia. Minimal spanning tree (MST) is employed to construct the financial network and uses cross-correlation as an input. The impact of the global financial crisis on the companies is evaluated using centrality measurements such as degree, betweenness, closeness and eigenvector centrality. The results indicate that there are some changes on the linkages between securities after the financial crisis, that can have some significant effect in investment decision making. PubDate: Sep 2019

Abstract: Publication date: Sep 2019 Source:Mathematics and Statistics Volume 7 Number 4 Mihail Cocos The Fundamental Theorem of Riemannian geometry states that on a Riemannian manifold there exist a unique symmetric connection compatible with the metric tensor. There are numerous examples of connections that even locally do not admit any compatible metrics. A very important class of symmetric connections in the tangent bundle of a certain manifolds (afinnely flat) are the ones for which the curvature tensor vanishes. Those connections are locally metric. S.S. Chern conjectured that the Euler characteristic of an affinely at manifold is zero. A possible proof of this long outstanding conjecture of S.S. Chern would be by verifying that the space of locally metric connections is path connected. In order to do so one needs to have practical criteria for the metrizability of a connection. In this paper, we give necessary and sufficient conditions for a connection in a plane bundle above a surface to be locally metric. These conditions are easy to be veri ed using any local frame. Also, as a global result we give a necessary condition for two connections to be metric equivalent in terms of their Euler class. PubDate: Sep 2019

Abstract: Publication date: Sep 2019 Source:Mathematics and Statistics Volume 7 Number 4 Zurab Kvatadze and Beqnu Pharjiani On the probabilistic space (Ω ,F , P ) we consider a given two-component stationary (in the narrow sense) sequence , where is the controlling sequence and the members of the sequence are the observations of some random variable which are used in the construction of kernel estimates of Rosenblatt-Parzen type for an unknown density of the variable . The cases of conditional independence and chain dependence of these observations are considered. The upper bounds are established for mathematical expectations of the square of deviation of the obtained estimates from . PubDate: Sep 2019

Abstract: Publication date: Sep 2019 Source:Mathematics and Statistics Volume 7 Number 4 Roselaine Neves Machado and Luiz Guerreiro Lopes There are many simultaneous iterative methods for approximating complex polynomial zeros, from more traditional numerical algorithms, such as the well-known third order Ehrlich–Aberth method, to the more recent ones. In this paper, we present a new family of combined iterative methods for the simultaneous determination of simple complex zeros of a polynomial, which uses the Ehrlich iteration and a correction based on King's family of iterative methods for nonlinear equations. The use of King's correction allows increasing the convergence order of the basic method from three to six. Some numerical examples are given to illustrate the convergence behaviour and effectiveness of the proposed sixth order Ehrlich-like family of combined iterative methods for the simultaneous approximation of simple complex polynomial zeros. PubDate: Sep 2019

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: Nov 2019 Source:Mathematics and Statistics Volume 7 Number 5 Llesh Lleshaj and Alban Korbi In this study analyzed 20 different countries that are the origin state of foreign investors, which have invested in Albania (this sample represents 95% of FDI (Foreign Direct Investments) stocks, 2007 - 2014). The analysis technic used is the gravity model of FDI stocks in Albania. The main independent variables in this analysis are GDP, the level of business taxes, the difference of GDP per capita, the similarity economies, etc. The result of this study: The level of FDI stocks in Albania is lower than its potential compare with FDI stock average in the States of the Balkan Region. PubDate: Nov 2019

Abstract: Publication date: Nov 2019 Source:Mathematics and Statistics Volume 7 Number 5 Anuradha Seema Mehra and Said Broumi Motivated by the concepts of fuzzy metric and m-metric spaces, we introduced the notion of Non- Archimedean fuzzy m-metric space which is an extension of partial fuzzy metric space. We present some examples in support of this new notion. Regarding this notion, its topological structure and some properties are specified simultaneously. At the end, some fixed point results are also provided. PubDate: Nov 2019

Abstract: Publication date: Nov 2019 Source:Mathematics and Statistics Volume 7 Number 5 Igor Sinitsyn and Vladimir Sinitsyn Analytical methods of the mathematical statistics of random vectors and matrices based on the parametrization of the distributions are widely used. These methods permit to design practically simple software when it is possible to have the definite information about analytical properties of the distributions under research. The main difficulty in practical applications of the methods based on the parametrization of the distributions is the rapid increase of the number of equations for the moments, the semiinvariants or the coefficients of the truncated orthogonal expansions of the dimension or the state vector (extended in the general case) and the maximal order of the moments involved. The number of equations for the parameters becomes exceedingly large in such cases. For structural parametrization and/or approximation of the probability densities of the random vectors we shall apply the ellipsoidal densities, i.e. the densities whose planes of the levels of equal probability are similar concentric ellipsoids (the ellipses for two-dimensional vectors, the ellipsoids for three-dimensional vectors, the hyperellipsoids for the vectors of the dimension more than three). In particular, a normal distribution in any finite-dimensional space has an ellipsoidal structure. The distinctive characteristics of such distributions consists in the fact that their probability densities are the functions of positively determined quadratic form where is an expectation of the random vector is some positively determined matrix. Ellipsoidal approximation method (EAM) cardinally reduces the number of parameters till () where being the number of probabilistic moments. While using ellipsoidal linearization method (ELM) we get Basic EAM and ELM foundations and applications to problems of mathematical statistics and ellipsoidal distributions with invariant measure in populational Volterra differential stochastic nonlinear systems are considered. PubDate: Nov 2019

Abstract: Publication date: Nov 2019 Source:Mathematics and Statistics Volume 7 Number 5 Aripov M. Mukimov A. and Mirzayev B. We study the asymptotic behavior (for ) of solutions of the Cauchy problem for a nonlinear parabolic equation with a double nonlinearity, describing the diffusion of heat with nonlinear heat absorption at the critical value of the parameter ᵝ. For numerical computations as an initial approximation we used founded the long time asymptotic of the solution. Numerical experiments and visualization were carried for one and two dimensional case. PubDate: Nov 2019

Abstract: Publication date: Nov 2019 Source:Mathematics and Statistics Volume 7 Number 5 Emil V. Veitsman This paper is aimed to find a connection between i-dimensional spaces (i=0,…, ‘n') and the long-range j-dimensional attractive forces (j=0,…, ‘m') creating these spaces. The connection is fundamental and unrelated to any processes going in the spaces being studied. A theorem is formulated and strictly proved showing in which cases the long-ranged attractive forces can form real spaces of different dimensions ( i=0,…,n). The existence of the attraction between masses is defined by divergence of the vector of interaction between masses. Weak anisotropic real spaces are studied by rotating an ellipsoid for (3ζ)D-cases when its eccentricity ε PubDate: Nov 2019

Abstract: Publication date: Nov 2019 Source:Mathematics and Statistics Volume 7 Number 5 Taehan Bae and Maral Mazjini Recent studies on correlated Poisson processes show that the backward simulation methods are computationally efficient, and incorporate flexible and extremal correlation structures in a multivariate risk system. These methods rely on the fact that the past arrival times of a Poisson process given the number of events over a time interval, [0; T], are the order statistics of uniform random variables on [0; T]. In this paper, we discuss an extension of the backward methods to a correlated negative binomial L´evy process which is an appealing model for over-dispersed count data such as operational losses. To obtain the conditional uniformity for the negative binomial L´evy process, we consider a particular setting in which the time interval is partitioned into equally spaced sub-intervals with unit length and the terminal time T is set to be the number of sub-intervals. Under this setting, the resulting joint probability of the increment series, conditional on the number of events over [0; T], say l, is uniform for any points in the support of a [T; l]-simplex lattice. Based on this result, we establish a backward simulation method similar to that of Poisson process. Both the conditional independence and conditional dependence cases are discussed with illustrations of the corresponding time correlation patterns. PubDate: Nov 2019

Abstract: Publication date: Nov 2019 Source:Mathematics and Statistics Volume 7 Number 5 Mykola Bokalo and Olha Sus In this paper, we consider the initial-value problem for parabolic variational inequalities (subdifferential inclusions) with Volterra type operators. We prove the existence and the uniqueness of the solution. Furthermore, the estimates of the solution are obtained. The results are achieved using the Banach's fixed point theorem (the principle of compression mappings). The motivation for this work comes from the evolutionary variational inequalities arising in the study of frictionless contact problems for linear viscoelastic materials with long-term memory. Also, such kind of problems have their application in constructing different models of the injection molding processes. PubDate: Nov 2019

Abstract: Publication date: Nov 2019 Source:Mathematics and Statistics Volume 7 Number 5 Benjamin Kedem Lemeng Pan and Paul J. Smith Chen Wang It is shown how to estimate any threshold probability from data below or even far below the threshold through repeated fusion of the data with externally generated random samples. This is referred to as repeated out of sample fusion (ROSF). A comparison of the approach with peaks-over-threshold (POT) across different tail types shows that ROSF provides more precise point and interval estimates based on moderately large samples. PubDate: Nov 2019

Abstract: Publication date: Nov 2019 Source:Mathematics and Statistics Volume 7 Number 5 Sh. A. Dildabayev and G. K. Zakir'yanova Up to now remains open the question of constructing fundamental solutions of the two-dimensional statics of an elastic body with arbitrary anisotropy. Also in the scope of BEM method, the question of calculating stresses in boundary points and points located close to the boundary of the region still remains actual. In this work, fundamental solutions of the static problem for elastic plane with arbitrary anisotropic properties are obtained as the sum of residues with complex variable function. The assessments of fundamental solution and theirs derivatives are presented in closed form. In the distribution space obtained are the regular representations for the Somigliana formulas and the stress calculation formulas. The numerical implementation of the BIE method in direct formulation has been realized in standard way. The test results performed for circular hole in anisotropic plane of rhombic system show a higher compliance with the boundary values of displacements and stresses and with nodes placed close to boundary. The results of analysis of the stress-strain state in the vicinity of rectangular mining chambers located deep from day surface are presented in tables and pictures of isolines. PubDate: Nov 2019

Abstract: Publication date: Nov 2019 Source:Mathematics and Statistics Volume 7 Number 5 D. A. Karpov and V. I. Struchenkov This article deals with the problem of approximation of plane curves defined by a sequence of points by a spline of a given type. This task arises when developing methods for computer-aided design of linear structures: railways and roads, trenches for laying pipelines, canals, etc. Its fundamental differences from the problems are considered in the theory of splines and its applications are as follows: spline elements are of various types (straight line segments and circles joined by clothoids), the boundaries of the elements and even their number is unknown; also there are restrictions - inequalities on the parameters of the elements. Continuity of the curve, the tangent, and the curvature is provided. Clothoids are missing if curvature continuity is not required, for example, when designing pipelines. The above mentioned features of the task do not allow using the achievements of the theory of splines and nonlinear programming. We cannot recognize the individual elements of the desired spline by a given sequence of points. Therefore, it is not possible to implement their selection separately. We must search for the spline as a whole. The article presents a mathematical model and a new algorithm for solving the problem using dynamic programming. PubDate: Nov 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