Abstract: In this paper we solve numerically Volterra integral equations of the first kind with separable kernels. This is done by first converting the first-kind Volterra integral equations into those of the second kind and then applying the fourth-order block-by-block method in conjunction with Simpson’s rule to find approximate solutions. Approximate solutions based on several numerical examples are given and confirm the convergence of the method. A comparison of numerical results from the block-by-block method with those from other existing methods available in the literature proves its superiority over those other methods. Mathematics Subject Classification: 45A05, 45D05, 46N20

Abstract: In the last decades, crime has become a major issue against local decision-makers in the Pekanbaru city region. The incidence of criminality in a region depends not only on local socio-economic conditions, but also on the ones in nearby regions, due to significant population mobility. Understanding the relationship between crime and its surrounding environment can reveal possible strategies that can reduce crime in a neighborhood. Techniques account for such territorial correlations, such as use of spatial weights that capture the influence of each region upon its neighbors. Among the spatial methods, the geographically weighted regression (GWR) is a valuable instrument that allows estimating local coefficients, specific to each location, thus providing useful information for appropriate policy design at the regional level. In this context we employed a criminality GWR model in an attempt to find the local determinants, both economic and demographic, that explain the spatial distribution of criminal offenses in Pekanbaru city region. The results indicated that the incidence of this phenomenon in Pekanbaru is linked to factors largely acknowledged in the literature, such as poverty, unemployment, and population. Thirty novelty brought about by the GWR model compared to previous 292 Risa Wara Elzati et al. research is that it also revealed important spatial variations in the impacts of the variables and indicated which region is more vulnerable to specific factors. From a modeling perspective the GWR model represents a better fit than the classic OLS model, in addition to capturing the spatial variation in coefficients’ estimation.

Abstract: A time-changed mixed fractional Brownian motion by inverse αstable subordinator with index α ∈ (0, 1) is an iterated process Y H Tα(a, b) constructed as the superposition of mixed fractional Brownian motion NH(a, b) and an independent inverse α-stable subordinator Tα. In this paper we prove that the process Y H Tα(a, b) is of long range dependence property for every H > 1 2 . We deduce that the time-changed fractional Brownian motion by inverse α-stable subordinator has long range dependence for all H ∈ (0, 1). Mathematics Subject Classification: 60G20; 60G18; 60G15; 60G10

Abstract: In this paper, the Gaussian curvatures of closed parallel ruled surfaces are calculated. We consider parallel ruled surfaces from indicatrix curves associated to Frenet vectors of the curve created on the unit dual sphere. Mathematics Subject Classification: 53A04, 53A05, 53A17

Abstract: Let A denote the class of functions which are analytic in the open unit disc U = {z ∈ C : |z| < 1}. In this paper, we introduce new classes of analytic functions involving q-derivative operator defined on U. Furthermore, we obtain the Fekete-Szeg¨o functional for functions f(z) belongs to these classes.

Abstract: In this study, the performance of radial basis function neural networks (RBFNNs) architecture was examined. Firefly algorithm (FFA) and prey-predator algorithm (PPA) are metaheuristic algorithms with high-level strategies. These algorithms are used for the training of RBFNNs. Two and twelve the hidden neurons with ten different classification data sets are used to test RBFNNs architecture. To evaluate the performance and effectiveness of algorithms, the Schwarz Bayesian criterion (SBC) and the error functions are utilized. The simulation results revealed that the algorithms are appropriate to use in learning ANNs.

Abstract: An assignment problem (AP) is a particular case of a transportation problem, in which the objective is to assign (or allocate) a number of resources (say facilities) to an equal number of activities (say jobs) at an overall minimum total cost, distance, time (or maximum total profit). It occupies a very significant role in the real physical world for e.g. production planning, particular job tasks, economic etc. The most common method used to solve the APs is the Hungarian assignment method (HAM). In this paper, we make an effort to introduce a new approach to APs namely TERM for solving a wide range of APs with minimum effort of mathematical calculations. The proposed TERM method is based on the principle of reducing the given cost matrix to a matrix of opportunity costs (MOC) having at least one zero in each row and column and making assignments to the selected zero-entry cells of MOC which ensures best solution for a given AP. To verify the performance of the TERM method, 30 classical benchmark instances from the literature have been tested. Simulation results authenticate that the proposed TERM method is the most efficient method which produces optimal solution directly to 24 instances (i.e. 80% cases) next to the HAM. 802 R. Murugesan and T. Esakkiammal

Abstract: The flow of an inelastic fluid subject to shear thinning phenomenon is considered. Using the Williamson constitutive equation to model the pseudoplastic effects, the governing boundary layer equations for steady laminar flow near a horizontal flat rigid surface, have been subjected to a similarity analysis. Two specific flow configurations corresponding to (i) Blasius flow and (ii) Sakiadis flow, have been investigated. The resulting non-linear boundary value problem for each flow has been solved using a perturbation expansion followed by numerical integration. The focus of this work is on bringing out the effect of the rheological parameter, and also the relative higher order effects on the flows. It is concluded that higher order effects arising due to the non-Newtonian effects, do influence the flows to varying degrees. 60 Tayfour El-Bashir, Pallath Chandran and Nirmal C. Sacheti Mathematics Subject Classification: 76A05, 76D10

Abstract: In this article, we present a new family of simultaneous iterative method for determining all the roots of non-linear equation. Using King’s family of iterative methods as corrections, we accelerate the convergence order of basic weierstrass method from 2 to 5. Convergence analysis, basins of attraction, computational efficiency, numerical test examples and log of residual demonstrate the performance and efficiency of the newly constructed simultaneous method as compared to other existing methods in the literature.

Abstract: We find numerical solutions of nonlinear Volterra integral equations of the first kind by first converting them into linear Volterra integral equations of the second kind. We then apply the fourth-order blockby-block method in conjunction with Simpson’s rule. The approximate solutions obtained, based on a sampling of numerical examples, are then compared with those from other existing methods in the literature. Mathematics Subject Classification: 45A05, 45D05, 46N20

Abstract: This paper proposes a deteriorating inventory model with a generalised exponential increasing demand where the deterioration rate is a time-varying linear function of time and the holding cost is constant. Shortages are not allowed. A numerical example is presented to demonstrate the application of the model and sensitivity analysis is carried out to see the effect of parameter changes on the solution.

Abstract: Goodness of fit (GOF) tests of logistic regression attempt to find out the suitability of the model to the data. The null hypothesis of all GOF tests is the model fit. R as a free software package has many GOF tests in different packages. A Monte Carlo simulation has been conducted to study two situations; the first, studying the ability of each test, under its default settings, to accept the null hypothesis when the model truly fitted. The second, studying the power of these tests when assumptions of sufficient linear combination of the explanatory variables are violated (by omitting linear covariate term, quadratic term, or interaction term). Moreover, checking whether the same test in different R packages had the same results or not. As the sample size supposed to affect simulation results, so the pattern of change of GOF tests results under different sample sizes as well as different model settings was estimated. All tests accept the null hypothesis (more than 95% of simulation trials) when the model truly fitted except modified Hosmer-Lemeshow test in "LogisticDx" package under all different model settings and Osius and Rojek’s (OsRo) test when the true model had an interaction term between binary and categorical covariates. In addition, le Cessie-van Houwelingen-Copas-Hosmer unweighted sum of squares (CHCH) test gave unexpected different results under different packages. Concerning the power study, all tests had a very low power when a departure of missing covariate existed. Generally, stukel’s test (package ’LogisticDX) and CHCH test (package "RMS") reached a power in detecting a missing quadratic term greater than 80% under lower sample size while OsRo test (package ’LogisticDX’) was better in detecting missing interaction term. Beside the simulation study, we evaluated the performance of GOF tests using the breast cancer dataset.

Abstract: Quantitative and qualitative analysis of the Averaging methods for the parabolic partial differential equation appears as an exciting field of the investigation. In this paper, we generalize some known results due to Krol on the averaging methods and use them to solve the parabolic partial differential equation.

Abstract: In this paper we introduce a generalized quaternion with generalized Fibonacci number components. For this quaternion we obtain the two types of Catalan’s identities and d’Ocagne’s identity. Mathematics Subject Classification: 11B39, 11B37, 11B52

Abstract: Ancient Egyptians represented a fraction as a sum of inverses of natural numbers, with the smallest possible number of terms. In our previous paper, we explained that this representation makes sense since it leads to the optimal way of solving a problem frequently mentioned in the Egyptian papyri: dividing bread between workers. However, this does not explain why ancient Egyptians preferred some representations with the same number of terms but not others. For example, to represent 2/3, they used the sum 1/2 + 1/6 but not the sum 1/3 + 1/3 with the same number of terms. In this paper, we use a more detailed analysis of the same dividing-bread problem to explain this preference. Namely, in our previous explanation, we assumed that each cut requires the same amount of time. If we take into account that in practice, each consequent cut of the same loaf – just like any other repetitive action – takes a little less time, we get the desired explanation of why ancient Egyptians preferred, e.g., 1/2 + 1/6. 1 Egyptian Fractions – What and Why: A Reminder Egyptian fractions – what is it. In ancient Egypt, fractions were represented as the sum of inverse numbers with the smallest possible number of terms; see, e.g., [1, 2, 3] and references therein. For example, 5 6 was represented as 5 6 = 1 2 + 1 3 . (1) Egyptian fractions – why. One of the possible explanations for the above representation is that it leads to the optimal solution of a problem actively

Abstract: A one-dimensional convective-diffusion problem is considered. To improve the quality of difference schemes, the method of moving nodes is used in combination with Richardson interpolation. Approximate analytical solutions and improved schemes are obtained. Numerical experiments carried out.

Abstract: An assignment problem (AP) is a particular case of a transportation problem, in which the objective is to assign (or allocate) a number of resources (say facilities) to an equal number of activities (say jobs) in such a way that the overall cost, time, distance, is minimized (or the overall profit is maximized). It plays a vital role in the real physical world for e.g. production planning, particular job tasks, economic etc. The most common method used to solve the APs is the Hungarian assignment method (HAM) due to H.W. Kuhn (1955), which produces optimal assignment plan almost all the time. In the recent years several methods have been projected by several researchers for solving APs. Among them some methods have been introduced which arrive at the optimal assignment plan directly. In this paper, we have tried to expose that the proposed direct methods namely New Method (NM), Innovative Method (TVAM), Advanced Method (NS-AVSNM), New Methodology (MAP) for finding optimal solution of an assignment problem do not produce optimal assignment constantly. We give examples of the APs where the direct methods fail to find their optimal assignment plan. 824 R. Murugesan and T. Esakkiammal

Abstract: There is an intrinsic and mutualistic dependence between the bio-economic performance of banks and that of enterprises. This supposition is supported by correlations identified in a comprehensive analysis of the Italian banking sector, which reveal particularly strong relations between financial intermediaries and smaller enterprises. Concentrating on developments within the bank-enterprise system (and by extension, in households), we discuss the positive effects, including on macroeconomics, generated when the banking sector supplies funding to productive infrastructure to understand how the industry remains healthy and efficient. The negative effects produced by the disappearance of such a cycle are also considered. This paper thus presents a mathematical argument through dynamic modelling to evaluate the structural trends in bank and company populations that result from more and less expansive credit strategies assumed by banks. 1 Corresponding author; Economist and Credit Financial Advisor – Practitioner 2 Independent Economist and Credit Financial Advisor 680 Marco Desogus and Elisa Casu Empirical observations of this data also reflect the critical stress factor of the (micro)enterprise population that allows it to generate positive economic variations as financial leverage decreases. The ensuing assessment of stable and unstable points of equilibrium as well as bifurcations and their irreversibility (hysteresis) reveals that banks have stagnating profits and increasing numbers of non-performing loans. Finally, we investigate the possibility of an optimal minimum level of credit leverage and how to improve the stabilizing measures that are conferred to the system itself, especially given the uncertainty caused by the COVID-19 pandemic. JEL Codes: C61, C62, E32, E44, G21

Abstract: Some new Hermite-Hadamard type inequalities will be presented in this work for functions whose second derivative in absolute value at certain power is exponential type convex.

Abstract: Ebola virus disease (EVD), is a savere, often fatal disease in humans with very high mortality rate. Currently, there are neither licenced vaccines nor approved medication for the disease. In this study, a within host model of Ebola virus disease incorporating treatment as a control strategy has been formulated. Local and global stability analyses of the infection free, (IFE) and endemic equilibrium, (EE) points of the model have been done. It is shown that if the basic reproduction number Rw 0 < 1 , the IFE is both locally and globally assymptotically stable and that when Rw 0 > 1 , the disease persists in the population of the cells. The impact of treatment on the infection has also been established. The study indicates that a higher efficacy of treatment helps to tackle the disease within an individual.

Abstract: Abstract We study the behavior of a solution of mixed stochastic differential equation driven by independent standard Brownian motion and fractional Brownian motion with Hurst index H ∈ (0; 1). On this we first look at the case where the drift is zero and the diffusion coefficients are equal to 1 then we generalize the study in the case where the drift is not zero. Our study is done via the large deviation principle on the set of continuous square integrable functions in the dual of Schwartz space.

Abstract: The assignment problem (AP) is a particular case of the transportation problem, in which the objective is to assign a number of resources to an equal number of activities at an overall minimum cost (or overall maximum profit). It has great implication in the real physical world. In 2012, Hadi Basirzadeh introduced a new approach to APs namely, Ones Assignment Method, for solving a wide range of such problems. This method is based on creating ones in the assignment matrix and then tries to find a complete assignment to these ones. In 2013, Ghadle K.P. and Muley Y.M. presented a new method namely, Revised Ones Assignment (ROA) method for solving wide range of APs, which is different from the preceding method. This method is also based on creating some ones in the assignment matrix and then tries to achieve exact optimal assignment, which is same as that of Hungarian method, in terms of ones. In 2014, M. Khalid et al. [7] introduced the New Improved Ones Assignment (NIOA) method, which overcomes the drawbacks of older algorithms and outperforms them by a considerable margin. In this paper, we have tried to reveal that the presented ROA method as well as the NIOA method for solving APs do not present optimal solution at all times. We give examples of the AP where the ROA and the NIOA 900 R. Murugesan and T. Esakkiammal methods fail to find their optimal solution. Also, a new set of rules, called ME rules, for covering all the 1s in a resultant assignment matrix by drawing minimum number of lines and also for testing the conditions for the achievement of a complete assignment are presented in this paper.

Abstract: In this paper, we prove a set of sufficient optimality conditions with a current-value Hamiltonian for a family of age-structured optimal control problems with a discount factor in the objective functional. Mathematics Subject Classification: 49K20, 49N90, 91B55

Abstract: Principal component analysis (PCA) is one of the successful dimensionality reduction approaches for color face recognition. For various PCA methods, the experiments show that the contribution of eigenvectors is different and different weights of eigenvectors can cause different effects. Based on this, a modified and simplified color two-dimensional quaternion principal component analysis (M2D-QPCA) method is proposed along the framework of the color two-dimensional quaternion principal component analysis (2D-QPCA) method and the improved two-dimensional quaternion principal component analysis (2D-GQPCA) method. The shortcomings of 2D-QPCA are corrected and the CPU time of 2D-GQPCA is reduced. The experiments on two real face data sets show that the accuracy of M2D-QPCA is better than that of 2D-QPCA and other PCA-like methods and the CPU time of M2D-QPCA is less than that of 2D-GQPCA.

Abstract: A new generalized Poisson mixed distribution is proposed in this study called New Generalized Poisson-Sujatha distribution (NGPSD). The properties and application of the distribution are studied. The two parameter distribution is obtained by compounding Poisson distribution with a two parameter generalized Sujatha distribution. The distribution has a tendency to account for over-dispersion in count data. The first four moments, variance and coefficient of variation of the distribution are also obtained. The estimators of its parameters are obtained via maximum likelihood method using R-software. The goodness-of-fit of the distribution is compared with other distributions such as Poisson distribution (PO), negative binomial (NB), Generalized Poisson-Lindley (GPL) and a New Generalized Poisson-Lindley (NGPL) Distributions. It can be seen that the test statistic, AIC and BIC for the NGPSD are lower than those of competing distributions implying that the proposed distribution satisfactorily fits better to the data set.

Abstract: Different forms of discriminant functions and the essence of their appearances were considered in this study. Various forms of classification problems were also considered, and in each of the cases mentioned, classification from simple functions of the observational vector rather than complicated regions in the higher-dimensional space of the original vector were made. Ever since the emergence of the Linear Discriminant Function (LDF) by Fisher, several other classification statistics have emerged and violation of condition of equal variance covariance matrix for Linear Discriminant Function (LDF) results to Quadratic Discriminant Function (QDF). While the Best Linear Discriminant Function (BLDF) is referred to Best Sample Discriminant Function (BSDF) when the parameters are estimated from a sample and also optimal in the same sense as Quadratic Discriminant Function (QDF), Rao statistic is best for discriminating between options that are close each other. The relationships among the classification statistics examined were established: Among the methods of classification statistics considered, Anderson’s (W) and Rao’s (R) statistics are equivalent when the two sample sizes n1 and n2 are equal, and when a constant is equal to 1, W, R and John-Kudo’s (Z) classification statistics are asymptotically comparable. A linear relationship is also established between W and Z classification.

Abstract: A non-traditional formulation of the Gaussian probability distribution in two dimensions did not require the constant pi and mathematically resembled the exponential formula of radioactive decay. Shifting the position of reference did not affect the effective span of its remaining existence on the farther side of that reference position. Isolation prevailed like a black hole behind a circular boundary when observing outward from there. Consequently, any observer at any possible location, could as well view itself to be just in the center of that distribution, if the distribution was perfectly Gaussian. Utility of this viewpoint could include development of alternative tests of normality. Such tests might be useful for exploring random distribution of errors in unknown data sets in many areas of science from cosmology to virology.