Open Access Opinion Article

A Comparative Study of Solving Methods of Transportation Problem in Linear Programming Problem

Farzana Sultana Rafi, Safiqul Islam

Journal of Advances in Mathematics and Computer Science, Page 45-67
DOI: 10.9734/jamcs/2020/v35i530281

The paper is related with the basic transportation problem (TP)which is one kind of linear programming problem (LPP). There are some existing methods for solving transportation problem and in this paper all the standard existing methods has been discussed to understand which one is the best method among them. Among all of existing methods, the Vogel’s Approximation Method (VAM) is considered the best method which gives the better optimal result then other methods and North-West Corner Rule is considered as simplest but gives worst result. A C programming code for Vogel’s Approximation Method have been added in the appendix.

Open Access Original Research Article

On A Class of Idealized Near-Rings Admitting Frobenius Derivations

Ojiema M. Onyango, Onyango B. Achieng, Abuga J. Motanya

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/jamcs/2020/v35i530277

In this paper, we use the idealization procedure for finite rings to construct a class of quasi-3 prime Near-Rings N with a Jordan ideal J(N) and admitting a Frobenius derivation. The structural characterization of N; J(N) and commutation of N via the Frobenius derivations have been explicitly determined.

Open Access Original Research Article

Mean Square Asymptotic Boundedness of Stochastic Complex Networks via Impulsive Control

Xiaoyi Zhu, Danhua He

Journal of Advances in Mathematics and Computer Science, Page 10-21
DOI: 10.9734/jamcs/2020/v35i530278

In this paper, the mean square asymptotic boundedness of a class of stochastic complex systems with different dynamic nodes represented by Ito stochastic differential equations is studied.  By using the Lyapunov function and Ito formula, the mean square asymptotic boundedness and mean square asymptotic stability conditions of stochastic complex systems with different dynamic nodes are obtained.

Open Access Original Research Article

Improved Model for Facial Expression Classification for Fear and Sadness Using Local Binary Pattern Histogram

Adebola K. Ojo, Temitope Ololade Idowu

Journal of Advances in Mathematics and Computer Science, Page 22-33
DOI: 10.9734/jamcs/2020/v35i530279

In this study, a Local Binary Pattern Histogram model was proposed for Facial expression classification for fear and sadness. There have been a number of supervised machine models developed and used for facial recognition in past researches. The classifier requires human effort to perform feature extraction which has led to unknown changes in the expression of human face and incomplete feature extraction and low accuracy. This study proposed a model for improving the accuracies for fear and sadness and to extract features to distinguish between fear and sadness. Images of different people of varying ages were extracted from two datasets got from Japanese female facial expression (jaffe) dataset and Cohn cade got from Kaggle. In other to achieve an incremental development, classification was done using Linear Support Vector Machine (LSVM) and Random Forest Classifier (RFC). The accuracy rates for the LSVM models, LSVM1 and LSVM2 were 88% and 87% respectively while the RFC models, RFC1 and RFC2, were 81% and 82% respectively.

Open Access Original Research Article

Combined PCA-Daugman Method : An Effcient Technique for Face and Iris Recognition

Md. Mahbubul Alam, Md. Ashikur Rahman Khan, Zayed Us Salehin, Main Uddin, Sultana Jahan Soheli, Tanvir Zaman Khan

Journal of Advances in Mathematics and Computer Science, Page 34-44
DOI: 10.9734/jamcs/2020/v35i530280

Face and iris are very common individual bio-metric features for person identification. Face recognition is the method of identification a person uniquely using face. Principal component analysis is one of the algorithms for face recognition. Iris recognition in another method of person identification using iris. Very popular iris recognition method is Daugman algorithm. Unimodal biometric system has various difficulties to detect a person like noisy and unusual data. Multimodal biometric system combined more than one individual modalities like face and iris to increase the efficiency. In this work, we combined principal component analysis and Daugman algorithm with ORL, YALE, CASIA and Real face dataset to combine face and iris recognition to improve the recognition efficiency.

Open Access Original Research Article

Experimental and Mathematical Model for the Antimalarial Activity of Methanolic Root Extract of Azadirachta indica (Dongoyaro) in Mice Infected with Plasmodium berghei NK65

Adeniyi Michael Olaniyi, Momoh Johnson Oshiobugie, Aderele Oluwaseun Raphael

Journal of Advances in Mathematics and Computer Science, Page 68-82
DOI: 10.9734/jamcs/2020/v35i530283

The study determines the experimental and mathematical model for the anti-plasmodial activity of methanolic root extract of Azadirachta indica in Swiss mice infected with Plasmodium berghei NK65. Phytochemical analyses, antimalarial activity of the methanolic root extract of A. indica was determined in mice infected with Plasmodium berghei NK65 using standard procedure. Liver biomarker enzymes were also determined. The model P. berghei induced free and P. berghei infected equilibrium were determined. The stability of the model equilibrium points was rigorously analyzed. The phytochemicals present in the extract include: alkaloid, flavonoid, saponin and phenolic compounds etc. The experimental study consists of five groups of five mice each per group. Group A, B, C, D and E were healthy, infected without treatment, infected mice treated with fansidar (10 mg/kg), chloroquine (10 mg/kg) and 250 mg/kg body weight of A. indica methanolic root extract respectively. The extract showed anti-plasmodial activity of 73.96%. The result was significant when compared with group B mice, though it was lower than that exhibited by fansidar (88.91%) and chloroquine (92.18%) for suppressive test. There were significant decrease (P<0.05) in plasma AST and ALT levels in the treated infected mice compared to the infected untreated mice. The results of the model showed that the P.berghei induced free equilibrium is locally and globally asymptotically stable at threshold parameter,  less than unity and unstable when  is greater than unity. Numerical simulations were carried out to validate the analytic results which are in agreement with the experimental analysis of this work.

Open Access Original Research Article

A Modified Ant Colony Optimization Algorithm for Solving a Transportation Problem

E. M. U. S. B. Ekanayake, S. P. C. Perera, W. B. Daundasekara, Z. A. M. S. Juman

Journal of Advances in Mathematics and Computer Science, Page 83-101
DOI: 10.9734/jamcs/2020/v35i530284

Transportation of products from sources to destinations with minimal total cost plays a key role in logistics and supply chain management. The transportation problem (TP) is an extraordinary sort of Linear Programming problem where the objective is to minimize the total cost of disseminating resources from several various sources to several destinations. Initial feasible solution (IFS) acts as a foundation of an optimal cost solution technique to any TP. Better is the IFS lesser is the number of iterations to reach the final optimal solution. This paper presents a meta-heuristic algorithm, modified ant colony optimization algorithm (MACOA) to attain an IFS to a Transportation Problem. The proposed algorithm is straightforward, simple to execute, and gives us closeness optimal solutions in a finite number of iterations. The efficiency of this algorithm is likewise been advocated by solving validity and applicability examples An extensive numerical study is carried out to see the potential significance of our modified ant colony optimization algorithm (MACOA). The comparative assessment shows that both the MACOA and the existing JHM are efficient as compared to the studied approaches of this paper in terms of the quality of the solution. However, in practice, when researchers and practitioners deal with large-sized transportation problems, we urge them to use our proposed MACOA due to the time-consuming computation of JHM. Therefore this finding is important in saving time and resources for minimization of transportation costs and optimizing transportation processes which could help significantly to improve the organization’s position in the market.

Open Access Original Research Article

Simulation Study of H1N1 Transmission through Immigrants and Vaccination

Nita H. Shah, Nehal Shukla, Foram Thakkar, Moksha Satia

Journal of Advances in Mathematics and Computer Science, Page 102-120
DOI: 10.9734/jamcs/2020/v35i530285

H1N1 influenza, is a disease caused by the Type A strain of negative-sense single stranded RNA virus which has unique characteristics of reassortment making it different and difficult to control. Due to the unique nature of the virus, the constant globalization of the international population, and the lack of effective immunization, this virus is a great threat to public health. There is only limited data available on impacts of immigrants on H1N1 transmission. So, there is real need to study impacts of immigrants on H1N1 transmission as well as vaccination. We have studied a mathematical model for simulation study of H1N1 transmission through immigrants and vaccination. The class of susceptible people is divided in two types: vaccinated immigrants and non-vaccinated immigrants. The medications and hospitalizations are the remedial steps to get cured. The rate at which people get medicated or hospitalized is analyzed using SEIR model. The system of non-linear ordinary differential equation is formulated for the given model and the reproduction number is then calculated using next generation matrix method which indicates the recovery rate of an individual stability. Numerical simulations are then carried out. Our study showed that increasing the awareness among the general population, immigrants about clinical features and modes of transmission of H1N1 and improving the vaccination rate helps decrease the transmission of H1N1.

Open Access Original Research Article

An Optimal Algorithm for the Solution of the Helmholtz Equation

Richard O. Akinola, Blessing Okwudo Ogbeh, Isaac Chukle

Journal of Advances in Mathematics and Computer Science, Page 121-133
DOI: 10.9734/jamcs/2020/v35i530286

Aims/Objectives: The Helmholtz equation is a partial differential equation which is used in numerical weather prediction. Angwenyi et. al., used a five point finite difference stencil in discretizing the partial differential equation and solved the resulting square system of equations using eight iterative methods and concluded that the BICGSTAB was the most computationally efficient using just one example. However, based on a comparison of the norm of the residual and CPU time of four methods presented in this work on the same example in their paper and others; we not only discovered that the Gauss Seidel method out performed the BICGSTAB contradicting the claim of the authors but also the Thomas Block Tridiagonal Algorithm (TBTA)
in the absence of round off errors.
Methodology: We compared the performance of the Gauss Seidel Method, BICGSTAB, Matlab backslash, and the Thomas Block Tridiagonal Algorithm (TBTA) for the numerical solution of the Helmholtz equation with different step sizes.

Results: We discovered that in the absence of round off errors, not only did the Gauss Seidel method but also the Thomas Block Tridiagonal Algorithm (TBTA) out performed the BICGSTAB contradicting the claim of Angwenyi et. al.
Conclusion: We do not recommend the BICGSTAB for the solution of the linear system of equations arising from the discretization of the Helmholtz equation as claimed by Angwenyi et al. Rather, the Thomas Block Tridiagonal Algorithm should be used and if one is thinking of an iterative method for the numerical solution of the Helmholtz equation, the Gauss-Seidel method should be the method of choice rather than the BICGSTAB.

Open Access Original Research Article

Mathematical Model on Optimal Combination of Vaccination and Antiviral Therapy to Curb In uenza in Kenya

Derrick M. Nzioki, James K. Gatoto

Journal of Advances in Mathematics and Computer Science, Page 134-147
DOI: 10.9734/jamcs/2020/v35i530287

Human influenza is a contagious disease which, if proper precautions are not taken to control the disease, can lead to massive mortality rates and high costs will be incurred to control the disease in case of an outbreak. As a result, we investigate how the cost of implementing both vaccination and antiviral therapy can be minimized and at the same time minimize the number of infected individuals. We have developed a system of ordinary differential equations from our formulated SVIR model and used vaccination and antiviral therapy to study influenza dynamics. We have the basic reproductive number determined using the next generation matrix. The equilibria and stability of the model has also been determined and analyzed. We have used the maximization theory of Pontryagin to define the optimal control rates and then used MATLAB program to do the numerical simulations. The numerical simulations done indicate that an ideal combination of vaccination and antiviral therapy decreases the number of infected individuals which in turn reduces the cost of applying the two control measures.