##### Inventory Model for Three–parameter Weibull Deterioration and Partial Backlogging

Naresh Kumar Kaliraman

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/jamcs/2019/v33i530189

This paper develops an economic order quantity inventory model for time dependent three parameters Weibull deterioration. Partially backlogged shortages are considered. The demand rate is deterministic and time dependent. The rate of deterioration is time dependent. We have derived the most favorable order quantity model by minimizing the entire inventory cost. A numerical illustration has been carried out to evaluate the result of parameters on decision variables and the total average cost of the model. The research focus of this paper is to derive the optimum order quantity by minimizing the total inventory cost.

##### Mathematical Modelling of Tungiasis Disease Dynamics Incorporating Hygiene as a Control Strategy

Faith Kabura Mbuthia, Isaac Chepkwony

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/jamcs/2019/v33i530190

Tungiasis is a disease that mostly affects the children,the disabled,alcoholics and the aged in Kenya and other parts of the world.Despite the intensive research that has been doneon tungiasis disease,the disease remains a threat in Muranga County.In this research, weformulated a model which is mathematical in nature and derived a system of ordinary differentialequations from it,which we used to study the dynamics of tungiasis disease, incorporating properhygiene as a control measure.The basic reproduction number, R0, is calculated using the nextgeneration matrix.We determined the equilibrium points of the model and also carried out theirstability analysis. From stability, both disease free equilibrium and endemic equilibrium points of the model were found to be locally asymptotically stable when R0 < 1 and R0 > 1 respectively.Numerical simulation of the model carried out showed that effective proper hygiene leads to afaster decrease in the spread of tungiasis.

##### On Nonsingularity of RSFPLR Circulant Matrices

Xiyou Cui, Nan Jiang

Journal of Advances in Mathematics and Computer Science, Page 1-7
DOI: 10.9734/jamcs/2019/v33i530191

In this paper, we discuss the non-singularity of a row skew rst-plus-last right (RSFPLR) circulant matrices with the rst row (a1; a2; : : : ; an),which is determined by entries of the first row. First,the suffient condition for the matrix to be nonsingular is that,there exists an element ai0 belonging to the first row,whose absolute value is greater than the sum of the corresponding power of 2 and the absolute values of the remaining (n − 1) elements, that is, $$|a_{i_0}|>\sum_{{i=1},{i\neq i_0}}^{n}2^{i-i_0}|a_i|.$$ Moreover, we derive other suffcient conditions for judging the non-singularity of the matrix.

##### Credit Card Fraud Detection Using Autoencoder Model in Unbalanced Datasets

M. A. Al-Shabi

Journal of Advances in Mathematics and Computer Science, Page 1-16
DOI: 10.9734/jamcs/2019/v33i530192

Fraudulent credit card transaction is still one of problems that face the companies and banks sectors; it causes them to lose billions of dollars every year. The design of efficient algorithm is one of the most important challenges in this area. This paper aims to propose an efficient approach that automatic detects fraud credit card related to insurance companies using deep learning algorithm called Autoencoders. The effectiveness of the proposed method has been proved in identifying fraud in actual data from transactions made by credit cards in September 2013 by European cardholders. In addition, a solution for data unbalancing is provided in this paper, which affects most current algorithms. The suggested solution relies on training for the autoencoder for the reconstruction normal data. Anomalies are detected by defining a reconstruction error threshold and considering the cases with a superior threshold as anomalies. The algorithm's performance was able to detected fraudulent transactions between 64% at the threshold = 5, 79% at the threshold = 3 and 91% at threshold= 0.7, it is better in performance compare with logistic regression 57% in unbalanced dataset.

##### Aspects of the Fourier-Stieltjes Transform of C*-algebra Valued Measures

Koami Gbemou, Yaogan Mensah

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/jamcs/2019/v33i530193

This paper deals with the Fourier-Stieltjes transform of C∗-algebra valued measures. We construct an involution on the space of such measures, define their Fourier-Stieltjes transform and derive a convolution theorem.