Journal of Applied & Computational Mathematics

In the seventeenth century Fermat defined a sequence of numbers Fn=22n +1 for n ≥ 0 known as Fermat’s number . If Fn happens to be prime then Fn is called Fermat prime. All the Fermat’s number are of the form n!k+ Σnk for some fixed value of k and n. Further we will prove that after F4 no other Fermat prime exist upto 1050 .

Spatial modeling has largely been applied in epidemiology and disease modeling. Different methods such as generalized linear models (GLMs), Poisson regression models, and Bayesian Models have been made available to predict the claim frequency for forthcoming years. However, due to the heterogeneous nature of policies, these methods do not produce precise and reliable prediction of future claim frequencies; these traditional statistical methods rely heavily on limiting assumptions including linearity, normality, predictor variable independence, and an established functional structure connecting the criterion and predictive variables. This study investigated how to construct a spatial nonparametric regression model estimator tor for prediction of claim frequency of insurance claims data. The study adopted a nonparametric function based on smoothing Spline in constructing the model. The asymptotic properties of the estimators; normality and consistency were derived and the inferences on the smooth function were derived. The simulation study showed that the estimator that incorporated spatial effects in predicting claims frequency is more efficient than the traditional Simultaneous Autoregressive model and Nonparametric model with Simultaneous Autoregressive error. The model estimator was applied to claims data from Cooperative Insurance Company insurance in Kenya with n = 6500 observations and the findings showed that the proposed model estimator is more efficient compared to the Local Linear fitted method, which does not account for spatial correlation. Therefore, the proposed method (Nonparametric spatial estimator) based on the findings has significant statistical improvement of the existing methods that are used for the prediction of claims. The study had a number of limitations, where the data used in the study is Lattice data (without a coordinate system); therefore, there was difficulty in classifying the claims to a specific area in the region (County).

This paper is to study the contributions, analyze the professional handling of patients needs by the globally recognized a European, non-governmental organization Médecins Sans Frontiéres MSF-Spain, on Nurse Scheduling, through the most less cost effective and workload sharing techniques, in area called Pulka Community that is approximately 5killometers away from Camp Zero called Sambisa forrest, a former Boko Haram stronghold that was formally declared as the insurgents hideout location or headquaters referred as the Caliphate on the 7th August, 2014 by their Leadership. The most difficult and highly volatile, risk area in Borno State Northeast- Nigeria that was classified as a red zone by the security intelligence reports. The task of Nurse Scheduling to meet up with the community counselling, traumatized patients by the armed gunmen, hetherto the hectic and herculean task, when considered the services rendered during the crisis period at the peak of the insurgency, Military hostility and subsequent Government declaration and pronouncement of curfew on all sorts of movements sometimes between the 1000hours to 0700hours without any provision for alternative arrangement for the special health-care workers. We proposed a model to improve both the process and the quality of scheduling techniques. The objective is to maximize the fairness of the schedule among personnel. A numerical illustration and example of workload scheduling for a maximum of 8 hours is obtained and solved by correct simplex method, through elementary row operation, the hospital needs a minimum of professional nurses to meet up with the patients needs to be more effective and efficient.