In this paper we introduced the definition of perfect foldingof graphs and we proved that cycle graphs of even number ofedges can be perfectly folded while that of odd number ofedges can be perfectly folded to C3 . Also we proved thatwheel graphs of odd number of vertices can be perfectlyfolded to C3. Finally we proved that if G is a graph of n verticessuch that 2 < clique number =chromatic number=k < n ,then the graph can be perfectly folded to a clique of order k.
Spatial modeling has largely been applied in epidemiology and disease modeling. Different methods such as Generalized linear models (GLMs) have been made available to prediction of the claim frequencies. However, due to heterogeneity nature of policies, the methods do not generate precise and accurate claim frequencies predictions; these parametric statistical methods extensively depend on limiting assumptions (linearity, normality, independence among predictor variables, and a pre-existing functional form relating the criterion variable and predictive variables). This study investigates how to derive a spatial nonparametric model estimator based on smoothing Spline for predicting claim frequencies. The simulation results showed that the proposed estimator is efficient for prediction of claim frequencies than the kernel based counterpart. The estimator derived was applied to a sample of 6500 observations obtained from Cooperative Insurance Company, Kenya for the period of 2018-2020 and the results showed that the proposed method performs better than the kernel based counterpart. It is worth noting that inclusion of the spatial effects significantly improves the estimator prediction of claim frequency.
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 .
The Goldbach’s Strong Conjecture is one of the oldest unsolved problem in number theory in Mathematics. We have created a pair of formulae to the Goldbach's strong conjecture because the statement is based with the basic concept of Mathematics. The main focus before creation was, If we can create a formula or a pair of formulae to the said conjecture, that will bring an interesting events among the students (readers) who love Mathematics, the creations will give them a huge pleasure, when they can solved, the primes whose sum are equal to the positive integer say 46,by applying our created formulae.
This paper is to study the contributions, analyze the professional handling of patients needs by the globally recognized a European, non-governmental organization Medecins Sans Frontieres 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.
