In a previous paper, we have shown how to obtain sequences of numbers proved random : these sequences can be regarded as a sample of IID sequences of random variables. By using Fibonacci congruences, we transformed sequences of noises yn such that the conditional probabilities have Lipschitz coecients not too large. Then, we obtained sequences xn which admited the IID model for correct model, i.e. Fibonacci congruences behave as extractors. This method allowed to value the CD-ROM of Marsaglia. But we did not use Rap Music (as Marsaglia), but texts les. In this paper, we show that this technique can be applied for a vast majority of possible noises. In order to prove this, we shall provide all nite sequences of random variables with a well chosen measure. Then, with a probability very close to 1, the functions of Fibonacci are very good extractors. It is therefore a very ecient method to obtain sequences proved IID from almost any sequence of noises.

Wave breaking is a phenomenon well-studied in the context of shallow water waves. This paper attempts to connect wave breaking to the global existence of solutions for the periodic peakon b-family of equations. New results on existence of global strong solutions to periodic b-family equations are presented. Periodic initial profile is considered because of strong physical evidence of such behavior of ocean (shallow) waves.

A nonlinear evolution equation in the AKNS hierarchy is presented. The symmetries for this equation are given. The exact traveling wave solutions are obtained by using the tanh-expand and sine-cosine methods.

Fortune’s Conjecture is extended from a relatively short interval after each primorial to an infinite numbers of similar intervals on both sides of primorials, where n is a positive integer.

In addition, it is shown that for every prime in the interval ,there is a number in the interval that is also a prime or 1, such that.

Since n can take infinitely many values, it is highly probable that the reverse of the above theorem is also true. Accordingly, it is conjecture that for every prime , there exist a prime in the interval that gives a much larger prime when added to or subtracted from the primorial multiplied by an integer n.

The paper discusses the core problem error in variables for statistical Least Squares which have noise in the data using polynomial fit of order three. Via Mobius transformation for complex disk in the sense of Petkovic, the exact inversion of a disk was described. Its pitfall was noted and Modified Certifylss relaxed refinement Cholesky decomposition in the sense of Rump comes in handy as a useful alternative for the solution of resulting interval linear system with guaranteed error bounds. The well known Oettli-Prager theorem was used as a measure of performance to the described method using the united solution set for the interval Hull as was described in the sense of Shary. It was discovered that the proposed technique performed as good with high yield of certainty in comparison with well known Oettli-Prager theorem. We also obtained results for traditional floating point arithmetic in the absence of noise in the data.

The mining of association rules and frequent item sets are the main area of interest in recent research activities. The multiple level association rules provide the more meaningful information in comparison to single level association rules which describes only single level concept hierarchy. The Apriori algorithm is most established algorithm for mining the single level association rules. In this study, the fast implementation of Apriori algorithm has been used to generate 3rd level association rules with some modifications in the algorithm. The data coding and data cleaning techniques are used to find the multilevel association rules as they are prerequisite to implement the modified algorithm.

The beta generalized inverse Weibull distribution (BGIW) is suggested in this paper. The mathematical properties of the BGIW distribution are provided and the expression for the moment generating function is derived. Also, the analytical shapes of the corresponding probability density function, reliability function, hazard rate function, and mode are derived with graphical illustrations. Expressions for the r-th positive and negative moments are calculated and the variation of the skewness and kurtosis measures is investigated. Moment and likelihood estimators of the parameters are derived. The observed information matrix is obtained. Simulation study is carried out to investigate the performance of the maximum likelihood method of estimation. Moreover, analysis of real data set is conducted to demonstrate the usefulness of the proposed distribution.

Aims: To investigate the optimal control strategy for Plasmodium knowlesi malaria in humans and macaques. Methodology: A Plasmodium knowlesi malaria model was developed using a deterministic system of differential equation and extended to include an optimal control of the disease. The optimal control model was analysis dynamically and numerically. Results: if the cost of biological control against the mosquito Larvae, the forest dwelling mosquitoes and chemical control against the adult mosquitoes is more than cost of treatment of the infected human, we observed that the control strategy yields increase in susceptible humans, decrease in the infected humans, infected macaques and mosquito population. This is one of the best strategies but treatment is very important for total elimination of Plasmodium knowlesi malaria in a community. Conclusion: Numerical simulations of the problem, suggest that applying the three control measure can effectively reduce if not eliminate the spread of Plasmodium knowlesi malaria in a community.

Aims: To study the implications of power transformations namely; inverse-square-root, inverse, inverse-square and square transformations on the error component of the multiplicative error and determine whether the unit-mean and constant variance assumptions of the model are either retained or violated after the transformation. Methodology: We studied the distributions of the error component under the various distributional forms of the generalized gamma distribution namely; Gamma (a, b, 1), Chi-square, Exponential, Weibull, Rayleigh and Maxwell distributions. We first established the functions describing the distributional characteristics of interest for the generalized power transformed error component and secondly applied the unit-mean conditions of the untransformed distributions to the established functions. Results: We established the following important results in modeling using a multiplicative error model, where data transformation is absolutely necessary;(i) For the inverse-square-root transformation, the unit-mean and constant variance assumptions are approximately maintained for all the distributions under study except the Chi-square distribution where it was violated. (ii) For the inverse transformation, the unit-mean assumptions are violated after the transformation except for the Rayleigh and Maxwell distributions. (iii) For the inverse-square transformation, the unit-mean assumption is violated for all the distributions under study. (iv) For the square transformation, it is only the Maxwell distribution that maintained the unit-mean assumption. (v) For all the studied transformations the variances of the transformed distributions were found to be constant but greater than those of the untransformed distribution. Conclusion: The results of this study though restricted to the distributional forms of the generalized gamma distribution, however they provide a useful framework in modeling for determining where a particular power transformation is successful for a model whose error component has a particular distribution.