Access to age-appropriate essential medicines: a retrospective survey of compounding of medicines for children in hospitals in Nigeria and implications for policy development

Policies to improve access to medicines for children in Nigeria do not include compounding as a source of medicines. Compounding is often applied as a last resort in health institutions to provide age-appropriate formulations usually for oral use in young children; but it bears some risk. Some countries have adopted policies aimed at reducing the risk based on available data. There is not much data for Nigeria. This retrospective study examined compounding records from January to December 2011 in a sample of seven hospitals to describe what medicines for oral use were commonly compounded in Nigeria. It then determined if these medicines were commercially available in forms suitable for use in children in selected countries-the United Kingdom, United States and India. The study found that out of 2845 items compounded, over 65% were medicines for cardiovascular conditions, diarrhoea or tuberculosis. The main reason (96%, n = 2399) for compounding was the unavailability of age-appropriate formulations. Medicines were almost all compounded using simple syrup, vitamin C or vitamin B syrups as suspending vehicles. Final products were all oral liquids. Comprehensive stability testing was not reported for the products. Almost all of the commonly compounded medicines were found to be commercially available in dosage forms suitable for use in children in the selected countries. These medicines were all listed in the World Health Organization Essential Medicines List for children as well as in the current edition of the Essential Medicines List of Nigeria. The fact that they were compounded highlights the need for improved access to age-appropriate dosage forms for children in Nigeria. The study recommends policy expansion through a three-pronged approach to improving access: increased supply through facilitated importation/accelerated product registration, or in-country manufacturing; rational drug use including therapeutic substitution, and establishment of a national formulary for compounding

Properties of Sequences Generated by Summing the Digits of Cubed Positive Integers

Having established some properties of sequences generated by summing the digits of squared positive integers (Okagbue et al, 2015), we go a step further to explore the properties and characteristics of sequences generated by summing the digits of cubed positive integers. The results are different from summing the digits of squared positive integers. Two distinct sequences were obtained: one generated by summing the digits of cubed positive integers and the other sequence as the complement of the first but the domain remains the positive integers. The properties of these two sequences are discussed. The properties include their decompositions, subsequences, algebraic, additive, multiplicative, divisibility, uniqueness and ratios

A Novel Approach For Solving Quadratic Riccati Differential Equations

In this paper, a numerical technique-differential transform method (DTM) is presented for the solution of Riccati differential equations. Three illustrative examples involving both constant and variable coefficients are solved. The DTM applied provides results that converge rapidly to the exact solution. To see the accuracy of this method, the results are compared with the exact solutions

Numerical Solution of Two-Point Boundary Value Problems via Differential Transform Method

This paper considers the solution of two-point boundary value problems by the application of Differential Transform method. Two examples are solved to illustrate the technique and the results are compared with the exact solutions. The numerical results obtained show strong agreement with their corresponding exact solutions, and as such demonstrate reliability and great accuracy of the metho

A Numerical-Computational Technique for Solving Transformed Cauchy-Euler Equidimensional Equations of Homogeneous Type

This work considers the solution of Transformed-Cauchy-Euler differential equations via Differential Transform method (DTM). For illustration and application of the method’s efficiency and reliability, two examples of order 2 and 3 are solved. The results agreed with the exact solution obtained via Laplace transform method

Classes of Ordinary Differential Equations Obtained for the Probability Functions of Exponentiated Generalized Exponential Distribution

In this paper, the differential calculus was used to obtain some classes of ordinary differential equations (ODE) for the probability density function, quantile function, survival function, inverse survival function, hazard function and reversed hazard function of the exponentiated generalized exponential distribution. The stated necessary conditions required for the existence of the ODEs are consistent with the various parameters that defined the distribution. Solutions of these ODEs by using numerous available methods are new ways of understanding the nature of the probability functions that characterize the distribution. The method can be extended to other probability distributions and can serve an alternative to approximatio

Sequence of Integers Generated by Summing the Digits of their Squares

Objectives: To establish some properties of sequence of numbers generated by summing the digits of their respective squares. Methods/Analysis: Two distinct sequences were obtained, one is obtained from summing the digits of squared integers and the other is a sequence of numbers can never be obtained be obtained when integers are squared. Also some mathematical operations were applied to obtain some subsequences. The relationship between the sequences was established by using correlation, regression and analysis of variance. Findings: Multiples of 3 were found to have multiples of 9 even at higher powers when they are squared and their digits are summed up. Other forms are patternless, sequences notwithstanding. The additive, divisibility, multiplicative and uniqueness properties of the two sequences yielded some unique subsequences. The closed forms and the convergence of the ratio of the sequences were obtained. Strong positive correlation exists between the two sequences as they can be used to predict each other. Analysis of variance showed that the two sequences are from the same distribution. Conclusion/Improvement: The sequence generated by summing the digits of squared integers can be known as Covenant numbers. More research is needed to discover more properties of the sequence

Convection Flow of MHD Couple Stress Fluid in Vertical Microchannel with Entropy Generation

Entropy generation of fully developed steady, viscous, incompressible couple stress fluid in a vertical micro-porous-channel in the presence of horizontal magnetic field is analysed in this work. The governing equations for the flow are derived, and nondimensionalised and the resulting nonlinear ordinary differential equations are solved via a rapidly convergent technique developed by Zhou. The solution of the velocity and temperature profiles are utilised to obtain the flow irreversibility and Bejan number. The effects of couple stresses, fluid wall interaction parameter (FSIP), effective temperature ratio (ETR), rarefaction and magnetic parameter on the velocity profile, temperature profile, entropy generation and Bejan number are presented and discussed graphically

Classes of Ordinary Differential Equations Obtained for the Probability Functions of Gompertz and Gamma Gompertz Distributions

In this paper, the differential calculus was used to obtain some classes of ordinary differential equations (ODE) for the probability density function, quantile function, survival function, inverse survival function, hazard function and reversed hazard function of the Gompertz and gamma Gompertz distributions. The stated necessary conditions required for the existence of the ODEs are consistent with the various parameters that defined the distributions. Solutions of these ODEs by using numerous available methods are a new ways of understanding the nature of the probability functions that characterize the distributions. The method can be extended to other probability distributions and can serve an alternative to approximation especially the cases of the quantile and inverse survival functions. Finally, the link between distributions extended to their differential equations as seen in the case of the ODE of the hazard function of the gamma Gompertz and exponential distributions

Some Notes on the 3-Factor Analysis of9x9 Sudoku

In this study, we consider a 9x9 post-filled Sudoku puzzle as an example of a three factorial design without blocking. Because of the rigidity of Sudoku, the all main effects and two factors interactions are all statistically insignificant. The three factor interaction is can be statistically significant or not. The use of column or row additions in the computation of the 3-factor interactions of a chosen Sudoku yields complementary results. If the rows addition gives an interaction effect that is statistically significant then the column result will be insignificant and vice versa. The treatment effects of the 3-factor effect of a post-filled Sudoku depend on whether the column or row sllllls are used in the computation of the interaction effect