On Recognizability of Groups by Bottom Layer

The bottom layer of a group is a set of its elements of prime order. A group is called recognizable by bottom layer under additional conditions if it is uniquely restored by bottom layer under these conditions. A group is called almost recognizable by bottom layer under additional conditions, if there are a finite number of pairwise non-isomorphic groups satisfying these conditions, with bottom layer that is the same as that of the group. A group is called unrecognizable by bottom layer under additional conditions if there are an infinite number of pairwise non-isomorphic groups satisfying these conditions, with bottom layer that is the same as that of the group. In the paper we consider examples of groups recognized by bottom layer, by spectrum and, simultaneously, by spectrum and by bottom layer. We have also proved some results of recognizability of groups by bottom layer.

An Analytical Solution of Spatially Dependent One-Dimensional Advection-Dispersion Equation for a Varying Pulse Type Input Source

In present study, solution of advection-dispersion equation is obtained to determine concentration distribution of solute introduced from a varying pulse type point source in one-dimensional heterogeneous semi-infinite porous medium. Heterogeneity of the medium gives rise to space dependent groundwater velocity, dispersion coefficient and retardation factor. Groundwater velocity is some exponent ξ to a linear function of space. The dispersion and retardation factor are also exponents of same linear function with exponents (ξ+1) and (ξ-1), respectively, where ξ takes the value 0 or 1. At one end of the domain, a time dependent varying nature source, which involves step-size increasing function of time, acts along the flow up to a certain time the n eliminated while concentration gradient is considered zero at the other end of the domain. Initially, medium is uniformly polluted. Firstly, the advection-dispersion equation is reduced into constant coefficients by using certain transformations and then Laplace Integral Transformation Technique is utilized to get the solution. The obtained result is illustrated with numerical examples to study the effect of various parameters.

An Evaluation of the Chemical Composition of Soft Drinks in Nigeria: A Principal Component Analysis Approach

This study aims to determine the relationship between the chemical compositions of twenty-five (25) soft drinks sold in Nigeria. Sample concentration of twenty-five (25) soft drinks used in the study was collected from the National Agency for Food and Drug Administration and Control (NAFDAC). Principal Component Analysis (PCA) was employed to explain the relationship between the chemical compositions and determine the soft drinks' chemical composition distribution. The result has shown that all except acidity and antioxidant has a significantly strong positive relationship among the chemical structures. PCA suggested retaining three components that explained about 82.465 per cent of the data set's total variability. It was observed that carbonated water, fructose, sucrose, main concentration, stabiliser, E412, colouring and gelatin were the major compositions of the soft drinks in Nigeria, Base on the findings in this study, it is recommendations that; Consumers who are allergic to sugar or diabetic should avoid taking any of the soft drinks with high sugar concentration. Soft drinks companies producing drinks with high sugar content should consider their customers who are diabetic and allergic to high sugar levels.