We consider the almost similarity property which is a new class in operator theory and was first introduced by A. A. S. Jibril.   We establish that almost similarity is an equivalence relation.  Some results on almost similarity and isometries, compact operators, hermitian, normal and projection operator are also shown.  By characterization of unitary equivalence operators in terms of almost similarity we prove that operators that are similar are almost similar.  We also claim that quasi-similarity implies almost similarity under certain conditions (i.e. if the quasi-affinities are assumed to be unitary operators).

Fifty-four Forbush decrease (Fd) events had been studied during a period of twenty years. It was found that there exist dependence between the amplitude of (Fd) event and the rigidity at the point of observation. The spectrum responsible for the Forbush decrease is found to have a power law with an exponent which depends on the profile of the event. (Fd) events can be classified into three different classes depending on the shape of its decreases and recovery.

This research work investigated the expert system design and control of crude oil distillation column (CODC) using artificial neural network model which was validated using experimental data obtained from functioning crude oil distillation column of Port-Harcourt Refinery, Nigeria. MATLAB program was written for the artificial neural network back-propagation algorithm using the implementation steps of the artificial neural network. Out of the one-hundred and thirty (130) experimental data sets obtained, ninety percent (90%) were used for training the network while the remaining ten percent (10%) were used for testing the network to determine its prediction accuracy. The neural network architecture for the design of the crude oil distillation column was fourteen inputs with one hidden layer and seven outputs (14-1-7); and thirteen (13) inputs with one hidden layer and six (6) outputs (13-1-6) for the neural network controller. The accuracies obtained for the design were 94%, 99%, 92%, 93%, 81%, 95% and 90% for temperature at which 100% (T₁₀₀) of Kerosene, 90% (T₉₀) of Diesel and 10% (T₁₀) of AGO were distilled; and naphtha, kerosene, diesel and AGO flow rates respectively. The maximum relative error between the experimental data and the calculated data obtained from the output variables of the neural network for CODC design was 1.98% error. The accuracies obtained for the neural network controller (NNC) were 98%, 99%, 99%, 93%, 97% and 97% for the stripping steam to main column, LDO stripper, HDO stripper, reflux flow 1, reflux flow 2 and reflux flow 3 respectively. The little deviation between the output variables of the experimental and calculated data for the cases of NNC predictions for reflux flows 1, 2 and 3 resulted from their excessive usage by the PID controller of the refinery considered to meet the product specifications. Hence, artificial neural network model is an effective tool for the design and control of crude oil distillation column.