All meromorphic solutions for two forms of odd order algebraic differential equations and its applicatio

Abstract

The performance of many reactors found in the mining and metals industry is closely related to the physical properties of aggregate material in the burden, for example particle size distribution. Specifically, the presence of excessive amounts of fine particles in feed material of, for example, fluidised bed gasification reactors and metallurgical furnaces, can impair the gas permeability of the coal or ore burden. This results in non-ideal conditions required for the reacting phases and, subsequently, an adverse effect on plant performance. Therefore, monitoring and control of particle size distribution profiles of such aggregate material on reactor feed streams is critical to minimise or avoid the effect of changing feed conditions on plant performance. Sieve analysis using stock or belt cut samples, which is widely used in industry for this purpose, is inadequate for online control, owing to poor representativeness of samples, rapidly changing feed material, and poor turnaround times of laboratory analysis, among others. In this paper we propose a better framework for real-time monitoring and control, which incorporates image analysis and adaptive learning. The spatial organisation of patterns contained in image data is characterised using the notion of texture and statistically represented as nonlinear localised features or textons. In light of the practical problem of the lack of sufficient annotated data typically required in supervised learning schemes, semi-supervised learning is used instead. In contrast to supervised learning, semi-supervised learning involves direct mapping of given test image features to the estimated labels without the need to learn a decision rule. The benefits of texton representation and semi-supervised learning are highlighted on pilot plant data.