A duality theorem for L-R crossed product

Abstract

In this work, the notion of an L-R crossed product is introduced as a unified approach for L-R smash product and crossed product. Then the duality theorem for L-R crossed product is given. As the applications of the main result, some classical results in some materials can be obtained.

Application of artificial neural networks to X‐ray fluorescence spectrum analysis

“…Find better M and k through multiple experiments. [20] Lu Wei combined the Ensemble Empirical Mode Decomposition (EEMD) and Deep Belief Network (DBN) for fluorescence spectroscopy to predict the germination rate of rice seeds, even in the case of less data and weak signals, the prediction accuracy is very high. [62] 3 | GENERALIZATION The generalization ability of a neural network refers to the ability of a trained neural network model to predict data that is not in its training sample.…”

“…In this review, we mainly demonstrated several kinds of typical ANN models (variants) to overcome the challenges in quantitative analysis applied in XRF, such as Self-improving Segmented Particle Swarm Optimization (SPSO) Adaptive Neural Network (SANN), Deep Sparse Auto-encoder Neural Network (DSAENN), Single Component Prediction Based On Backward Error Propagation (SCP-BEP), Multiple Component Prediction Based On Backward Error Propagation (MCP-BEP), Backward Propagation Network Model Based On Principal Component Analysis (PCA-BP), Genetic Algorithm Backward Propagation (GA-BP), Mind Evolutionary Algorithm Backward Propagation (MEA-BP), and Probabilistic Neural Network (PNN). [19][20][21][22][23][24] We did not discuss all available models in this field; instead, the focus of this review is on overfitting problem, generalization ability, and iteration efficiency. Representative samples are discussed in more details because of their reliability and applicability.…”