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The purpose of this paper is to examine the criteria of uniqueness of the equilibrium point and the new stability criteria for stability of the equilibrium point. The new stability condition is dependent on the size of delays.

The global asymptotic stability of a class of delayed bi‐directional associative memory (BAM) neural networks is studied. Some new sufficient conditions are presented for the unique equilibrium point and the global stability of BAM neural networks with time delays by constructing Lyapunov functions and using the linear matrix inequality. A numerical example is presented to illustrate the effectiveness of the theoretical results.

Based on the mathematical method and matrixes inequality skill, some criteria are obtained which contain the unique equilibrium point and the global stability of BAM neural networks.

The paper proposes the new Lyapunov function and new skill to compose matrixes inequality.

A very useful method for BAM neural network to judge the uniqueness of the equilibrium point and stability.

The new mathematical model is proposed about the production process, and the new control method is used in the temperature system for a double layers welded pipe in welding process.

Internet + and Electronic Business in China is a comprehensive resource that provides insight and analysis into E-commerce in China and how it has revolutionized and continues to revolutionize business and society. Split into four distinct sections, the book first lays out the theoretical foundations and fundamental concepts of E-Business before moving on to look at internet+ innovation models and their applications in different industries such as agriculture, finance and commerce. The book then provides a comprehensive analysis of E-business platforms and their applications in China before finishing with four comprehensive case studies of major E-business projects, providing readers with successful examples of implementing E-Business entrepreneurship projects.

Internet + and Electronic Business in China is a comprehensive resource that provides insights and analysis into how E-commerce has revolutionized and continues to revolutionize business and society in China.

The purpose of this paper is to summarize the advances in grey system theory research and various application achievements in science and engineering. At the same time, it commemorates the 40th anniversary of the birth of grey system theory and the 10th anniversary of Grey Systems–Theory and Application.

Firstly, the innovations of theoretical research in grey system theory were summarized and some of the widely recognized new results are briefly described. By searching and combing the research results of grey system theory in China national knowledge infrastructure (CNKI) database and Web of Science by Institute for Scientific Information (ISI), this paper shows the rapid development trend of grey system theory in the past 40 years, and the successful applications of grey system theory in the fields of social sciences, natural sciences and engineering technologies.

More than 227 thousands literature were found by input 10 phrases such as grey system, grey number and sequence operator etc. in CNKI database. After entering the new century, the number of grey system papers included in CNKI database is increasing rapidly. Since 2008, more than 10 thousands papers have been included per year and more than 15 thousands papers have been included per year since 2014. Grey system method and model are widely used in physics, chemistry, biology and other fields of natural science, as well as transportation, electric power, machinery and other fields of engineering technology, and a large number of valuable results have been achieved.

It can be seen that the grey system theory plays an important role in promoting China’s scientific and technological progress, innovation and development and high-level talent training from tens of thousands of literatures marked with important national science and technology projects and a large number of grey system literatures published by China’s double first-class universities and double first-class discipline construction universities.

Both innovations of theoretical research and practical application play important role in the growth of new theory. The innovations of theoretical research provide methods and tools for practical application, which is conducive to improve application efficiency and broaden application fields. A large number of practical applications needs have become the source of theoretical innovation and the solid background for the birth of theoretical innovation achievements.

The purpose of this paper is to attempt to establish the pattern of multi‐objective and multi‐dimensional grey fuzzy forecasting with feedback based on the theories of grey system and fuzzy recognition.

First, according to the given weights, the weighting integrated value of samples were computed. Second, the method of fuzzy recognition with single index was employed to calculate the fuzzy classification of the integrated value. According to the cause analysis, the fuzzy classification of the integrated value is used to compute the weights of indexes. In the same way, repeating the above processes, the weighting integrated value and fuzzy classification with given accuracy are retrieved at the same time. Finally, the authors calculate the correlation coefficient between the weighting integrated values and forecasting objects, according to the principle of maximal relativity, optimizing the weighting integrated value of samples, establishing the fuzzy forecasting pattern, and checking the model's precision. A numeric example is also computed in the last part of the paper.

The results are convincing: not only that the pattern of multi‐objective and multi‐dimensional grey fuzzy forecasting with feedback based is valid, but also the model's applied prediction accuracy is higher, where the test samples' mean forecast accuracy of groundwater dynamic levels is 96.50 percent.

The method exposed in the paper can be used to predict groundwater dynamic levels and even for other similar forecast problems.

The paper succeeds in realising both a prediction pattern and application of predicting groundwater dynamic levels by using the newest developed theories of grey system and fuzzy recognition.