In the realm of information security, the nonlinearity of an S-Box is a pivotal attribute for ensuring its effectiveness. S-Boxes randomly generated with chaotic maps, however, often exhibit insufficient nonlinearity. To construct a robust S-Box with enhanced nonlinearity, we have developed a nondegenerate two-dimensional hyper chaotic map (2D-NDHCM). We rigorously evaluated its dynamic properties through bifurcation and phase diagrams, Lyapunov exponents, Kolmogorov entropy, correlation dimension, and randomness tests to assess the map’s resilience. Subsequently, we employed the 2D-NDHCM to devise a novel algorithm for constructing and optimizing a keyed strong S-Box, leveraging simulated annealing technique to achieve superior nonlinearity. Finally, We conducted performance analyses of the optimized S-Box using the classic six criteria, and the results confirmed the algorithm’s practicality and effectiveness.

Based on different carbon quota trading mechanisms, the price and emission reduction strategies of oligopoly manufacturers in the low-carbon market and the government carbon quota mechanism are considered. A dynamic game evolution model of the two oligopoly manufacturers with competitive relations is established. The stability of the equilibrium point of the game model, the price adjustment speed of the decision variable, the impact of carbon emission reduction investment, and the government carbon quota on the system are discussed. Through nonlinear dynamics research, it is found that the advantage of the grandfathering method is that it is conducive to maintaining market stability when the government’s carbon quota decision changes; the advantage of the benchmarking method is that when manufacturers formulate price adjustment strategies, the benchmarking method carbon quota mechanism has a stronger stability range for the market, the manufacturer’s profit price adjustment speed is positively correlated, and the government carbon quota decision and emission reduction investment are also positively correlated. Decision makers need to choose appropriate carbon quota mechanisms and manufacturers’ emission reduction strategies according to actual market changes to maintain supply chain stability.

In this study, based on a morpheme segmentation framework, we researched a text keyword extraction method for Uyghur, Kazakh and Kirghiz languages, which have similar grammatical and lexical structures. In these languages, affixes and a stem are joined together to form a word. A stem is a word particle with a notional meaning, while the affixes perform grammatical functions. Because of these derivative properties, the vocabularies used for these languages are huge. Therefore, pre-processing is a necessary step in NLP tasks for Uyghur, Kazakh and Kirghiz. Morpheme segmentation enabled us to remove the suffixes as the auxiliary unit while retaining the meaningful stem and it reduced the dimension of the feature space present in the keyword extraction task for Uyghur, Kazakh and Kirghiz texts. We transformed the morpheme segmentation task into the problem of labeling the morpheme sequences, and we used the Bi-LSTM network to bidirectionally obtain the position feature information of character sequences. We applied CRF to effectively learn the information of the preceding and following label sequences to build a highly accurate Bi-LSTM_CRF morpheme segmentation model, and we prepared morpheme-based experimental text sets by using this model. Subsequently, we used the stem vectors’ similarity to modify the TextRank algorithm, subsequent to the training of the stem embedding vector using the Doc2vec algorithm, and then we performed a text keyword extraction experiment. In this experiment, the highest F1 scores of 43.8%, 44% and 43.9% were obtained for three datasets. The experimental results show that the morpheme-based approach provides much better results than the word-based approach, which shows the stem vector similarity weighting is an efficient method for the text keyword extraction task, thus proving the efficiency of morpheme sequence for morphologically derivative languages.