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Research on self-supervised pre-training for recommender systems Jiyuan YANG,Muyang MA,Pengjie REN,Zhumin CHEN,Zhaochun REN,Xin XIN,Fei CAI,Jun MA JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (7): 1-26.   DOI: 10.6040/j.issn.1671-9352.1.2023.043 Abstract （1255）   HTML （7）    PDF（pc） （7266KB）（4899）       Save Plenty of recent studies explores the application of pre-training techniques within the context of recommendation scenarios and the design of pre-training tasks in order to enhance the overall performance of recommendation. This paper extensively reviews the progress in research of recommendation models based on pre-training, classifies and compares different pre-training methods, and conducts extensive experiments and analyses on some representative models using three benchmark datasets for recommendation systems. The datasets and codes have been made open source. Finally, we summarize and prospect the future development trend of recommendation models based on pre-training. Table and Figures | Reference | Related Articles | Metrics

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Dimensionality reduction and retrieval algorithms for high dimensional data Wei SHAO,Gaoyu ZHU,Lei YU,Jiafeng GUO JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (7): 27-43.   DOI: 10.6040/j.issn.1671-9352.1.2023.062 Abstract （1318）   HTML （21）    PDF（pc） （1007KB）（3922）       Save At present, most studies use some dimensionality reduction methods to convert high-dimensional vectors into low-dimensional vector representations, and then apply related vector retrieval optimization technology to achieve fast similarity retrieval, thereby improving the application performance of large models. Currently, there are many and scattered dimensionality reduction methods for high-dimensional data, and the dimensionality reduction methods used in different research backgrounds are different. Similarly, there are also many different retrieval ideas and optimization methods in vector retrieval technology. By reviewing the main ideas and optimization methods of recent dimensionality reduction and retrieval algorithms, this paper helps to generate inspiring connections between the two and support the development and in-depth research of subsequent high-dimensional vector retrieval optimization algorithms. Table and Figures | Reference | Related Articles | Metrics

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Research progress on fabrication and application of self-healing superhydrophobic materials WANG Yutao, LIAN Yuechang, ZHAO Shengyuan, LIU Wendong JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2025, 60 (10): 59-78.   DOI: 10.6040/j.issn.1671-9352.0.2025.155 Abstract （480）      PDF（pc） （20350KB）（2032）       Save Superhydrophobic materials have been widely applied in anti-fouling, oil-water separation, and fluid manipulation due to their excellent liquid repellency. As a result of the synergistic effect between surface micro/nano structures and low surface energy substances, the surface wettability of superhydrophobic materials is highly susceptible to physical damage, UV irradiation, chemical corrosion, etc., which significantly limits their practical applications. Therefore, developing durable superhydrophobic materials is desirable. In the past decade, researchers have extended the service life of superhydrophobic materials by endowing them with self-healing properties, which not only enhances their practical performance but also broadens the application fields. In this review, an overview of the recent development of self-healing superhydrophobic materials focusing on fabrication strategies and possible applications is provided. Finally, an outlook on the future fabrication direction and application of self-healing superhydrophobic materials is presented. Reference | Related Articles | Metrics

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Category-wise knowledge probers for representation learning of graph neural networks Xingyu HUANG,Mingyu ZHAO,Ziyu LYU JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (7): 85-94.   DOI: 10.6040/j.issn.1671-9352.1.2023.064 Abstract （600）   HTML （2）    PDF（pc） （3615KB）（1696）       Save In order to solve the problem that the graph neural network model lacks corresponding probes, a knowledge detection framework for graph neural network representation learning is proposed, and two kinds of class-aware knowledge probes are designed based on the category attributes of data in different domains, namely clustering probes and contrastive clustering probes. The two probe the characterization effect of different models and give corresponding scores. On 8 datasets in 3 neighborhoods, including reference networks, social networks and biological networks, the representation learning of 7 classical graph neural network models realizes systematic knowledge detection and evaluation experiments, and summarizes the detection and evaluation conclusions. Table and Figures | Reference | Related Articles | Metrics

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Creditrisk assessment based on Logistic regression and credit strategy optimization modeling of small and medium-sized enterprises Zhongfeng QU,Honghua WU,Fanjun LI JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (8): 94-102.   DOI: 10.6040/j.issn.1671-9352.0.2023.206 Abstract （1409）   HTML （11）    PDF（pc） （1260KB）（1546）       Save In order to facilitate banks to assess the credit risk of small and medium-sized enterprises, and formulate the optimal credit strategy, an indicator system composed of four primary risk assessment indicators, namely, business income ability, profitability, customer stability, and transaction vitality, is constructed by using the bank flow information of enterprises with upstream and downstream partners. The enterprise credit risk is predicted based on Logistic regression, and compares it with error back-propagation neural network. Combining the probability of default and the retention rate under different interest rates, taking the maximum expected return of banks on small and medium-sized enterprises as the objective function, the credit strategy optimization model is established. In order to verify the effectiveness of the model, the credit risk assessment and credit strategy optimization models are empirically analyzed. The results indicate that Logistic regression has high accuracy and recall, and the area under the curve of receiver operating characteristic reaches 0.964, which is suitable for credit risk prediction and assessment of small and medium-sized enterprises. The credit strategy optimization model can determine the loan amount and loan interest rate of each lending enterprise, and maximize the expected return of the bank. Table and Figures | Reference | Related Articles | Metrics

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Staining methods on arbuscular mycorrhizal fungi in Lycium barbarum roots and the relationship between colonization rate and soil factors Mu YANG,Shenglian JI,Huan GUO,Guozhen DUAN,Guanghui FAN,Jianling LI,Zhanlin WANG JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (11): 40-50.   DOI: 10.6040/j.issn.1671-9352.0.2023.488 Abstract （872）   HTML （41）    PDF（pc） （7023KB）（1485）       Save Understanding the infection and colonization of arbuscular mycorrhizal fungi (AMF) is the basis for mobilizing indigenous AMF to improve plant resistance. Lycium barbarum in nine fields of the Qaidam Basin were the subject. Based on the basic staining method of AMF, previous studies were optimised to investigate the main factors influencing the observation of AMF on the roots of perennial field-grown L.barbarum. The influence of different regions, soil pH, soil physicochemical properties and the colonization rate of AMF on L.barbarum were also compared. The results showed that the optimal observation effect of AMF colonization rate on the roots of Perennial field-grown L.barbarum in the Qaidam Basin was achieved by the following steps. First, the fixed root segments were placed in a 10% KOH 90 ℃ for 90 min, then in the boiling alkaline peroxide (3 mL NaOH+30 mL 10% H2O2+H2O to 600 mL) for 15-20 min, followed by 5 min of H2O2 bleaching, 5 min of lactic acidification, 5 min of acetone ink staining and 30 min of lactic acid glycerol 90 ℃ decolourisation. This method can clearly observe the structures of vesicles and hyphae in the roots of perennial field-grown L.barbarum. The average AMF colonization rate of perennial field-grown L.barbarum in the Qaidam Basin was about 41.32%. RDA analysis showed that the AMF colonization rate in L.barbarum roots was mainly affected by factors such as soil pH, available phosphorous content(xAP), and available potassium content(xAK), among which the soil pH showed a significant positive correlation with the AMF colonization rate, while xAP and xAK showed a significant negative correlation with the colonization rate. Table and Figures | Reference | Related Articles | Metrics

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A prompt learning approach for telecom network fraud case classification Jie JI,Chengjie SUN,Lili SHAN,Boyue SHANG,Lei LIN JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (7): 113-121.   DOI: 10.6040/j.issn.1671-9352.1.2023.040 Abstract （1432）   HTML （17）    PDF（pc） （3845KB）（1286）       Save For the automatic classification technology of telecom fraud cases, a classification system of telecom network fraud based on situational analysis is formulated, the privacy protection method of case text de-identification is realized, and accuracy and F1-score of a classification method of telecom network fraud cases based on prompt learning is proposed. The experimental results show that the method is on average 1 to 2 percentage points higher than the BERT-based classification method on the data set constructed in the paper. Table and Figures | Reference | Related Articles | Metrics

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Comprehensive credit evaluation of transportation enterprises based on game theory combinatorial weighting-TOPSIS method Antao LYU,Yongbin GAO,Wen HAN,Ying DONG,Zhenfang ZHONG,Qingchun MENG JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (9): 88-97.   DOI: 10.6040/j.issn.1671-9352.0.2023.153 Abstract （665）   HTML （13）    PDF（pc） （1970KB）（1040）       Save Firstly, the index system of comprehensive credit evaluation of transportation enterprises is constructed from four aspects: basic information, reward recognition, reputation assessment and administrative penalty. Secondly, the weights of each index are obtained by using game theory combination assignment method, and the comprehensive credit evaluation model of enterprises by game theory combination assignment-TOPSIS method is constructed. Finally, the data of transportation enterprises in Shandong Province are used for experimental analysis to obtain the credit evaluation results. The study shows that: the weighting of each first-level index is ranked as administrative penalty, award recognition, reputation assessment, basic information, indicating that the relevant departments should focus on assessing the administrative punishment index of enterprises; the credit evaluation results are consistent with the actual, which verifies the rationality of the evaluation model. Table and Figures | Reference | Related Articles | Metrics

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Noise network alignment method integrating multiple features Ning XIAN,Yixing FAN,Tao LIAN,Jiafeng GUO JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (7): 64-75.   DOI: 10.6040/j.issn.1671-9352.1.2023.102 Abstract （563）   HTML （4）    PDF（pc） （1975KB）（797）       Save A multi-round iterative network alignment method is proposed to address the challenges of large structural differences and high noise sensitivity in anchor nodes in network alignment tasks. The method calculates node features of different dimensions using various heuristic approaches at each iteration, utilizing the combination of multiple features to assess the reliability of anchor nodes, filter potential noise, and enhance the confidence of each alignment round. Additionally, a graph neural network is employed to improve the consistency between nodes without attributes, mitigating the impact of structural differences in networks. Experimental results demonstrate that this method achieves high accuracy under high noise conditions, verifying its effectiveness. Table and Figures | Reference | Related Articles | Metrics

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A document-level event extraction method based on core arguments Chengjie SUN,Zongwei LI,Lili SHAN,Lei LIN JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (7): 53-63.   DOI: 10.6040/j.issn.1671-9352.1.2023.080 Abstract （820）   HTML （2）    PDF（pc） （3665KB）（735）       Save A document-level event extraction method based on core arguments(CA-DocEE) is proposed, which defines criteria for selecting core arguments based on their distributions in document-level events, uses heterogeneous graph convolutional neural networks to augment document contextual information for encoding argument entities, and captures deep semantic information in sentences based on machine reading comprehension methods for classifying the role of arguments. On the document-level event extraction dataset, the method proposed in this paper achieves a micro-average F1 value of 80.1%, which is comparable with the state-of-the-art methods. Table and Figures | Reference | Related Articles | Metrics

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Differential game in supply chain of innovative products with double regrets of consumers Yi ZHU,Zhenwei LIU JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (9): 56-63.   DOI: 10.6040/j.issn.1671-9352.0.2023.174 Abstract （565）   HTML （12）    PDF（pc） （3317KB）（730）       Save In the context of a long-term dynamic environment, this study investigates the impact of consumer regret behavior after purchasing innovative durable products on a manufacturer-led secondary dynamic supply chain. By establishing a differential game model and solving Hamilton equation, the optimal path for manufacturers' wholesale prices and retailers' retail prices in the supply chain is obtained. Through numerical simulation, the data changes are presented in the form of images to further analyze the impact of consumer purchase regret behavior on various decision variables in the supply chain. The results show that consumer purchase regret can lead to a decrease in sales of innovative durable products in the supply chain, and the long-term profits of manufacturers and retailers also decrease accordingly. But as the time for innovative durable products to enter the market increases, the sales volume of the products and the long-term profits of manufacturers and retailers also increase. In addition, when the proportion of consumer regret behavior is relatively small and the product market investment time is relatively long, the long-term profits of retailers will experience a bifurcation phenomenon. Therefore, when the proportion of purchase regret behavior is low, extending the product's market investment time can significantly increase the profit of this innovative durable product. Table and Figures | Reference | Related Articles | Metrics

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Probability distribution optimization model for learning to rank Fengxu ZHAO,Jian WANG,Yuan LIN,Hongfei LIN JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (7): 95-104.   DOI: 10.6040/j.issn.1671-9352.1.2023.026 Abstract （591）   HTML （4）    PDF（pc） （1775KB）（719）       Save Existing learning to rank (LTR) models rely on the scores output by models to represent the partial order among documents. Considering the limitation of treating scores as deterministic values, this paper proposes a probability distribution optimization method for the LTR model, which introduces the uncertainty of the ranking score. It smooths the scores in the form of probability distributions, thereby transforming the comparison of ranking scores into the probability estimation of score partial orders. The proposed method is applied to LTR models such as RankNet, LambdaRank, and LambdaMART. It effectively bridges the gap between the modeled probability and the target probability, leading to optimization of the LTR models. The paper conducts experiments on multiple large-scale real datasets, and the experimental results show that the optimized models outperform the original ones, which validates the effectiveness of the proposed method. Table and Figures | Reference | Related Articles | Metrics

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Factual error detection in knowledge graphs based on dynamic neighbor selection Liang GUI,Yao XU,Shizhu HE,Yuanzhe ZHANG,Kang LIU,Jun ZHAO JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (7): 76-84.   DOI: 10.6040/j.issn.1671-9352.1.2023.097 Abstract （902）   HTML （5）    PDF（pc） （1844KB）（688）       Save The construction and updating of the knowledge graph(KG) usually depend on a wide range of web data and automated methods, inevitably resulting in factual inaccuracies in the modeled and acquired knowledge. To tackle this problem, a novelapproach for identifying factual inaccuracies within the knowledge graph is proposed. This method actively selects adjacent nodes of the facts to be checked, detecting errors by measuring the intricate associations linking the head and tail entities. More specifically, it first utilizes graph structure information to identify potential neighbors for each entity. Then, based on contextual information, it dynamically selects relevant neighbors and uses an efficient graph attention network to encode node features. Finally, by calculating the consistency of head and tail entity representations, it determines if the fact under consideration is erroneous. Experimental results on multiple public KG datasets demonstrate that this method outperforms existing approaches in error detection. Table and Figures | Reference | Related Articles | Metrics

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On w-FPn-projective modules Jie WANG,Wenjing CHEN JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (6): 64-70.   DOI: 10.6040/j.issn.1671-9352.0.2022.650 Abstract （485）   HTML （2）    PDF（pc） （740KB）（679）       Save Let n≥1 be an integer or n=∞. The definitions of w-FPn-projective modules and w-FPn-projective dimensions of modules are introduced, and their properties are studied. At the same time, some properties of w-FPn-projective modules over n-coherent rings are discussed. Reference | Related Articles | Metrics

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Analysis of correlation and evolutionary of risk sources in aviation industry based on risk disclosure data of listed companies Chang XU,Yuqiao HUI,Wen HAN,Mengdi CAO,Zhenfang ZHONG,Qingchun MENG JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (9): 79-87, 118.   DOI: 10.6040/j.issn.1671-9352.0.2023.421 Abstract （681）   HTML （11）    PDF（pc） （2586KB）（677）       Save This study analyzes the risk sources disclosed by passenger airlines, airport service companies and air logistics companies based on the risk identification results of 255 listed companies in the aviation industry from 2005 to 2022 obtained by LDA method. The results of the study show that: in terms of risk correlation, there is a certain inner correlation between the risk sources of different sub-industries, and this correlation is closely related to the business attributes of the industry, and the risk correlation between the passenger airline industry and the air transportation logistics industry is higher, which suggests that there is a common risk or a similar risk characteristic between, and the results obtained by word covariance indicate that cost risk and operational risk have the highest degree of correlation with the other types of risk; and in terms of risk evolution. The five types of risks, including reputation risk, have increased, while the other three types of risks, such as stock volatility risk, have shown a decreasing trend, and the exponential smoothing method predicts that the total risk size of the passenger aviation industry and the air logistics industry in the future are both showing an increasing trend, and the airport service industry has shown a decreasing trend while the passenger aviation industry has the fastest rising trend. Table and Figures | Reference | Related Articles | Metrics

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Number of homomorphisms between finitely generated Abelian groups and finite groups Yanxia LI,Jinke HAI JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (6): 103-107.   DOI: 10.6040/j.issn.1671-9352.0.2022.627 Abstract （685）   HTML （3）    PDF（pc） （617KB）（658）       Save Let $G$ be a finite group, and $F=F_{r} \times A$ be a finitely generated Abelian group, where $A$ is finite and $F_{r}$ is a free Abelian group of rank $r$. It is proved that the number of homomorphisms from $F$ to $G$ is a multiple of $|A|$ and $|G|$ greatest common divisor. The results generalize the famous T.Yoshdia theorem. Reference | Related Articles | Metrics

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Competitive strategies among supply chains considering tariff and local identity of consumers Mingwu LIU,Ling GUO,Yue YAN,Shuoming DU JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (9): 18-32.   DOI: 10.6040/j.issn.1671-9352.0.2023.315 Abstract （667）   HTML （11）    PDF（pc） （5262KB）（624）       Save Considering the factors of tariff and local identity of consumers, a competitive game model of two supply chains with two manufacturers as Stackelberg leaders is constructed, studies the optimal pricing strategies of two competitive supply chains are studied, and the influence of tariff and local identity of consumers on the profit elasticity of supply chains is analyzed. The results show that: (1) with the increase of tariffs, the wholesale price of domestic manufacturers decreases, while the sales price of retailer 1, the wholesale price of foreign manufacturers and the sales price of retailer 2 increase; with the enhancement of consumers' awareness of local identity, the pricing of each member of the two chains increases, and when consumers' awareness of local identity is weak, product A has more price advantage than product B. (2) With the increase of tariffs, the profits of domestic manufacturers and retailers 1 decrease, while the profits of foreign manufacturers and retailers 2 increase, and the impact of tariff changes on consumer surplus is related to the strength of consumers' local identity consciousness; with the enhancement of consumers' awareness of local identity, the profits of each member of the two chains increase, and the impact of changes in consumers' awareness of local identity on consumer surplus is related to the level of tariff rate. (3) When the local identity consciousness is weak (the tariff rate is low), the profit elasticity of multinational supply chain members is greater than that of foreign local supply chain members, that is, the profits of multinational supply chain members are more sensitive to the change of tariff rate (local identity consciousness); properly enhancing consumers' local identity can slightly slow down the losses caused by the rising tariff rate to the members of transnational supply chains, without causing damage to foreign local supply chains themselves. Table and Figures | Reference | Related Articles | Metrics

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Construction of evaluation index system of university literature resources Hong XIAO,Zhen GAO JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (9): 119-126.   DOI: 10.6040/j.issn.1671-9352.0.2024.264 Abstract （834）   HTML （16）    PDF（pc） （1875KB）（615）       Save By clarifying the current status of literature resource evaluation systems in domestic and foreign libraries, and combining with the actual needs of university libraries, the analytic hierarchy process (AHP) is used for weight allocation to achieve quantitative evaluation methods, improve the speed of literature resource updates, expand coverage, and more efficiently allocate resources, a literature resource evaluation system that adapts to the needs of the "Four New" disciplines is constructed. Table and Figures | Reference | Related Articles | Metrics

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Block triangular splitting and its preconditioning iterative algorithms for a class of complex symmetric linear systems Yang WANG JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (10): 1-9.   DOI: 10.6040/j.issn.1671-9352.0.2023.225 Abstract （689）   HTML （13）    PDF（pc） （1013KB）（593）       Save Based on block triangular splitting for block 2×2 matrix, the block triangular splitting(BTS) iteration method and the preconditioned block triangular splitting (PBTS) iteration method for a class of complex symmetric linear system are proposed. Theoretical analysis shows that the BTS and PBTS methods converge under certain conditions. The optimal iteration parameters of these two methods are obtained. Numerical experiments demonstrate the effectiveness and superiority of the BTS method and the PBTS iterative methods. Table and Figures | Reference | Related Articles | Metrics

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Matrix product operator based sequential recommendation model Peiyu LIU,Bowen YAO,Zefeng GAO,Wayne Xin ZHAO JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (7): 44-52, 104.   DOI: 10.6040/j.issn.1671-9352.1.2023.042 Abstract （600）   HTML （4）    PDF（pc） （930KB）（578）       Save The task of sequential recommendation confronts challenges characterized by high complexity and substantial diversity. The paradigm of pre-training and fine-tuning is extensively employed for learning item representations based on sequential data in recommendation scenarios. However, prevalent approaches tend to disregard the potential underfitting and overfitting issues that may arise during model fine-tuning in new domains. To address this concern, a novel neural network architecture grounded in the framework of matrix product operator (MPO) is introduced, and two versatile fine-tuning strategies are presented. Firstly, a lightweight fine-tuning approach that involves updating only a subset of parameters is proposed to effectively mitigate the problem of overfitting during the fine-tuning process. Secondly, an over-parameterization fine-tuning strategy is introduced by augmenting the number of trainable parameters, robustly addressing the issue of underfitting during fine-tuning. Through extensive experimentation on well-established open-source datasets, the efficacy of the proposed approach is demonstrated by achieving performance achievements. This serves as a compelling testament to the effectiveness of the proposed approach in addressing the challenge of general item representation in recommendation systems. Table and Figures | Reference | Related Articles | Metrics

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n-copure Gorenstein AC modules Nana GAO,Gang YANG JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (6): 71-75,90.   DOI: 10.6040/j.issn.1671-9352.0.2022.652 Abstract （488）   HTML （2）    PDF（pc） （671KB）（578）       Save Let R be a ring, n a fixed nonnegative integer and $\mathscr{G} \mathscr{I}_n$ (resp., $\mathscr{G} \mathscr{F}_n$) the class of all left (resp., right) R-modules of Gorenstein AC injective (resp., Gorenstein AC flat) dimension at most n. A left R-module M (resp., right R-module M) is called n-copure Gorenstein AC injective (resp., n-copure Gorenstein AC flat) if ExtR1 (N, M)=0 (resp., Tor1R (M, N)=0) for any N ∈ $\mathscr{G} \mathscr{I}_n$. It is proven that a finitely presented right R-module M is n-copure Gorenstein AC flat if and only if M is a cokernel of a $\mathscr{G} \mathscr{F}_n$- preenvelope K→F of a right R-module K with F flat. Reference | Related Articles | Metrics

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Vertex reducible edge coloring of the Lexicographic product of graphs Fei LEI,Fei WEN,Zepeng LI,Muchun LI JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (10): 107-114.   DOI: 10.6040/j.issn.1671-9352.0.2023.032 Abstract （597）   HTML （13）    PDF（pc） （1511KB）（572）       Save Let $f: E(G) \rightarrow\{1, 2, \cdots, k\}$ be a non-proper k-edge coloring of G, and 1≤k≤Δ. If for any two adjacent vertices u, v ∈ V(G) with d(u)=d(v) satisfy C(u)=C(v), f is called a k-vertex-reducible edge coloring, where C(u) denotes the set of colors of edges incident with u. The maximum positive integer k is called vertex-reducible edge chromatic number of G. According to the characters of the lexicographic product graphs, we apply combinatorial analysis to give a lower bound of the vertex reducible edge chromatic number of the lexicographic product G[H] for simple graphs G and H. As applications, the vertex-reducible edge chromatic numbers of $K_{n}\left[\overline{K_{2 m}}\right], K_{n}[H]$ and Pn[H] are obtained. Table and Figures | Reference | Related Articles | Metrics

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Chinese disease text classification model driven by medical knowledge Chao LI,Wei LIAO JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (7): 122-130.   DOI: 10.6040/j.issn.1671-9352.0.2023.291 Abstract （963）   HTML （7）    PDF（pc） （3349KB）（566）       Save This study proposes a Chinese disease text classification model that integrates knowledge graph. Firstly, by introducing structured knowledge from external medical knowledge graph, a knowledge enhanced disease text vector representation is obtained; Secondly, the global semantic features and local semantic features of the disease text are extracted by using bidirectional long short-term memory network and convolutional neural network respectively. At the same time, the joint attention mechanism improves the efficiency of the model in extracting effective features information; Finally, the extracted features are concatenated and fused, and a classifier is used to output the classification result. The experimental results on the Chinese disease text dataset show that the proposed model has a classification accuracy, recall, and the harmonic mean value F1 of 95.21%, 95.64%, and 95.42%, respectively, which shows better classification performance compared to other models. Table and Figures | Reference | Related Articles | Metrics

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A note on fractional S-acts Xingliang LIANG,Yuhang LI JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (8): 1-8.   DOI: 10.6040/j.issn.1671-9352.0.2023.362 Abstract （745）   HTML （11）    PDF（pc） （460KB）（565）       Save Let S be a commutative monoid, in the category of S-acts, by the injectivity and surjectivity of the mapping of pullback diagrams, a new proof that fractional functors (the category of S-acts to the category of fractional S-acts) preserve flatness properties is given. The relationship between fractional functors and directed colimits is investigated. A sufficient condition for fractional S-acts having a cover is presented. Table and Figures | Reference | Related Articles | Metrics

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Sufficient maximum principle for one kind of nonzero-sum stochastic differential game involving noisy memory Feng ZHANG,Jiawei LIANG JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (10): 46-52.   DOI: 10.6040/j.issn.1671-9352.0.2023.281 Abstract （748）   HTML （14）    PDF（pc） （718KB）（546）       Save One nonzero-sum stochastic differential game is considered, whose main feature is that several kinds of delays of the state and the control are involved. The state process can contain distributed delays, discrete delays, and noisy memory, and control processes can contain distributed delays and discrete delays. The control domains are convex sets. Sufficient conditions for the equilibrium point of the game are established by means of the stochastic maximum principle. Finally, an illustrative example is considered for which the equilibrium point is obtained in explicit form. Reference | Related Articles | Metrics

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An ultra-weak discontinuous Galerkin method for drift-diffusion model of semiconductor problem Lulu AI,Yunxian LIU JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (10): 10-21.   DOI: 10.6040/j.issn.1671-9352.0.2023.089 Abstract （827）   HTML （15）    PDF（pc） （2625KB）（544）       Save An ultra-weak discontinuous Galerkin (UWDG) method is developed for the drift-diffusion model of the semiconductor problem with the error analysis. The UWDG method has the advantage of the classical discontinuous Galerkin (DG) method. Compared to the local discontinuous Galerkin method, this method can solve partial differential equations with higher-order spatial derivatives without introducing auxiliary variables, which is simpler in scheme and more direct in calculation. The main technical difficulty is to select the appropriate projection for error analysis. A numerical simulation is performed to validate the numerical stability of the UWDG method. Table and Figures | Reference | Related Articles | Metrics

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Linear arboricity in graphs of low treewidth Hongyu CHEN JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (6): 25-28, 35.   DOI: 10.6040/j.issn.1671-9352.0.2023.109 Abstract （540）   HTML （3）    PDF（pc） （626KB）（537）       Save Let G=(V, E) be a graph, a map φ from E(G) to {1, 2, …, t} is called a t-linear coloring if the induced subgraph of edges having the same color α is a linear forest for 1≤α≤t. The linear arboricity la(G) is the minimum number t over all t-linear coloring of G. In this paper, we determine $\operatorname{la}(G)=\left\lceil\frac{\Delta}{2}\right\rceil$ for graphs with maximum degree Δ and treewidth at most $\frac{\Delta+1}{4}$. Reference | Related Articles | Metrics

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Spectra of product operation signed graphs Ziqiang FANG,Longjie LI,Haizhen REN JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (10): 101-106.   DOI: 10.6040/j.issn.1671-9352.0.2023.048 Abstract （576）   HTML （12）    PDF（pc） （684KB）（530）       Save A graph whose edges are labeled either as positive or negative is called a signed graph. The product operations, i.e. symmetric product, direct product, semi-strong product and strong product, of signed graphs are given, respectively. The adjacency matrices of these product operation signed graphs in tensor form are obtained, and some relations on the eigenvalues of signed graphs on product operations (direct product, semi-strong product, strong product) are also formulated. Reference | Related Articles | Metrics

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Differential quadrature method for solving the generalized Burgers-Fisher equations ALI Adil,RAHMAN Kaysar JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (10): 30-39.   DOI: 10.6040/j.issn.1671-9352.0.2023.112 Abstract （655）   HTML （14）    PDF（pc） （2761KB）（525）       Save In this paper, a high accuracy numerical scheme is constructed for the generalized Burgers-Fisher equation with Dirichlet boundary or Neumann boundary conditions. Firstly, the Lagrange interpolation polynomial differential quadrature method with uniform grid and Chebyshev-Gauss-Lobatto grid is used in space, and the third-order strong stability-preserving Runge-Kutta scheme is used in time. Secondly, the stability of the scheme is analyzed by using the matrix method. Finally, two numerical examples with different boundary conditions are calculated, and the results are compared with other numerical methods to verify the effectiveness of the proposed scheme. Table and Figures | Reference | Related Articles | Metrics

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An efficient outlier detection method based on multi-factor fusion Zhiqiang YANG,Shan FENG,Yi YIN,Huijia WU JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (8): 118-126.   DOI: 10.6040/j.issn.1671-9352.0.2023.250 Abstract （617）   HTML （6）    PDF（pc） （937KB）（516）       Save Based on granularity characteristics of relative ratio of object neighborhood and importance of objects in neighborhood rough sets, an improved outlier detection method (neighborhood rough entropy-based outlier, NREOD) based on neighborhood rough entropy and multi-factor fusion is proposed. Comparison experiments on standard data sets in University of CaliforniaIrvine (UCI) databases show that the NREOD algorithm has a lower false positive rate for outlier detection in different types of data sets, and has better adaptability and effectiveness. This algorithm provides a new effective way for the research and application of outlier detection in mixed attribute data sets. Table and Figures | Reference | Related Articles | Metrics

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Sub-Z-Quantales and their properties Ling WANG,Bin ZHAO JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (6): 76-83.   DOI: 10.6040/j.issn.1671-9352.0.2022.491 Abstract （556）   HTML （2）    PDF（pc） （714KB）（515）       Save Firstly, the concept of the sub-Z-Quantales is introduced and some properties of sub-Z-Quantales are studied. In particular, the binary operation ⊙ on the set of all sub-Z-Quantales of a unital Z-Quantale containing the identity element is constructed such that the set is a Quantale. Secondly, the definition of join sub-Z-Quantales is given, and it is proved that every join sub-Z-Quantale of a Z-Quantale with a maximum (minimum) element has a maximum (minimum) element. Finally, the concept of conuclei on Z-Quantales is introduced, and it is proved that the join sub-Z-Quantales and conuclei on a Z-Quantale are one-to-one correspondence. Table and Figures | Reference | Related Articles | Metrics

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Sombor index on four operation graphs Yinzhen MEI,Huifeng FU JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (6): 56-63.   DOI: 10.6040/j.issn.1671-9352.0.2023.042 Abstract （713）   HTML （3）    PDF（pc） （732KB）（511）       Save Let G be a simple graph, E(G) be the edge set of G, and, du, dv be the degree of vertex u, v, respectively. In this paper, we focuse on the definition of F- sum of graphs combined with four transformation operations S(G), R(G), Q(G), T(G) and Cartesian product of two graphs, and calculate the upper bound of the Sombor index of the four kinds of related graphs by using the maximum degree and classification, and characterize their extreme values. Table and Figures | Reference | Related Articles | Metrics

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Financing models of low-carbon supply chain under capital constraints and cross-shareholding Yuyan WANG,Yulin SUN,Fei LIN JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (9): 64-78.   DOI: 10.6040/j.issn.1671-9352.0.2023.102 Abstract （699）   HTML （15）    PDF（pc） （1630KB）（510）       Save This paper explores the issue of supplier-led supply chain financing decisions in a low-carbon and cross-holding environment. Considering cross-shareholding, this paper studies the supply chain composed of a well-funded supplier and a capital-constrained manufacturer. Three models of non-financing, bank financing, and trade credit financing are constructed respectively. On this basis, the financing models that the manufacturer preferred and the supplier preferred are given. Also, the impacts of the cross-shareholding ratio and consumers' environmental awareness on the economic performance and emission-reduction level are discussed. The conclusions are as follows. Trade credit financing can achieve a win-win situation of reducing emissions and easing capital constraints. However, the capital-constrained manufacturer will always choose bank financing for a higher profit, and the manufacturer increasing shareholdings in the supplier enhances its preference for bank financing. The supplier prefers the manufacturer to choose trade credit financing and is always willing to provide trade credits. Under the trade credit financing model, the manufacturer will not gain more decision power even if it has more shareholdings in the supplier. Under the bank financing model, the manufacturer increasing shareholdings in the supplier can narrow the profit gap and alleviate the unfair profit distribution. The supplier increasing shareholdings in the manufacturer will increase the supplier's profit, but will not always increase the manufacturer's profit. Table and Figures | Reference | Related Articles | Metrics

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Key preparation processes and applications of arabinoxylan Guang CHEN,Jiangtao LYU,Xueliang QIU,Libing DING,Yichen CAI,Yue CHEN,Zhenxue LIU,Lushan WANG JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (11): 20-30.   DOI: 10.6040/j.issn.1671-9352.0.2023.481 Abstract （1008）   HTML （41）    PDF（pc） （7133KB）（509）       Save Arabinoxylan (AX) was an important component of hemicellulose in plant cell walls, which wa s found in grains such as corn, wheat, barley and rice. AX not only had antioxidant, prebiotic potential, and immunomodulatory activity but also had water retention, biocompatibility, and mechanical properties. At the same time, it could be converted into clean energy. Therefore, it was widely used in food, medical, industrial, and other fields. The biological activity of AX was closely related to its chemical structure. The fine structures and the functional properties of AX depended on different cereal sources and different extraction methods. In this paper, we summarized several aspects of AX, which contained the structural characteristics, biological activities, serval methods of extraction and purification from various raw materials, and the application. Table and Figures | Reference | Related Articles | Metrics

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Sharp constant for reverse fractional Hardy inequality on higher-dimensional product spaces Xiaoyu LIU,Mingquan WEI,Pengchao SONG JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (8): 20-27.   DOI: 10.6040/j.issn.1671-9352.0.2023.331 Abstract （507）   HTML （6）    PDF（pc） （390KB）（505）       Save The conditions for the validity of the reverse fractional Hardy inequality in power-weighted Lebesgue spaces are studied, and the sharp constant for the inequality is given. Reference | Related Articles | Metrics

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A method of online teaching platform selection based on online reviews Xia LIANG,Jie GUO JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (9): 108-118.   DOI: 10.6040/j.issn.1671-9352.0.2023.334 Abstract （720）   HTML （13）    PDF（pc） （959KB）（498）       Save To better select online teaching platforms, give college students a better online course learning experience, and provide a reference for future online education and teaching, a method for selecting online teaching platforms based on online reviews is proposed. Firstly, user reviews from alternative online teaching platforms are collected by the crawler technology, and NLPIR-ICTCLAS Chinese word separation system is used to separate online words. Next, attribute word extraction is conducted using TF-IDF algorithm, along with a method that was manually selected to obtain the attribute set. The weights of attributes are determined using the mean square deviation method. Subsequently, sentiment analysis is carried out on the online reviews, with user emotional orientations represented as probability distributions regarding the evaluation scale. On this basis, the extended VIKOR method is used to select the optimal online teaching platform. Finally, the feasibility of the method proposed in this paper is demonstrated through an example and comparative analysis. Table and Figures | Reference | Related Articles | Metrics

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Combinatorial properties and algebraic characterization of the strict mono-affix languages Jing TIAN,Jiahao GONG JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (6): 91-97, 107.   DOI: 10.6040/j.issn.1671-9352.0.2023.044 Abstract （521）   HTML （2）    PDF（pc） （686KB）（495）       Save A class of mono-affix languages is the union of the strict prefix language class and strict suffix language class on a finite alphabet Σ, whose element can be described as an independent set of some partial order over Σ+. Equipping two binary operations, the class of mono-affix languages forms a semiring, which is a model of free object for an ai-semiring class. Table and Figures | Reference | Related Articles | Metrics

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Identification of nonlinear heat transfer law of heat conduction equation Le DU,Liu YANG,Tao ZHANG JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (8): 56-66.   DOI: 10.6040/j.issn.1671-9352.0.2023.232 Abstract （664）   HTML （5）    PDF（pc） （468KB）（491）       Save The identification of temperature-dependent heat transfer coefficients in heat conduction equations by boundary control is considered. Based on the optimal control theory, the general heat conduction equation parameter inversion problem is transformed into a variational problem, and then the existence and necessary conditions of the minimum value are discussed. Finally, by using the energy norm estimation method, the uniqueness and stability of the minimum value are proved under the assumption that the terminal time is small. Reference | Related Articles | Metrics

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Online and offline supply chain coordination with competition and cooperation considering product quality and bilateral service level Wenbing SHUI,Dongmin ZHOU,Shaomei GUO JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (9): 33-41, 55.   DOI: 10.6040/j.issn.1671-9352.0.2022.620 Abstract （630）   HTML （12）    PDF（pc） （939KB）（491）       Save Aiming at the supply chain coordination issues that the demand is affected by product quality, platform service level, service of team leaders, and the competition and cooperation relationship between the platform and team leaders, the supply chain decision-making models of centralized decision-making, decentralized decision-making, and coordination contracts are respectively built. The traditional cost sharing contract, two-part pricing contract, and "revenue sharing+commission" hybrid contract are designed. This paper explored the impact of product quality and bilateral service levels on the profits and optimal decisions of members before and after coordination in a competitive and cooperative supply chain. The results show that the two-part pricing contract and the "revenue sharing+commission" hybrid contract can effectively coordinate competing supply chains compared to traditional cost sharing contracts; the increase of consumers' preference for product quality and bilateral services contributes to expand the market demand for products, and improves the profits of the overall members of the competitive and cooperative supply chain under coordination. Table and Figures | Reference | Related Articles | Metrics

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Good congruences on r-wide semigroups whose idempotents form normal band Chunmei GONG,Jiao PENG,Xuena bai JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (6): 6-12.   DOI: 10.6040/j.issn.1671-9352.0.2023.045 Abstract （690）   HTML （3）    PDF（pc） （666KB）（486）       Save The definition of good congruence pairs is established by means of quasi-spined product structure of r-wide semigroups whose idempotents form normal band, and then, any good congruences of r-wide semigroups whose idempotents form normal band are characterized by using the good congruence pairs. Reference | Related Articles | Metrics