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25 May 2021, Volume 2021 Issue 3 Previous Issue    Next Issue

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Mathematics

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Commuting variety of r-tuples over the Witt algebra Yufeng YAO, Yajing ZHANG 2021, 2021 (3):  1-7.  doi: 10.3969/j.issn.1000-5641.2021.03.001 Abstract ( 438 )   HTML ( 1449 )   PDF (603KB) ( 135 )   Save Let ${\mathfrak{g}}$ be the Witt algebra over an algebraically closed field of characteristic $p>3$ , and $r\in\mathbb{Z}_{\geqslant 2}$ . The commuting variety ${{\cal{C}}_{r}}\left( \mathfrak{g} \right)$ of $r$ -tuples over ${\mathfrak{g}}$ is defined as the collection of all $r$ -tuples of pairwise commuting elements in ${\mathfrak{g}}$ . In contrast with Ngo’s work in 2014, for the case of classical Lie algebras, we show that the variety ${{\cal{C}}_{r}}\left( \mathfrak{g} \right)$ is reducible, and there are a total of $\frac{p-1}{2}$ irreducible components. Moreover, the variety $ {{\cal{C}}_{r}}\left( \mathfrak{g} \right) $ is not equidimensional. All irreducible components and their dimensions are precisely determined. In particular, the variety ${{\cal{C}}_{r}}\left( \mathfrak{g} \right)$ is neither normal nor Cohen-Macaulay. These results are different from those for the case of classical Lie algebra, $\mathfrak{sl}_2$ . References | Related Articles | Metrics

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Modules and induced modules of 3-Lie algebra Aω δ Ruipu BAI, Yue MA 2021, 2021 (3):  8-16.  doi: 10.3969/j.issn.1000-5641.2021.03.002 Abstract ( 322 )   HTML ( 1418 )   PDF (598KB) ( 155 )   Save For the infinite dimensional simple 3-Lie algebra $A_{\omega}^{\delta}$ over a field $\mathbb F$ of characteristic zero, we construct two infinite dimensional intermediate series modules $(V, \rho_{\lambda, 0})=T_{\lambda, 0}$ and $(V, \rho_{\lambda, 1})=T_{\lambda, 1}$ of $A_{\omega}^{\delta}$ as well as a class of infinite dimensional modules $(V, \psi_{\lambda,\mu})$ of ad $(A_{\omega}^{\delta})$ , where $\lambda, \mu\in \mathbb F$ . The relation between 3-Lie algebra $A_{\omega}^{\delta}$ -modules and induced modules of ad $(A_{\omega}^{\delta})$ are discussed. It is shown that only two of infinite dimensional modules, namely $(V, \psi_{\lambda, 1})$ and $(V, \psi_{\lambda, 0})$ , are induced modules. References | Related Articles | Metrics

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Tilting modules for the nonrestricted representations of modular Lie algebra Yiyang LI 2021, 2021 (3):  17-22, 46.  doi: 10.3969/j.issn.1000-5641.2021.03.003 Abstract ( 317 )   HTML ( 1303 )   PDF (845KB) ( 157 )   Save Let $ G $ be a connected reductive algebraic group over an algebraically closed field $ k $ of prime characteristic $ p $ , and let $ {\frak {g}} = {\rm{Lie}}(G) $ , $U_{\chi}({\frak {g}}) $ be the reduced enveloping algebra. In this paper, when $ p $ -character $ \chi $ has the standard Levi form, we prove that a $ U_{\chi}({\frak {g}}) $ -module $ Q $ is a tilting module if and only if it is projective. Figures and Tables | References | Related Articles | Metrics

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Kastler-Kalau-Walze type theorems for an even dimensional manifold with boundary Kaihua BAO, Aihui SUN, Lingyuan XIA 2021, 2021 (3):  23-33.  doi: 10.3969/j.issn.1000-5641.2021.03.004 Abstract ( 277 )   HTML ( 160 )   PDF (607KB) ( 149 )   Save In this paper, we establish a Kastler-Kalau-Walze type theorem for an even dimensional manifold with boundary about Dirac operators with torsion; in addition, we provide a simple theoretical explanation to the Einstein-Hilbert action for any even dimensional manifold with boundary. References | Related Articles | Metrics

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Continuous dependence of primitive equations of the atmosphere with vapor saturation Yuanfei LI, Shengzhong XIAO, Peng ZENG 2021, 2021 (3):  34-46.  doi: 10.3969/j.issn.1000-5641.2021.03.005 Abstract ( 289 )   HTML ( 53 )   PDF (634KB) ( 85 )   Save In this paper, we study the primitive equations of the atmosphere in the presence of vapor saturation; these equations are often used in forecasting weather in a cylindrical region. By using the technique of differential inequality and the method of energy estimation, we obtain the prior bounds of the solutions for the equations, and we prove the continuous dependence of the equations on the boundary parameters. References | Related Articles | Metrics

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Analysis of vector-borne infectious disease model with age-structured and horizontal transmission Shuangshuang LIANG, Linfei NIE, Lin HU 2021, 2021 (3):  47-55.  doi: 10.3969/j.issn.1000-5641.2021.03.006 Abstract ( 432 )   HTML ( 57 )   PDF (601KB) ( 222 )   Save Considering the prevalence of variations in virus strains and the age of infection, a vector-borne infectious disease model with latent age and horizontal transmission is proposed. An exact expression for the basic reproduction number, ${\cal R} _0 $ , is given, which characterizes the existence of the disease-free equilibrium and the endemic equilibrium for this model. Next, by using a combination of linear approximation methods, constructing suitable Lyapunov functions, LaSalle invariance principles, and other methods, we prove that if ${\cal R}_0 <1 $ , then the disease-free equilibrium has global asymptotic stability, and the disease will eventually become extinct; if ${\cal R}_0>1$ , then the endemic equilibrium is globally asymptotically stable, and the disease will continue to form an endemic disease. References | Related Articles | Metrics

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An n-order expansion method for determining the upper bound of the order of finite series solutions Chenwei SONG, Yinping LIU 2021, 2021 (3):  56-64.  doi: 10.3969/j.issn.1000-5641.2021.03.007 Abstract ( 366 )   HTML ( 61 )   PDF (587KB) ( 147 )   Save A number of algebraic methods used for constructing exact finite series solutions of nonlinear evolution equations are based on the homogeneous balance principle, such as the tanh function method, the Jacobi elliptic function method, the Painlevé truncated expansion method, the CRE method, etc. In each of these methods, the order of required solutions is determined by the homogeneous balance principle. In this paper, the homogeneous balance principle is further extended by considering additional balance possibilities. An n-order expansion method is proposed to determine possible new orders of required solutions. By applying the proposed method to several examples, we show that higher orders and new solutions can be obtained. Figures and Tables | References | Related Articles | Metrics

Computer Science

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An algorithm for precise image registration based on priori mark features Tianbi LIU, Rui FENG 2021, 2021 (3):  65-77.  doi: 10.3969/j.issn.1000-5641.2021.03.008 Abstract ( 391 )   HTML ( 54 )   PDF (1387KB) ( 118 )   Save The use of a gene sequencer requires that the lens and gene chip are aligned accurately before base-calling. We propose an algorithm to calculate the deviation of the field of view (FOV) from the ideal position. Marks are set at locations on the gene chip in advance, so that the deviation in position of the lens relative to the gene chip can be analyzed. Firstly, the marked locations are captured by extracting grayscale features of the image to initially align the center of the FOV; secondly, the coordinates for multiple key points on the marks are captured; and finally, the location and angle deviations are calculated by mapping coordinates for the key points. Practical and experimental analysis show that the image registration algorithm designed in this paper can achieve a high-precision estimate for the position deviation between the FOV and the gene chip. Figures and Tables | References | Related Articles | Metrics

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The design and implementation of a scalable Internet of things teaching development system Ming ZHU, Jianhua SHEN, Jiacai WANG 2021, 2021 (3):  78-95.  doi: 10.3969/j.issn.1000-5641.2021.03.009 Abstract ( 376 )   HTML ( 62 )   PDF (1330KB) ( 153 )   Save Internet of things (IoT) technology is booming, and from the viewpoint of embedded experimental teaching, it is worth thinking about how to lead students to conduct preliminary exploration in the field of Internet of things with embedded technology. In order to reduce the difficulties and costs of student learning and development, we designed and implemented a scalable IoT teaching and development system that integrates management and development functions. We adopted the open-source framework of Spring Boot and Vue to complete the development for the cloud side of the system. Using a micro-service architecture, we solved the typical challenges of strong coupling and poor scalability. In order to cope with high concurrency scenarios, we designed a load balancing optimization algorithm based on threshold filtering. Experimental results showed that the algorithm enhances the average response speed of the cloud and improves load balancing in complex network environments. Based on the MSP432 development platform and the EMW3080 Wi-Fi module, we implemented an easy-to-use SDK(Software Development Kit) that supports network distribution and data communication on the hardware side. The SDK reduced the complexity of the underlying hardware work and learning costs, allowing developers to focus on implementing business logic. Combining the work of software and hardware, the proposed IoT teaching development system provides a complete set of personalized IoT development solutions and an embedded teaching management system. Figures and Tables | References | Related Articles | Metrics

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Chinese text relation extraction based on a multi-channel convolutional neural network Yanchun LIANG, Ailian FANG 2021, 2021 (3):  96-104.  doi: 10.3969/j.issn.1000-5641.2021.03.010 Abstract ( 406 )   HTML ( 67 )   PDF (702KB) ( 300 )   Save This paper presents an end-to-end method for Chinese text relation extraction based on a multi-channel CNN (convolutional neural network). Each channel is stacked with a layered neural network; these channels do not interact during recurrent propagation, which enables a neural network to learn different representations. Considering the nuances of the Chinese language, we employed the attention mechanism to extract the semantic features of a sentence, and then integrate structural information using piecewise average pooling. After the maximum pooling layer, the final representation of the sentence is obtained and a relational score is calculated. Finally, the ranking-loss function is used to replace the cross-entropy function for training. The experimental results show that the MCNN_Att_RL (Multi CNN_Att_RL) model proposed in this paper can effectively improve the precision, recall, and F1 value of entity relation extraction. Figures and Tables | References | Related Articles | Metrics

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The impact of coupling patterns on transport in multilayer networks Yaqin HU, Ming TANG 2021, 2021 (3):  105-113.  doi: 10.3969/j.issn.1000-5641.2021.03.011 Abstract ( 620 )   HTML ( 71 )   PDF (924KB) ( 138 )   Save Multilayer networks can better reflect the structure and characteristics of many systems in the real world. In recent years, multilayer networks have become a focus area for many researchers. Based on the degree-degree correlation of interlayer nodes, we propose an intermediate degree coupling pattern to enhance the traffic capacity of multilayer networks at a low relative cost. In addition, the effectiveness of the intermediate degree coupling pattern is verified using two classic routing strategies, namely shortest path and efficient routing. Compared with the three coupling methods-assortative coupling, disassortative coupling, and random coupling-the intermediate coupling pattern makes the traffic load distribution more uniform on multilayer networks; hence, the traffic capacity of multilayer networks is greatly improved, and the average transport time of packets is effectively reduced. With lower coupling probability, the intermediate coupling pattern can significantly enhance the traffic capacity of a multilayer network when an efficient routing strategy is used. Meanwhile, simulation results show that more uniform network topology results in higher traffic capacity. Figures and Tables | References | Related Articles | Metrics

Life Sciences

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Preparation and stability study of lyophilized lentiviral vector Hongwei SHEN, Minghao LI, Nan XU, Jiaqi SHAO, Jing WANG, Lei YU 2021, 2021 (3):  114-127.  doi: 10.3969/j.issn.1000-5641.2021.03.012 Abstract ( 848 )   HTML ( 56 )   PDF (1003KB) ( 497 )   Save In this paper, we studied a new preparation technique for lyophilized lentiviral vectors. We determined the optimal formulation for a freeze-drying protective agent by screening and optimizing potential candidates. The candidates were evaluated on the basis of physical and chemical properties of the freeze-drying process, including appearance, excipient, color, and solubility. The optimal formulation was determined to be trehalose 0.30 g/mL, L-histidine 0.31 mg/mL, L- alanine 0.178 mg/mL, CaCl2 0.020 mg/mL, and MgSO4 0.015 mg/mL. With this technique, the prepared lyophilized lentiviral vector had good appearance, low residual water content, intact structure, and good re-dispersibility. The biological titer of the lentiviral vector reached 9.37 × 107 IU/mL, and the recovery rate of the titer was 50.15%. We also conducted research on potential influencing factors, including a high temperature accelerated experiment and repeated freeze-thaw stability experiments. These experiments showed that the lyophilizing technology can be used for the preparation of lentiviral vector solids and can be effectively used to improve the storage of lentiviral vectors under different temperature conditions, exposure to repeated freeze-thaw cycles, and tolerance to adverse environments (e.g., high temperatures). Figures and Tables | References | Related Articles | Metrics

Ecological and Environmental Sciences

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Relationship between air pollution purification and forest belt width of the Shanghai green belt in the summer season Xiaoling WANG, Kun SONG, Ying LE, Jing CHEN, Hao JIANG, Yongjia ZHANG, Heyi GONG, Zifei WANG, Yi DING, Tianhui SHI, Liangjun DA 2021, 2021 (3):  128-137.  doi: 10.3969/j.issn.1000-5641.2021.03.013 Abstract ( 343 )   HTML ( 50 )   PDF (16410KB) ( 127 )   Save In this study, ground-level air pollutants (i.e., particulate matter (PM), NO2, and CO) were monitored at two transects of an urban-road-green-belt of Shanghai for one month during the summer season. Four monitoring sites at 100m intervals were set along each transect from the road to the inside. The air pollution was evaluated for each site based on China’s national standard, and the variation in air pollution purification ability (i.e., removal percentage) was compared among sites with different distances to the road. The effects of meteorological condition and pollution background on maximum removal percentage of each air pollutant were evaluated by multiple regression analysis. The results showed that the green belt greatly contributed to reducing PM2.5, PM10, and NO2; however, the green belt also produced a cumulative effect on CO generation within its boundaries. The green belt had the greatest air pollution purification performance at sites with 300m distance to the road for most pollutants in both transects. The maximum removal percentages of PM2.5 and PM10 were correlated to air humidity difference and air temperature difference between outer and inner of forests mostly, while the maximum removal percentages of NO2 were correlated to the pollution background and maximum removal percentages of CO were correlated to air temperature difference. The results can provide a theoretical foundation for forest transform and arrangement aimed at air pollution purification in the green belt. Figures and Tables | References | Related Articles | Metrics

Estuary and Coastal Research

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Application of a surface and river network coupled model on waterlogging distribution analysis and risk assessment for a region suffering from extreme storm surges Fei TENG, Lu LI, Zhuyuan BEI, Jun WANG, Jufei QIU, Xiaojie ZHANG 2021, 2021 (3):  138-150.  doi: 10.3969/j.issn.1000-5641.2021.03.014 Abstract ( 345 )   HTML ( 40 )   PDF (10376KB) ( 230 )   Save Extreme precipitation and floods may occur during a storm surge hazard, accompanied by typhoon conditions and high tide levels. The combination of these factors intensifies the risk of flooding in coastal regions suffering from a storm surge. Thus, multi-impact analysis should be applied to determine flood risk during a storm surge. River networks play an important role in flood processes. The storage and transportation capacity provided by rivers can directly change the distribution of a flood. In this paper, a 1-D river network model and a 2-D surface model were respectively established and coupled to simulate the flood processes during an assumed storm surge in Jinshan District, Shanghai. The cumulative influence of the concurrent storm surge, typhoon, rainfall, and upstream flooding was explored to support hazard risk analysis for Jinshan District. The coupled model’s simulation indicated a clear decrease in the number of waterlogged areas in Jinshan District after considering the river network’s storage and transportation capacity during a storm surge event. The distribution of predicted waterlogged areas also changed; according to the simulation results, the flood risk grade decreased in the central and northern Jinshan District and rose in the Northwest corner. Figures and Tables | References | Related Articles | Metrics

Chemistry and Chemical Engineering

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Study on Fe2O3/g-C3N4 photocatalytic degradation of Rhodamine B Qinghua XI, Yiqiang HUANG, Jiaxiang CHEN, Er NIE, Zhuo SUN 2021, 2021 (3):  151-160.  doi: 10.3969/j.issn.1000-5641.2021.03.015 Abstract ( 387 )   HTML ( 47 )   PDF (1416KB) ( 124 )   Save In order to improve the low specific surface area of g-C3N4, three-dimensional (3D) porous g-C3N4 was prepared using high temperature thermal polymerization. Fe2O3/g-C3N4 catalyst was prepared by compositing the g-C3N4 with Fe2O3 to improve its visible light response. The decolorization rate of the Fe2O3/g-C3N4 catalyst reached 100% in 30 minutes with a g-C3N4 content of 900 mg, Rhodamine B (RhB) concentration of 20 mg·L–1, and H2O2 content of 15 mmol. The Fe2O3/g-C3N4 catalyst also demonstrated good performance in degrading other organics; the degradation rates of Methyl orange (MO) and Tetracycline (TC) reached 80% and 90%, respectively, in 30 minutes. This photocatalytic mechanism was explored by active group capture experiments, and the results show that h+ and ·OH play an important role in the progress of photocatalysis. Figures and Tables | References | Related Articles | Metrics