S1 | First-order Sensitivity, which is local sensitivity |

GSA | Global Sensitivity Analysis |

CWS | Connection Weight Sensitivity |

LHS | Latin Hypercube Sampling |

ANN | Artificial Neural Network |

BPM/BPPM | Building performance Model/Building Parametric Performance Model |

CDD/HDD | Cooling/Heating Degree-Days (CDD/HDD) |

SALib | A Sensitivity Analysis Library in Python |

RBD-FAST | Random Balance Designs - Fourier Amplitude Sensitivity Test |

DMIM | Delta Moment-Independent Measure |

UDI | Useful Daylight Index |

sDA | Spatial Daylight Autonomy |

PMV | Predicted Mean Vote |

R^{2} | Coefficient of Determination |

MAE | Mean absolute Error |

MSE | Mean Square Error |

RMSE | Root Mean Squared Error |

Loss | Loss function curve during ANN training |

MOEA | Multi-objective Evolutionary Algorithm |

The progress of human society is reflected in the comprehensive optimisation of building performance, which is promoted by the joint efforts of architectural research and design practice. With the progress of scientific and technological civilisation, people’s necessities for visual and thermal comforts of the living environment are also improved accordingly. At present, the maintenance of building indoor environment comfort is still dependent on active energy supply, which makes the building energy consumption in the operation stage accounts for a large proportion of the global total energy consumption [1]. The building is like a complex machine that is easily affected by various parameters such as environment, materials, equipment, form and human behaviour. Therefore, the design of buildings with better performance is an important strategy to achieve sustainable development [2].

This study can provide more accurate results for the optimisation of envelope enclosure. However, most previous studies can only discuss samples under certain specific design situations due to the research’s complexity. With the further development of computer simulation technology, many building performance simulation tools (such as EnergyPlus, DeST, ESP-R, DOE2, TRNSYS and IES VE) have been applied in architectural research and design practice. In particular, the Ladybug Tools for building performance are maturing, providing researchers with a more flexible and diverse solution for building optimisation. Ladybug Tools can analyse EPW format files of building weather data and visualisation methods to perform some basic building performance simulations [3,4,5]. Honeybee (HB) uses visual programming to structure and input building morphological parameters and meteorological data to the computing engine (such as EnergyPlus, Radiance, Daysim and Thermal) to realise the construction of building performance simulation schemes and data conversion in the GH platform. Based on this, HB reads the numerical calculation results into GH for analysis and visualisation [6]. EnergyPlus (EP) [7, 8] is a building energy simulation engine developed by the Department of Energy (DOE) of the United States, which can simulate and analyse the overall energy consumption of heating, refrigeration, lighting, ventilation and other energy consumption of the building. Besides, HB realises the collaborative optimisation of indoor lighting and energy consumption through the coupling calculation of Radiance and EP [9, 10].

Sensitivity analysis (SA) is a method used to quantitatively describe the importance of model input variables to output results, which plays an essential role in understanding complex models [11,12,13,14,15]. Meanwhile, it can help to identify the influence of input parameters on the results, make model builders fully aware of the uncertain response caused by changes in model inputs and provide decision-makers with rich insights on management issues [16, 17]. The optimisation of building performance is a multi-objective optimisation problem under the comprehensive action of multiple parameters. In previous studies, Sanchez et al. [18] analysed and illustrated the potential use of integrating first-order and second-order sensitivity analyses into building energy models (ESPR). Taking an apartment building as an example, the sensitivity analysis is carried out by using the principal effect method (Morris), including the analysis of the interaction between the input parameters (secondary analysis). To effectively perform the interval size of multi-level sensitivity analysis variables, nonlinear management and the availability of various outputs, Hughes et al. [19] used two global sensitivity analysis techniques, such as the necessary effect and the variance-based method, to determine the U value and demand temperature of SAP wall as the most critical uncertainty parameters so far. The U values of SAP roofs, windows and floors together explain 96% of the observed yield changes. Kulhanek and Poyraz [20] studied three different exterior wall (Clay) designs, which were convenient in suggesting the energy characteristics of passive house design in general. They proved the feasibility of using the dominant weight method to carry out a sensitivity analysis of envelope enclosure parts containing energy. Sun [21] made a systematic sensitivity analysis of large parameters in near-zero energy building (NZEB) and carefully selected more accurate design parameters (especially those with serious sensitivity effects), which is of great value to help designers to improve the design of the NZEB system. Maltais and Gosselin [22] conducted a sensitivity analysis based on daylight simulations of an office building in Montreal to identify the most influential architectural design variables on the 15 feature lists. Finally, it is concluded that the WWR and the overhang size are among the most influential parameters of AEL and AGI, while the direction and aspect ratio of the building and the visible light transmittance have relatively little influence.

In the recent study, Ostergard et al. [23] introduced a novel approach to explore multi-dimensional design spaces and guide multifactor decision-making in sustainable building design. Sensitivity metrics and metamodels show the combined effect of changing individual inputs and how to correct unnecessary output changes. The proposed approach has been developed and tested by using standard models to assess energy requirements, thermal comfort and lighting in real building cases. Al-Saadi and Al-Jabri [24] studied the optimal design of envelope enclosure under hot climate by using genetic algorithm (GA) technology and carried out life cycle cost (LCC) analysis with EP simulation programme. A sensitivity analysis was performed using a validated housing model to determine the upper and lower limits for optimising the search domain. The results show that the window shading is thermoresistant and economically viable in the selected climate. Depending on the energy cost, the insulation cost of an enclosure system in a hot climate will be 2.5–5 cm more than that of an enclosure system in a warm and humid climate. Liu et al. [25] built a simulation model through the energy consumption simulation analysis method and verified the reliability of the model by comparing it with the actual energy consumption. In order of energy-saving sensitivity, the thermal design parameters of six building envelopes, including the heat transfer coefficient of external walls, were analysed. According to the results of sensitivity analysis, suggestions for each factor are put forward. Delgarm et al. [26] studied the integration of factor-based OFAT and variance-based sensitivity analysis methods with EnergyPlus through MATLAB to define the main variables that affect building energy efficiency at the early stage of building design. It is proved that in the selected typical case studies, the window size is the main parameter for annual cooling, heating and total building energy consumption, while visible light transmittance of glass has little effect on annual lighting in the selected climate conditions.

According to the research of the existing literature, it is found that most of the previous research is the sensitivity analysis under the action of a single computing engine or method, and there is still a gap in the sensitivity analysis of multiple performance tags under the action of multi-parameters coupling. The improvement of this study is not only to evaluate the sensitivity analysis of space energy consumption, comfort and lighting performance under the action of multi-dimensional design parameters but also to use various sensitivity analysis methods to evaluate the quantitative results obtained and ensure the applicability of the calculation method.

Residential buildings in dry-hot and dry-cold climate zones were selected as the research object of this paper. Local buildings were investigated and operation data were obtained. Through simulation verification, the parameterised envelope performance evaluation model is reconstructed, while on this basis the simulated sample data are obtained, and the sensitivity analysis is carried out. The overall technical route is shown in Figure 1.

Build the energy consumption model of the original building, and obtain the simulated data of energy consumption through the simulation technology;

Fit the simulation data with the building operation data to verify the applicability of the simulation tool on the premise of ensuring accuracy;

By extracting the optimised performance design parameters, the parameterised performance coupling simulation model was reconstructed;

Latin hypercube sampling (LHS) was used to sample and save the combination table of design parameters;

Colibri plug-in in GH platform is used to automatically control the cycle solution and write out the calculation results;

ANN modelling was carried out between the sampled samples and the simulation results, and the accuracy of the model was verified;

Calculate the weight value of the neural network in the process of (6), and calculate CWS with the improved Garson algorithm;

RBD-S1 was calculated by using RBD-FAST in SALib;

DMIM-S1 and DMIM-delta were calculated by using the DMIM algorithm in SALib;

Various sensitivity indexes were verified and comprehensively analysed.

The area represented by the Turpan is located in the Cold B area of the China Building Thermal Design Division. The climatic condition of the area is characterised by abundant sunshine, rare rainfall, average annual precipitation <20 mm, >100 hot days higher than 35°C, extreme high temperature in summer up to 49.6°C and extreme minimum temperature in winter −28.7°C [27]. According to the CDD/HDD [28] calculation method provided by ASHARE, the CDD and HDD in this area are 579 and 2758, respectively. So it has the characteristics of dry-hot and dry-cold, which are alternating.

The New Energy Demonstration Zone of Turpan is the first large residential area in western China to fully utilise multi-energy complementarity, which is a high-quality object in terms of architectural design and energy utilisation. On the one hand, the residential buildings in this area are modern residential buildings, and the design techniques and materials adopted are quite different from the traditional local dwellings (Figure 2). And to adapt to the continuous evolution of the local climate and environment, traditional dwellings in Turpan generally use ‘thick walls’ and ‘small windows’ to sacrifice indoor lighting to improve the indoor thermal environment. Therefore, indoor lighting and vision are mightily imperfect, which need to put forward a reasonable improvement plan through the design intervention.

In addition, the heating and air conditioning in this area adopt solar-ground source heat pump technology, which is a multi-source complementary system in the right operating conditions. According to the field investigation and interview of the buildings in this area, most villagers are more acceptable to central heating, but there are also terrible operation cases. Because of its lack of independent control and high overall operating cost, some residents even give up the central heating system and choose to install an independent control system. Also, from the initial design scheme’s perspective, the shading system for the building’s exterior windows was not implemented in the later construction process, which was also one of the problems that increased energy consumption and reduced comfort.

Many design parameters affect building energy consumption. In this paper, based on the original design parameters, the original building energy consumption evaluation model is established (Figure 3). First, the simulation parameter settings were adjusted according to the original architectural design parameters (Table 1). The mean relative error between simulation data and operation data is calculated, and the result is 14.68%. Energy consumption during the life of a building is influenced by a complex set of factors, such as uncontrolled human factors and changes in meteorological conditions. Based on this, it can be concluded that the model has high accuracy. Parameters that can be used for design optimisation are extracted to construct the parameterised building performance model (PBPM), which were set as adjustable intervals. Finally, the LHS [29,30,31,32,33] was used to generate design parameter combination samples (Table 2).

Building materials parameters for simulation.

Roughness | Rough | Rough | Rough | Rough | Thickness (m) | – |

Thickness (m) | 0.20 | – | 0.12 | – | Conductivity (W/m∗K) | 0.08 |

Conductivity (W/m∗K) | 1.74 | 0.03 | 1.74 | 0.03 | Solar transmittance (%) | 2.4 |

Density (kg/m^{3}) | 2,500 | 38 | 2,500 | 38 | Solar reflectance (%) | – |

Specific heat (KJ/(kg∗K)) | 1,010 | 1,010 | 1,010 | 1,010 | Visible transmittance (%) | 0.7 |

Roughness (optics) | 0.1 | 0.1 | 0.1 | 0.1 | Roughness (optics) | 0.02 |

Reflection coefficient ( | 0.4 | – | 0.3 | – | Reflection coefficient ( | 0.78 |

1. Property (opaque): non-transparent material property; Property (transparent): transparent material property.

2. Insulation layer (W): external wall insulation; insulation layer (R): external roof insulation.

Parameters value ranges and sampling.

Window-to-wall ratio in north | WWR_N | 0.15–0.7 | 3,000 |

Window-to-wall ratio in south | WWR_S | 0.15–0.7 | |

Window-to-wall ratio in west | WWR_W | 0.15–0.7 | |

Window-to-wall ratio in east | WWR_E | 0.15–0.7 | |

Window heat transfer coefficient | WHTC | 0.8–2.8 | |

Wall insulation | WI | 0.05–0.12 | |

Roof insulation | RI | 0.06–0.15 | |

Depth of shading | S-D | 0.1–1.2 | |

Numbers of shading | S-N | 1–10 | |

Angle of shading | S-A | −60–60 |

In this paper, literature research is carried out through commonly used building parameters. In most cases, the main differences of the modern residential building envelope in different climate zones of China are the control of the building, the size of the window, the thermal performance of the envelope and whether to take corresponding shading measures. In terms of parameter variable selection, the window-wall area ratio (WWR_N, WWR_S, WWR_W and WWR_E), wall insulation layer thickness (WI), roof insulation layer thickness (RI) and comprehensive heat transfer coefficient of external windows (WHTC) are mainly selected in each orientation according to the local residential building design and construction feasibility. Due to the various forms of shading systems outside the building, this paper selects stationary blinds as the test objects. The depth (S-D), numbers (S-N) and angle (S-A) of the shading components on the exterior windows of the building were selected. LHS sampled a total of 10 envelope performance design parameters that could be optimised in the design stage.

In terms of the selection of performance labels, lighting energy consumption and heating energy consumption may be increased under the effect of improving heat insulation and shading in summer. Therefore, main energy consumption labels, such as the heating load of the building, the cooling load of air conditioning and lighting load that meets the requirement of illumination, are selected. By extracting the whole space’s relevant values, the PMV calculation module in EP is adopted to calculate the spatial PMV values of the corresponding samples.

The remaining simulated parameters are not taken as the main discussion object, and the original design is selected because of its small impact on the research. UDI and sDA [34] values were calculated through the coupling of Radiance and DaySim, which were used as an essential basis for evaluating the lighting quality of building space. Because the two labels’ data changed in the same direction and had a high correlation, UDI and sDA were merged into a comprehensive spatial lighting evaluation label DWS [Eq. (1)].

According to the existing research, artificial neural network (ANN) [35,36,37] has been applied in various industries to solve the related problems of pattern recognition and prediction. ANN can build models with predictive ability according to the characteristics of existing operational data. However, due to the inherent uncertainty (black box) in the model constructed by the researchers, the understanding and optimisation of the model are greatly troubled. To solve the black box effect of ANN, many researchers have made outstanding contributions in this aspect: Garson [38] proposed the Garson algorithm in 1991; Olden and Jackson proposed the randomisation test in 2002 and Muriel Gevery proposed the PaD2 method in 2005 [39]. This paper uses Python to code an improved Garson algorithm [Eq. (2)] [39], while CWS values are calculated based on the high precision of ^{2} [Eq. (3)], MAE [Eq. (4)] and RMSE [Eq. (5)] of ANN regression model evaluation indexes. In addition, MSE [Eq. (6)] is adopted as the Loss function of the training process in this paper, so the optimal Loss value of the ANN model can also be used as the performance evaluation index of the model.

With the popularity of parameter sensitivity analysis in research and practice in various industries, the tools available for parameter sensitivity analysis have also been developed. Among them, the SA analysis modules in Simlab software and R software are more commonly used. Besides, a sensitivity analysis library, SALib [40,41], based on Python programming language, has also attracted researchers’ attention. It can select different sampling methods according to specific problems and provide more comprehensive sensitivity analysis methods (such as Sobol, Morris, FAST and DMIM). SALib provides a separate workflow, which means it is not directly linked to mathematical or computational models. Besides Sobol and Morris methods, RBD-FAST [40,41,42] and DMIM [42, 43] are representative first-order sensitivity and global sensitivity analysis methods in SALib, which make the sensitivity analysis of given sample data possible. RBD-FAST is an improvement on FAST [42, 43], which aims to make sensitivity analysis easier than any other available methods and significantly reduce the computational cost of the analysis. The main development idea of DMIM, combined with the methods proposed by Borgonovo and Plischke, can simultaneously evaluate the first-order sensitivity (DMIM-S1) and the global sensitivity (DMIM-delta). Because the calculation process of RDB-FAST and DMIM is relatively complicated, and there are some application examples in SALib, this paper will not introduce the calculation method in detail.

To ensure the effectiveness of the model established by ANN, the accuracy of the data modelling used in this paper is evaluated. The ANN established in this paper adopts a three-layer full-link structure (one input layer, one hidden layer and one output layer) and adopts MSE as the loss function. In the ANN training process, 10-fold cross-validation [44, 45] is used to prevent over-fitting of the model, and the best model is selected to calculate the sensitivity index. The loss curve of the model (Figure 5) is drawn, which can be seen that the model reaches the best accuracy around 235 times of running, with the value of ^{2} is 0.91, the value of RMSE is 0.31 and MAE is 0.18 (Table 3) meeting the standard of a high-precision regression model.

Performance evaluation indexes of models or methods in different stages.

^{2} | ||||
---|---|---|---|---|

ANN-BPM | 0.91 | 0.31 | 0.18 | 0.05 |

SA (RBD-FAST and DMIM-S1) | 0.98 | 0.001 | 0.001 | – |

SA (ANN + Garson and DMIM-delta) | 0.8 | 0.15 | 0.01 | – |

The design parameters of the performance models discussed in this paper may influence each other and relate to each other in terms of performance labels. The results of sensitivity analysis are better verified to understand the characteristics and applicability of each calculation method. The sensitivity indexes obtained by different methods were verified (Figure 6). There was little difference between RDB-S1 and DMIM-S1, so the two methods can verify each other to predict the reliability of the DMIM-delta (Table 3). And there are some differences between CWS and the other three sensitivity indexes, which are between the first-order sensitivity and the global sensitivity. The advantage of using full-link ANN combined with the improved Garson algorithm lies in the correlation between multiple performances. In contrast, the DMIM algorithm’s advantage lies in the full calculation of global sensitivity under the interaction of multiple parameters. Therefore, to ensure the accuracy of the analysis results, this paper mainly uses CWS and DMIM-delta as the main consequence of the discussion. To further check the performance of ANN Garson and DMIM-delta in sensitivity analysis, the calculation of correlation coefficient and error-index between the two sets of results is beneficial to better evaluate the reliability of the calculation results (Table 3).

According to the sensitivity analysis results of different methods (Figure 7), all four calculation results can better identify the design parameters with significant sensitivity in the model, while there are some differences in the design parameters with low sensitivity. Generally speaking, the analysis can be divided into three situations: (1) Local sensitivity analysis CWS for the interaction among indicators of multiple performances (Figure 7a); (2) The global sensitivity DMIM-delta (Figure 7b) of the interaction among parameters of multiple designs, but the interaction among indicators multiple performances is not calculated; (3) Only consider the influence of a single parameter change on a single performance label RBD-S1 and DMIM-S1 (Figures 7c and d). Based on the analysis of sensitivity index values, the envelope enclosure of residential buildings in this area has a high sensitivity on the five parameters of external shading components (S-D, S-N and S-A), south window-wall area ratio (WWR_S) and north window-wall area ratio (WWR_N). The sensitivity of S-D, S-N and S-A was significant, and the sum of them was >60% in various performance labels. The sensitivity of the sum of WWR_S and WWR_N was also >20%. And the sensitivity of the other design parameters is <20% accumulatively, which has little effect on the performance within the adjustable range.

Due to the lack of operational data on building performance, it is hard to establish the building envelope performance model based on the real situation. Meanwhile, the operation data can only reflect the performance of a specific design portfolio. It is not easy to obtain the same result as the actual operation through simulation. Therefore, the simulation study can obtain the variation trend of various parameters which can accelerate the evolution process of modern architecture to adapt to the environment, and then promote the development of architecture towards sustainable development. Sensitivity analysis of the model can improve the interpretability and simplify the complexity of the model.

In later research and practice, a more detailed model can be established according to the leading factors of the design. For example, shading measures and ventilation devices are used only in summer, and transparent enclosures utilise solar radiation as much as possible in winter which reduces heat loss at night. Besides, due to the numerous design parameters of the envelope structure, the comprehensive influence of more dimensional design parameters and performance labels should be studied in the later research to improve the model’s accuracy and applicability. On the choice of performance labels, computational fluid dynamics (CFD) may be combined to calculate indoor air quality and air distribution to optimise the indoor environment calculation model, while is also an expandable research programme.

This paper investigated the new energy demonstration zone of Turpan and established a multi-performance parameterised solution model under the action of multi-parameter coupling. LHS was used to generate samples of different combinations, and parameterised performance simulation tools were used to solve each combination. Through the sensitivity analysis and discussion of the results, the research conclusions are as follows:

The sensitivity analysis results of RBD-FAST and Dimim-S1 are almost the same, so it can be generally inferred that the calculation results of DMIM-delta have high reliability. Moreover, the results of DMIM-delta and ANN Garson’s calculation are highly consistent. Therefore, the calculation results of ANN Garson and DMIM-delta have certain reliability.

The envelope enclosure of residential buildings in this area has a high sensitivity on the five parameters of external shading components (S-D, S-N and S-A), south window-wall area ratio (WWR_S) and north window-wall area ratio (WWR_N). The sensitivity of S-D, S-N and S-A was significant, and the sum of them was >60% in various performance labels. The sensitivity of the sum of WWR_S and WWR_N was also >20%.

Draw P-C for the performance model established by ANN, which can better explain the performance model and further verify the correctness of sensitivity analysis results. From the curve, the four parameters of S_A, S_N, S_D and WWR_S have strong volatility. Through the analysis of the P-C, it can be seen that there is no optimal solution for the performance design of the residential building envelope in this area, and through the multi-objective optimisation method, it is necessary to obtain a reasonable parameter combination under different dominant factors.

After the sensitivity analysis process, the calculation efficiency of the model can be improved as far as possible without reducing the accuracy of the model in the later simplified calculation and multi-objective optimisation. Parameters with weak sensitivity can be set to a fixed value in the later optimisation process of the model to reduce the complexity of the model when the dimension of characteristic parameters is too high.

#### Performance evaluation indexes of models or methods in different stages.

^{2} | ||||
---|---|---|---|---|

ANN-BPM | 0.91 | 0.31 | 0.18 | 0.05 |

SA (RBD-FAST and DMIM-S1) | 0.98 | 0.001 | 0.001 | – |

SA (ANN + Garson and DMIM-delta) | 0.8 | 0.15 | 0.01 | – |

#### Building materials parameters for simulation.

Roughness | Rough | Rough | Rough | Rough | Thickness (m) | – |

Thickness (m) | 0.20 | – | 0.12 | – | Conductivity (W/m∗K) | 0.08 |

Conductivity (W/m∗K) | 1.74 | 0.03 | 1.74 | 0.03 | Solar transmittance (%) | 2.4 |

Density (kg/m^{3}) | 2,500 | 38 | 2,500 | 38 | Solar reflectance (%) | – |

Specific heat (KJ/(kg∗K)) | 1,010 | 1,010 | 1,010 | 1,010 | Visible transmittance (%) | 0.7 |

Roughness (optics) | 0.1 | 0.1 | 0.1 | 0.1 | Roughness (optics) | 0.02 |

Reflection coefficient ( | 0.4 | – | 0.3 | – | Reflection coefficient ( | 0.78 |

#### j.amns.2021.2.00033.tab.004.w2aab3b7b1b1b6b1ab1ab1Aa

S1 | First-order Sensitivity, which is local sensitivity |

GSA | Global Sensitivity Analysis |

CWS | Connection Weight Sensitivity |

LHS | Latin Hypercube Sampling |

ANN | Artificial Neural Network |

BPM/BPPM | Building performance Model/Building Parametric Performance Model |

CDD/HDD | Cooling/Heating Degree-Days (CDD/HDD) |

SALib | A Sensitivity Analysis Library in Python |

RBD-FAST | Random Balance Designs - Fourier Amplitude Sensitivity Test |

DMIM | Delta Moment-Independent Measure |

UDI | Useful Daylight Index |

sDA | Spatial Daylight Autonomy |

PMV | Predicted Mean Vote |

R^{2} | Coefficient of Determination |

MAE | Mean absolute Error |

MSE | Mean Square Error |

RMSE | Root Mean Squared Error |

Loss | Loss function curve during ANN training |

MOEA | Multi-objective Evolutionary Algorithm |

#### Parameters value ranges and sampling.

Window-to-wall ratio in north | WWR_N | 0.15–0.7 | 3,000 |

Window-to-wall ratio in south | WWR_S | 0.15–0.7 | |

Window-to-wall ratio in west | WWR_W | 0.15–0.7 | |

Window-to-wall ratio in east | WWR_E | 0.15–0.7 | |

Window heat transfer coefficient | WHTC | 0.8–2.8 | |

Wall insulation | WI | 0.05–0.12 | |

Roof insulation | RI | 0.06–0.15 | |

Depth of shading | S-D | 0.1–1.2 | |

Numbers of shading | S-N | 1–10 | |

Angle of shading | S-A | −60–60 |

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system for automobiles based on torsional vibration damping Application research on piano teaching in colleges and universities based on remote wireless network communication Construction of a mathematical modeling teaching quality assessment system for universities based on Eviews model Construction of Financial Risk Evaluation Index System for Biomass Graphene Fibre Industrialisation Project Innovative model of teaching in law experiment center based on LETS software A Study on the Implications of Critical Discourse Analysis Theory for College English Teaching in the Context of Big Data Computational research on flat image design and style based on perceptual feature quantification The artistic aesthetic and cultural value orientation of 3D printing A multidimensional interpretation of Marxist theory based on a decentralized Internet perspective Student management model of college student associations based on ant colony Algorithm Analysis of the evolution of China’s energy legal system under the background of discrete model theory and dual carbon Design of Morlet wavelet neural network to solve the non-linear influenza disease system An online statistical analysis of the hotel management and operation performance model Research on the relationship between the construction of school teachers’ team literacy and the educational environment Research on the post-purchase behaviour tendency of the product quality to customers in fast-selling marketing Motion about equilibrium points in the Jupiter-Europa system with oblateness Design of an embedded machine vision system for smart cameras Ultra-short-term power forecast of photovoltaic power station based on VMD–LSTM model optimised by SSA Optimal preview repetitive control for impulse-free continuous-time descriptor systems Design of information management system based on wireless communication under the background of Internet of Things The impact of global warming on the small Scottish Fishing Company Research on heat transfer properties of graphene composites Development of main functional modules for MVB and its application in rail transit Analysis of agricultural economic development and optimisation measures under the strategy of rural revitalisation Study on the impact of forest fire prevention policy on the health of forest resources Value Creation of Real Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Research on the relationship between government subsidies, R&D investment and high-quality development of manufacturing industry Research on the protection and inheritance of intangible cultural heritage under the background of rural revitalisation Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment Computer vision recognition and tracking algorithm based on convolutional neural network Innovative reform strategy of artistic practice of university folk dance education based on information fusion technology A review of the treatment techniques of VOC Study on structural parameter design and life analysis of large four-point contact ball bearing channel Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}Digital marketing solutions based on consumer data and homomorphic encryption The consistency method of linguistic information and other four preference information in group decision-making Research on the driving principle and guiding strategy of the public's collaborative supervision of the sharing economy in my country Influence of innovative human capital on economic development of China through the STI model New ideas of precision teaching development based on the background of big data Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development Application research of bel canto performance based on artificial intelligence technology Research on the path of integrating blockchain technology into the teaching of film and television courses in higher education institutions Combined application of employment education and big data internet technology based on the context of vocational education reform Fractal structure of magnetic island in tokamak plasma College students' innovation and entrepreneurship model based on probability theory statistics Exploring the path of network security and student privacy protection in smart campus based on Markov model Innovation and entrepreneurship model of higher vocational college students based on probability theory statistics Application of knowledge graph in smart grid fault diagnosis Research on the innovation of youth network media literacy education in the context of Internet + education Research on the optimisation of logistics parcel intelligent sorting and conveying chain combined with variable clustering mathematical method Research on power quality assessment based on ubiquitous power IoT Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Analysis of network information security issues under the background of big data Research on SOC estimation of residual power of lithium-ion batteries for electric vehicles based on extended Kalman filtering algorithm Harmonic current variation characteristics of shunt capacitors based on full-phase FFT algorithm Urban Public Epidemic Prevention and Control Model Based on Nonlinear Differential Equations Research on computer vision technology based on BP-LSTM hybrid network Research progress of computer vision tasks based on deep learning and SAE network Application of Discriminative Training Algorithm Based on Intelligent Computing in English Translation Evaluation Research on the application of GLE teaching mode in English-medium colleges The application of directional derivative in the design of animation characters and background elements Research on product process design and optimisation model based on IoT intelligent computing Simulation research on music feature recognition based on mobile big data and smart sensors Digital design and experimental testing of a compressor's suction muffler transmission loss LTE wireless network coverage optimisation based on corrected propagation model SCP model based on the new energy vehicle collaborative detection configuration method research Study on tourism development income index calculation of finite element ordinary differential mathematical equation The cardiovascular promotion of college taekwondo based on fractional differential equation Analysis and research on the economic benefits of employee labor in enterprises in the context of the Internet Application of renewable energy decorative materials in modern architectural design under low-carbon concept The boundedness of functional differential equations of hospital financial software under information Deep learning model-based brand design 3D image construction The character image setting of 3D animation works based on Poisson equation Research on the interaction between university physical culture education and college students’ physical exercise in the context of big data The optimization path of core literacy of innovative talents in universities based on the improved Markov model Analysis of the innovation path of university education management informatization in the era of big data Impact of ASEAN-China free trade area on fishery value chain based on difference-in-difference method Research on indoor environment design of comprehensive commercial shopping center based on numerical simulation Empirical analysis of the economic absolute income hypothesis based on mathematical statistics Realization of Book Collaborative Filtering Personalized Recommendation System Based on Linear Regression Equation Study on Interactive Relations between Enterprise Social Media and Decision Style Based on a vector Autoregressive Model Research on Dynamics of Flexible Multibody System with Deployable Antenna Based on Static Lagrangian Function The Optimization of Mathematics Teaching Models in Colleges and Universities Based on Nonlinear Differential Equations Study on spatial planning and design of learning commons in university libraries based on fuzzy matrix model The Stability Model of Piano Tone Tuning Based on Ordinary Differential Equations Construction and application of automobile user portrait based on k-mean clustering model The Homework Model of Screening English Teaching Courses Based on Fractional Differential Equations MATLAB-based simulation of industrial robots in water environment monitoring An innovative teaching model of automotive manufacturing process based on ADDIE model The train of thought and design of university talents training based on ADDIE model from the perspective of ideological and political education Research on the innovation of model based on the cultivation of talents in higher vocational art and design Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer Football Offense Training Strategy Based on Fractional Differential Mathematical Modeling The Mathematical Analysis Model of Educational System in Music Courses in Colleges and Universities Continuing Education Network Data Center Model Based on Fractional Differential Mathematical Equations Study on the factors influencing the evolution mechanism of cobalt trade network from the perspective of national competition Computer Art Design Model Based on Nonlinear Fractional Differential Equations The Optimization Model of Public Space Design Teaching Reform Based on Fractional Differential Equations The Approximate Solution of Nonlinear Vibration of Tennis Based on Nonlinear Vibration Differential Equation Graphical Modular Power Technology of Distribution Network Based on Machine Learning Statistical Mathematical Equation Reliability analysis of reinforced concrete beams based on the stochastic model of resistance calculation Employment and Professional Education Training System of College Graduates Based on the Law of Large Numbers Economic Research on Multiple Linear Regression in Fruit Market inspection and Management Nonlinear Differential Equations in Preventing Financial Risks Lagrange’s Mathematical Equations in the Sports Training of College Students Simulation Research of Electrostatic Precipitator Power Supply Voltage Control System Based on Finite Element Differential Equation Research on the effect of generative adversarial network based on wavelet transform hidden Markov model on face creation and classification Research on Lightweight Injection Molding (CAE) and Numerical Simulation Calculate of New Energy Vehicle Power Flow Calculation in Smart Distribution Network Based on Power Machine Learning Based on Fractional Differential Equations Demonstration of application program of logistics public information management platform based on 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Financial Markets Fractional Differential Equations in the Model of Vocational Education and Teaching Practice Environment Information transmission simulation of Internet of things communication nodes under collision free probability equation Image denoising model based on improved fractional calculus mathematical equation Random Fourier Approximation of the Kernel Function in Programmable Networks The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models University Library Lending System Model Based on Fractional Differential Equations Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Intelligent Matching System of Clauses in International Investment Arbitration Cases Based on Big Data Statistical Model Evaluation and Verification of Patent Value Based on Combination Forecasting Model Financial Institution Prevention Financial Risk Monitoring System Under the Fusion of Partial Differential Equations Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model Calculus Logic Function in Tax Risk Avoidance in Different Stages of Enterprises The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations Optimization Simulation System of University Science Education Based on Finite Differential Equations The Law of Large Numbers in Children's Education Optimization System of Strength and Flexibility Training in Aerobics Course Based on Lagrangian Mathematical Equation Data structure simulation for the reform of the teaching process of university computer courses A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes Garment Image Retrieval based on Grab Cut Auto Segmentation and Dominate Color Method Financial Risk Prediction and Analysis Based on Nonlinear Differential Equations Constructivist Learning Method of Ordinary Differential Equations in College Mathematics Teaching Multiple Effects Analysis of Hangzhou Issuing Digital Consumer Coupons Based on Simultaneous Equations of CDM Model Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations Pressure Image Recognition of Lying Positions Based on Multi-feature value Regularized Extreme Learning Algorithm English Intelligent Question Answering System Based on elliptic fitting equation Precision Machining Technology of Jewelry on CNC Machine Tool Based on Mathematical Modeling Application Research of Mathematica Software in Calculus Teaching Computer Vision Communication Technology in Mathematical Modeling Skills of Music Creation Based on Homogeneous First-Order Linear Partial Differential Equations Mathematical Statistics Technology in the Educational Grading System of Preschool Students Music Recommendation Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation Construction of an enterprise financial risk management system based on F-score model Research on education management system based on machine learning and multidimensional data modeling Multi-featured multi-scale combination of high-resolution remote sensing images for building extraction Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Electronic properties of diamond semiconductor materials: based on response surface model Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching Deep learning techniques in modern women’s smart clothing design Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology A study on the aesthetic characteristics of ethnic music based on radial basis neural network model The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Analysis of the application methods of film and television media and images in the era of big data cloud Air data computer simulation and design credibility assessment considering ADC calculation model Analysis of news communication strategies in the era of full media based on big data mining On the improvement, innovation and inheritance of stage makeup styling in opera under the background of big data Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Evaluation Mechanism of Teaching Staff’s Building in Local Vocational Colleges Based on Big Data Technology Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Research on detection of parking space based on the combination of magnetoresistance and microwave radar sensor under IoT platform Research on sustainable development mechanism of regional ‘Artisan Workshop’ under big data environment Application of hybrid kernel function in economic benefit analysis and evaluation of enterprises The analysis method of the impact of missing audit information on the securities investment decisions based on Logistic regression models Research on the innovation theory of college students’ ideological and political education under the background of big data Research on classification of e-commerce customers based on BP neural network Research on the problems and reform strategies of government statistics based on big data technology The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Adaptive fusion of multi-exposure images based on perceptron model Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Exploring the Path of Integrating Excellent Traditional Culture into Civic Education in Universities in the Internet+ Era Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate Design and research of environmentally friendly field sewage purification mechanical device 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System An analysis of time commitment for college students to online English writing and peer assessment learning Research on network security management monitoring platform based on Internet of things technology Study of frictional wear properties of materials for mechanical seals Fractional Differential Equations in Electronic Information Models Exploring the construction of an all-round cost management system for investment control in university engineering construction BIM Engineering Management Oriented to Curve Equation Model Relationship Between Physical Activity Sedentary Behavior and Body Mass Index in Children and Adolescents Based on FIT Modelo Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Grid data asset relationship and intelligent classification integrating knowledge graph and Internet of Things Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Analysis of digital humanistic knowledge production based on natural language processing Design of language assisted learning model and online learning system under the background of artificial intelligence Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering The Construction of Judgment Model for Cultivating Intelligent Accounting Professionals in Universities Based on Logarithmic Periodic Power Law Model Action of Aut( G ) on the set of maximal subgroups ofp -groupsDigital Regeneration and Database Construction of Hunan Embroidery Needlework under the Perspective of Artificial Intelligence Research on the practice of innovation and entrepreneurship education in universities under the environment of big data Application of digital technology in environmental art design Research on loyalty prediction of e-commerce customer based on data mining Research on the evaluation system of tourism management classroom teaching based on multimedia big data analysis The application of ARCS motivation model in college oral English teaching Research on Innovation of Translation Teaching and Translation Strategies for College Students in Multimedia Background A multi-channel convolutional neural network based on attention mechanism fusion for facial expression recognition Exploring the development of cultural and creative tourism under the perspective of ecological theory of tourism destination management Modeling Analysis of User Consumption Data of Internet Culture Industry in the Context of Emerging Technologies Reference: An algorithm for recognizing the main melody of orchestral music based on artificial intelligence of music melody contour Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Evaluation and prediction of regional human capital based on optimised BP neural network Study on inefficient land use determination method for cities and towns from a city examination perspective A study of local smoothness-informed convolutional neural network models for image inpainting The construction of a practical platform for party building and ideological and political education based on information fusion A study on the influence of the spread of Yangming Studies in Japan on the psychology of the Japanese people based on big data analysis Research on personalized recommendation algorithm for micromechanical sensors based on cloud model Research on the value of modern vernacular literature in contemporary rural construction based on ADDIE model Robust speech recognition based on deep learning for sports game review Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Model Construction of Influencing Factors of Physical Education Core Quality Cultivation Based on Multiple Linear Regression Application of Nonlinear Differential Equation in Electric Automation Control System Research on the operation and management mechanism of cross-border e-commerce shared practice training base Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Strategies for improving Chinese language proficiency based on artificial intelligence technology The success rate model of college students’ new entrepreneurship based on nonlinear differential equations Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Research on the application of marketing strategy of national fitness exercise and dance events in the construction of sports culture based on big data technology Decisions of competing supply chain with altruistic retailer under risk aversion Strategies for constructing mathematical models of nonlinear systems based on multiple linear regression models Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations Research on human resource management performance evaluation based on BP algorithm The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network Law of interest rate changes in financial markets based on the differential equation model of liquidity Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Badminton players’ trajectory under numerical calculation method Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Innovation of Economic Management Risk Control in Retailer Supply Chain Based on Differential Equation Model Statistical Model of College Ideological and Political Learning Based on Fractional Differential Equations Nonlinear Differential Equation in Anti-aging Test of Polymer Nanomaterials Mechanics of Building Structural Materials Based on Lagrangian Mathematical Model Analysis The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations Application of regression function model based on panel data in financial risk management of bank resource allocation University Ideological and Political Learning Model Based on Statistical Memory Curve Mathematical Equation Research on Resonance Properties of Semantic Wave Fractal Fractals Based on Quantitative Analysis of English Corpus Research on urban landscape big data information processing system based on ordinary differential equations Modeling of fractional differential equation in cloud computing image fusion algorithm Conventional Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of E-commerce Platform The Security of Database Network Model Based on Fractional Differential Equations Electric Vehicle Mechanical Transmission System Based on Fractional Differential Equations The Practice System of Physics and Electronics Courses in Higher Vocational Colleges Based on Fractional Differential Equations The Economic Model of Rural Supply and Demand Under the Data Analysis Function Based on Ordered Probit 3D Modeling System of Indoor Environment Art Landscape Design under Statistical Equation Electronic Information Security Model of Nonlinear Differential Equations The Optimization Model of College Students' Physical Exercise Motivation and Self-control Ability Based on the Mathematical Model of Probability Theory Health monitoring of Bridges based on multifractal theory Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Application and risk assessment of the energy performance contracting model in energy conservation of public buildings Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas Criminal law imputation path for biometric information Research on composite dynamic disaster prevention and control system of mine earthquake and shock in thick and hard rock mines Research on urban energy Internet planning based on fuzzy comprehensive method Research on innovative strategies of college students’ English teaching under the background of artificial intelligence Electromagnetic interference prediction technology of new energy motor drive system Research on the intelligent path of college students’ network ideological and political education based on big data mining technology Research on the application of PLC technology in electrical automation engineering Application of matrix multiplication in signal sensor image perception Analysing the variation of metadiscourse verb patterns in English academic papers from within and between disciplines Impact of COVID-19 policy on stock prices of listed property companies Research on the experimental principle of deep integration of LETS software and criminal procedure under the background of artificial intelligence VR-based computer maintenance practical training platform development design and application research Design and implementation of an integrated management system for discipline construction and postgraduate education in universities Research on innovative human capital for China’s economic development based on STI model In-depth analysis of the artistic expression of paper-cut elements in the design of boat space Knowledge graph construction and Internet of Things optimisation for power grid data knowledge extraction Modeling the pathway of breast cancer in the Middle East Construction and intelligent analysis of power grid physical data knowledge graph based on Internet of Things for power system Research on industrial Internet of Things and power grid technology application based on knowledge graph and data asset relationship model Research on the effects of financial literacy on rural household credit constraint Research on educational resource recommendation system based on MRLG Rec Visual analysis of the trend of mental health changes among Chinese college students in the context of the normalisation of the new crown epidemic A study on the phenomenon of anaphoric correction in college students’ English conversation Limit cycles of a generalised Mathieu differential system Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Application of data mining in basketball statistics The nonlinear effects of ageing on national savings rate – An Empirical Study based on threshold model Design of fitness walker for the elderly based on ergonomic SAPAD model Research on the innovation of collaborative education model of scientific research and teaching in colleges and universities based on the theory of process reengineering AtanK-A New SVM Kernel for Classification The innovative path of diversified vocal music education reform in colleges and universities under the advanced educational concepts of China and the West Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Rhino application in ceramic packaging design teaching Study of a linear-physical-programming-based approach for web service selection under uncertain service quality Analysis and countermeasures of cultivating independent learning ability in colleges teaching English based on OBE theory A mathematical model of plasmid-carried antibiotic resistance transmission in two types of cells Projection of Early Warning Identification of Hazardous Sources of Gas Explosion Accidents in Coal Mines Based on NTM Deep Learning Network Burnout of front-line city administrative law-enforcing personnel in new urban development areas: An empirical research in China RETRACTION NOTE Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Research on non-linear visual matching model under inherent constraints of images Good congruences on weakly U-abundant semigroups Can policy coordination facilitate unimpeded trade? An empirical study on factors influencing smooth trade along the Belt and Road Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Research on design of customer portrait system for E-commerce Research on rule extraction method based on concept lattice of intuitionistic fuzzy language Fed-UserPro: A user profile construction method based on federated learning Design and evaluation of intelligent teaching system on basic movements in PE Research on identifying psychological health problems of college students by logistic regression model based on data mining Research on evaluation system of cross-border E-commerce platform based on the combined model A mathematical model of PCNN for image fusion with non-sampled contourlet transform Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Retraction: Wei, Wei and Lu, Liu. “The influence of X fuzzy mathematics method in basketball tactics scoring” Applied Mathematics and Nonlinear Sciences, vol.7, no.1, 2022, pp.677-684 Retraction Retraction: Retraction of: Mundewadi, R. A. and S, Kumbinarasaiah. “Numerical Solution of Abel's Integral Equations using Hermite Wavelet” Applied Mathematics and Nonlinear Sciences, vol.4, no.2, 2019, pp.395-406