The development of ink art in China has a history of >1,300 years . The production of ink and wash art is closely related to landscape painting. To some extent, landscape painting has contributed to the emergence and development of ink and wash arts. As a unique art form in China, ink art has an unquestionable position in traditional Chinese painting, and is recognised as the art form that best represents the Chinese spirit . From the perspective of its historical development process, the ups and downs of >1,300 years, the sea and the stormy fields, are enough to witness its indelible historical achievements and status in the field of Chinese art creation . Ink art masters who appeared in various historical periods have made immeasurable contributions to the development of ink art and laid a solid foundation for the development of modern ink art. With the progress of the times and the development of economy and society, China's graphic design is gradually moving towards the direction of internationalisation and diversification. It constantly adapts to the requirements of the commercial society and has made a lot of contributions to the development of the market economy. However, while making progress, this paper should also think carefully about the overall development of graphic design in China .
The trend of modern packaging design has pointed to the global environmental protection principle, and at the same time, more emphasis is on humanised design than ever before, to achieve the coordination of people, packaging and environment. This forces the packaging of products to change . The inheritance and development of traditional ink painting art is constantly reflected in modern packaging design, and seeking innovation, difference and change, integrating the essence of traditional ink painting art with modern design concepts has become a necessity. Under the trend of more and more frequent international exchanges, to adapt to the competition in the modern international market, it is necessary to meet people's pursuit of product personality, fashion and cultural taste, which requires packaging designers to establish new design concepts and further strengthen the cultural connotation and taste of products, and put forward higher requirements for modern packaging design. Therefore, the inheritance and transcendence of traditional culture is a problem that packaging design needs to face and solve, and it is also the only way to make the packaging of Chinese local products with Chinese characteristics [6, 7].
The traditional ink art form comes from the daily life of this article, so it is often endowed with traditional cultural connotation and spirit. Using it in packaging design not only enriches the appearance but also enhances the taste of the product . For example, tea culture can be combined with the art of calligraphy and reflected in modern packaging design. The auspicious patterns in the traditional ink art elements are also the artistic expressions often used in modern packaging design. For example, dragon and phoenix patterns, plant patterns, symbol patterns, etc. and the use of auspicious patterns is the embodiment of the people's longing and pursuit of a better life in all dynasties. Applying these patterns to packaging design can give the product a charming traditional charm . The traditional ink art provides a wealth of design materials for the design of this article, and the unique national attribute reflected by this has become the distinctive feature of modern Chinese packaging design. The modern packaging design of this paper is rooted in the profound cultural background, combined with the current advanced concepts and methods, to create a modern packaging design with distinctive Chinese characteristics. This not only brings beautiful visual experience to consumers, but also easily arouses the aesthetic identity and emotional resonance of modern people, so that the traditional Chinese culture can be displayed and spread .
The function of the ink-wash image preprocessing system is that, after processing input ink-wash image, we get an output which is the processed result data called primitives. In fact, the output primitives are organically combined into ‘objects’ of this module. The area of interest in the ink image is separated, and then it is segmented, fused, then skeleton extraction and other processing are performed, and finally we get the primitive information as the output. The ink and wash image preprocessing system is the first processing module designed in this paper. If the ink wash image preprocessing system to the stylised rendering system is regarded as an ink wash image data processing process, then the preprocessing system and every other subsystem again are associated input and output data . Ink image preprocessing is the premise of the design of ink painting artistic style. Only on the basis of good ink image preprocessing specific feature analysis and feature extraction can be carried out effectively. Therefore, it is very important to choose a stable preprocessing algorithm. First of all, for the result of ink image processing, as these primitive information will be transmitted to the style learning system, they will be called input samples in the style learning system. It is stipulated here that in the ink-wash image preprocessing subsystem, the results of the ink-wash image processing are collectively referred to as primitives .
The skeleton information obtained from the skeleton extraction of the texture describes the extension direction of the primitive pixels to a certain extent. The length of the skeleton in this system is normalised to [0, 1]; the position coordinate (x, y) of any point on the skeleton in the primitive texture area is the
The system not only needs to extract the various primitives of the original ink image, but also organically combine the discrete primitives into different ‘objects’.
An object is a collection of primitives that are relatively close in the spatial and colour domains. From the perspective of the whole system, combining primitives into objects is the process of extracting objects of different ink styles from ink works . Therefore, the ink image segmentation algorithm in this paper consists of two parts namely region growing and object extraction. Region growing is a process of aggregating pixels or seed regions into large regions according to pre-defined criteria; the basic method is to start with a set of ‘seed’ points and attach adjacent pixels with similar properties to the seed to each seed of the growing region, until no pixels meet the conditions for joining a region. The most important part of the region growing method is the selection algorithm of seed points and the similarity measure function between regions. Here, the description of the two parts selected for this topic is given first, and then the details of the region growing algorithm process are described in general .
The inter-region similarity measure employed during growth is based on the region-averaged colour distance. Here, the colour distance is defined in the a*b colour space, not the RGB colour space. Because the visual perception of colour in the RGB colour space is non-linear. The a*b colour space is suitable for the representation and calculation of all light source colours or object colours. It is a space that reflects the uniformity of object colours in human perception. The colour space distance obtained in this space is more in line with human visual perception; Perceptual properties of colour differences. Since the ink images processed by this system are mainly stored in RGB colour format, this paper needs to know the conversion formula between the two. To make the conversion easier, this paper first introduces the CIEXYZ space as the transition space. The formula for converting RGB colour space to CIEXYZ space is as Eq. (2):
The conversion formula from CIEXYZ space to a*b space is as follows
In the a*b space, the colour difference between the two colours (L1, a1, b1) and (L2, a2, b2) is defined as the Euclidean distance between them in this space, as shown in Eq. (7)
Skeletons, also known as regional centrelines, are a way to express the structure of a target shape. From the definition of primitives, we can see that the skeleton largely expresses the extension direction of a primitive texture, and at the technical level, it also reflects the path and direction of the painter's strokes when depicting objects . In addition, the texture features of the primitive itself are usually generated along this path, and the average width of the texture that the system needs is to be calculated based on the skeleton information. In general, skeletons have three main properties: continuity, minimum width of 1 and centrality. The traditional technique for extracting the skeleton of a region is the mid-axis transformation. For the skeleton extraction algorithm, first mark the known target point as 1 and the background point as 0; consider the 8-neighbourhood with the boundary point as the centre, denote the centre point as
After checking all boundary points, delete all marked points, and repeat the above steps until no boundary points are marked. The skeletons generated by this method have a disadvantage and are prone to glitches, i.e., short skeleton branches due to unsmooth region boundaries . The glitches interfere with the analysis process in this paper and should be removed. Using the burr culling algorithm, the generated skeleton can be very smooth.
In the skeleton calculation, this paper obtains the shape description of the pixel area, which guarantees the extraction of other information of the primitives in this section. This paper will describe the extraction algorithm of each component data of the primitive . The geometric area refers to the size of the smallest rectangular bounding box representing the pixel area of the primitive itself and its coordinate position in the original image. Since the index number of the segmentation area to which each pixel in the original image belongs has been marked in the ink image segmentation stage, it is natural to get the pixel coordinates of the lower left corner of a certain pixel area when scanning the original image from bottom to top and from left to right and top right position. Here, the lower left corner is marked as (
Primitive ink density represents the average grey level of the primitive texture. In this system, the average grey level of the primitives is normalised to [0, 1] for the convenience of ink colour analysis.
The main colour of the primitive is actually the average colour information of the statistical primitive. Since this information will be used for colour recovery of greyscale primitive textures, this paper should consider extracting the average colour information of the primitives instead of simple RGB colour values. An optional algorithm used here to describe colour information is the HSI colour model . The HSI value is a triple (
In the above three evaluation formulas, if the
The average width of the primitive is the average of the lengths of the vertical segments at all points on the skeleton line (the vertical segments are marked by red lines). The calculation formula is Eq. (15):
As most Chinese ink landscape paintings are drawn with brushes, the brushes are a special painting tool, and the lines drawn by the brush are also very special. It is not difficult to find that the ink lines have a certain width, so the ink line rendering is performed. Previously, the outline of the ink image needs to be further processed, and the concept of the spline model is introduced for this purpose. The so-called spline model represents the ink outline with a strip of a certain width. The purpose is that the spline model can help to use texture mapping technology to complete the rendering of ink lines and make the drawn ink lines more realistic .
The ink and wash line rendering algorithm is completed in three parts: one part is the vectorisation of the ink and wash outline, which simplifies the complete ink and wash outline by reducing the number of coordinates; the second part is the drawing of the spline, by translating and rotating the simplified outline stagnation point. The stagnation point coordinates of the spline are obtained, and the spline model is obtained; the third part is to obtain the real brushstrokes of the painter, and design the algorithm according to the texture mapping technology to complete the outline rendering of the ink and wash lines . Finally, using texture synthesis technology, the hand-painted chapped texture is synthesised into the mountain of the real picture, and the ink painting of the mountain is completed. Then integration the ink mountain and the outline of the ink line is performed to complete the line rendering of the ink landscape painting.
The outer contour vectorisation algorithm of ink images is also applicable to the inner contour. By observing the inner contour obtained after edge detection, it is found that the trend of the inner contour is obviously smooth, and the length of the inner contour is smaller than that of the outer contour. Therefore, the outer contour vectorisation algorithm is applied to the inner contour. When contouring, two principles are followed in threshold selection: one is to choose a larger angle threshold and the other is to choose a smaller sampling interval [23, 24]. Referring to the outer contour vectorisation algorithm, each line array of the inner contour of the ink image is processed separately, and the vectorised coordinates are stored in the array.
Contour vectorisation greatly reduces the number of pixel coordinates, obtains a vectorised mountain contour, and stores the stationary point coordinates in an array. In this section, an algorithm is designed to translate, rotate and connect the stagnation point, so that a mountain contour line evolves from a line to a strip. Let the width of the spline be
Description of spline drawing algorithm: Traverse the pixel coordinates
After calculating the mirror point of
The purpose of colour segmentation of ink and wash images is to determine the information of the sky, trees, waterfalls and people in the image, and to finally find the area that reflects the outline of the ink and wash image. Based on the Euclidean distance formula mentioned previously, according to the calculation of the colour difference of two pixels, all the pixels whose colour difference Δ
Greyscale the ink image after colour segmentation to obtain a greyscale image of the ink image. However, although the ink image in the greyscale image preserves the internal mountains and veins of the ink image, it also preserves information such as trees and rivers. These trivial information will interfere with the extraction of the inner contour of the ink image. The purpose of filtering the image is to reduce the interference of useless information such as trees and rivers on the internal vein texture of the ink image, and to highlight the edges of the internal concave and convex texture of the ink image for easy extraction. The filtering of ink images often starts from the spatial domain, rather than the frequency domain filtering commonly used for signals . Spatial domain filtering is a very important application in ink image processing, which is of great help in reducing noise in ink images. The greyscale image preprocessing of the ink image is filtered by calculating the edge gradient features of the ink image, and the interference is filtered while maintaining the original edge. Its filter formula is shown in Eq. (19)
The gradient magnitude of the boundary taken by
According to the mathematical relationship, the boundary gradient magnitude function Δ
Through the above analysis of the principle of the PM model, the sharpening spatial filter that uses the gradient magnitude function as the control function of the PM model will filter the part with large gradient changes in the ink image, which is obviously contrary to preserving the gradient in the greyscale image. The original intention is of clearly changing lines. Since it is necessary to suppress the filtering in the gradient direction, the filtering control function
The gradient magnitude (Δ
In ink image processing, bilinear interpolation algorithm completes the enlargement or reduction of the original ink image by generating new pixels. Adjust the size of the painter's strokes through bilinear interpolation, so that the real ink strokes can match the width of the spline model. Using bilinear interpolation to calculate the pixel value of a point in the target ink image is to find the 2*2 adjacent pixels of the point in the source ink image, and then use the pixel weighted average of the 2*2 area to obtain the pixel value of a point in the target ink image. The formulas for calculating the bilinear interpolation in the x direction are as follows
In the implementation process,
If the ink image consists of pixels, there will be
Through linear interpolation in the x and y directions, the pixels of the source point are finally transported to the target position to achieve the scaling of the original ink image. The effect of the ink image calculated by the bilinear interpolation algorithm is relatively good, and there will be no obvious distortion and discontinuity, which is a good anti-aliasing technology. The size of the ink stroke is adjusted by the bilinear interpolation algorithm to fit the width of the spline model.
How to use ink art elements precisely in design is a very important issue. The information contained in a graphic element is a complex set. Considering the complexity of the overall style analysis of ink images, the article focuses on the analysis and research; on the characteristics of local brush strokes and technical styles of ink and wash images. The application of ink art elements in packaging design is by no means isolated, but the comprehensive application of concepts, aesthetic techniques and other elements, and only in this way can the characteristics of ink art elements be brought into full play in packaging design. With its unique aesthetic characteristics and profound cultural heritage, ink art is a huge treasure trove to enrich the connotation and expression of packaging design. Integrating the essence of the traditional culture and art of the nation into modern packaging design is beneficial to us – the road of packaging design with Chinese characteristics. It is the essence of national design to carry forward the art of ink painting and to create a packaging design with a rich national meaning. Only the design art based on the local area can better show the due national charm.
Law of interest rate changes in financial markets based on the differential equation model of liquidity Research and implementation of smart city public information mining analysis system based on mobile edge model of game theory Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Design of college education evaluation based on accompanying data acquisition and mathematical analysis Enterprise financial strategy and performance management analysis based on principal component analysis Study on the Dynamic Change of Regional Water Level and Climate Based on Forecast Equation Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Municipal Civil Engineering Construction Based on Finite Element Differential Equations Financial Risk Prevention Model of Financial Institutions Based on Linear Partial Differential Equation Influence of heterogeneity of local officials on the economy of resource-based cities developed with high quality Analysis of influencing factors of SPOC course teaching effect using structural equation modelling Training Model of Basketball Offensive Route Based on Nonlinear Differential Equation Research on the construction of rural interface style based on aesthetic rules Optimization Algorithm of New Media Hot Event Push Based on Nonlinear Differential Equation Mathematical Differential Equation in Calculating the Strength of Building Beam Structure Impact Resistance Stability of Building Structural Engineering Based on Fractional Differential Equations The Technical Research on the Assessment of Network Security Situation Based on D-S Evidence Theory Computer big data modeling system based on finite element mathematical equation simulation Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation The Composition System of Pop Music Movement Based on Finite Element Differential Equations The Structure and Influencing Factors of Innovation and Entrepreneurship Ability of Higher Vocational Students Based on Structural Equation Model Model System Study of Accordion Score Based on Fractional Differential Equations Data mining of Chain convenience stores location Parameter Id of Metal Hi-pressure State Equation P-Matrix Reasoning and Information Intelligent Mining Symmetry Analysis and Exact Solutions of Extended Kadomtsev-Petviashvili Equation in Fluids Research on Detection Model of Abnormal Data in Engineering Cost List Research on deformation monitoring of tunnel engineering based on 3D laser scanning Solidification treatment effect of wellsite waste mud based on physical adsorption of a composite curing agent A study of immersive technology for product usability improvement design based on comprehensive value evaluation Intelligent Recommendation System for English Vocabulary Learning – Based on Crowdsensing Application of Nonlinear Fractional Differential Equations in Computer Artificial Intelligence Algorithms Application of calculus function and value chain analysis method in the quantification of financial flexibility management indicators Optimal Research in Piano Shape Sound and Sound Propagation Model Based on Nonlinear Differential Equations Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Badminton players’ trajectory under numerical calculation method Mathematical methodology in the seismic resilience evaluation of the water supply system Prediction of surface quality in end milling based on modified convolutional recurrent neural network Analysis of IPO pricing efficiency under the registration system Case application data research of traditional ink art elements in packaging design Research on an early warning model of effectiveness evaluation in ideological and political teaching based on big data Application of intelligent teaching resource organisation model and construction of performance evaluation model Secure transmission of simultaneous wireless information and power transfer system for Internet of things Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Numerical simulation of vortex vibration in main girder of cable-stayed bridge based on bidirectional fluid–structure coupling Research on location algorithm of new energy vehicle charging station based on multi-objective decision Optimisation of construction mode of residential houses based on the genetic algorithm under BIM technology A study on the reform of college English education inspired by the cultural differences between China and the United States Research on innovative strategies of college students’ English teaching under the blessing of big data Research on multi-dimensional optimisation design of user interface under Rhino/GH platform Has the belt and road initiative boosted the resident consumption in cities along the domestic route? – evidence from credit card consumption Attitude control for the rigid spacecraft with the improved extended state observer A long command subsequence algorithm for manufacturing industry recommendation systems with similarity connection technology Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Evaluation of spoken English self-study system considering speech knowledge recognition algorithm Application research on piano teaching in colleges and universities based on remote wireless network communication Construction of Financial Risk Evaluation Index System for Biomass Graphene Fibre Industrialisation Project System dynamics model of output of ball mill Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel 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 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 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 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 Innovation of Economic Management Risk Control in Retailer Supply Chain Based on Differential Equation Model Computer vision recognition and tracking algorithm based on convolutional neural network 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 p m− x+ δ) s+ ax p m+ bxover F p2 m 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 Statistical Model of College Ideological and Political Learning Based on Fractional Differential Equations Research on the driving principle and guiding strategy of the public's collaborative supervision of the sharing economy in my country Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development Nonlinear Differential Equation in Anti-aging Test of Polymer Nanomaterials Application research of bel canto performance based on artificial intelligence technology Fractal structure of magnetic island in tokamak plasma 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 Application of knowledge graph in smart grid fault diagnosis University Ideological and Political Learning Model Based on Statistical Memory Curve Mathematical Equation Research on the optimisation of logistics parcel intelligent sorting and conveying chain combined with variable clustering mathematical method Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations 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 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 Conventional Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education LTE wireless network coverage optimisation based on corrected propagation model The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of E-commerce Platform Study on tourism development income index calculation of finite element ordinary differential mathematical equation 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 Impact of ASEAN-China free trade area on fishery value chain based on difference-in-difference method 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 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 application of PLC technology in electrical automation engineering Research on indoor environment design of comprehensive commercial shopping center based on numerical simulation Application of matrix multiplication in signal sensor image perception Empirical analysis of the economic absolute income hypothesis based on mathematical statistics 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 Realization of Book Collaborative Filtering Personalized Recommendation System Based on Linear Regression Equation Research on the experimental principle of deep integration of LETS software and criminal procedure under the background of artificial intelligence 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 VR-based computer maintenance practical training platform development design and application research 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 Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer Football Offense Training Strategy Based on Fractional Differential Mathematical Modeling Research on educational resource recommendation system based on MRLG Rec 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 A study on the phenomenon of anaphoric correction in college students’ English conversation 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 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 fuzzy constrained programming mathematical model Basketball Shooting Rate Based on Multiple Regression Logical-Mathematical Algorithm The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis Similarity Solutions of the Surface Waves Equation in (2+1) Dimensions and Bifurcation Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns Game theoretic model for low carbon supply chain under carbon emissions reduction sensitive random demand 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 AtanK-A New SVM Kernel for Classification Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Study of a linear-physical-programming-based approach for web service selection under uncertain service quality The Relationship Between College Students’ Taekwondo Courses and College Health Based on Mathematical Statistics Equations 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 Fractional Differential Equations in the Exploration of Geological and Mineral Construction AdaBoost Algorithm in Trustworthy Network for Anomaly Intrusion Detection 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 Enterprise Financial Risk Early Warning System Based on Structural Equation Model A Study on the Application of Quantile Regression Equation in Forecasting Financial Value at Risk in 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 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 A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes Design and evaluation of intelligent teaching system on basic movements in PE 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 Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching 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 Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method 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 Application of hybrid kernel function in economic benefit analysis and evaluation of enterprises Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model 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 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 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 Action of Aut( G) on the set of maximal subgroups of p-groups Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Research on loyalty prediction of e-commerce customer based on data mining 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 sentiment analysis method based on bidirectional long short-term memory networks A study of local smoothness-informed convolutional neural network models for image inpainting Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations 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