Geometrical Classification of Self-Similar Motion of Two-Dimensional Three Point Vortex System by Deviation Curvature on Jacobi FieldRead the full article
Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches.
Chief Editor, Prof Di Matteo (Department of Mathematics, King’s College London), engages in world-leading multidisciplinary and data-driven research focussed on the analysis of complex data from the perspective of a statistical physicist.
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A Partial Differential Equation-Based Image Restoration Method in Environmental Art Design
With the rapid development of networks and the emergence of various devices, images have become the main form of information transmission in real life. Image restoration, as an important branch of image processing, can be applied to real-life situations such as pixel loss in image transmission or network prone to packet loss. However, existing image restoration algorithms have disadvantages such as fuzzy restoration effect and slow speed; to solve such problems, this paper adopts a dual discriminator model based on generative adversarial networks, which effectively improves the restoration accuracy by adding local discriminators to track the information of local missing regions of images. However, the model is not optimistic in generating reasonable semantic information, and for this reason, a partial differential equation-based image restoration model is proposed. A classifier and a feature extraction network are added to the dual discriminator model to provide category, style, and content loss constraints to the generative network, respectively. To address the training instability problem of discriminator design, spectral normalization is introduced to the discriminator design. Extensive experiments are conducted on a data dataset of partial differential equations, and the results show that the partial differential equation-based image restoration model provides significant improvements in image restoration over previous methods and that image restoration techniques are exceptionally important in the application of environmental art design.
Automatic Recognition of Financial Instruments Based on Anisotropic Partial Differential Equations
In this paper, anisotropic partial differential equations are used to conduct an indepth study and analysis of automatic recognition of financial bills. Firstly, it obtains the invoices of the group enterprise, uses scanning technology and related image recognition technology to capture, process, compress and slice the paper bill content, and then carries out data identification and verification of the image. It classifies the obtained electronic data information into bills, converts it into electronic information related to bills according to the corresponding categories of the bill template, and stores it in the bill table of the database to achieve the management operation of formatted electronic files. After categorizing the bills according to the electronic information of bills to match the business scenarios, financial journal vouchers can be generated according to the preconfigured voucher templates of the corresponding business scenarios, and the financial journal vouchers are converted into voucher messages using XML technology. Finally, we use agent technology to design middleware for heterogeneous financial systems to realize the function of communicating voucher messages to each other in different business systems. The system automatically extracts the key information of invoices through OCR technology and performs real-time verification and cyclical feedback to the verification results to the suppliers. The system has realized the intelligent management of the power company’s VAT invoices, thus greatly enhancing the efficiency of VAT invoice verification and settlement. The automatic tax invoice recognition system adopts a network structured tax invoice recognition model, which eliminates the cumbersome steps of character decomposition and character classification in traditional OCR character recognition. After several trials, it has obtained better experimental results in terms of recognition accuracy, with an accuracy rate of over 93% in the recognition of tax invoice data set.
Asymptotic Behavior of Solution for Functional Evolution Equations with Stepanov Forcing Terms
Through the use of the measure theory, evolution family, “Acquistapace–Terreni” condition, and Hölder inequality, the core objective of this work is to seek to analyze whether there is unique -pseudo almost periodic solution to a functional evolution equation with Stepanov forcing terms in a Banach space. Certain adequate conditions are derived guaranteeing there is unique -pseudo almost periodic solution to the equation by Lipschitz condition and contraction mapping principle. Finally, an example is used to demonstrate our theoretical findings.
Fast Decomposition Algorithm Based on Two-Dimensional Wavelet Transform for Image Processing of Graphic Design
Graphic design is an important part of the design field today. In this era of information explosion, designs that can deliver information faster and more accurately are bound to gain popularity among the public. In this paper, we propose a fast decomposition algorithm image processing method based on a new transform of the wavelet transform, which mainly addresses the problems of large computation of feature points and long-time consumption of traditional image processing algorithms. Firstly, the second-order decomposition of the image is performed by wavelet function to obtain the low-frequency components of the image, and the wavelet gradient vector is used to extract feature points from the overlapping regions of the low-frequency image so that the transformation parameters of feature points can be obtained quickly under the low-frequency image to guide the feature point extraction under the high-frequency image; on this basis, an improved algorithm of image processing based on the fast decomposition algorithm of two-dimensional wavelet transform with planar design is proposed. Using the properties of one-way matching and directional consistency of feature point constraints, the mismatched point pairs are effectively eliminated to improve the feature point matching accuracy and real-time performance. Finally, the effectiveness and feasibility of the proposed method are verified by two sets of experiments.
Identification of Fuzzy Information in English Interpretation Based on the Digital Elevation Model
With the rapid development of information society, a large amount of vague or uncertain English interpretation information appears in daily life. Uncertain information processing is an important research content in the field of artificial intelligence. In this paper, we combine the three-branch concept lattice and linguistic values with the digital elevation model and propose the three-branch fuzzy linguistic concept lattice as well as the attribute approximation method. In this paper, an improved serial algorithm for sink accumulation is proposed. The improved algorithm changes the order of cell calculation; after the cumulative amount of a “sub-basin” is calculated, all cells of the next “sub-basin” are calculated until all cells are calculated. The improved algorithm reduces the overhead space in the calculation process, reduces the pressure of cells entering and leaving the queue, and improves the calculation efficiency. The improved cumulant algorithm is compared with the commonly used recursive cumulant algorithm and the nonrecursive cumulant algorithm, and the improved algorithm improves by about 17% compared with the nonrecursive algorithm at 106 cell level, and the computation time of the recursive algorithm is about 3 times of the improved algorithm. Because the sink accumulation serial algorithm is an important part of the parallel calculation of sink accumulation, and the execution time is shorter by using the improved algorithm, this paper applies the proposed improved accumulation serial algorithm to the process of parallel calculation of accumulation.
The Statistical Analysis of Multidimensional Psychological Characteristics and User Feedback Willingness
The purpose of this paper is to study the influence of multidimensional psychological characteristics on users’ feedback intention by using several statistical analysis methods based on information theory. The feedback process can be described as a communication process based on information theory. The feedback information entropy is associated with the degree of uncertainty elimination of the users who provide feedback information. Many factors are related to this uncertainty, such as information senders often stopped feedback process for some reasons and information senders may have provided fake or spam information. In order to encourage more useful feedback information, a model of a user’s willingness to provide feedback was established with personality traits and cognitive styles as independent variables, feedback motivation as intermediary variables, and feedback willingness as the dependent variable. 206 online and offline questionnaires were obtained to be analyzed by correlation analysis, regression analysis, and structural equation analysis. Cronbach’s coefficient was used to test the reliability of the questionnaire, and exploratory factor analysis method was used to verify the validity of the questionnaire. First, correlation analysis was used to explore the correlation between personality traits, cognitive styles, and motivation factors. Second, we further explored the strength of the relationship of the five correlated groups of variables through linear regression analysis. At last, we conducted structure equation analyses to test the hypotheses. The results show that both personality traits and cognitive styles can have a significant impact on feedback motivation factors and also show that self-efficacy may be the only evident feedback motivation to encourage useful feedback information. The results show that the willing users with extraversion trait are more likely be motivated by self-efficacy and thus have evident feedback willingness.