rss_2.0Mathematics FeedSciendo RSS Feed for Mathematics Feed adaptive watermark embedding and detection algorithm based on phase function equation<abstract> <title style='display:none'>Abstract</title> <p>In order to improve the video watermark embedding strength and balance the transparency of the watermark system, this paper proposes a combination of all phase Biorthogonal Transform and watermark embedding to complete the experiment. Firstly, the all phase biorthogonal transform is described. Referring to the construction process of APBT, combined with APDF and DST, a new all phase biorthogonal transform, all phase discrete sinusoidal biorthogonal transform (APDSBT), is proposed. This paper makes full use of MPEG-2 compression format to embed watermark directly in DCT domain. The low-frequency coefficients in the DCT block of the brightness space of I frame are selected as the watermark embedding space. The brightness component of each image block is transformed by two-dimensional DCT in the unit of 8×8 image blocks. By introducing the idea of energy receiver into the detection of digital watermark, the following correlation detector can be obtained. Implemented with MATIAB and VC + +. In the experiment, the foreman video test sequence is used as the watermark carrier, and the copyright logo image designed by ourselves is used as the watermark image to test the video watermarking system. The results show that when the coding rate is 3Mvps, the accuracy of each plane is 100%, 98.48%, 98.12% and 96.27% respectively. When the coding rate is 2.6Mvps, the accuracy of each plane is 100%, 96.38%, 94.87% and 95.21% respectively. This algorithm selects the frame of video to embed watermark. On the premise of ensuring video quality, this algorithm is robust to common video watermark attacks (MPEG compression, frame loss, frame clipping and frame rearrangement).</p> </abstract>ARTICLE2022-07-15T00:00:00.000+00:00Research on Resonance Properties of Semantic Wave Fractal Fractals Based on Quantitative Analysis of English Corpus<abstract> <title style='display:none'>Abstract</title> <p>Aiming at the increasing research demand of the resonance properties of semantic waves in quantitative analysis of English corpus, this paper constructs a three-dimensional integrated fractal model of semantic waves, and extends the transformation of semantic waves in system functional linguistics to the lexical grammar level. The in-depth analysis provides objective and explicit analysis and identification criteria for the study of semantic waves in the legalized code theory. Through the experimental method, the type resonance characteristics between different types of semantic waves in English popular science discourses are investigated. The experimental results show that the frequency of peaks and troughs varies from 2 to 153 based on different characters, and the construction of different types of semantic waves presents the legalized communication process of knowledge popularization, embodies the social education essence of popular science practice, and is the basis of popular science discourse. The legal representation of persuasive and informative discourse features in the process of knowledge construction provides a reference standard.</p> </abstract>ARTICLE2022-07-15T00:00:00.000+00:00A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations<abstract> <title style='display:none'>Abstract</title> <p>In order to solve the system of compatible nonlinear equations, the author proposes a hybrid computational intelligence method of Newton's method and genetic algorithm. First, the Quasi-Newton Methods (QN) method is given. Aiming at the local convergence of the algorithm, it is easy to cause the solution to fail. By embedding the QN operator in the Genetic Algorithm (GA) and defining the appropriate fitness, thus, a hybrid computational intelligence algorithm of CNLE is obtained that combines the advantages of GA and QN method, which has both faster convergence and higher probability of solving. Experimental results show that: The value of the selection probability <italic>p<sub>n</sub></italic> of the QN operator also directly affects the solution efficiency. Generally speaking, for strong nonlinear CNLE composed of multimodal functions, <italic>p<sub>n</sub></italic> can be larger; For weakly nonlinear CNLE composed of functions with fewer extreme points and stronger monotonicity, <italic>p<sub>n</sub></italic> can be smaller. It is demonstrated that the computational results show that this method significantly outperforms the GA and QN methods.</p> </abstract>ARTICLE2022-07-15T00:00:00.000+00:00Financial customer classification by combined model<abstract> <title style='display:none'>Abstract</title> <p>This paper explores the pros and cons of different algorithm models on the same selection problem, and then uses the combined prediction theory to obtain a new combined prediction model to explore its prediction accuracy. The actual problem to be solved is to help financial institutions to scientifically classify customers who choose financial products. We select the bank data set in the UCI database, which is derived from the survey data of a customer conducted by a financial institution in Portugal for a wealth management product. Decision tree C5.0 algorithm, naive Bayes classification algorithm and binary logit model are individually used to carry out a single model of empirical research on financial product customer classification. Through the empirical analysis of the five combination models, it is concluded that in the model that uses the least squares weighting method to determine the weight, the weight appears negative, which does not conform to the actual situation. The model that is based on the least squares weighting method and the model that is based on the simple weighting method are excluded. In contrast, the arithmetic mean weighted model is better than the reciprocal variance weighted model and the reciprocal mean square model. The accuracy reaches 89.91%, which is 0.43% higher than the accuracy of a single model. It can be concluded that the model that is based on the arithmetic average weighting is a better combination forecasting model.</p> </abstract>ARTICLE2022-05-31T00:00:00.000+00:00The Technical Research on the Assessment of Network Security Situation Based on D-S Evidence Theory<abstract> <title style='display:none'>Abstract</title> <p>With the increasing importance of network security, more attention is paid to the research on network security situation awareness, while network security situation assessment is the core of situation awareness. The existing situation assessment technology has many problems, such as unitary methodology, large-scale subjective factors and so on, affecting the accuracy of situation assessment. Combined with the traditional network security technology, this paper sets up a three-layer evaluation index system, and puts forward an overall network security situation evaluation model based on hidden Markov model, PageRank algorithm and D-S evidence theory, through which, the overall situation is evaluated after using different fusion algorithms in different fusion stages. The simulation result shows that the above assessment method is more accurate and efficient than the method using single model.</p> </abstract>ARTICLE2022-07-15T00:00:00.000+00:00Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval<abstract> <title style='display:none'>Abstract</title> <p>The basic theory of the neural network model used in this research is particle swarm optimization, applied to English-Chinese translation retrieval and model optimization. The decoded form obtains the translation task sequence. This topic uses TensorFlow to complete the construction of the translation system. This research solves the typical lack of semantic information in the hierarchical model. The demonstration of examples shows that the neural network model based on particle swarm optimization can significantly improve the quality of machine translation.</p> </abstract>ARTICLE2022-07-15T00:00:00.000+00:00Enterprise financial strategy and performance management analysis based on principal component analysis<abstract> <title style='display:none'>Abstract</title> <p>Under the condition of social and economic growth rate continues to slow down, enterprises put forward environmental protection policies from the perspective of long-term development of resource construction, and enterprises will face more and more competitive pressure. If an enterprise wants to break through its own development bottleneck and become one of the enterprises drafting national standards in the industry, it must have a comprehensive understanding of its financial strategy and performance management program. This paper studies using the principal component analysis (pca), after consulting relevant financial performance evaluation literature, based on an enterprise's financial performance data for principal component analysis, will have access to financial performance evaluation results ranking and scoring, not only can be found that there were problems, also will use modern management theory to replace the traditional financial performance evaluation methods, Give priority to scientific and comprehensive financial indicators for performance evaluation, so as to put forward effective solutions to help enterprises to clarify their own competitive pressure and market positioning.</p> </abstract>ARTICLE2022-07-15T00:00:00.000+00:00Research on deformation monitoring of tunnel engineering based on 3D laser scanning<abstract> <title style='display:none'>Abstract</title> <p>The paper mainly studies the deformation monitoring of tunnel engineering based on 3D laser scanning. First, the principle and characteristics of 3D laser scanning technology are expounded, which lays a theoretical foundation for the research. Then, the flow and main technologies of tunnel engineering deformation monitoring are analysed. Among them, the general process includes four stages: preliminary preparation, point cloud data capture, point cloud data processing and deformation analysis. The main technologies include point and data pre-processing technology and tunnel axis fitting. Finally, combined with the case, deformation monitoring is implemented to analyse the deformation of the tunnel in detail.</p> </abstract>ARTICLE2022-06-15T00:00:00.000+00:00ℋ-compactness in GTS<abstract> <title style='display:none'>Abstract</title> <p>Using the notion of operations on a generalized topological space (<italic>X, µ</italic>) and a hereditary class we have introduced the notion of <italic><sub>γµ</sub></italic>-compactness modulo a hereditary class ℋ termed as <italic><sub>γµ</sub></italic>ℋ -compactness. We have studied <italic><sub>γµ</sub></italic>ℋ-compact spaces and <italic><sub>γµ</sub></italic>ℋ-compact sets relative to <italic>µ</italic>.</p> </abstract>ARTICLE2022-09-25T00:00:00.000+00:00A simpler method to get only the true solutions of cubic and quartic equations using Tschirnhaus transformation<abstract> <title style='display:none'>Abstract</title> <p>The classic method of solving the cubic and the quartic equations using Tschirnhaus transformation yields true as well as false solutions. Recently some papers on this topic are published, in which methods are given to get only the true solutions of cubic and quartic equations. However these methods have some limitations. In this paper the author presents a method of solving cubic and quartic equations using Tschirnhaus transformation, which yields only the true solutions. The proposed method is much simpler than the methods published earlier.</p> </abstract>ARTICLE2022-09-25T00:00:00.000+00:00On Traczyk’s BCK-sequences<abstract> <title style='display:none'>Abstract</title> <p>BCK-sequences and <italic>n</italic>-commutative BCK-algebras were introduced by T. Traczyk, together with two related problems. The first one, whether BCK-sequences are always prolongable. The second one, if the class of all <italic>n</italic>-commutative BCK-algebras is characterised by one identity. W. A. Dudek proved that the answer to the former question is positive in some special cases, e.g. when BCK-algebra is linearly ordered. T. Traczyk showed that the answer to the latter is a˚rmative for <italic>n</italic> = 1, 2. Nonetheless, by providing counterexamples, we proved that the answers to both those open problems are negative.</p> </abstract>ARTICLE2022-09-25T00:00:00.000+00:00Multiple Effects Analysis of Hangzhou Issuing Digital Consumer Coupons Based on Simultaneous Equations of CDM Model<abstract> <title style='display:none'>Abstract</title> <p>With the comprehensive development of informatization, digital consumption provides a market space for various consumer coupons. Taking the consumption voucher stimulus method of the Hangzhou Municipal Government as an example, the relevant departments issued a certain amount of electronic consumption vouchers to citizens within the city online, and at the same time tracking the subsequent consumption records to promote the sluggish market economy affected by the new crown epidemic. And stimulation. This article constructs a CDM model to assist in analyzing the joint equation of the economic impact of Hangzhou's digital consumer coupons. The multiple effects of electronic consumer coupons on the market economy and society are discussed and analyzed. After research and discussion, this method can promote the sluggish consumer market in the context of the epidemic.</p> </abstract>ARTICLE2022-07-15T00:00:00.000+00:00Professional English Translation Corpus Under the Binomial Theorem Coefficient<abstract> <title style='display:none'>Abstract</title> <p>This paper proposes a professional English translation corpus based on the binomial theorem coefficients. This paper combines the binomial theorem with the vector space model to analyze the similarity between machine translation and human translation in English translation. The study results show that both human translation and machine translation can experience translation inaccuracies. The English translation based on the binomial theorem is more objective and accurate. The professional English translation corpus established by this method can help us solve the problem of professional terminology translation. The research in this paper has a specific reference value for improving the accuracy of the English translation.</p> </abstract>ARTICLE2022-07-15T00:00:00.000+00:00English Intelligent Question Answering System Based on elliptic fitting equation<abstract> <title style='display:none'>Abstract</title> <p>The elliptic equation intelligent question answering system based on the elliptic equation intelligent question answering system is an intelligent device that combines natural language and data retrieval technology. Knowledge domains used for different purposes are divided into open domains and restricted domains. In order to simplify the existing knowledge of English intelligence answer and elliptic algebra and reduce the efficiency of the questionnaire, a similar algorithm is designed and implemented in the process of English intelligence answer, and the method of distance ellipse switching is adopted. The experimental results show that the accuracy of the questionnaire answering the questions described in this paper is 17% higher than that of general research answers, which confirms the authenticity of the questionnaire algorithm mentioned in this paper. The system not only provides accurate answers to English questions for primary school students, but also plays an important role in the cultivation of English question and answer skills in primary and secondary schools.</p> </abstract>ARTICLE2022-07-15T00:00:00.000+00:00Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation<abstract> <title style='display:none'>Abstract</title> <p>In order to solve the problem of Bragg equation, a research on retrieval and feature of multimedia testing machine is proposed. Firstly, this paper investigates the various stages of multimedia retrieval system and some mainstream multimedia retrieval algorithms, in order to cover all aspects of relevant algorithms. Secondly, on the basis of investigation, eight representative algorithms are selected. These algorithms cover three stages of multimedia retrieval system, including feature extraction stage, feature matching stage and geometric verification stage. Based on the above observed characteristics, finally, some relevant suggestions on architecture design and system optimization are put forward, including the design of single node processor, the design in parallel environment and the suggestions for simulation and evaluation using this test set.</p> </abstract>ARTICLE2022-07-15T00:00:00.000+00:00Financial Risk Prediction and Analysis Based on Nonlinear Differential Equations<abstract> <title style='display:none'>Abstract</title> <p>This paper attempts to use nonlinear differential equations as a research model. The purpose of this paper is to analyze the risk of financial management. This paper uses the chaos theory of a general nonlinear system to study the differential relationship of financial trouble. We use them to research and solve the management problems of the economic system. Then, this paper proposes a model related to the evolution of the economic system and the prediction of financial and financial risks. The research results show that the method proposed in this paper can realize the synchronization and balance point control of general economic chaotic systems.</p> </abstract>ARTICLE2022-07-15T00:00:00.000+00:00Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function<abstract> <title style='display:none'>Abstract</title> <p>Research on the geometric tolerance control method of precision machinery based on image modeling and new saturation function. First, image-based modeling techniques provide a new way to control the saturation function with a dynamic boundary layer from a computer graphics perspective. Then, it proposes a method to represent the dimensional and geometric tolerances of precision machines using changes in the position of control points of geometric elements. Finally, the main content of the tolerance analysis method based on Monte Carlo simulation is proposed, that is, the position of the azimuth control point of all geometric elements on the measurement chain is determined experimentally by using a random number generator. Experiments have shown that the nominal distance between the control points is the nominal size of the geometric elements, and by comparing the variation of the control points with the nominal distance of the control points, it is easy to determine the relationship between tolerance and tolerance. accuracy.</p> </abstract>ARTICLE2022-07-15T00:00:00.000+00:00Music Recommendation Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function<abstract> <title style='display:none'>Abstract</title> <p>This paper proposes a simulation algorithm of transition probability function based on logistic distribution. This method mainly models popularity and state transition probability functions by acquiring consumers' music preferences and likes. Through this mathematical model, this paper obtains the best results that are more in line with consumer preference. This paper conducts a simulation experiment by collecting Netease cloud music data. Finally, through the comparison with the empirical data, it is further demonstrated that the algorithm model in this paper has particular practical value.</p> </abstract>ARTICLE2022-07-15T00:00:00.000+00:00Study on the Dynamic Change of Regional Water Level and Climate Based on Forecast Equation<abstract> <title style='display:none'>Abstract</title> <p>Because there are too many factors affecting the change of hydrometeorological elements in the long term, it is necessary to use a single linear relationship to construct the forecast equation, which will omit too many forecast factors. Therefore, it is necessary to use a variety of nonlinear function types of correlation coefficient calculation and comparison, clear optimization of forecast factors to build the corresponding forecast equation. In this paper, we study spatial change of water in the understanding of trend test principle, analysis method and dynamic time series model, on the basis of based on regional water level change to build the corresponding forecast equation, the design and implementation of the regional water level change and climate dynamics forecasting system software, the empirical analysis found that the regional water level has a close relationship between dynamic change and climate change.</p> </abstract>ARTICLE2022-07-15T00:00:00.000+00:00Stability of Building Structural Engineering Based on Fractional Differential Equations<abstract> <title style='display:none'>Abstract</title> <p>The compression rod is an important stress member of house building and bridge structure. When the load on the compression rod reaches the critical load, the entire structure will lose its stability. We use the fractional-order differential equation of the curvature of the member to bend and apply the fourth-order differential equation's general solution to establish the compression rod's stability model in construction engineering. In this paper, the discrete boundary conditions are applied to the algebraic equation system by the substitution method to obtain the characteristic equation about the buckling load of the compression rod. The research found that the method proposed in the paper is simple. The critical load relation deduced in this paper is reasonable and efficient.</p> </abstract>ARTICLE2022-07-15T00:00:00.000+00:00en-us-1