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With the rapid development and wide application of the digital media technology,the information security problem is becoming more and more highly attention.Because of the various kinds of medias,previous research works have focused on a specific digital media from,such as text,image,audio and video.As a fact that all the objects were expressed in digital forms under the environment of computer and network,a unified form for all kinds of digital media under the complex number base system was proposed.The algorithm of the digital media signal and the complex number intercom version were given,so the relationship among the digital media could be converted to the corresponding geometric relationship on the complex plane.In the experiments,the proposed method was applied to the application of the digital media information hiding.

Retailers are facing with a variety of product information, how to help retailers access to effective commodity sales strategy effectively and accurately is an urgent problem. Based on complex network theory, this paper constructed a complex weighted network model of retail product association. Beginning with the relationship of retail product purchase in the consumer purchase record, retail products wrere nodes and the relationship of different product purchase wrere directed edge, and product sales volume wrere weights. And then, it calculated the node strength. Finally, it used the sales bill data from the K-commerce sites and supermarket to verify the algorithm. This study provided a reference basis for bundling sales, discount promotions and display layout strategies for E-commerce websites or large retailers. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Xinjiang University (Natural Science Edition) is the property of Xinjiang University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Objective Image representation has always been a basic problem in image processing. This paper studies the approach of a digital image expressed as a complex number. The new approach has been applied to image disguise, and the result is satisfying.Method A one-to-one correspondence established between an image and a point in a complex plane based on complex bases under positional number system notation. The relationships between different images can be converted into a plain vector operation, which helps image study using geometric method. Thus, a new image disguise method is realized.Result This image disguise algorithm can not only disguise one or many images, but also allows an image to be disguised many times.Conclusion Experimental results show that our method is numerically stable, can accurately restore secret images in an ideal transmission environment, and can restore secret images with some satisfaction even in a noisy transmission environment. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Cryptologic Research (2097-4116) is the property of Editorial Board of Journal of Cryptologic Research and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Evaluation & Analysis of Drug-Use in Hospitals of China is the property of Evaluation & Analysis of Drug-Use in Hospitals of China Editorial Board and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In order to further improve the self-learning and noise reduction ability of speech enhancement model, a speech enhancement method based on multi-domain fusion and neural architecture search was proposed. The multi-spatial domain mapping and fusion mechanism of speech signals were designed to realize the mining of real complex number correlation. Based on the characteristics of convolution pooling of the model, a complex neural architecture search mechanism was proposed, and the speech enhancement model was constructed efficiently and automatically through the designed search space, search strategy and evaluation strategy. In the comparison and generalization experiment between the optimal speech enhancement model and the baseline model, the two indexes of PESQ and STOI increase by 5.6% compared with the optimal baseline model, and the number of model parameters is the lowest. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Beijing University of Technology is the property of Journal of Beijing University of Technology, Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Molecular Science is the property of Journal of Molecular Science Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Research in Education Sciences is the property of National Taiwan Normal University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Mass resolution of Foureir transform mass spectrometer (FTMS) highly depends on the acquisition time of image charge/current signal. In order to achieve higher resolution with a shorter transient time, apart from increasing the field strength of the analyzer, the high order harmonics in the image charge signal may also be exploited. The image charge or current signal obtained from the planar electrostatic ion trap has a non-sinusoidal waveform which contains many high-order harmonic components. However, presence of high harmonics increases the complexity of spectral analysis, such as identification of a peak for its correct harmonic order, and avoiding quantitation error due to the peak overlapping from different harmonic groups. A new quantitative algorithm consists of a scoring-based peak classification and the least square fitting (SC-LSF), which has been developed to convert image charge or current signal to mass spectrum. The scoring process will go through all the peaks identified above the noise background, for assumptions that the peak belongs to a certain harmonic order. The score will go up when a relevant lower harmonic peak is confirmed. The harmonic order which achieves the highest score, is assigned to the peak so its fundamental frequency can be determined. Through the SC tests, the candidates of all fundamental frequencies are found for all possible m/z of ions. The basis signals for all possible m/z are constructed using the identified fundamental frequencies and are brought to the LSF to determine the intensities of each species. The SC-LSF algorithm was tested using simulated signal from a mixture of 48 different m/z ions. Different levels of artificial noise were added to the signal to challenge the algorithm. The results show a wide range of mass and ion numbers in the sample mixture can be accurately returned through the SC-LSF algorithm even if the transient signal is under high noise condition. LSF in frequency domain is more efficient than in time domain because a subset of frequency points may be selected, so the amount of calculation is massively reduced. In addition, the test proves that good quantitation can be achieved only when LSF is carried out using data in complex number, while fitting with magnitude data results in large errors for ions in the closed mass group. This is because those closed mass peaks are overlapping at certain low-order harmonics and the amplitudes of a FFT spectrum are not addable, thus leading to the fitting errors.

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Southern Energy Construction is the property of Southern Energy Construction Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Hydrographic Surveying & Charting / Haiyang Cehui is the property of Hydrographic Surveying & Charting Editorial Board and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Signal Processing is the property of Journal of Signal Processing and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Advanced Engineering Science / Gongcheng Kexue Yu Jishu is the property of Advanced Engineering Science Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Dalian Polytechnic University is the property of Journal of Dalian Polytechnic University Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Lotus seed has very high nutritional and medicinal value, which consists of lotus shell, lotus kernel and lotus core. Because of the bitter taste, the lotus cores need to be removed before eating. The existing equipment for removing core can remove the lotus core fast by operating the coring bit. Before drilling, the lotus kernel has to be centered in the centering working position. The centering device generally consists of two rotating rollers. Under the action of gravity and friction force, the lotus kernel can be centered in the rotating process. However, the position of the coring bit is fixed in the centering working position, and therefore the drilling deviation occurs due to the diameter variation of lotus kernels, and the lotus cores cannot be removed effectively, which lowers the quality of lotus kernels directly. To solve the above problems, the classification process is applied widely. However, it is ineffective owing to the inaccuracy of the classification process and the high requirement for staff and equipment. In order to avoid this situation, the shape parameters of lotus kernels are firstly measured and analyzed in this paper. The results show that the maximum cross section of the lotus kernel is almost round with a mean roundness deviation of 0.46 mm and the diameter ranges from 9 to 16 mm; the average chordwise curvature radius is 7.764 mm, and the average longitudinal curvature radius is 5.177 mm, therefore, the shape of a lotus kernel can approximate to an ellipsoid. Moreover, the centering deviation of the double roller rolling centering method presents a maximum value of 6.654 mm. Aiming at solving the problem of drilling deviation in the automated coring of lotus seeds, this paper proposes a self-adaptive centering method for lotus seeds based on a slider-crank mechanism and a parallel crank mechanism. By utilizing this method, the position of the coring bit can be automatically adjusted according to the lotus kernel size. A mathematical model of self-adaptive centering is established by the complex number vector method. Once the parameters of the linkages are selected, the centering deviation value is determined. For the self-adaptive centering mechanism, the optimization of the linkage parameters is complicated and difficult to meet the demand through traditional optimization methods. Therefore, in order to make the centering deviation minimum, by utilizing the stochastic optimization algorithm of Cuckoo Search, this paper optimizes the linkage parameters in MATLAB. The initial parameters are as follows: the nest number is 25, the probability of detection is 0.25, and the maximum iteration number is 4×105. The optimized parameters of connecting rod are 88.51, 135.72, 0.12828, and 125.35 mm respectively, and the coaxial deviation between the coring bit axis and lotus kernel axis is lower than 0.05mm. Based on the above study, a self-adaptive machine for removing core of lotus seed was developed and a coring experiment with 400 samples of lotus seeds was carried out. The experimental parameters were as follows: the working cycle was 1.5 s, the roller's rotating speed was 238 r/min, the pressure of the pressing wheel was 25 N, the coring bit diameter was 2.5 mm and the drill speed was 2800 r/min. By measuring the circle run-out value at the maximum cross section of the lotus kernel, the drilling accuracy of lotus seeds were calculated. The results show that the drilling accuracy of a self-adaptive machine for removing core of lotus seed is 91.25%, much higher than that of the existing equipment, which is 60%-70%; moreover, this machine can handle different sizes of lotus kernels. The experimental results verify the effectiveness and practicability of this self-adaptive centering method. [ABSTRACT FROM AUTHOR]

Copyright of Chinese Journal of Preventive Veterinary Medicine / Zhongguo Yufang Shouyi Xuebao is the property of Chinese Journal of Preventive Veterinary Medicine Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Engineering for Thermal Energy & Power / Reneng Dongli Gongcheng is the property of Journal of Engineering for Thermal Energy & Power and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Modern Food Science & Technology is the property of Editorial Office of Modern Food Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Image & Graphics is the property of Editorial Office of Journal of Image & Graphics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

本研究以幼兒階段數感與基本算術能力的發展為目標，設計以心理數線為理論背景的數位數線遊戲，探究心理數線遊戲對幼兒數感與基本算術能力的學習成效，並進行心理數線遊戲及非心理數線遊戲的成效差異比較。本研究採前、後測實驗研究設計，實際研究參與對象為臺灣東部地區的幼兒共105位，將研究對象分為三組（心理數線遊戲組、非心理數線遊戲組與控制組）。結果顯示，以心理數線概念所建構的數位數線遊戲，在數感能力的提升上確實能獲得顯著的學習成效，且傳統的非心理數線概念所設計的數字概念學習遊戲亦同樣能提升幼兒的數感能力。然而，在基本算術能力（加減法）的學習成效上，心理數線遊戲的學習成果明顯比非數線遊戲來得好。研究結果建議，幼教相關教學人員在建構幼兒的數感能力與基礎算術能力時，使用心理數線遊戲是一個很好的教學工具選項。 Background and Purpose The main purpose of teaching number sense to young children is to establish a core knowledge framework for number concepts, thereby enabling young children to understand a wide range of number problems and providing a basis for children to learn more complex number concepts in the future. Number sense is also fundamental for learning formal mathematics later in life. Studies have associated a lack of number sense in early childhood with a subsequent decline and difficulty in mathematical learning. Therefore, cultivating number sense in early childhood is essential for future mathematics achievement. The development of young children’s numerical cognition and mathematical skills is closely linked to the establishment of a mental number line. Additionally, studies have discovered a strong correlation between an individual’s innate perception of the mental number line and their proficiency in a range of mathematical abilities, including understanding number concepts, estimating quantities, and performing arithmetic. With the goal of developing young children’s number sense and basic arithmetic skills, this study designed a set of targeted intervention tools in the form of digital number line games. These tools were designed to help young children develop an understanding of mental number lines, thereby improving their number sense and basic arithmetic skills. This study also compared the improvement effects of the number line game and a non-number line game on the aforementioned learning objectives to determine which game was more effective at improving the relevant learning outcomes. Literature Review The meaning of number sense Number sense can be described as an individual’s ability to understand, relate, and connect numbers. Children with number sense can understand the relevant concepts and principles of numbers. Number sense includes several mathematical aspects, such as the ability for estimating small quantities, counting and cardinality, comparing numbers, recognizing number patterns, and transforming numbers. The concept of number sense in early childhood refers not to a single mathematical ability but rather encompasses a set of essential cognitive components that aid in comprehending numbers and abstract numerical symbols. These components include a conceptual understanding and the ability to perform practical numerical operations. Development of a mental number line and the relationship between a mental number line and number sense in children The ability to place numbers on a mental number line is associated with the development of number sense, which is the ability to understand, relate, and connect numbers. Relevant studies have suggested that an individual’s perception of the mental number line influences their development of several number sense components (e.g., estimating, counting, and transforming numbers). Therefore, as soon as young children are capable of counting, connecting, and estimating the size of numbers and have learnt the numeral system and the spatial arrangement of numbers, they may acquire the ability to perceive a mental number line. Through educational activities, children can learn how to spatially arrange numbers (i.e., visualize a mental number line) and effectively develop a complete understanding of advance number concepts, including number transformation. Relationship between the construction of a mental number line and basic arithmetic The construction of a mental number line involves spatially arranging numbers by size in the mind. Numbers are arranged in a continuous, quantity-based analogical format in ascending order (from left to right). When constructing a mental number line, basic arithmetic is performed. For example, the number after 6 is 7. To arrive at 7, addition arithmetic (6 + 1) must be performed. Therefore, the construction of a mental number line plays an important role in the development of basic arithmetic skills. Methods This study employed an experimental research design. A total of 105 preschool children from rural areas in eastern Taiwan were enrolled into this study. Participants were randomly divided into three groups: two experimental groups and a control group. A pretest-posttest analysis was performed to explore the influence of number line games on number sense and basic arithmetic skills. One-way analysis of covariance was performed to determine whether significant differences were present between the pretest and posttest results and between the three groups to eliminate the influence of confounding variables. Results Results for the number sense Covariate analysis revealed significant differences in posttest scores between the three groups (F(2,101) = 64.47, p < .05, eta squared η 2 = .56). Furthermore, the improvement in number sense in the two experimental groups was significant. Both interventions (a number line game and a non-number line game) significantly improved the number sense to a similar extent. Results for basic arithmetic skills Significant differences were observed in the improvement of addition and subtraction skills between the two experimental groups and the control group. Basic arithmetic skills were better in the two experimental groups than in the control group. Additionally, the group that played the number line game performed significantly better than the group that played the non-number line game. Conclusion This research is one of the few studies that has explored the development of number sense among young children by using a number line game. The findings indicate that the number line game, which was designed in accordance with the mental number line concept, can effectively enhance number sense among young children. However, in terms of improving number sense, similar learning outcomes can also be achieved by using non-number line games. In terms of improving basic arithmetic skills (addition and subtraction), the number line game was more effective than the non-number line game (traditional number decomposition and synthesis game). Furthermore, the non-number line game was more effective than the intervention in the control group. Overall, the digital game intervention aimed at improving mathematical learning among young children (whether it involves a number line game or a traditional non-number line game) had a positive effect on improving numerical ability, including number sense and basic arithmetic. The number line game was more effective than the non-number line game and the intervention in the control group. These findings are expected to advance the theoretical literature of mathematics education in early childhood and the teaching practices of mathematics for young children.

Copyright of Journal of Image & Graphics is the property of Editorial Office of Journal of Image & Graphics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Hebei University of Science & Technology is the property of Hebei University of Science & Technology, Journal of Hebei University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Geomatics & Information Science of Wuhan University is the property of Geomatics & Information Science of Wuhan University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In order to obtain a stable beam pattern and further improve the performance of adaptive beamforming for polarization sensitive array, a Quaternion-Amplitude and Phase Estimation (Q-APES) algorithm is presented for polarization- space adaptive filtering in the paper. First, the quaternion signal model is given and the inherent orthogonal structure of the two component signal output of each sensor has been kept well by using the quaternion signal model. It is obvious that the quaternion signal model is more suitable for two component vector sensor array signal processing than the conventional long vector signal model which is based on the complex number. Second, the conventional APES algorithm for spatial domain filtering has been expanded to the polarization-space adaptive beamforming. The proposed Q-APES algorithm is derived theoretically and the quaternion optimal weight vector is obtained following. Finally, computer simulation results are shown to verify the correctness of the proposed algorithm. The results indicate that Q-APES algorithm can achieve a better filtering performance than the existing Q-MVDR algorithm under the circumstances of strong desired signal power or low sampling snapshot numbers. Moreover, Q-APES algorithm can also perform well even if the incident interference signals are fully correlated with the desired signal. [ABSTRACT FROM AUTHOR]

In the study of the terrain classification based on the Polarimetric Synthetic Aperture Radar (PolSAR), the algorithms based on general CNN do not fully utilize the phase information in different channels, and the pixel-by-pixel classification strategy with extensive redundant computation is inefficient. To mitigate these problems, a deep pixel-to-pixel mapping model in the complex domain is used for achieving a fast and accurate PolSAR terrain classification at a low sampling rate. To completely utilize the phase information, this study uses Group-Cross CNN to extend the original model to the complex domain allowing complex-number input signals and significantly improving the classification accuracy. In addition, to speed up the algorithm, a Fine-tuned Dilated Group-Cross CNN (FDGC-CNN) was adopted to directly achieve pixel-to-pixel mapping as well as improve accuracy. We verified the adopted model on two PolSAR images comprising 16 classes terrains from the AIRSAR and 4 classes terrains from the E-SAR. According to our model, the overall classification accuracies were 96.94% and 90.07% respectively while the running time was 4.22 s and 4.02 s respectively. Therefore, FDGC-CNN achieved better accuracy with higher efficiency compared to SVM and traditional CNN.

In order to deeply understand the influence of driving position of vibrating flip-flow screen on motion characteristic of main and floating screen frame, mechanical model and vibration differential equation of the vibrating flip-flow screen were established with consideration of the effect of damping.The formulas of amplitude and phase of main and floating screen frame were derived using complex number method under different forms, and the method of determining phase through quadrant was also proposed based on practical problems in Engineering.In addition, the feasibility of vibrating flip-flow screen driven by floating screen frame was also analyzed theoretically.The motion characteristics of main and floating screen frame of vibrating flip-flow screen driven by main screen frame and driven by floating screen frame were compared under the condition that only position of vibration exciter was changed while the first natural frequency and the second natural frequency remain unchanged.Eventually, characteristics of the floating driving flip-flow screen were obtained, such as, low resonance frequency, wide frequency modulation area and large amplitude of main and floating screen frame.

In order to obtain the classification of 4-dimensional associative algebras with principal generators over complex number C under isostructuralism, by using the ring theory and distribution of roots of the equations satisfied by the principal generators: one quadruple root, four different roots, one triple root and one simple root, two different double roots, one double root and two different simple roots, the above equations are translated and stretched, then the more simple equations are obtained. By using linear algebras, quotient algebras and maple to make a large number of operations, it is concluded that each isomorphism type has nothing to do with parameters. Finally by comparing each isomorphism type, the complete classification is obtained, which deepens the realization of structure of asso ciative algebra, and provides reference for relative study.

To realize the controllable of the motion state of double generating- wave swing- rod movable tooth drive,the reverse design of wave generator tooth profile is carried out by using the complex number vector method based on the given motion law of the swing- rod. The tooth profile equation of wave generator is built,and the tooth profile equation of central wheel is deduced in detail based on converted gear train and envelope principle to get the same form theoretical tooth profile equations of wave generator and central wheel. The change law of central wheel curvature radius is illustrated based on the same mathematical model analysis,the non- interference conditions of equidistant teeth profile are given. The effect of structure parameters for the minimum profile curvature radius during the process of designing is analyzed and the principle of choosing the parameters is formulated. The change law of the velocity of swing rod movable teeth is analyzed during the transmission process. The results of the design example contribute to the series design and parametric design of double generating- wave swing- rod movable tooth drive while the operating condition is given.

The kinematics characteristic of the closed chain two degree of freedom planar five-bar mechanism is analyzed by using the closed vector polygon projection method,complex number-vector method and matrix method.The kinematics equations are deduced,furthermore,the characteristic and application situations of each method are compared and analyzed.The kinematics equations are validated according to the example designed.By using the Solid Works motion simulation software,the motion path is changed with the original position of driving link,and the inner link between kinematics equations and output motion path is achieved.The reference for solving kinematic characteristic of hybrid driven mechanism in analytic method can be provided.

Copyright of Applied Mathematics & Mechanics (1000-0887) is the property of Applied Mathematics & Mechanics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)