Measurement Analysis and Evaluation of Twenty-Five Years of Mathematics Education Research in China:Visual Econometric Analysis Based on CiteSpace Knowledge Mapping(1999-2024)

Since the new century,China’s mathematics curriculum reform in basic education has continued to move forward in attempts and explorations,presenting many new changes,trends,movements,and developments.Sorting out,analyzing,and summarizing the achievements,experiences,problems,and challenges in this journey are conducive to providing insights for the reform and development of the Chinese basic education mathematics curriculum in the new era.This paper analyses the research on mathematics education in China(1999-2024)using the visual measurement of CiteSpace knowledge mapping,hoping to provide directions for the future of mathematics education in China.

Source Separation of Diesel Engine Vibration Based on the Empirical Mode Decomposition and Independent Component Analysis

Vibration signals from diesel engine contain many different components mainly caused by combustion and mechanism operations,several blind source separation techniques are available for decomposing the signal into its components in the case of multichannel measurements,such as independent component analysis（ICA）.However,the source separation of vibration signal from single-channel is impossible.In order to study the source separation from single-channel signal for the purpose of source extraction,the combination method of empirical mode decomposition（EMD） and ICA is proposed in diesel engine signal processing.The performance of the described methods of EMD-wavelet and EMD-ICA in vibration signal application is compared,and the results show that EMD-ICA method outperforms the other,and overcomes the drawback of ICA in the case of single-channel measurement.The independent source signal components can be separated and identified effectively from one-channel measurement by EMD-ICA.Hence,EMD-ICA improves the extraction and identification abilities of source signals from diesel engine vibration measurements.

Separation of Comprehensive Geometrical Errors of a 3-DOF Parallel Manipulator Based on Jacobian Matrix and Its Sensitivity Analysis with Monte-Carlo Method

Parallel kinematic machines （PKMs） have the advantages of a compact structure,high stiffness,a low moving inertia,and a high load/weight ratio.PKMs have been intensively studied since the 1980s,and are still attracting much attention.Compared with extensive researches focus on their type/dimensional synthesis,kinematic/dynamic analyses,the error modeling and separation issues in PKMs are not studied adequately,which is one of the most important obstacles in its commercial applications widely.Taking a 3-PRS parallel manipulator as an example,this paper presents a separation method of source errors for 3-DOF parallel manipulator into the compensable and non-compensable errors effectively.The kinematic analysis of 3-PRS parallel manipulator leads to its six-dimension Jacobian matrix,which can be mapped into the Jacobian matrix of actuations and constraints,and then the compensable and non-compensable errors can be separated accordingly.The compensable errors can be compensated by the kinematic calibration,while the non-compensable errors may be adjusted by the manufacturing and assembling process.Followed by the influence of the latter,i.e.,the non-compensable errors,on the pose error of the moving platform through the sensitivity analysis with the aid of the Monte-Carlo method,meanwhile,the configurations of the manipulator are sought as the pose errors of the moving platform approaching their maximum.The compensable and non-compensable errors in limited-DOF parallel manipulators can be separated effectively by means of the Jacobian matrix of actuations and constraints,providing designers with an informative guideline to taking proper measures for enhancing the pose accuracy via component tolerancing and/or kinematic calibration,which can lay the foundation for the error distinguishment and compensation.

Single channel source separation of radar fuze mixed signal based on phase difference analysis

A new method based on phase difference analysis is proposed for the single-channel mixed signal separation of single-channel radar fuze.This method is used to estimate the mixing coefficients of de-noised signals through the cumulants of mixed signals,solve the candidate data set by the mixing coefficients and signal analytical form,and resolve the problem of vector ambiguity by analyzing the phase differences.The signal separation is realized by exchanging data of the solutions.The waveform similarity coefficients are calculated,and the time鈥攆requency distributions of separated signals are analyzed.The results show that the proposed method is effective.

Blind Separation of Speech Signals Based on Wavelet Transform and Independent Component Analysis

Speech signals in frequency domain were separated based on discrete wavelet transform (DWT) and independent component analysis (ICA). First, mixed speech signals were decomposed into different frequency domains by DWT and the subbands of speech signals were separated using ICA in each wavelet domain; then, the permutation and scaling problems of frequency domain blind source separation (BSS) were solved by utilizing the correlation between adjacent bins in speech signals; at last, source signals were reconstructed from single branches. Experiments were carried out with 2 sources and 6 microphones using speech signals at sampling rate of 40 kHz. The microphones were aligned with 2 sources in front of them, on the left and right. The separation of one male and one female speeches lasted 2.5 s. It is proved that the new method is better than single ICA method and the signal to noise ratio is improved by 1 dB approximately.

Performance analysis of an O_2/ CO_2 power plant based on chemical looping air separation

The process of an O2//CO2 power plant based on chemical looping air separation （CLAS） is modeled using the Aspen Plus software. The operating parameters and power consumption of the CLAS unit are analyzed. The CLAS system, thermal power generation system and flue gas cooling and compression unit （CCU） are coupled and optimized, and the temperature and flow of the flue gas extraction are determined. The results indicate that the net plant efficiency of CLAS O2/CO2 power plant is 39.2%, which is only 3.54% lower than that of the conventional power plants without carbon capture. However, the O2/CO2 power plant based on cryogenic air separation technology brings 8% to 10% decrease in the net plant efficiency. By optimizations, the net plant efficiency increases by 1.65%. The energy consumption of the CCU accounts for 59.7% and the pump accounts for 27.1%. The oxygen concentration from the chemical looping air separation unit is 12.2%.

Global-Local Finite Element Analysis for Predicting Separation in Cord-Rubber Composites of Radial Truck Tires

A global-local finite element modeling technique is employed in this paper to predict the separation in steel cord-rubber composite materials of radial truck tires. The local model uses a finite element analysis in conjunction with a glob-al-local technique in ABAQUS. A 3-dimensional finite element local model calculates the maximum cyclic shear strain of an interface between steel cord and rubber materials at the carcass ply shoulder region. It is found that the maximum cyclic shear strain is reliable as a result of the analysis of carcass ply separation in radial truck tires. Using the analysis of the local model, a study of the cyclic shear strain is performed in the shoulder region and used to deter-mine the carcass ply separation. The effect of the change of carcass ply design on the separation in steel cord-rubber composite materials of radial truck tires is discussed.

Greek Texts and the Rigorization of Analysis:An Inquiry into J.L.Lagrange's Work on the History of Mathematics

This paper offers a study of J.L.Lagrange's research on history of mathematics,aiming to clarify Lagrange's intention in carrying out historical work.To this end,I first document how Lagrange worked with and exerted his influence on other scholars in the translation and diffusion of ancient Greek texts.Second,investigating Lagrange's style in doing and writing history of mathematics,this paper takes a new perspective and elucidates his motivation in these activities.In particular,it focuses on Lagrange's presentation of the history of calculus while he was teaching analysis at the Ecole Polytechnique(1795-1799)so as to clarify the function of history in Lagrange's mathematical works.My thesis is that Lagrange's intention in examining the different methods employed by his predecessors was to find inspiration and useful contents in his search for the proper approach to mathematical problems.I thus argue in this paper that history served as a guide or methodology for Lagrange's mathematics.Meanwhile,through an analysis of his historical writing,this paper points to four epistemological values according to which Lagrange judged various historical methods of differential calculus:generality,simplicity,clarity,and rigor.Lagrange's move to rigorize analysis was connected to his interest in and research of Greek texts;he was attempting to introduce the rigor of the ancient Greeks'demonstration in his works of analysis.

MATHEMATICAL AND EXPERIMENTAL ANALYSIS OF AIR SEPARATION BY HOLLOW FIBER MEMBRANES

Approximate solutions for gas separation by hollow fiber membranes have been developedby several investigators.However,there are few reports of experimental verification of the models forhigh stage cut separations.In this work,an approximate mathematical model was developed and wasexperimentally verified for high stage cut air separation.Both countercurrent and cocurrent now pat-terns were used.In addition,the applicability of feed-inside mode for low stage cut air separation byhollow fiber membrane was examined.It was found that feed-inside mods was more advantageousthan feed-outside mode when used for the generation of oxygen-enriched air.

Study on Fractional Separation and GC-MS Analysis of Flash Coal Tar Pyrolysed at Low Temperatures

The composition of low temperature pyrolysis coal tar has an effect on its further processing and reasomble utlization In this paper, the compeition or coal tars produced from both low temperature pyroysis in a fluidized bed aud flash pyrolysis with solid heat carrier have been investigated by the methch of fractional seperation and Gas Chromatography-Mass Spectrometry (GC-MS)- It is observed that the degree of coalification maceral and secondary reaction temperature (freeboard temperature in a fluidized bed) have some iufluence on the composition of coal tars- The main compoundes are phenol cresols,xylenols, naphthalene, alkylnaphthalenes, antbraceue, phenanthrene,acenaphthylene, fluoren, indene and so

Verification of Existence of Harmonic Suppression in Error Separation by Prony Spectrum Analysis

Prony spectrum analysis is employed in this paper to analyze the harmonics of estimation of radial runout of axis in error separation. The result of analysis verifies the existence of harmonic suppression in multi-step method, thereby advancing the study of harmonic suppression which stayed at the theoretical level for years.

Compressed data separation via dual frames based split-analysis with Weibull matrices

In this paper, we consider data separation problem, where the original signal is composed of two distinct subcomponents, via dual frames based Split-analysis approach. We show that the two distinct subcomponents, which are sparse in two diff erent general frames respectively, can be exactly recovered with high probability, when the measurement matrix is a Weibull random matrix （not Gaussian） and the two frames satisfy a mutual coherence property. Our result may be significant for analysing Split-analysis model for data separation.

Aptamer-Based DNA Materials for the Separation and Analysis of Biological Particles

DNA is a biological macromolecule that carries genetic information in organisms.It provides a series of predominant bio-logical advantages,such as sequence programmability,high biocompatibility,and low biotoxicity.As such,it is a unique polymer material that shows great potential for application in biological and medical fields.DNA aptamers are short DNA sequences with a specific ability of molecular recognition.With its discovery,the application prospect of DNA materials has broadened,especially for the separation and analysis of biological particles.In this review,the functions and characteristics of DNA aptamers are introduced,and the applications of DNA materials in cell/exosome separation and cancer detection are summarized.The application prospect and possible challenges of DNA materials are predicted.

Separation work analysis of cohesive law and consistently coupled cohesive law

An appropriate coupled cohesive law for predicting the mixed mode failure is established by combining normal separation and tangential separation of surfaces in the cohesive zone model （CZM） and the cohesive element method. The Xu-Needleman exponential cohesive law with the fully shear failure mechanism is one of the most popular models. Based on the proposed consistently coupled rule/principle, the Xu-Needleman law with the fully shear failure mechanism is proved to be a non-consistently coupled cohesive law by analyzing the surface separation work. It is shown that the Xu-Needleman law is only valid in the mixed mode fracture when the normal separation work equals the tangential separation work. Based on the consistently coupled principle and the modification of the Xu-Needleman law, a consistently coupled cohesive （CCC） law is given. It is shown that the proposed CCC law has already overcome the non-consistency defect of the Xu-Needleman law with great promise in mixed mode analyses.

Multiple transformation analysis for interference separation in TDCS

Various types of interference signals limit the practical application of transform domain communication systems(TDCSs)in the severe electromagnetic field,an orthogonal basis learning method of transformation analysis(OBL-TA)is proposed to effectively address the problem of obtaining an optimal transform domain based on sparse representation.Then,the sparse availability is utilized to obtain the optimal transformation analysis by the iterative methods,which yields the sparse representation for transform domain(SRTD)in unrestricted form.In addition,the iterative version of SRTD(I-SRTD)in unrestricted form is obtained by decomposing the SRTD problem into three sub-problems and each sub-problem is iteratively solved by learning the best orthogonal basis.Furthermore,orthogonal basis learning via cost function minimization process is conducted by stochastic descent,which is assured to converge to a local minimum at least.Finally,the optimal transformation analysis is developed by the effectiveness of different transform domains according to the accuracy of the sparse representation and an optimal transformation analysis separately(OPTAS)is applied to the synthesized signal forms with conic alternatives,dualization,and smoothing.Simulation results demonstrate that the superiorities of the proposed methods achieve the optimal recovery and separation more rapidly and accurately than conventional methods.

The Impact of Peer Instruction on Students’ Achievement in Mathematics Analysis

In this research,we investigated the effect of peer instruction method on the first course mathematics education students’academic achievement and the attitudes of students by using peer instruction method.The implementation was carried out seven weeks with 60 participants in an introduction to mathematics analysis lesson in Suleyman Demirel University in Kazakhstan.Two first course groups were randomly assigned to treatment and control groups.The final results were obtained to measure students’academic achievement and questionnaires used to indicate attitudes towards peer instruction.Data were analyzed,using analysis of t-test(p=0.029)with an alpha significance level of 0.05.The results of final questions indicated,peer instruction has a significant positive effect on students’achievement in the introduction to mathematics analysis course and the results of questionnaires demonstrated peer instruction(PI)has a positive impact on peers’understanding by making learning interesting and interactive,and it also creates conducive atmosphere in the class.

Analysis and Strategy Research on the Mathematics Learning Situation of the Postgraduate Candidates

This study takes the students who intend to study for graduate students as the research object,and makes a questionnaire survey on the mathematics learning situation and learning platform of the postgraduate candidates.Questionnaires were distributed online and offline,and a total of 326 valid questionnaires were collected.Based on 326 questionnaires,this paper analyzes the current learning situation of mathematics in the postgraduate entrance examination and studies the strategies based on the present situation,which points out the direction for the construction of mathematics learning and communication platform based on the needs of postgraduate entrance examination.

Simplified quantitative analysis method and its application in the insitu synthesized copper-based azide chips

Copper-based azide(Cu(N_(3))2 or CuN_(3),CA)chips synthesized by in-situ azide reaction and utilized in miniaturized explosive systems has become a hot research topic in recent years.However,the advantages of in-situ synthesis method,including small size and low dosage,bring about difficulties in quantitative analysis and differences in ignition capabilities of CA chips.The aim of present work is to develop a simplified quantitative analysis method for accurate and safe analysis of components in CA chips to evaluate and investigate the corresponding ignition ability.In this work,Cu(N_(3))2 and CuN_(3)components in CA chips were separated through dissolution and distillation by utilizing the difference in solubility and corresponding content was obtained by measuring N_(3)-concentration through spectrophotometry.The spectrophotometry method was optimized by studying influencing factors and the recovery rate of different separation methods was studied,ensuring the accuracy and reproducibility of test results.The optimized method is linear in range from 1.0-25.0 mg/L,with a correlation coefficient R^(2)=0.9998,which meets the requirements of CA chips with a milligram-level content test.Compared with the existing ICP method,component analysis results of CA chips obtained by spectrophotometry are closer to real component content in samples and have satisfactory accuracy.Moreover,as its application in miniaturized explosive systems,the ignition ability of CA chips with different component contents for direct ink writing CL-20 and the corresponding mechanism was studied.This study provided a basis and idea for the design and performance evaluation of CA chips in miniaturized explosive systems.

Rapid and real-time analysis of multi-component dissolved gas in seawater by Raman spectroscopy combined with continuous gas-liquid separator

Rapid and sensitive detection of dissolved gases in seawater is quite essential for the investigation of the global carbon cycle.Large quantities of in situ optical detection techniques showed restricted measurement efficiency,owing to the single gas sensor without the identification ability of multiple gases.In this work,a novel gas-liquid Raman detection method of monitoring the multi-component dissolved gases was proposed based on a continuous gas-liquid separator under a large difference of partial pressure.The limit of detection(LOD)of the gas Raman spectrometer could arrive at about 14 μl·L^(-1)for N_(2)gas.Moreover,based on the continuous gas-liquid separation process,the detection time of the dissolved gases could be largely decreased to about 200 s compared with that of the traditional detection method(30 min).Effect of equilibrium time on gas-liquid separation process indicated that the extracted efficiency and decay time of these dissolved gases was CO_(2)>O_(2)>N_(2).In addition,the analysis of the relationship between equilibrium time and flow speed indicated that the decay time decreased with the increase of the flow speed.The validation and application of the developed system presented its great potential for studying the components and spatiotemporal distribution of dissolved gases in seawater.

Detection and Separation of Event-related Potentials from Multi-Artifacts Contaminated EEG by Means of Independent Component Analysis

Event-related potentials (ERP) is an important type of brain dynamics in human cognition research. However, ERP is often submerged by the spontaneous brain activity EEG, for its relatively tiny scale. Further more, the brain activities collected from scalp electrodes are often inevitably contaminated by several kinds of artifacts, such as blinks, eye movements, muscle noise and power line interference. A new approach to correct these disturbances is presented using independent component analysis (ICA). This technique can effectively detect and extract ERP components from the measured electrodes recordings even if they are heavily contaminated. The results compare favorably to those obtained by parametric modeling. Besides, auto-adaptive projection of decomposed results to ERP components was also given. Through experiments, ICA proves to be highly capable of ERP extraction and S/N ratio improving.