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从“Long time no see”说起
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作者 倪相玉 《中学英语园地(高中一二年级)》 2004年第7期35-36,共2页
前几天,我在20多年前教过的一位学生来看我。我们谈话时,他随手拿起我书桌上的一本英语口语教材翻看,他说:“呀,老师,教材里怎么有错句?”我拿起教材一看,是“Long time no see”。我笑了。“老师,我清楚地记得,我们在中学时... 前几天,我在20多年前教过的一位学生来看我。我们谈话时,他随手拿起我书桌上的一本英语口语教材翻看,他说:“呀,老师,教材里怎么有错句?”我拿起教材一看,是“Long time no see”。我笑了。“老师,我清楚地记得,我们在中学时,您不止一次地在黑板上纠正过类似的错句,怎么20年后它又成对的了?”我说:“你问得好。”接着我对此作了解释。 展开更多
关键词 long time no see 口语表达 语法 习惯用语 高中 英语
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Origin of “Long time,no see”
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作者 张可科 《海外英语》 2013年第8X期208-209,212,共3页
"Long time no see" is a very interesting English expression used as a greeting by people who have not seen each other for a while. The essay shows how Chinese people and native English speaker think about &q... "Long time no see" is a very interesting English expression used as a greeting by people who have not seen each other for a while. The essay shows how Chinese people and native English speaker think about "Long time no see". Meanwhile, it does research upon the historical appearances of the phrase. 展开更多
关键词 long time no see native English SPEAKER CHINGLISH
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A Time Series Intrusion Detection Method Based on SSAE,TCN and Bi-LSTM
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作者 Zhenxiang He Xunxi Wang Chunwei Li 《Computers, Materials & Continua》 SCIE EI 2024年第1期845-871,共27页
In the fast-evolving landscape of digital networks,the incidence of network intrusions has escalated alarmingly.Simultaneously,the crucial role of time series data in intrusion detection remains largely underappreciat... In the fast-evolving landscape of digital networks,the incidence of network intrusions has escalated alarmingly.Simultaneously,the crucial role of time series data in intrusion detection remains largely underappreciated,with most systems failing to capture the time-bound nuances of network traffic.This leads to compromised detection accuracy and overlooked temporal patterns.Addressing this gap,we introduce a novel SSAE-TCN-BiLSTM(STL)model that integrates time series analysis,significantly enhancing detection capabilities.Our approach reduces feature dimensionalitywith a Stacked Sparse Autoencoder(SSAE)and extracts temporally relevant features through a Temporal Convolutional Network(TCN)and Bidirectional Long Short-term Memory Network(Bi-LSTM).By meticulously adjusting time steps,we underscore the significance of temporal data in bolstering detection accuracy.On the UNSW-NB15 dataset,ourmodel achieved an F1-score of 99.49%,Accuracy of 99.43%,Precision of 99.38%,Recall of 99.60%,and an inference time of 4.24 s.For the CICDS2017 dataset,we recorded an F1-score of 99.53%,Accuracy of 99.62%,Precision of 99.27%,Recall of 99.79%,and an inference time of 5.72 s.These findings not only confirm the STL model’s superior performance but also its operational efficiency,underpinning its significance in real-world cybersecurity scenarios where rapid response is paramount.Our contribution represents a significant advance in cybersecurity,proposing a model that excels in accuracy and adaptability to the dynamic nature of network traffic,setting a new benchmark for intrusion detection systems. 展开更多
关键词 Network intrusion detection bidirectional long short-term memory network time series stacked sparse autoencoder temporal convolutional network time steps
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Deep Learning for Financial Time Series Prediction:A State-of-the-Art Review of Standalone and HybridModels
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作者 Weisi Chen Walayat Hussain +1 位作者 Francesco Cauteruccio Xu Zhang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第4期187-224,共38页
Financial time series prediction,whether for classification or regression,has been a heated research topic over the last decade.While traditional machine learning algorithms have experienced mediocre results,deep lear... Financial time series prediction,whether for classification or regression,has been a heated research topic over the last decade.While traditional machine learning algorithms have experienced mediocre results,deep learning has largely contributed to the elevation of the prediction performance.Currently,the most up-to-date review of advanced machine learning techniques for financial time series prediction is still lacking,making it challenging for finance domain experts and relevant practitioners to determine which model potentially performs better,what techniques and components are involved,and how themodel can be designed and implemented.This review article provides an overview of techniques,components and frameworks for financial time series prediction,with an emphasis on state-of-the-art deep learning models in the literature from2015 to 2023,including standalonemodels like convolutional neural networks(CNN)that are capable of extracting spatial dependencies within data,and long short-term memory(LSTM)that is designed for handling temporal dependencies;and hybrid models integrating CNN,LSTM,attention mechanism(AM)and other techniques.For illustration and comparison purposes,models proposed in recent studies are mapped to relevant elements of a generalized framework comprised of input,output,feature extraction,prediction,and related processes.Among the state-of-the-artmodels,hybrid models like CNNLSTMand CNN-LSTM-AM in general have been reported superior in performance to stand-alone models like the CNN-only model.Some remaining challenges have been discussed,including non-friendliness for finance domain experts,delayed prediction,domain knowledge negligence,lack of standards,and inability of real-time and highfrequency predictions.The principal contributions of this paper are to provide a one-stop guide for both academia and industry to review,compare and summarize technologies and recent advances in this area,to facilitate smooth and informed implementation,and to highlight future research directions. 展开更多
关键词 Financial time series prediction convolutional neural network long short-term memory deep learning attention mechanism FINANCE
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LÉVY AREA ANALYSIS AND PARAMETER ESTIMATION FOR FOU PROCESSES VIA NON-GEOMETRIC ROUGH PATH THEORY
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作者 Zhongmin QIAN Xingcheng XU 《Acta Mathematica Scientia》 SCIE CSCD 2024年第5期1609-1638,共30页
This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting.To tackle this problem,we propose a novel approach based on r... This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting.To tackle this problem,we propose a novel approach based on rough path theory that allows us to construct pathwise rough path estimators from both continuous and discrete observations of a single path.Our approach is particularly suitable for high-frequency data.To formulate the parameter estimators,we introduce a theory of pathwise Itôintegrals with respect to fractional Brownian motion.By establishing the regularity of fractional Ornstein-Uhlenbeck processes and analyzing the long-term behavior of the associated Lévy area processes,we demonstrate that our estimators are strongly consistent and pathwise stable.Our findings offer a new perspective on estimating the drift parameter matrix for fractional Ornstein-Uhlenbeck processes in multi-dimensional settings,and may have practical implications for fields including finance,economics,and engineering. 展开更多
关键词 Itôintegration Lévy area non-geometric rough path fOU processes pathwise stability long time asymptotic high-frequency data
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基于Informer的CFB机组长序列NO_(x)排放预测研究与教学实践
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作者 任燕燕 龙嘉豪 +2 位作者 郭晓桐 韦德生 周怀春 《实验技术与管理》 CAS 北大核心 2024年第10期171-179,共9页
为了研究循环流化床机组NO_(x)排放预测问题,采用Informer神经网络模型对某350 MW超临界循环流化床机组NO_(x)排放进行建模研究。首先,获取机组运行数据,对有关数据进行标准化处理;其次,确定实验方案,进行了6种不同NO_(x)排放长序列时... 为了研究循环流化床机组NO_(x)排放预测问题,采用Informer神经网络模型对某350 MW超临界循环流化床机组NO_(x)排放进行建模研究。首先,获取机组运行数据,对有关数据进行标准化处理;其次,确定实验方案,进行了6种不同NO_(x)排放长序列时序预测的仿真实验,并进行分析;最后,利用Transformer模型、RNN模型与LSTM模型按照相同实验方案进行NO_(x)排放预测,并与Informer模型的预测结果进行对比。研究结果表明,Informer模型通过注意力机制、蒸馏机制获得了较好的特征提取能力和长序列输入能力,该模型的NO_(x)排放预测效果在预测精度与时效性两个方面均明显优于其他三种对比模型,能够为循环流化床机组NO_(x)排放预测提供有效技术支持。该能源动力类学生的创新与实践教育项目,有助于锻炼学生的科研思维,能够为能源动力类专业实践教学发展提供一定借鉴。 展开更多
关键词 循环流化床机组 Informer模型 no_(x)排放 长序列时序预测 创新与实践教育
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Long-time Convergence of Numerical Approximations for Semilinear Parabolic Equations (Ⅱ) 被引量:1
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作者 武海军 李荣华 《Northeastern Mathematical Journal》 CSCD 2001年第1期75-84,共10页
In this article we extend ours framework of long time convergence for numeracal approximations of semilinear parabolic equations prorided in “Wu Haijun and Li Ronghua, Northeast. Math. J., 16(1)(2000), 1—28”, to t... In this article we extend ours framework of long time convergence for numeracal approximations of semilinear parabolic equations prorided in “Wu Haijun and Li Ronghua, Northeast. Math. J., 16(1)(2000), 1—28”, to the Gauss Ledendre full discretization. When apply the result to the Crank Nicholson finiteelement full discretization of the Navier Stokes equations, we can remore the grid ratio restriction of “Heywood, J. G. and Rannacher, R., SIAM J. Numer. Anal., 27(1990), 353—384”, and weaken the stability condition on the continuous solution. 展开更多
关键词 long time convergence semilinear porabolic equations Gauss Legendre method
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Binaural Speech Separation Algorithm Based on Long and Short Time Memory Networks 被引量:1
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作者 Lin Zhou Siyuan Lu +3 位作者 Qiuyue Zhong Ying Chen Yibin Tang Yan Zhou 《Computers, Materials & Continua》 SCIE EI 2020年第6期1373-1386,共14页
Speaker separation in complex acoustic environment is one of challenging tasks in speech separation.In practice,speakers are very often unmoving or moving slowly in normal communication.In this case,the spatial featur... Speaker separation in complex acoustic environment is one of challenging tasks in speech separation.In practice,speakers are very often unmoving or moving slowly in normal communication.In this case,the spatial features among the consecutive speech frames become highly correlated such that it is helpful for speaker separation by providing additional spatial information.To fully exploit this information,we design a separation system on Recurrent Neural Network(RNN)with long short-term memory(LSTM)which effectively learns the temporal dynamics of spatial features.In detail,a LSTM-based speaker separation algorithm is proposed to extract the spatial features in each time-frequency(TF)unit and form the corresponding feature vector.Then,we treat speaker separation as a supervised learning problem,where a modified ideal ratio mask(IRM)is defined as the training function during LSTM learning.Simulations show that the proposed system achieves attractive separation performance in noisy and reverberant environments.Specifically,during the untrained acoustic test with limited priors,e.g.,unmatched signal to noise ratio(SNR)and reverberation,the proposed LSTM based algorithm can still outperforms the existing DNN based method in the measures of PESQ and STOI.It indicates our method is more robust in untrained conditions. 展开更多
关键词 Binaural speech separation long and short time memory networks feature vectors ideal ratio mask
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基于MIC-CFS-LSTM的SCR出口NO_(x)浓度动态预测 被引量:4
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作者 吴康洛 黄俊 +4 位作者 李峥辉 阮斌 罗圣 卢志民 姚顺春 《洁净煤技术》 CAS CSCD 北大核心 2023年第6期142-150,共9页
针对燃煤机组选择性催化还原(SCR)系统出口氮氧化物(NO_(x))预测模型精度不高的问题,提出一种基于最大信息系数(MIC)和长短期记忆(LSTM)神经网络的预测模型方法。首先采用MIC估计各变量的延迟时间,对数据进行时延重构;然后采用重构后数... 针对燃煤机组选择性催化还原(SCR)系统出口氮氧化物(NO_(x))预测模型精度不高的问题,提出一种基于最大信息系数(MIC)和长短期记忆(LSTM)神经网络的预测模型方法。首先采用MIC估计各变量的延迟时间,对数据进行时延重构;然后采用重构后数据的MIC值作为评价各输入变量和输出变量间相关性大小的指标,并结合基于关联性的特征选择算法(CFS)进行输入变量筛选;最后基于时延重构和变量筛选后的数据,采用LSTM神经网络建立了SCR出口氮氧化物浓度动态预测模型。该模型被用于广东某320 MW燃煤机组实际运行数据分析。结果表明,经时延重构和变量筛选后所建立的LSTM预测模型具有较高精度,优于深度神经网络(DNN)模型和径向基函数(RBF)神经网络模型,平均绝对百分比误差达2.58%,均方根误差达2.02,可满足现场运用要求。 展开更多
关键词 SCR no_(x)浓度预测 时延分析 变量选择 最大信息系数 长短期记忆神经网络
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Asymptotics of estimators for nonparametric multivariate regression models with long memory
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作者 WANG Li-hong WANG Ming 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2019年第4期403-422,共20页
In this paper,a nonparametric multivariate regression model with long memory covariates and long memory errors is considered.We approximate the nonparametric multivariate regression function by the weighted additive o... In this paper,a nonparametric multivariate regression model with long memory covariates and long memory errors is considered.We approximate the nonparametric multivariate regression function by the weighted additive one-dimensional functions.The local linear smoothing and least squares method are proposed for the one-dimensional regression estimation and the weight parameters estimation,respectively.The asymptotic behaviors of the proposed estimators are investigated. 展开更多
关键词 ADDITIVE model local linear estimation long MEMORY time series
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Time Series Forecasting Fusion Network Model Based on Prophet and Improved LSTM 被引量:1
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作者 Weifeng Liu Xin Yu +3 位作者 Qinyang Zhao Guang Cheng Xiaobing Hou Shengqi He 《Computers, Materials & Continua》 SCIE EI 2023年第2期3199-3219,共21页
Time series forecasting and analysis are widely used in many fields and application scenarios.Time series historical data reflects the change pattern and trend,which can serve the application and decision in each appl... Time series forecasting and analysis are widely used in many fields and application scenarios.Time series historical data reflects the change pattern and trend,which can serve the application and decision in each application scenario to a certain extent.In this paper,we select the time series prediction problem in the atmospheric environment scenario to start the application research.In terms of data support,we obtain the data of nearly 3500 vehicles in some cities in China fromRunwoda Research Institute,focusing on the major pollutant emission data of non-road mobile machinery and high emission vehicles in Beijing and Bozhou,Anhui Province to build the dataset and conduct the time series prediction analysis experiments on them.This paper proposes a P-gLSTNet model,and uses Autoregressive Integrated Moving Average model(ARIMA),long and short-term memory(LSTM),and Prophet to predict and compare the emissions in the future period.The experiments are validated on four public data sets and one self-collected data set,and the mean absolute error(MAE),root mean square error(RMSE),and mean absolute percentage error(MAPE)are selected as the evaluationmetrics.The experimental results show that the proposed P-gLSTNet fusion model predicts less error,outperforms the backbone method,and is more suitable for the prediction of time-series data in this scenario. 展开更多
关键词 time series data prediction regression analysis long short-term memory network PROPHET
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Dynamics and Long Time Convergence of the Extended Fisher-Kolmogorov Equation under Numerical Discretization
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作者 Wang Jue Ma Fu-ming 《Communications in Mathematical Research》 CSCD 2013年第1期51-60,共10页
We present a numerical study of the long time behavior of approxima- tion solution to the Extended Fisher-Kolmogorov equation with periodic boundary conditions. The unique solvability of numerical solution is shown. I... We present a numerical study of the long time behavior of approxima- tion solution to the Extended Fisher-Kolmogorov equation with periodic boundary conditions. The unique solvability of numerical solution is shown. It is proved that there exists a global attractor of the discrete dynamical system. Furthermore, we obtain the long-time stability and convergence of the difference scheme and the upper semicontinuity d(Ah,τ, .A) → O. Our results show that the difference scheme can effectively simulate the infinite dimensional dynamical systems. 展开更多
关键词 Extended Fisher Kolmogorov equation finite difference method global attractor long time stability and convergence
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Analysis of long-term dependence phenomenon in Benue River flow process and its hypothesis testing
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作者 Martins Y. OTACHE 李致家 Mohammad BAKIR 《Chinese Journal of Oceanology and Limnology》 SCIE CAS CSCD 2008年第3期313-322,共10页
In this paper, the long-term dependence phenomenon (the Hurst Effect) which characterizes hydrological and other geophysical times series is studied. The long-term memory is analysed for both daily and monthly strea... In this paper, the long-term dependence phenomenon (the Hurst Effect) which characterizes hydrological and other geophysical times series is studied. The long-term memory is analysed for both daily and monthly streamflow series of the Benue River at Makurdi, Nigeria by using heuristic methods and testing specifically the null hypothesis of short-term memory in the monthly flow series. Results obtained by applying heuristic procedures indicated that there may be the presence of long-term memory component in mean daily flow series but there is no discernible reason to suspect the presence in both average monthly and maximum monthly flow series (extreme event). Hypothesis testing was conducted by using original and modified versions of rescaled range statistic. When the modified rescaled range, which accounts for short-term memory in the series, is used, the null hypothesis is accepted for both the average monthly and maximum monthly flow series, indicating little or no probable presence of long-term memory in the series. An identical conclusion is also arrived at when second null hypothesis for independence of the monthly flow series is tested. Therefore, apart from the mean daily flow series, there is little evidence of long-term dependence in the Benue River streamflow series at Makurdi. However, considering the limited length of data used, the results are inconclusive. 展开更多
关键词 Hurst exponent hydrological method time series river flow long memory NIGERIA
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Source time functions of the 1999, Jiji (Chi-Chi) earthquake from GDSN long period waveform data using aftershocks as empirical Green's functions 被引量:1
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作者 许力生 G.Patau 陈运泰 《Acta Seismologica Sinica(English Edition)》 EI CSCD 2002年第2期121-133,共13页
A large earthquake (Mw=7.6) occurred in Jiji (Chi-Chi), Taiwan, China on September 20, 1999, and was followed by many moderate-size shocks in the following days. Two of the largest aftershocks with the magnitudes of M... A large earthquake (Mw=7.6) occurred in Jiji (Chi-Chi), Taiwan, China on September 20, 1999, and was followed by many moderate-size shocks in the following days. Two of the largest aftershocks with the magnitudes of Mw=6.1 and Mw=6.2, respectively, were used as empirical Green's functions (EGFs) to obtain the source time functions (STFs) of the main shock from long-period waveform data of the Global Digital Seismograph Network (GDSN) including IRIS, GEOSCOPE and CDSN. For the Mw=6.1 aftershock of September 22, there were 97 pairs of phases clear enough from 78 recordings of 26 stations; for the Mw=6.2 aftershock of September 25, there were 81 pairs of phases clear enough from 72 recordings of 24 stations. For each station, 2 types of STFs were retrieved, which are called P-STF and S-STF due to being from P and S phases, respectively. Totally, 178 STF individuals were obtained for source-process analysis of the main shock. It was noticed that, in general, STFs from most of the stations had similarities except that those in special azimuths looked different or odd due to the mechanism difference between the main shock and the aftershocks; and in detail, the shapes of the STFs varied with azimuth. Both of them reflected the stability and reliability of the retrieved STFs. The comprehensive analysis of those STFs suggested that this event consisted of two sub-events, the total duration time was about 26 s, and on the average, the second event was about 7 s later than the first one, and the moment-rate amplitude of the first event was about 15% larger than that of the second one. 展开更多
关键词 Jiji (Chi-chi) earthquake long-period waveform source time function
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Non-stationary Buffeting Response Analysis of Long Span Suspension Bridge Under Strong Wind Loading
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作者 Wenfeng Huang Kongqing Zou 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2016年第6期9-16,共8页
The non-stationary buffeting response of long span suspension bridge in time domain under strong wind loading is computed. Modeling method for generating non-stationary fluctuating winds with probabilistic model for n... The non-stationary buffeting response of long span suspension bridge in time domain under strong wind loading is computed. Modeling method for generating non-stationary fluctuating winds with probabilistic model for non-stationary strong wind fields is first presented. Non-stationary wind forces induced by strong winds on bridge deck and tower are then given a brief introduction. Finally,Non-stationary buffeting response of Pulite Bridge in China,a long span suspension bridge,is computed by using ANSYS software under four working conditions with different combination of time-varying mean wind and time-varying variance. The case study further confirms that it is necessity of considering non-stationary buffeting response for long span suspension bridge under strong wind loading,rather than only stationary buffeting response. 展开更多
关键词 noN-STATIONARY long span suspension bridge strong wind loading time domain analysisCLC number: TU311.3 Document code: A Article ID: 1005-9113(2016)06-0009-08
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Longtime Convergence of Numerical Approximations for Semilinear Parabolic Equations (Ⅰ)
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作者 武海军 李荣华 《Northeastern Mathematical Journal》 CSCD 2000年第1期99-126,共28页
The numerical approximations of the dynamical systems governed by semilinear parabolic equations are considered. An abstract framework for long time error estimates is established. When applied to reaction diffusion... The numerical approximations of the dynamical systems governed by semilinear parabolic equations are considered. An abstract framework for long time error estimates is established. When applied to reaction diffusion equation, Navier Stokes equations and Chan Hilliard equation, approximated by Galerkin and nonlinear Galerkin methods in space and by Runge Kutta method in time, our framework yields error estimates uniform in time. 展开更多
关键词 semilinear parabolic equation Runge Kutta method long time error estimate
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Expression signatures of long non-coding RNA and mRNA in human traumatic brain injury 被引量:8
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作者 Li-Xiang Yang Li-Kun Yang +3 位作者 Jie Zhu Jun-Hui Chen Yu-Hai Wang Kun Xiong 《Neural Regeneration Research》 SCIE CAS CSCD 2019年第4期632-641,共10页
Long non-coding RNAs(lncRNAs) play a key role in craniocerebral disease, although their expression profiles in human traumatic brain injury are still unclear. In this regard, in this study, we examined brain injury ti... Long non-coding RNAs(lncRNAs) play a key role in craniocerebral disease, although their expression profiles in human traumatic brain injury are still unclear. In this regard, in this study, we examined brain injury tissue from three patients of the 101 st Hospital of the People's Liberation Army, China(specifically, a 36-year-old male, a 52-year-old female, and a 49-year-old female), who were diagnosed with traumatic brain injury and underwent brain contusion removal surgery. Tissue surrounding the brain contusion in the three patients was used as control tissue to observe expression characteristics of lncRNAs and mRNAs in human traumatic brain injury tissue. Volcano plot filtering identified 99 lncRNAs and 63 mRNAs differentially expressed in frontotemporal tissue of the two groups(P < 0.05, fold change > 1.2). Microarray analysis showed that 43 lncRNAs were up-regulated and 56 lncRNAs were down-regulated. Meanwhile, 59 mRNAs were up-regulated and 4 mRNAs were down-regulated. Gene Ontology(GO) and Kyoto Encyclopedia of Genes and Genomes(KEGG) analyses revealed 27 signaling pathways associated with target genes and, in particular, legionellosis and influenza A signaling pathways. Subsequently, a lncRNA-gene network was generated, which showed an absolute correlation coefficient value > 0.99 for 12 lncRNA-mRNA pairs. Finally, quantitative real-time polymerase chain reaction confirmed different expression of the five most up-regulated mRNAs within the two groups, which was consistent with the microarray results. In summary, our results show that expression profiles of mRNAs and lncRNAs are significantly different between human traumatic brain injury tissue and surrounding tissue, providing novel insight regarding lncRNAs' involvement in human traumatic brain injury. All participants provided informed consent. This research was registered in the Chinese Clinical Trial Registry(registration number: ChiCTR-TCC-13004002) and the protocol version number is 1.0. 展开更多
关键词 nerve REGENERATION HUMAN TRAUMATIC brain injuries long noncoding RNA messenger RNA GO ANALYSIS real-time quantitative POLYMERASE chain reaction biomarkers microarray ANALYSIS biological processes medical informatics neural REGENERATION
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RHEOLOGICAL BEHAVIOUR FOR AN ANHYDRITE SPECIMEN AND DETERMINATION OF ITS LONG TIME STRENGTH
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作者 李宏 《Journal of Wuhan University of Technology(Materials Science)》 SCIE EI CAS 1999年第3期59-62,共4页
Based on the method of torsional creep, the creep laws of ananhydrite specimen are studied in this paper. When a shearing stressapplied to the specimen is less than a value, only the primary stagetakes place. How- eve... Based on the method of torsional creep, the creep laws of ananhydrite specimen are studied in this paper. When a shearing stressapplied to the specimen is less than a value, only the primary stagetakes place. How- ever, when the shearing stress is more than anothervalue, all the three stages of a creep curve, i. e. primary, steady-state and accelerated are exhibited. 展开更多
关键词 CREEP RHEOLOGY long-time strength of rock
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LONG-TIME CONVERGENCE OF GENERALIZED DIFFERENCE METHOD FOR NAVIER-STOKES EQUATIONS
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作者 Wu Haijun(武海军) +1 位作者 Li Ronghua(李荣华) 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2001年第2期193-208,共16页
In this paper, we first provide a generalized difference method for the 2-dimensional Navier-Stokes equations by combing the ideas of staggered scheme m and generalized upwind scheme in space, and by backward Euler ti... In this paper, we first provide a generalized difference method for the 2-dimensional Navier-Stokes equations by combing the ideas of staggered scheme m and generalized upwind scheme in space, and by backward Euler time-stepping. Then we apply the abstract framework of to prove its long-time convergence. Finally, a numerical example for solving driven cavity flows is given. 展开更多
关键词 generalized DIFFERENCE method staggered scheme UPWIND scheme long-time covergence.
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Long-time limit behavior of the solution to an atom's master equation
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作者 陈俊华 范洪义 姜年权 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第8期161-166,共6页
We study the long-time limit behavior of the solution to an atom's master equation. For the first time we derive that the probability of the atom being in the α-th (α = j + 1 -jz, j is the angular momentum quantu... We study the long-time limit behavior of the solution to an atom's master equation. For the first time we derive that the probability of the atom being in the α-th (α = j + 1 -jz, j is the angular momentum quantum number, jz is the z-component of angular momentum) state is {(1 - K/G)/[1 - (K/G)2j+1]}(K/G)^α-1 as t → +∞, which coincides with the fact that when K/G 〉 1, the larger the a is, the larger the probability of the atom being in the α-th state (the lower excited state) is. We also consider the case for some possible generaizations of the atomic master equation. 展开更多
关键词 master equation angular momentum long-time limit behavior
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