Dynamics and Long Time Convergence of the Extended Fisher-Kolmogorov Equation under Numerical Discretization

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.

Origin of “Long time,no see”

"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.

A Long Time Coming

South Sudan,Africa’s newest nation,carries much hope on its shoulders IF joy and happiness could be measured, then millions of South Sudanese would have pushed the meter off the charts when their country got its independence on July 9,2011. The foot-thumping,hip-swaying and shoulder-shaking crowd chanted and danced rhythmically to celebrate their new country,their own President Salva

A Long Time Coming

EGYPTIANS moved further along the path of change after ousting Hosni Mubarak and 15 months of military rule. In June Mohamed Morsi of the Muslim Brotherhood beat his military-backed rival, Ahmed Shafik to become the first ever Islamist head of state in the Arab world.

RHEOLOGICAL BEHAVIOUR FOR AN ANHYDRITE SPECIMEN AND DETERMINATION OF ITS LONG TIME STRENGTH

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.

Symbolic representation based on trend features for knowledge discovery in long time series

The symbolic representation of time series has attracted much research interest recently. The high dimensionality typical of the data is challenging, especially as the time series becomes longer. The wide distribution of sensors collecting more and more data exacerbates the problem. Representing a time series effectively is an essential task for decision-making activities such as classification, prediction, and knowledge discovery. In this paper, we propose a new symbolic representation method for long time series based on trend features, called trend feature symbolic approximation （TFSA）. The method uses a two-step mechanism to segment long time series rapidly. Unlike some previous symbolic methods, it focuses on retaining most of the trend features and patterns of the original series. A time series is represented by trend symbols, which are also suitable for use in knowledge discovery, such as association rules mining. TFSA provides the lower bounding guarantee. Experimental results show that, compared with some previous methods, it not only has better segmentation efficiency and classification accuracy, but also is applicable for use in knowledge discovery from time series.

Research on fuzzy self-adaptive PI-Smith control in long time-delay system

The long time-delay often exists in industrial process. In order to overcome the big overshoot and long regulating time of the long time-delay system control, a new fuzzy self-adaptive PI-Smith control method is proposed. This method combines the Smith predictive control with fuzzy self-adaptive proportional-integral （PI） control. The traditional proportional-integral-derivative （PID） controller in Smith predictive control is replaced by fuzzy PI controller which utilizes the principle of fuzzy control to tune parameters of PI controller on-line. The results of simulation for electric furnace show that the method has the advantages of shortening regulating time, no overshoot, no steady-state error, excellent control accuracy, and good adaptive ability to the change of system model.

“The Insider’s Guide to Beijing rates as one of the best,new,imaginative and informative guidebooks in a long time”—South China Morning Post

Immersion Guides,Beijing’s leading English-language publisher of guidebooks for Beijing and beyond,is proud to present the 2008 edition of the Insider’s Guide to Beijing (November 2007,ISBN: 978-7-5085-1172-6,90 yuan).This is not the run-of-the-mill guide- book written by travelers who spend a few harried days getting to know their destination.Combining the knowledge of 40 long-term residents, this is the guidebook that knows Beijing inside and out.Now in its fourth edition,this'Beijing Bible'(Beijing Today) is the most compre- hensive resource available for both travelers and residents. Fully updated annually to keep pace with the rate of change in Beijing,the Insider’s Guide provides readers with practical informa-

Boltzmann Equations with Quantum Effects (1):Long Time Behavior of Spatial Decay Solutions

The Boltzmann equations for Fermi-Dirac particles and Bose-Einstein particles, both in the absence of external force fields, are combined into a more general form called the Boltzmann equation with quantum effects (BQE). It is assumed that the initial data f(x,v,0) satisfies 0≤f(x,v,0)≤cΦ(x,v,0) for a positive constant c and certain types of control functions Φ(x,v,t). Then within a given function space B(Φ), we prove that f(x+tv,v,t) uniformly converges to f ∞(x,v) in a certain norm where f ∞(x,v)= limt→∞f(x+tv,v,t) and different initial data determines different long time limits.

Long Time Behavior of the Fokker-Planck-Boltzmann Equation

This paper is devoted to the existence and long time behavior of the global classical solution to Fokker-Planck-Boltzmann equation with initial data near the absolute Maxwellian.

For long和for a long time

有些学生在翻译“我认识他的时间不久”这个句子时把它译成:I haven’t known himfor a long time.当然,老师告诉他们这个翻译是错误的,正确的译法应该是:I haven’tknown him for long.其理由是for a

Long time data series and data stewardship reference model

The need for accessing historical Earth Observation(EO)data series strongly increased in the last ten years,particularly for long-term science and environmental monitoring applications.This trend is likely to increase even more in the future,in particular regarding the growing interest on global change monitoring which is driving users to request time-series of data spanning 20 years and more,and also due to the need to support the United Nations Framework Convention on Climate Change(UNFCCC).While much of the satellite observations are accessible from different data centers,the solution for analyzing measurements collected from various instruments for time series analysis is both difficult and critical.Climate research is a big data problem that involves high data volume of measurements,methods for on-the-fly extraction and reduction to keep up with the speed and data volume,and the ability to address uncertainties from data collections,processing,and analysis.The content of EO data archives is extending from a few years to decades and therefore,their value as a scientific time-series is continuously increasing.Hence there is a strong need to preserve the EO space data without time constraints and to keep them accessible and exploitable.The preservation of EO space data can also be considered as responsibility of the Space Agencies or data owners as they constitute a humankind asset.This publication aims at describing the activities supported by the European Space Agency relating to the Long Time Series generation with all relevant best practices and models needed to organise and measure the preservation and stewardship processes.The Data Stewardship Reference Model has been defined to give an overview and a way to help the data owners and space agencies in order to preserve and curate the space datasets to be ready for long time data series composition and analysis.

“The Insider’s Guide to Beijing rates as one of the best,new,imaginative and informative guidebooks in a long time”—South China Morning Post

Immersion Guides,Beijing’s leading English-language publisher of guidebooks for Beijing and beyond,is proud to present

Long-time Convergence of Numerical Approximations for Semilinear Parabolic Equations (Ⅱ)

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.

Binaural Speech Separation Algorithm Based on Long and Short Time Memory Networks

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.

LONG-TIME CONVERGENCE OF GENERALIZED DIFFERENCE METHOD FOR NAVIER-STOKES EQUATIONS

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.

Source time functions of the 1999, Jiji (Chi-Chi) earthquake from GDSN long period waveform data using aftershocks as empirical Green's functions

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.

Longtime Convergence of Numerical Approximations for Semilinear Parabolic Equations (Ⅰ)

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.

Long-time limit behavior of the solution to an atom's master equation

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.

LONG-TIME BEHAVIOR OF TRANSIENT SOLUTIONS FOR CELLULAR NEURAL NETWORK SYSTEMS

By establishing concept an transient solutions of general nonlinear systems converging to its equilibrium set, long-time behavior of solutions for cellular neural network systems is studied. A stability condition in generalized sense is obtained. This result reported has an important guide to concrete neural network designs.