Master equation describing the diffusion process for a coherent state

The evolution of a pure coherent state into a chaotic state is described very well by a master equation, as is validated via an examination of the coherent state＇s evolution during the diffusion process, fully utilizing the technique of integration within an ordered product （IWOP） of operators. The same equation also describes a limitation that maintains the coherence in a weak diffusion process, i.e., when the dissipation is very weak and the initial average photon number is large. This equation is dp/dt = -κ[a＋ap -a＋pa -apa＋ ＋ paa＋]. The physical difference between this diffusion equation and the better-known amplitude damping master equation is pointed out.

Analytically determining frequency and amplitude of spontaneous alpha oscillation in Jansen's neural mass model using the describing function method

Spontaneous alpha oscillations are a ubiquitous phenomenon in the brain and play a key role in neural information processing and various cognitive functions.Jansen＇s neural mass model（NMM） was initially proposed to study the origin of alpha oscillations.Most of previous studies of the spontaneous alpha oscillations in the NMM were conducted using numerical methods.In this study,we aim to propose an analytical approach using the describing function method to elucidate the spontaneous alpha oscillation mechanism in the NMM.First,the sigmoid nonlinear function in the NMM is approximated by its describing function,allowing us to reformulate the NMM and derive its standard form composed of one nonlinear part and one linear part.Second,by conducting a theoretical analysis,we can assess whether or not the spontaneous alpha oscillation would occur in the NMM and,furthermore,accurately determine its amplitude and frequency.The results reveal analytically that the interaction between linearity and nonlinearity of the NMM plays a key role in generating the spontaneous alpha oscillations.Furthermore,strong nonlinearity and large linear strength are required to generate the spontaneous alpha oscillations.

Acrostic Puzzle: Describing People

Instructions:Use the letters after the clues(information that helps you to find the answers)below to make words used to describe people.Then use the letters in the yellow boxes to make another word that describes someone.

On limit cycle chattering in sliding mode control systems under the influence of sampling intervals based on describing function approach

In this paper, the influence of sampling intervals on the chattering in sliding mode （SM） control systems is considered. The describing function （DF） approach is employed to analyze the chattering characteristics in the sampling SM control. By the DF calculations and limit cycle existence conditions, an unstable limit cycle and two stable limit cycles are found in the SM control system. The frequencies and amplitudes of the two limit cycles can also be estimated by graphical calculations. The estimation accuracy of chattering parameters is evaluated by the simulations. The results of simulations show that the system could converge to a large and a small limit cycle from different initial conditions.

Bound State Description of Particles from a Quantum Field Theory of Fermions and Bosons, Compatible with Relativity

Both, the dilemma to find a quantum field theory consistent with Einstein’s law of relativity and the problem to describe existing particles as bound states of matter has been solved by calculating bound state matrix elements from a dual fermion-boson Lagrangian. In this formalism, the fermion binding energies are compensated by boson energies, indicating that particles can be generated out of the vacuum. This yields quantitative solutions for various mesons ω (0.78 GeV) - Υ (9.46 GeV) and all leptons e, μ and τ, with uncertainties in the extracted properties of less than 1‰. For transparency, a Web-page with the address htpps://h2909473.stratoserver.net has been constructed, where all calculations can be run on line and also the underlying fortran source code can be inspected.

Describing a Process

星期六Tom和Li Hua一起去了KFC。他们各自要了一份火鸡三明治，边吃边聊。LiHua想知道火鸡三明治的制作方法，Tom当然知道了，我们来看看他们的对话吧!

Mental health in the post-COVID-19 era:challenges and the way forward

The COVID-19 pandemic has posed a serious threat to global mental health.Multiple lines of evidence suggest that there is a varying yet considerable increase in mental health issues among the general population and vulnerable groups.12 The aftermath is obscure and speculative from a social,economic,individual and public mental health perspective.Recently published studies support the existence of an emotional epidemic curve,describing a high probability of an increase in the burden of mental health issues in the post-pandemic era.34 Furthermore,previous major public health emergencies showed that more than half of the population devel-oped mental health problems and required mental health intervention.45 There is,therefore,an urgent need to reorganise existing mental health services to address the current unmet needs for mental health and to prepare for future challenges in the postpandemic era in terms of prevention and management.

Design of Robust Controller for Flexible Joint Robot with Nonlinear Friction Characteristics

A robust controller method for flexible joint robot considering the effect caused by nonlinear friction was presented.The nonlinear friction was denoted as inverse additive output uncertainty relative to the nominal model in our work,based on which the describing function was analyzed in frequency domain,and the weighting function of nonlinear friction was further calculated as well. By combining the friction uncertainty,the mixed sensitivity H∞optimization was proposed as the benchmark for controller design, which also leaded to good performance of robustness. Furthermore,unstructured perturbation to the system was analyzed so that the stability was guaranteed. Simulation results show that the proposed controller can provide excellent tracking and regulation performance.

A CLASS OF FIRST ORDER QUASILINEAR PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS TO MATHEMATICAL MODEL FOR MYOPIA ILLNESS

At present, the myopia illness of the students (including the students of university, middle schools andprimary schools) is a serious problem. For preventing and curing it, we must search for the developing lowsof myopia illness to provide the theory foundation for researches on and preventions from myopia illness.We provide the mathematial model on describing the poor eyesight of the students after analysing thedeveloping lows of the poor eyesight of the students as follows:where p(r,t) is the student’s myopia falling ill rate function at time t and age r, u(r) denotes the initial stagemyopia falling ill rate function and v(t), the baby myopia falling ill rate function. It is a first order quasi-

A SINGLE-CAVITY MULTIPLE-DEVICE HARMONIC OSCILLATOR AT W-BAND

The equivalent circuit of single-cavity multiple-device fundamentaloscillator(SCMDFO)and that of single-device harmonic oscillator(SDHO)proposed byK.Kurokawa and K.Solbach,respectively,are extended and applied to a single-cavitymultiple-device harmonic oscillator(SCMDHO).By means of describing the functions ofnonlinearity of Gunn diodes,the performances of the SCMDHO are analyzed.It is foundthat the voltage amplitudes are similar to those of SDHO,and the ratio of maximum pow-er of harmonic to that of fundamental is identical to that in SDHO when the devices havesame parameters.The harmonic injection locking behavior is also investigated.The injec-tion locking range is greater than that of SDHO if locking gain remains constant.A2-Gunn diode harmonic oscillator was designed.It delivers 30mW output power at103GHz.The mechanical tuning range is 4.15GHz when the output power remains morethan 10mW.The desired operation mode is stable.

A TIME FILTERING SCHEME FOR THE SHORT RANGE CLIMATE PREDICTION MODEL PRODUCTS AND ITS REAL CASE ANALYSIS

A filtering / extracting scheme for various timescale processes in short range climate model out-put is established by using the scale scattering method. And the climatological meanings as well as the impor-tance of the filtered series are discussed. In the latter part of work, the effectiveness of the filtering method and the performance of the prediction model are analyzed through a real case.

ANALYSING METHOD FOR THE FORMULATING PROCESS OF ENTERPRISE MERGER AND ACQUISITION STRAGEGIES BASED PETRI NET

For the first time, this paper introduces Petri net theory to the domain of enterprise strategy management, puts forword a new way by using Petri net to analyse and describe the formulating process of enterprise merger and acquisition strategies, provides a clear and simple tool for supporting the management bureau of enterprise to make its merger and acquisition strategies.

WHAT CAN WE LEARN FROM A(π^(+),n)B CHARGE EXCHANGE REACTION?

Within DWIA formalism,we calculate the η production cross sections from nuclear target by charge exchange reaction A(π^(+),η)B.For 13C target the cross sections at forward angles are of the order of 10yb/sr at T_(π)=660MeV,which can be measured experimentally.The high momentum component of the wave function of single particle bound state is essential for describing this reaction.

Rough set model based on variable universe

Rough set theory has a very good effect in information processing and knowledge discovery.In an information table,the current scholars regard all objects as a universe,and then establish various rough set models.However,in the analysis of many data problems,it is more reasonable to select parts of objects which are useful to us or can meet the actual needs as a universe.Therefore,in order to make up for the deficiency of traditional models,a new model is introduced from the perspective of variable universe.Then,some interesting properties of this model,such as approximation sets,reduct of attributes and maximum part of universe,are discussed.Through the study of this paper,it can be seen that the model developed in our paper is not only more accurate but also more effective in describing uncertain knowledge.

Exact Dynamic Modeling of PWM DC-to-DC Power Converters—Part I: Continuous Conduction Mode

A general approach is presented by which the exact frequency response of any transfer function of switched linear networks can be determined. This is achieved with a describing function approach using a state space equation formulation. This work presents a somewhat simplified set of equations to one previously given by one of the authors. To demonstrate application of the general formulation, the frequency responses of switched networks used as PWM DC-to-DC converters operating in continuous conduction mode (CCM) under voltage mode control are derived. (The accompanying paper, Part II, will present results for converters operating in discontinuous conduction mode (DCM)). From the general sets of equations developed here, both the control to output and input source variation to output frequency responses are derived. The describing function approach enables exact frequency response determination, even at high frequencies where the accuracy using average models may be compromised. Confirmation of the accuracy of the derived models is provided by comparing the responses with those obtained using the commercial simulator PSIM on a PWM boost converter. The magnitude and phase responses are shown to match perfectly over the full range of frequencies up to close to half the switching frequency. Matlab code that implements the models is given such that the user can easily adapt for use with other PWM converter topologies.

Exact Dynamic Modeling of PWM DC-to-DC Power Converters—Part II: Discontinuous Conduction Mode

This paper follows on from the first paper, Part I, where a general formulation of a describing function approach to frequency response determination of switched linear networks, such as PWM converters, was simplified and updated. The models assume a piecewise linear state space equation description of the system and results in a closed form solution for the sought after frequency response. In Part I, model derivation was demonstrated for the case of PWM converters operating in the continuous conduction mode (CCM). This operating mode does not feature any state dependent switching times. In this paper, Part II, frequency response models for any transfer function for PWM converters operating in discontinuous conduction mode (DCM) are derived based on the theory presented in Part I. This operating model features state dependent switching times. The describing function models developed are exact and therefore, in terms of accuracy, are to be preferred over averaged models which are widely used. The example of a boost dc-to-dc converter operating in DCM is simulated to obtain the control to output and input to output frequency responses and are compared with the models derived here. Excellent agreement between the simulated and model responses was found. Matlab code implementing the analytical models is also presented which the user can adapt for any other PWM converter topology. The models derived here may be used as a basis from which simplified models may be derived while still preserving required accuracy.

Western Opera in China

“ALTHOUGH the road islong and leads far,I’llsearch hard for truth.″Ithink these lines by Qu Yuan(c.340-278 B.C.)are most appropriatein describing Western opera inChina.Opera originated from musicaldrama in Italy.From Dafne by Flo-rentine composer Jacopo Peri in1597,opera has a history of nearly400 years,if we do not count folk,church or court music and danceor song dramas in Europe.Afterspreading from Italy to Austria,France,Germany,Britain,northernEuropean countries and Russia,op-era has developed many

Multi-range controller design for highly nonlinear systems with application to unmanned aerial vehicles

A new procedure for a design of multi-range controllers for use with highly nonlinear systems is developed.The procedure involves obtaining the describing function models of the nonlinear plant by software followed by designing a controller at nominal conditions.Then,the controller parameters are optimized to yield a satisfactory closed-loop response at all operating regimes.Finally,the performance and stability of the closed-loop system comprised of the designed controller and the nonlinear plant are verified.The procedure and the associated software are applied to a nonlinear control problem of the sort encountered in aerospace,and the results are compared with two other approaches.

Module 1 Life in the Future Period 2 Reading and vocabulary

Teaching aims:课时教学目标:Knowledge and skills:1.To understand the passage by keywords and the first sentence,and to sum the main idea and analyze the structure of the passage;2.To find out the sentences describing the future,and to imitate;To talk about the life in the future,to express their own opinion about future.Process and methods:Reading,discussion,presentation.Emotion,attitudes and values:The students will become more eager for the future,and fight for their dream.Teaching important points:教学重点To get the main idea and the structure of the passage.

ICSR Lab: Where Scientometrics Meets Big Data

ICSR Lab is a cloud-based computational platform that enables researchers to analyze large structured datasets,including data that power Elsevier solutions such as Scopus and PlumX Metrics.It was launched in March 2020 and is available at no cost for scholarly bibliometrics research into themes such as research impact,careers and practices,open science,inclusivity and sustainability.This paper introduces ICSR Lab,describing its key features and some aspects taken into consideration during its inception.