結(jié)構(gòu)相對數(shù)在結(jié)構(gòu)分析運用中的費解

結(jié)構(gòu)相對數(shù)在結(jié)構(gòu)分析運用中的費解*

游新彩

(吉首大學(xué)商學(xué)院，湖南 吉首 416000)

摘要：結(jié)構(gòu)相對數(shù)是綜合指標中最重要的指標之一，運用十分廣泛.其理論內(nèi)涵和算法似乎很完善，但在結(jié)構(gòu)分析運用中常出現(xiàn)令人費解的情形，說明結(jié)構(gòu)相對數(shù)還存在缺陷.通過推敲內(nèi)涵，列示典型實例，顯擺問題，分析產(chǎn)生問題的原因.指出必須區(qū)分總體基本結(jié)構(gòu)和派生結(jié)構(gòu)，在算法方面進一步細化，對派生結(jié)構(gòu)的計算作例外規(guī)定，才能適應(yīng)各種統(tǒng)計分析的需要.

關(guān)鍵詞：結(jié)構(gòu)相對數(shù)；推敲；完善；費解

文章編號：1007-2985(2015)01-0019-02

中圖分類號：O213 文獻標志碼：A

DOI:10.3969/j.issn.1007-2985.2015.01.006

收稿日期：*2014-03-11

作者簡介：游新彩(1963-)，男，湖南益陽人，吉首大學(xué)商學(xué)院教授，主要從事統(tǒng)計學(xué)理論研究.

DOI:10.3969/j.issn.1007-2985.2015.01.007

總體特征常會從其結(jié)構(gòu)上體現(xiàn)出來，結(jié)構(gòu)分析就成為各種統(tǒng)計分析的主要內(nèi)容.結(jié)構(gòu)相對數(shù)作為反映總體結(jié)構(gòu)唯一的綜合指標，運用十分普遍，似乎在理論和實際應(yīng)用都很成熟，但在某些方面還有進一步推敲的必要.

1費解實例

財務(wù)分析中結(jié)構(gòu)分析是重中之重，諸如收入結(jié)構(gòu)、成本結(jié)構(gòu)、利潤結(jié)構(gòu)和現(xiàn)金流結(jié)構(gòu)等，都是財務(wù)分析必須要深入研究的.文中以“三一重工”股份有限公司為例進行討論.表1系根據(jù)“三一重工”股份有限公司2011年年報綜合統(tǒng)計而得.

表1　三一重工2011年現(xiàn)金凈流量和利潤結(jié)構(gòu)

不難發(fā)現(xiàn)，表1中存在以下2個問題：

(1)總體中的一部分，籌資活動的現(xiàn)金凈流量比例已超過100%，主營業(yè)務(wù)利潤、投資收益、營業(yè)外收支凈額等3項比例之和也超過100%，這與結(jié)構(gòu)相對數(shù)的概念相矛盾.

(2)總體結(jié)構(gòu)是可以用平面或立體圖來形象地描述其狀況的，Excel和Spss等軟件都有總體結(jié)構(gòu)繪圖功能.表1中2種結(jié)構(gòu)卻無法用圖形來描述，違背常態(tài).

這種現(xiàn)象在公司財務(wù)結(jié)構(gòu)中并不少見，既不能說明指標數(shù)值的具體經(jīng)濟含義，也無法用結(jié)構(gòu)相對數(shù)的原理解釋其合理性.

2查根索源

之所以出現(xiàn)上述令人費解的問題，是因為結(jié)構(gòu)相對數(shù)的概念不夠完善而導(dǎo)致的.究其原因，主要體現(xiàn)在以下2個方面：

(1)總體基本結(jié)構(gòu)與派生結(jié)構(gòu)的差異.計算結(jié)構(gòu)相對數(shù)的基礎(chǔ)是統(tǒng)計分組，而統(tǒng)計分組是將總體單位按分組標志在各組間進行分配，形成次數(shù)分布數(shù)列.計算結(jié)構(gòu)相對數(shù)的第1層次是依據(jù)次數(shù)分布數(shù)列的總體單位分布狀況，也就是用總體單位總數(shù)這一總量指標來計算，稱為總體基本結(jié)構(gòu).總體單位是客觀存在的事物，它的數(shù)量不可能出現(xiàn)負數(shù)，當然不可能出現(xiàn)上述令人費解的問題.次數(shù)分布數(shù)列的進一步延伸就是計算各組和全總體的總體標志總量指標，延伸計算的總體標志總量也能反映總體結(jié)構(gòu)，稱之為總體派生結(jié)構(gòu)，當然有可能與總體單位總數(shù)反映的總體結(jié)構(gòu)不一致.如果某些總體單位的標志是負值，就可能出現(xiàn)上述令人費解的問題.

(2)統(tǒng)計指標與會計指標的差異.統(tǒng)計中的總量指標數(shù)值不允許有相反方向的值同時存在，一般是正數(shù).會計中某些財務(wù)指標允許有相反方向的值同時存在，可正可負.比如企業(yè)的“利潤”指標，統(tǒng)計上企業(yè)收大于支實現(xiàn)的贏利統(tǒng)計為“利潤”，企業(yè)收不抵支統(tǒng)計為“虧損”，“虧損”在統(tǒng)計上是不能稱之為“利潤”的.會計報表中“利潤”這一財務(wù)指標是可正可負的，實現(xiàn)的贏利在報表中用正數(shù)列示，出現(xiàn)虧損則用負數(shù)列示，正或負值都列在“利潤”這一指標下，這是會計方法所允許的.正因為2專業(yè)在指標處理上存在差異，所以使得財務(wù)結(jié)構(gòu)分析在運用結(jié)構(gòu)相對數(shù)時出現(xiàn)上述令人費解的問題.

3解題釋疑

要解決前面所述問題，應(yīng)從以下2方面考慮：

(1)細化結(jié)構(gòu)相對數(shù)的算法.設(shè)總體有N個總體單位，其總體標志總量為M，統(tǒng)計分組后可分組成N1,N2，N3，…，Nk個部分，各部分對應(yīng)的標志總量分別為M1，M2，M3，…，Mk，顯然，N1+N2+N3+…+Nk=N，M1+M2+M3+…+Mk=M，則總體結(jié)構(gòu)相對數(shù)的算法見表3.表3反映了總體結(jié)構(gòu)有2個層次，一是由總體單位總數(shù)計算的基本結(jié)構(gòu)，二是由總體標志總量計算的派生結(jié)構(gòu).

表3　結(jié)構(gòu)相對數(shù)的算法

(2)總體派生結(jié)構(gòu)的例外規(guī)定.極少數(shù)經(jīng)濟指標是一種合成指標.如“進出口凈額”，有“順差”和“逆差”2種情況，“順差”以正數(shù)列示，“逆差”以負數(shù)列示；又如“財政收支凈額”，財政“節(jié)余” 以正數(shù)列示，財政“赤字”以負數(shù)列示.財務(wù)指標中的“利潤”、“現(xiàn)金凈流量”、“投資收益”等最為典型，都是有正有負的.這類指標在運用結(jié)構(gòu)相對數(shù)作結(jié)構(gòu)分析時就有可能出現(xiàn)令人費解的情形，有必要作例外規(guī)定.

(a)總體各部分標志總量M1，M2，M3，…，Mk中出現(xiàn)了負值，其中某個部分標志總量Mi>M或︱-Mi︱>M，則不能計算結(jié)構(gòu)相對數(shù).表1中現(xiàn)金凈流量的后2項就是這種情況，此時不能計算結(jié)構(gòu)相對數(shù).

(b)總體各部分標志總量M1，M2，M3，…，Mk中出現(xiàn)了負值，其中任意Mi

總之，費解的情形已經(jīng)提出，也是統(tǒng)計學(xué)理論必須解決的問題.

參考文獻：

[1]栗方忠.統(tǒng)計學(xué)原理.沈陽：東北財經(jīng)大學(xué)出版社，2004.

[2]黃良文，陳仁恩.統(tǒng)計學(xué)原理.北京：中央廣播電視大學(xué)出版社，1996.

[3]陳少華.財務(wù)報表分析方法.廈門：廈門大學(xué)出版社，2011.

[4]張新民.財務(wù)報表分析.北京：中國人民大學(xué)出版社，2011.

[5]郭富初.財務(wù)分析學(xué).北京：首都經(jīng)濟貿(mào)易大學(xué)出版社，2008.

[6]李鷗.揭示奧秘之數(shù)—結(jié)構(gòu)相對數(shù).中國統(tǒng)計,2001(7)：51-53.

[7]王濤.結(jié)構(gòu)分析的統(tǒng)計方法與應(yīng)用.統(tǒng)計與咨詢,2011(5)：26-27.

Inexplicability of Structural Relative Number in Structure Analysis Application

YOU Xincai

(College of Business,Jishou University，Jishou 416000，Hunan China)

Abstract：Structural relative number is one of the most important indexes in the comprehensive indexes,and is widely used.The connotation of the theory and the algorithm seems to be perfect,but in the structural analysis,some puzzling situations often appear in operation,which suggests the presence of defects in the structural relative number.In this paper,through elaborating connotation,listing the typical examples,presenting the problems,and analysing the cause of the problem,it is pointed out that the general basic structure and derivative structure must be distinguished,further refinement must be made in the aspect of algorithm,exceptions must be provided for calculating the derived structure,so that the needs of various statistical analysis can be met.

Key words：structural relative number;refining;improvement;inexplicability

(責(zé)任編輯陳炳權(quán))

Article ID：1007-2985(2015)01-0021-07

Dynamical Dissipative Cooling of a Cavity Opto-Mechanical Oscillator*

MI Xianwu,LI Xiuhong

Abstract：The dynamical cooling process of a cavity opto-mechanical system is investigated by a master equation.The mean phonon number is calculated using the covariance approach.Firstly,the effect of different cavity dissipation rate on the mean phonon number is discussed in the strong coupling system.Then the variation of mean phonon number changing with different parameters in the weak and strong coupling system is compared.For strong coupling regime,the mean phonon number oscillates periodically with the increase of coupling strength and it decreases fast as the cavity dissipation rate increases.Finally,it reaches a cooling limit.In the weak coupling regime,the mean phonon number increases fast as the cavity dissipation rate increases and it reaches equilibrium in the end.

Key words：dynamical dissipative cooling,mean phonon number,strong coupling system

CLC number：O47Document code：A

*Received date：2014-08-12

Foundation item： Project supported by the National Science Foundation of China (10647132);Scientific Research Fundation of Hunan Provincial Education Department,China (10A100)

Biography：MI Xianwu(1973—),male,was born in Hunan,China;received the microelectronics and solic state electronics Ph. D degree from the graduate school of Chinese Academy of Sciences;research interests include theoretical aspects of semiconductor lasers and amplifiers and terahertz physics.

1Introduction

As we all know,optical micro-cavity,nano-mechanical and electrical systems have been widely used,but recently there is other two independent systems coupled together through interaction between radiation light pressures.Actually,in the past 50 years the radiation light pressure and the relevant physics research have long been recognized as an important subject in the atomic physics,and the resulting cavity mechanical system is closely related to them.The problem of cooling the mechanical oscillator has been a research hotspot in recent years.Now the most concerned problem is how to cool the oscillator to the ground state of energy.Because we want to see many fancy quantum phenomena after cooling the oscillator to the ground state,such as the Schr?dinger cat state,quantum entangled state,etc.For different vibration frequency of the oscillator,the corresponding ground state temperature is different.For 109Hz oscillator,the temperature is 50 mk.With the loss of the vibration frequency,the critical temperature also decreases.So for general NEMS system,it is useless to make it to the ground state by lowering the environment temperature.The only way is cooling it actively.In recent years,the progress of this experiment is large,but not a landmark experiment shows that the oscillator can be cooled to the ground state.However,in 2011 a team comes from California institute of technology and the University of Vienna,cooling the nanomechanical resonator to the ground state by a bunch of laser,namely the lowest energy state.This result paved the way for the research of highly sensitive sensors and quantum experiments.The relevant research report was published on the journal Nature .

In fact.For example,the coupling between optical and mechanical system has been observed by many research teams,for example,Walther observed radiation light pressure in their pioneering work and confirmed the existence of the bistable effect,of course,in the field of microwave,which was observed by Braginsky much earlier.In addition to that,the correction of mechanical oscillator stiffness coefficient caused by radiation light pressure (optical spring) has also been observed in the experiments[2-9].In this article,we will control the cooling and heating process of the system by changing the magnitude of the dissipation rate,at the same time,in different coupling system,we compare the influence of the dissipation rate and coupling strength to the whole system.

Fig.1　Diagram of a Cavity Optomechanical System

In order to understand how optical degree of freedom and mechanical degree of freedom coupling together,we consider a kind of typical cavity optical mechanical system,a standard Fabry-Perot resonant cavity,as illustrated in fig.1,in which a mirror at one side can vibrate freely,and the other side is fixed.When the cavity is driven by a bunch of laser,the cycle vibration light field in the optical cavity will generate a radiation pressure to the movable mirror.The force makes the mirror produce forced vibration;in turn,the tiny changes of the mirror’s position will change the effective length of optical cavity,and thus it changes the light intensity distribution in the cavity because the vibration mode of the optical cavity has changed.It is this dynamic coupling that leads to a series of interesting phenomenon.

Thus,the linearized system Hamiltonianis[10]

(1)

Considering the dissipation effect,the quantum master equation is

(2)

(3)

Now,taking the counter-rotating terms into consideration,we obtain the following differential equations

(4)

(5)

Here the first term is the classical cooling limit.The second term is the quantum cooling limit.In the strong coupling system,eq. (5) reduces as

(6)

However,in the weak coupling system,the final phonon occupancy can be writen as

(7)

(8)

whereΓ=4|G|2/κ is the cooling rate.

In the strong coupling system,neglecting the counter-rotating term and directly solving the eq.(3),the mean phonon number is

(9)

where

(10)

are the eigen-frequencies of the normalmode.Next,taking the counter-rotating terms into consideration,solving the equations (4) and settingnth=0,we obtain

(11)

Hence in the strong coupling system,the time evolution of the mean phonon number is (for details see supplementary material [16])

(12)

Here the first term comes from energy exchange between optical and mechanical modes;the second term is induced by quantum backaction.

(13)

(14)

So the instantaneous-state cooling limit is (see supplementary material [16])

(15)

2The Numerical Results and Discussion

In fact,we can realize the dynamic control of cavity dissipation experimentally by using a light absorber/scatter[17]or modulating free-carrier plasma density[18-20].In order to observe quantum effects experimentally,we have to overcome the thermal noise which is one of the ultimate goals in quantum physics.Cavity opto-mechanics is a remarkable example[21-22];however,the most important thing is to get the mechanical resonator into the quantum regime[23-25].In this paper,we take a generic opto-mechanical system as an example,discussing the cooling problem of the system and the variation of mean phonon number with the change of different parameters in the weak and strong coupling system.

The parameter values used for the numerical simulation are:dissipation rate of the mechanical mode isγ/ωm=10-5，and thermal phonon number at the environmental temperatureTisnth=103.Fig. 2 displays

Fig.2　Time Evolution of Mean Phonon Number N b with Different Cavity Dissipation Rate κ(t).

the time evolution of mean phonon numberNbwith different cavity dissipation rateκ/ωm=0.01,1 in the strong coupling system,the linear coupling strength |G|/ωm=0.1.In fig. 2,we plot the numerical results based on the master equation for variousκ.It shows that whenκ/ωm=0.01,the envelope of the mean phonon number decreases gradually with the increase of time;at last it reaches and remains near the steady-state cooling limit(the dash-dotted line),given by eq.(5),but it cannot reach the instantaneous-state cooling limit (the dotted line),given by eq.(15).However,whenκ/ωm=1,the oscillation frequency becomes larger and the envelope of the mean phonon number keeps at a stable level.Most importantly it always below the steady-state cooling limit (the dashed line),given by eq.(5) and the instantaneous-state cooling limit (the dotted line).That is to say,by increasing the cavity dissipation rate,we can accelerate the cooling process.

Fig.3　 Three Dimensional Diagram About the Mean Phonon Number in the Strong Coupling System

In fig.3 we plot the three dimensional figure about the mean phonon number in the strong coupling system forγ/ωm=10-5,nth=103andωmt=30.It shows that in the strong coupling regime,the mean phonon number decreases gradually before the cavity dissipation rateκ/ωm≈1;afterκ/ωm≈1 the mean phonon number decreases quickly;at last it reaches and remains a stable limit.As the increase of the coupling strengthG/ωm,the mean phonon number oscillates periodically,and whenG/ωm=0.02～0.05,there occurs a small crest which consist of many sine waves.After that there occurs a larger crest and cycles periodically as the same crest value.

In Fig 4,we plot the three dimensional figure about the mean phonon number in the weak coupling

Fig.4　 Three Dimensional Figure About the Mean Phonon Number in the Weak Coupling System

system forγ/ωm=10-5,nth=103andωmt=200.On the contrary,in the weak coupling regime,the mean phonon number increases gradually as the increase of the cavity dissipation rateκ(t)/ωm.At last it reaches and remains a limit.What’s more,as the increase of the coupling strengthG/ωm,the mean phonon number doesn’t show periodically oscillation.That is to say,in the weak coupling regime,increasing the cavity dissipation rate is able to accelerate the heating process.At the same time,it may also strongly cause the heating noise.

3Conclusion

In summary,we discussed the dynamic cooling problem of an opto-mechanic coupling system,compared the influence of different dissipation rate of the optical cavity mode on the mean phonon number in the strong coupling system.In a certain range，the larger of the cavity dissipation rate,the smaller of the mean phonon number,and with the larger cavity dissipation rate,the mean phonon number can reach the instantaneous-state cooling limit quickly.That is to say,by increasing the cavity dissipation rate,we can accelerate the cooling process.For strong coupling regime,with the increase of the coupling strength,the mean phonon number oscillates periodically;at the same time,the mean phonon number decreases fast as the cavity dissipation rate increases.In the end,it reaches a cooling limit.On the contrary,for weak coupling regime,the mean phonon number increases fast as the cavity dissipation rate increases,and then it reaches equilibrium.What’s more,with the increase of the coupling strength,the mean phonon number doesn’t occur periodically oscillation.So in the weak coupling system,increasing the cavity dissipation rate is able to accelerate the heating process.

References:

[1]CHAN J,MAYER ALEGRE T P,AMIR H,et al.Laser Cooling of a Nano Mechanical Oscillator into Its Quantum Ground State.Nature,2011,478:89-92.

[2]SHEARD B S,GRAY M B,MOW-LOWRY C M,et al.Observation and Characterization of an Optical Spring.Phys.Rev.A,2004,69(5)：051 801.

[3]BRAGINSKY V B,STRIGIN S E,VYATCHANIN S P.Parametric Oscillatory Instability in Fabry-Perot Interferometer.Physics Letters A,2001,287(5/6):331-338.

[4]KIPPENBERG T J,ROKHSARI H,CARMON T,et al.Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity.Phys.Rev.Lett.,2005,95：003 901.

[5]ARCIZET O,COHADON P F,BRIANT T,et al.Radiation-Pressure Cooling and Optomechanical Instability of a Micromirror.Nature,2006,444(7 115):71-74.

[6]SCHLIESSER A,DEL’HAYE P,NOOSHI N,et al.Radiation Pressure Cooling of a Micromechanical Oscillator Using Dynamical Backaction,.Phys.Rev.Lett.,2006,97(24):243,905.

[7]THOMPSON J D,ZWICKL B M,YARICH A M,et al.Strong Dispersive Coupling of a High Finesse Cavity to a Micromechanical Membrane,.ArXiv:0707.1724 (2007).

[8]POGGIO M,DEGEN C L,MAMIN H J,et al.Feedback Cooling of a Cantilever’S Fundamental Mode Below 5 mK.Phys.Rev.Lett.,2007,99(1)：017 201.

[9]MARSHALL W,SIMON C,PENROSE R,et al.Towards Quantum Superpositions of a Mirror.Phys.Rev.Lett.,2003,91(13)：130 401.

[10] LIU Y C,XIAO Y F,LUAN X S,et al.Dynamical Dissipation Cooling of a Mechanical Oscillator in Strong-Coupling Optomechanics.ArXiv:1303.3657 (2013).

[11] MARQUARDE F,CHEN J P,CLERK A A,et al.Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion.Phys.Rev.Lett.,2007,99:093 902.

[12] DOBRINDT J M,WILSON-RAE I,KIPPENBERG T J.Parametric Normal-Mode Splitting in Cavity Optomechanics.Phys.Rev.Lett.,2008,101:263 602.

[13] WILSON-RAE I,NOOSHI N,DOBRINDT J,et al.Cavity-Assisted Back Action Cooling of Mechanical Resonators.New J.Phys.,2008,10:095 007.

[14] WILSON-RAE I,NOOSHI N,ZWERGER W,et al.Theory of Ground State Cooling of a Mechanical Oscillator Using Dynamical Backaction.Phys.Rev.Lett.,2007,99:093 901.

[15] MARQUARDT F,CHEN J P,CLERK A A,et al.Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion.Phys.Rev.Lett.,2007,99:093 902.

[16] LIU Y C,XIAO Y F,LUAN X S,et al.Supplementary Material for:Dynamical Dissipation Cooling of a Mechanical Oscillator In Strong-Coupling Optomechanics.ArXiv:1303.3657 (2013).

[17] FAVERO I AND KARRAI K.Cavity Cooling of a Nanomechanical Resonator by Light Scattering.New J.Phys.,2008,10:095 006.

[18] XU Q,DONG P,LIPSON M.Breaking the Delay-Bandwidth Limit in a Photonic Structure.Nature Phys.,2007,3(6):406-410.

[19] KONDO K,SHINKAWA M.Ultrafast Slow-Light Tuning Beyond the Carrier Lifetime Using Photonic Crystal Waveguides.Phys.Rev.Lett.,2013,110:053 902.

[20] SOREF R A,BENNETT B R.Electrooptical Effects in Silicon.IEEE J.Quantum Electron.,1987,23(1):123-129.

[21] KIPPENBERG T J,VAHALA K J.Cavity Optomechanics:Back-Action at the Mesoscale.Science,2008,321:1 172-1 176.

[22] MARQUARDT F,GIRVIN S M.Optomechanics.Physics,2009(2):40.

[23] TEUFEL J D.Sideband Cooling of Micromechanical Motion to the Quantum Ground State.Nature (London),2011,475:359-363.

[24] CHAN J,MAYER ALEGRE T P,SAFAVI-NAEINI A H,et al.Laser Cooling of a Nanomechanical Oscillator Into Its Quantum Ground State.Nature (London),2011,478:89.

[25] VERHAGEN E,DELEGLISE S,WEIS S,et al.Quantum-Coherent Coupling of a Mechanical Oscillator to an Optical Cavity Mode.Nature (London),2012,482:63.