2009 GENERALIZED instantaneous reactive power theory in poly-phase power systems05279292

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09春夏纽约时装周关键词：科技

公开号：ＣＮ１４１８６１０公开号：ＣＮ１２２４６４２
申请人：江苏阳光股份有限公司
申请人：凯诺科技股份有限公司专利摘要：
专利摘要：
该发明涉及一利抗皱自洁舒适性精毛纺面
该发明涉及一种含再生动物蛋白纤维的羊料及其后整理工艺，其特点是：选用的抗皱、
物蛋白条与羊毛混条；将混合条进行纺纱；精
ＶｖｎｅＴｍ２０ｉ＇ｎａ０９春夏时装秀上．模特们纺纱线经整经、织造得到坯布；坯布经生修及ｉｅ手中紧握的不再是晚装包，而是红色牡丹图案的染整深加工后即得到羊毛精纺织物，其特点限量版笔记本。ｉｅｎａＶｉｅｍ将之命名为ｄｉｌ是：ａ对再生动物蛋白纤维进行染色前处理ｖｎＴｉｔｇａ）ｃｔｈ据悉。ｌｃ。ｕ会在明年春节时推向市场。时，在成球时加一层涤纶条或／和加入柔软剂；惠普公司称，这是电脑公司第一次与｛‘ ｝装ｂ采用染色的染料为活性染料或兰纳素、兰纳４）设计合作，而此前设计师们已经尝试与一些手洒脱、克牢素；ｃ再生动物蛋白纤维条与羊毛）机公司合作。比如为ＬＧ公司的最新电话】混条中，加入含抗静电剂的混合型和毛油纤Ｇ
Ｌｔｓｏｕ设计围巾。而ＰｌａｐａｒｎｏｏＲｌｈＬｕｅ最近也维；ｄ再生动物蛋白纤维与羊毛的重量百分比）
推出一项移动电话技术，让消费者能够通过电为：５４：０９。该发明使再生动物蛋白纤～０６～５话扫描条形码进行购物。ＫＹｔＤＮ￣使用条码技术维在毛精纺织品上成功应用。所生产的织物具Ｊ

矢量光束Cylindrical vector beams from

Cylindrical vector beams:from mathematical concepts to applications Qiwen ZhanElectro-Optics Graduate Program,University of Dayton,300College Park,Dayton Ohio45469-0245,qiwen.zhan@Received September10,2008;revised November18,2008;accepted November19, 2008;posted November19,2008(Doc.ID101448);published January29,2009 An overview of the recent developments in theﬁeld of cylindrical vectorbeams is provided.As one class of spatially variant polarization,cylindricalvector beams are the axially symmetric beam solution to the full vectorelectromagnetic wave equation.These beams can be generated via differentactive and passive methods.Techniques for manipulating these beams whilemaintaining the polarization symmetry have also been developed.Theirspecial polarization symmetry gives rise to unique high-numerical-aperturefocusing properties thatﬁnd important applications in nanoscale opticalimaging and manipulation.The prospects for cylindrical vector beams and theirapplications in otherﬁelds are also brieﬂy discussed.OCIS codes:140.0140,170.4520,180.0180,240.6680,260.1690,260.5430.1.Introduction (2)2.Mathematical Description of Cylindrical Vector Beams (3)3.Generation of Cylindrical Vector Beams (7)3.1.Active Generation Methods (7)3.2.Passive Generation Methods in Free Space (10)3.3.Passive Generation Methods Using Optical Fiber (13)4.Manipulation of Cylindrical Vector Beams (15)5.Focusing Properties and Applications (18)5.1.Tighter Focusing with Radial Polarization Explained by DipoleRadiation (18)5.2.Numerical Calculation Methods (19)5.3.Tighter Focusing and Applications in Imaging (23)5.4.Three-Dimensional Focus Engineering with Cylindrical VectorBeams (25)5.5.Phase Behavior Near the Focus (31)6.Plasmon Excitation and Focusing with Radial Polarization (37)7.Applications in Optical Trapping (42)8.Applications in Laser Machining (48)9.Summary and Prospects (50)Acknowledgments (51)References (52)Cylindrical vector beams:from mathematical concepts to applications Qiwen Zhan1.IntroductionPolarization is one important property of light.This vector nature of light and its interactions with matter make many optical devices and optical system designs possible.Polarization propagation and interaction with materials have been extensively explored in optical inspection and metrology,display technologies,data storage,optical communications,materials sciences,and astronomy,as well as in biological studies.Most past research dealt with spatially homogeneous states of polarization(SOPs),such as linear,elliptical, and circular polarizations.For these cases,the SOP does not depend on the spatial location in the beam cross section.Recently there has been an increasing interest in light beams with spatially variant SOPs.Spatially arranging the SOP of a light beam,purposefully and carefully,is expected to lead to new effects and phenomena that can expand the functionality and enhance the capability of optical systems.One particular example is laser beams with cylindrical symmetry in polarization,the so-called cylindrical vector(CV) beams.Because of their interesting properties and potential applications,there has been a rapid increase of the number of publications on CV beams.The purpose in the present paper is to provide a review of the recent developments.In Section2,I introduce commonly used mathematical descriptions of these CV beams.Since1972[1,2],various active and passive methods have been developed to generate CV beams.In Section3,an overview of these methods is provided.Manipulation methods that can redirect,rotate,and modulateCV beams are summarized in Section4.CV beams have attracted signiﬁcant recent attention largely because of their unique properties underhigh-numerical-aperture(NA)focusing.In Section5,an intuitive explanation of the focusing properties using electric dipole emission pattern is given,and the numerical computation formula is reviewed.Numerical calculations have shown that tighter focal spots can be obtained by using radial polarization, a subset of CV beams,owing to the existence of a strong and localized longitudinalﬁeld component[3].Such an effect has been experimentallyconﬁrmed by several groups[4–6]and has found applications in high-resolution imaging,plasmonic focusing,and nanoparticle manipulation.The perspectives of CV beam applications in otherﬁelds such as laser machining,remote sensing,terahertz technology,and singular optics will be brieﬂy mentioned toward the end of this paper.2.Mathematical Description of Cylindrical Vector BeamsThe CV beams are vector-beam solutions of Maxwell’s equations that obey axial symmetry in both amplitude and phase [7].Modes with radial andazimuthal polarization are well known in waveguide theory [8].However,their counterparts in free space are less familiar.For free space,the typical paraxial beamlike solutions with harmonic temporal dependence are obtained by solving the scalar Helmholtz equation:ٌ͑2+k 2͒E =0,͑2.1͒where k =2␲/␭is the wavenumber.For a beamlike paraxial solution inCartesian coordinates,the general solution for the electric ﬁeld takes the formE ͑x ,y ,z ,t ͒=u ͑x ,y ,z ͒exp ͓i ͑kz −␻t ͔͒.͑2.2͒By applying the slowly varying envelop approximation ץ2uץz 2 k 2u ,ץ2uץz 2 k ץu ץz ,the Hermite–Gauss solution HG mn modes can be obtained by separation of variables in x and y .Mathematically,these solutions have the following form:u ͑x ,y ,z ͒=E 0H m ͩͱ2xw ͑z ͒ͪH n ͩͱ2y w ͑z ͒ͪw 0w ͑z ͒exp ͓−i ␸mn ͑z ͔͒exp ͫi k2q ͑z ͒r 2ͬ,͑2.3͒where H m ͑x ͒denotes the Hermite polynomials that satisfy the differential equationd 2H mdx 2−2x dH mdx +2mH m =0and E 0is a constant electric ﬁeld amplitude,w ͑z ͒is the beam size,w 0is the beam size at the beam waist,z 0=␲w 02/␭is the Rayleigh range,q ͑z ͒=z −iz 0is the complex beam parameter,and ␸mn ͑z ͒=͑m +n +1͒tan −1͑z /z 0͒is the Gouy phase shift.For m =n =0,this solution reduces to the well-known fundamental Gaussian beam solution:u ͑r ,z ͒=E 0w 0w ͑z ͒exp ͓−i ␸͑z ͔͒exp ͫi k2q ͑z ͒r 2ͬ,͑2.4͒where ␸͑z ͒=tan −1͑z /z 0͒is the Gouy phase shift for the fundamental Gaussian beam.For beamlike paraxial solution in cylindrical coordinates,the solution takes the following general formula:E ͑r ,␾,z ,t ͒=u ͑r ,␾,z ͒exp ͓i ͑kz −␻t ͔͒.͑2.5͒Substituting Eq.(2.5)into the scalar Helmholtz equation (2.1)and applying the slowly varying envelop approximation leads to1r ץץr ͩr ץuץr ͪ+1r 2ץ2uץ␾2+2ik ץuץz =0.͑2.6͒From this equation,the Laguerre–Gauss solution LG pl modes can be obtained by using the separation of variables in r and ␾:u ͑r ,␾,z ͒=E 0ͩͱ2r ␻ͪlL p l ͩ2r 2␻2ͪw 0w ͑z ͒exp ͓−i ␸pl ͑z ͔͒exp ͫi k2q ͑z ͒r 2ͬexp ͑il ␾͒,͑2.7͒where L p l ͑x ͒is the associated Laguerre polynomials that satisfy the differential equationx d 2L p l dx 2−͑l +1−x ͒dL p l dx +pL p l =0and ␸pl ͑z ͒=͑2p +l +1͒tan −1͑z /z 0͒is the Gouy phase shift.For l =p =0,the solution also reduces to the fundamental Gaussian beam solution.For l 0,the LG mode has a vortex phase term e il ␾.Another type of solution of Eq.(2.6)that obeys rotational symmetry (independent of the azimuthal angle ␾)has also been found [9].These solutions take the general formu ͑r ,z ͒=E 0w 0w ͑z ͒exp ͓−i ␸͑z ͔͒exp ͫi k2q ͑z ͒r 2ͬJ 0ͩ␤r 1+iz /z 0ͪexp ͫ−␤2z /͑2k ͒1+iz /z 0ͬ,͑2.8͒where ␤is a constant scale parameter,␸͑z ͒is the Gouy phase shift,z 0is the Rayleigh range,and J 0͑x ͒is the zeroth-order Bessel function of the ﬁrst kind.This group of beamlike solution is the so-called scalar Bessel–Gauss beam solution.When ␤=0,the solution reduces to the fundamental Gaussian beam solution given in Eq.(2.4)as well.The solutions derived above (Hermite–Gauss,Laguerre–Gauss,and Bessel–Gauss)are the paraxial beamlike solutions to the scalar Helmholtz equation (2.1)that correspond to spatially homogeneous polarization or scalar beams.For these beams,the electric ﬁeld oscillation trajectory (i.e.,SOP)does not depend on the location of observation points within the beam cross section.However,if we consider the full vector wave equation for the electric ﬁeld [7],ٌϫٌϫE៝−k 2E ៝=0,͑2.9͒then an axially symmetric beamlike vector solution with the electric ﬁeld aligned in the azimuthal direction should have the form E ៝͑r ,z ͒=U ͑r ,z ͒exp ͓i ͑kz −␻t ͔͒e ៝␾,͑2.10͒where U ͑r ,z ͒satisﬁes the following equation under the paraxial and slowly varying envelope approximation:1r ץץr ͩr ץUץr ͪ−Ur 2+2ik ץUץz =0.͑2.11͒There is a clear difference in the second terms of Eqs.(2.6)and (2.11).The solution that obeys azimuthal polarization symmetry has the trial solutionU ͑r ,z ͒=E 0J 1ͩ␤r 1+iz /z 0ͪexp ͫ−i ␤2z /͑2k ͒1+iz /z 0ͬu ͑r ,z ͒,͑2.12͒where u ͑r ,z ͒is the fundamental Gaussian solution given in Eq.(2.4)and J 1͑x ͒is the ﬁrst-order Bessel function of the ﬁrst kind.This solution corresponds to an azimuthally polarized vector Bessel–Gauss beam solution.Similarly,there should exist a transverse magnetic ﬁeld solutionH ៝͑r ,z ͒=−H 0J 1ͩ␤r 1+iz /z 0ͪexp ͫ−i ␤2z /͑2k ͒1+iz /z 0ͬu ͑r ,z ͒exp ͓i ͑kz −␻t ͔͒h ជ␾,͑2.13͒where H 0is a constant magnetic ﬁeld amplitude and h ជ␾is the unit vector in the azimuthal direction.For this azimuthal magnetic ﬁeld solution,thecorresponding electric ﬁeld in the transverse plane is aligned in the radial direction.Hence Eq.(2.13)represents the radial polarization for the electric ﬁeld.Clearly there should be a z component of the electric ﬁeld as well.However,this component is weak and can be ignored under paraxial conditions.For comparison,examples of the spatial distributions of the instantaneouselectric ﬁeld vector for several linearly polarized Hermite–Gauss and Laguerre–Gauss modes and the CV modes are illustrated together in Fig.1.The SOPs of the modes shown in Figs.1(a)–1(f)are considered spatially homogeneous,although the electric ﬁeld may have an opposite instantaneous direction caused by the inhomogeneous phase distribution across the beam.The ﬁeld illustrated in Fig.1(g)has polarization aligned in the radial direction.This is called the radial polarization.Similarly,the polarization pattern shown inFig.1(h)is called the azimuthal polarization.The generalized CV beams shown in Fig.1(i)are a linear superposition of these two.Due to the transverse ﬁeld continuity,one of the features of these CV modes is the existence of a null of the transverse ﬁeld.In many applications,instead of the vector Bessel–Gauss solutions derived above,other simpliﬁed distributions have been used,especially for CV beams with large cross sections.For very small ␤,the vector Bessel–Gauss beam at the beam waist can be approximated asE ៝͑r ,z ͒=Ar exp ͩ−r 2w 2ͪe ៝i ,i =r ,␾.͑2.14͒The amplitude proﬁle is exactly the LG 01mode [10]without the vortex phase term exp ͑i ␾͒.Using Eqs.(2.3)and (2.7),it is easy to show that CV beams can also be expressed as the superposition of orthogonally polarized Hermite–Gauss HG 01and HG 10modes [11]:E ៝r =HG 10e ៝x +HG 01e៝y ,͑2.15͒E ៝␾=HG 01e ៝x +HG 10e ៝y ,͑2.16͒where E r and E ␾denote radial and azimuthal polarization,respectively.This is illustrated schematically in Fig.2.For some applications,particularly for those involving the generation of collimated CV beams through passivedevices in applications requiring high-NA focusing,annular distributions withthe center blocked by an opaque stop have also been frequently used.The ﬁeld after these devices or in the pupil plane is [12]E ៝͑r ͒=P ͑r ͒e ៝i ,i =r ,␾,͑2.17͒where P ͑r ͒is the beam cross section or pupil function.For uniform annular illumination,P ͑r ͒=ͭ1,r 1Ͻr Ͻr 20,0Ͻr Ͻr 1.͑2.18͒Spatial distribution of instantaneous electric vector ﬁeld for several conventional modes and CV modes:(a)x -polarized fundamental Gaussian mode;(b)x -polarized HG 10mode;(c)x -polarized HG 01mode;(d)y -polarized HG 01mode;(e)y -polarized HG 01mode;(f)x -polarized LG 01mode;(g)radially polarized mode;(h)azimuthally polarized mode;(i)generalized CV beams as a linear superposition of (g)and (h).3.Generation of Cylindrical Vector BeamsSince 1972,many methods of generating CV beams have been reported,especially in the past decade or so.Depending on whether the generation methods involve amplifying media,these methods can be categorized as active or passive.3.1.Active Generation MethodsT ypically,active methods involve the use of laser intracavity devices that force the laser to oscillate in CV modes.Intracavity devices can be axialbirefringent (intrinsic birefringent,form birefringent,or induced birefringent)component or axial dichroic component to provide mode discrimination against the fundamental mode.One of the earliest experiments utilized an intracavity axial birefringent component [1].In this setup (Fig.3),a calcite crystal is placed in a telescope setup with its crystal axis parallel to the optical axis of the cavity.Because of double refraction,the e polarization and o polarization experience slightly different magniﬁcations.With a central stop aperture,one polarization is discriminated more because of higher loss.The cylindrical symmetry of the entire system ensures that the oscillation mode has cylindrical polarization symmetry.Since calcite is negatively birefringent,the azimuthal polarization was generated directly in this setup.Radialpolarization was generated with optical active materials (quartz)to rotate the electric ﬁeld by 90°.It is important to have the optical axis of the lasing medium aligned with the optical axis of the resonator if the laser medium is also anisotropic.Other papers extended these early reports [13,14].However,owing to the lack of practical applications of these special polarization modes,little attention was paid to this ﬁeld until recently.Formation of radial and azimuthal polarizations using linear superposition of orthogonally polarized HG modes.Driven by the potential applications of CV beams in imaging,machining,particle trapping,data storage,remote sensing,etc.,this ﬁeld has seen rapidly growth in the past decade or so.Active CV beam generation was revisited,and new methods were developed.For examples,CV beam generation with axial intracavity birefringence was reinvented and improved [15–17].Besides axial birefringence,axial intracavity dichroism created with conical axicon[18]and Brewster angle reﬂectors [19,20]were also utilized to provide polarization mode selection.One such conﬁguration [20]is illustrated in Fig.4.The techniques mentioned above used bulk intracavity devices for creating axial birefringence or dichroism.The recent availability of microfabrication and nanofabrication tools enables the creation of diffractive phase plate orpolarization selective end mirror devices [14,21]for CV beam generation (Fig.5).This type of device allows a much more compact laser design and can be exploited to generate high output power.In addition to those methods that utilize either intracavity axial birefringence or dichroism to provide the necessary mode discrimination,CV beamscan also be generated with intracavity interferometric methods using folded mirrors or prisms based on the linear superposition principle given by Eqs.(2.15)and (2.16).A recently proposed intracavity Sagnac interferometerCalciteAperture+Stop Mirror Diagram of a ruby laser that generates CV beam output.The optical axis of the calcite crystal is parallel to the resonator axis.The combination of the calcite crystal,the telescope,and the aperture and stop provides the mode discrimination to force the laser operation in CV polarization mode.Figure adapted with permission from[1].©1972American Institute of Physics.4CBPLD pumpedNd:YAG rodSiO 2Nd:Y AG laser that generates CV beams by using axial dichroism created by a conical Brewster prism (CBP).The structure of the conical Brewster prism is shown to the right.Figure adapted with permission from [20].setup [22]is illustrated in Fig.6.In this example,linearly polarized HG 01modes are created by placing a thin wire across the center of the cavity.A dove prism provides the necessary rotation to create the orthogonally polarized HG 10and HG 01modes.The Sagnac interferometer combines the two modes and creates the CV output.Active mediumYb:YAG (thin disk)couplermirrorYb:Y AG thin-disk laser that generates CV beam outputs using a circular multilayer polarizing grating end mirror.The output beam proﬁle andpolarization pattern are shown to the right.Figure adapted with permissionfrom [21].6Diagram of a laser cavity design with Sagnac interferometer as an end mirror to create CV beam output.BS,beam splitter.Figure reprinted with permission from [22].3.2.Passive Generation Methods in Free SpacePassive methods have also been used to generate CV beams in free space.In general,these methods convert those more commonly known spatially homogeneous polarizations(typically linear or circular polarization)into spatially inhomogeneous CV polarizations.Consequently,devices with spatially variant polarization properties are normally required.For example,axial birefringence and dichroism have been applied to generate CV beam outside the laser cavity.Simple setups with a radial analyzer made either from birefringent materials[23]or from dichroic materials[24]can be used to generate the CV beams.A radial analyzer is a device that has its local polarization transmission axis aligned along either the radial or the azimuthal directions.In general,birefringent radial analyzers have better polarization purity than dichroic radial analyzers,while the setup for a dichroic radial analyzer is more compact.A circularly polarized collimated beam needs to be used as the input to the radial analyzer.The beam after the radial analyzerwill be polarized either radially or azimuthally,depending on the type of radial analyzer used.However,one important factor that requires caution is the Berry’s phase[24].For a circularly polarized input,theﬁeld can be expressed asE៝in=e៝x+je៝y=͑cos␾e៝r−sin␾e៝␾͒+j͑sin␾e៝r+cos␾e៝␾͒=e j␾͑e៝r+je៝␾͒,͑3.1͒where e៝x and e៝y are the unit vectors in Cartesian coordinates and e៝r and e៝␾are the unit vectors in the polar coordinate system.After the beam passes through the radial analyzer,since the transmission axis of the radial analyzer is aligned along the radial direction,the SOP becomesE៝out=e j␾e៝r.͑3.2͒This indicates that,although the electricalﬁeld is aligned along the radial direction,there is a spiral phase factor on top of it.The geometric spiral phase has been conﬁrmed by interferometric measurement (Fig.7)[24].To obtain a true CV beam,a spiral phase element(SPE)withthe opposite helicity is necessary to compensate for the geometric phase(Fig.8).A SPE can be fabricated with a variety of lithographic techniques,suchas electron-beam lithography and gray-scale lithography,or can be generated by a liquid crystal(LC)spatial light modulator(SLM).An interestingsimple tunable SPE using a deformed cracked glass plate was reported in[25]. Commercial SPE products are available now at several vendors[26].This generation method has been successfully implemented by several groups to generate both continuous wave(CW)and ultrafast CV beams[6,27,28]. Spatially variant polarization rotation can also be utilized to produce CV beams. In this case,linearly polarized light is typically used as input and thenlocally rotated to the desired spatial polarization pattern.One such example is a device with twisted nematic LC sandwiched between linearly and circularly rubbed plates[29,30].Owing to the circular rubbing of the second plate,the twisted nematic LC molecules continuously rotate from the initial linear rubbing direction to the corresponding spatially distributed rubbing direction on the other plate.An incident beam that is linearly polarized perpendicular or parallel to the linear rubbing direction will follow themolecules’rotation,creating a radial or azimuthal polarization on the exiting side.A ␲-step phase plate is necessary to correct a geometric phase similar to what we mentioned above.These types of devices are already available at several vendors [31].Another very popular and powerful passive method uses a LC SLM.Despite its relatively high cost,a LC SLM offers the ﬂexibility and capability to generate an almost arbitrary complex ﬁeld distribution.One such example is shown in Fig.9[32].In this setup,two LC SLMs were used.The ﬁrst SLM provides pure phase modulation to the incoming beam to either correct certain aberrations in the system or to add the desired phase pattern to the beam.The combination of the ␭/4plate and the second SLM essentially forms a polarization rotator[23,33],where the amount of rotation is determined by the phase retardation of each pixel on the SLM.Properly designing the phase pattern on the second He‐Ne beam Beam splitter λ/4plateanalyzer Mach–Zehnder interferometer setup to verify the spiral Berry’s phase given in Eq.(3.2).The Berry’s phase is shown in the lower right-hand corner.8λ/2plate λ/2plateSPE Radialanalyzer Cylindrical vectoroutputGeneration of CV beam using radial analyzer and SPE.A circularly polarized input is used.The cascaded two ␭/2plates rotate the polarization to the desired pattern.SLM allows the input linear polarization to be converted into any arbitrary polarization distribution,including CV beams.Besides spatially variant polarization rotation,another class of methods use spatially variant retardation axis arrangements.For example,for a linearpolarization input,␭/2plates with spatially variant fast axis directions can be used to convert the linear polarization into CV polarizations.This can be achieved by taping or gluing together several segmented ␭/2plates with different discrete crystal angles (Fig.10)[34].Because of the discreteness,this type of device provides only rough spatial alignment of the polarization.A mode selector can be used to further clean up the polarization distribution pattern.One example is shown in Fig.11[4].The polarization is initially roughly aligned by four segmented ␭/2plates.Then a near-confocal Fabry–Perot interferometer is used to ﬁlter out the undesired mode and keep the radialf 1f 2SLM 2φxyθxyA polarization mode converter setup with two SLMs.The ﬁrst SLM creates the desired phase pattern.The combination of the ␭/4plate and the secondreﬂection-type SLM converts the beam into the spatially variant polarization pattern.The second SLM can be programed to convert a linearly polarized beam into CV beam.Figure adapted with permission from [32].10Segmented spatially variant ␭/2plates that can convert linear polarization into CV polarization.Figure reprinted from [34]with permission from Elsevier.polarization component.Recently,continuous rotation of linear polarization input using stress-induced space-variant plate [35]and photoaligned LC polymers [36]were reported,eliminating the need for a mode selector.For circularly polarized input,a spatially variant ␭/4retarder with axially symmetric local axis arrangement can be used to convert the input intocylindrical polarization.This type of device can be realized with spatial-variant subwavelength gratings (Fig.12)[37].The form birefringence of thesubwavelength grating provides ␭/4retardation,and its local orientation is continuously varied through lithographic patterning.However,owing to the requirement of a subwavelength period,extension into the visible and UV would be difﬁcult.An interesting technique using a transparent electro-optic (EO)ceramic [Pb ͑Mg 1/3Nb 2/3͒O 3−PbTiO 3,PMN-PT]as a radial polarization retarder (Fig.13,EO-RPR)was reported recently [38].A voltage is applied across the electrodes to create ␭/4retardation with a radially aligned retardation axis.This technique in principle could provide tunable CV generation from 500to 7000nm,depending on the applied voltage.However,in both cases a geometrical spiral phase exists and needs to be compensated.In addition to the methods using the spatially variant polarization properties described above,interferometric methods have also been used to create CV beams in free space.Methods using a Mach–Zehnder interferometercombined with a spiral phase plate [39]or a spiral phase created by a LC SLM[5]have been developed.A simple technique using ␲-phase step plates was reported in [40].Recently a common path interferometer implemented with a LC SLM to generate CV beams and other more complex vector beams was also demonstrated (Fig.14)[41].3.3.Passive Generation Methods Using Optical FiberGeneration of CV beams with few-mode ﬁber is another technique that deserves special attention.It is known that a multimode step-index optical ﬁber can support the TE 01and TM 01annular modes possessing cylindrical polarization symmetry,with the TE 01mode being azimuthally polarized and the TM 01Experimental setup that uses a segmented ␭/2plates polarization converter and a near-confocal Fabry–Perot interferometer (NCFPI)as a mode selector to generate CV beams.OD,optical diode;HWP ,half-wave plate;PH,pinhole;TL1,TL2,telescope lenses;PC,polarization converter;FL,focusing lens;CL,collimating lens;M,four mirrors;MD,monitor diode;AS,aperture stop;MO,microscope objective;PD,photodiode.Figure reprinted with permission from [4](/abstract/PRL/v91/i23/e233901).©2003American Physical Society.mode being radially polarized (Fig.15).Under the weakly guidingapproximation,these modes have the same cutoff parameter that is lower than all the other modes except the HE 11fundamental mode.In general,it is difﬁcult to excite these modes in an optical ﬁber without exciting the fundamental mode.The presence of a strong fundamental mode would spoil the cylindrical polarization purity.CV mode excitation in ﬁber can be achieved with careful misalignment between a single-mode and amultimode ﬁber [42].However,the conversion efﬁciency is fairly low for this method.The efﬁciency can be improved by preforming the incidentpolarization either in phase or polarization [27,43].A laboratory picture for CV mode excitation using an SPE is shown in Fig.16.A collimated laser beam passes through a SPE.Then it is coupled into a ﬁber that is carefully chosen such that it supports only the fundamental mode and the second-higher-order modes.The optical ﬁber acts as a spatial ﬁlter and a polarization modeselector.The polarization symmetry is conﬁrmed by inserting a linear polarizer between the ﬁber output end and the observation plane (shown in Fig.16).Using optical ﬁber as mode selector,a tunable and narrow band CV beam laser source was demonstrated in [44].(a)Geometry of spatially variant subwavelength grating.A scanning electron microscope image of the device is also shown.Experimentally measured spatial polarization patterns for (b)right-hand circular polarization and (c)left-hand circular polarization are illustrated.Figure reprinted with permission from [37].4.Manipulation of Cylindrical Vector Beams To make use of the CV beams in different applications,devices that can perform basic manipulations such as reﬂection,polarization rotation,and retardation are necessary.The key for these operations is to maintain thepolarization symmetry.When CV beams are reﬂected and steered,polarization symmetry could be broken owing to the nonequal reﬂection coefﬁcients for s and p polarizations.Even if the magnitudes of these reﬂection coefﬁcients are close,the phase difference can still destroy the polarization symmetry.In principle,metallic mirrors should preserve the polarization symmetry better.However,many metallic mirrors have protective coatings that could give rise to different reﬂection coefﬁcients for s and p bination oftwo identical beam splitters (picked up from the same coating run)with twistedLG01generation SPEλ/2platesAn experimental setup using an EO radial polarization retarder (EO-RPR)to generate CV beams.Figure adapted with permission from [38].14A common-path interferometer setup implemented with a SLM to generate CV beams and other more complicated vector beams.Several CV beams with different polarization patterns are also shown to the right.Figure reprinted with permission from [41].。

TEM4 2009

英语专业四级真题词汇精选TEM4 20091.Take place: 发生进行e.g. The meeting will take place next week. 会议下周举行。

2.Spectacular: adj.&n. 壮观的e.g. It is a spectacular fireworks display. 这是一个壮观的烟火会。

3.Countdown: n. 倒数计秒e.g. The countdown to the Athens games has begun. 雅典奥林匹克运动会开始进入倒计时。

4.Resolution: n.坚定决心决定e.g. His resolution never sways. 他的决心从不动摇。

5.Eventually: adv.e.g. Eventually it stopped raining.最后雨停了。

6.Scratch: v.&n.抓痕，划痕e.g. That cat scratches. 那只猫会抓伤人。

7.Definitely: adv. 明确地一定地e.g. The team will defini tely lose if he doesn’t play.如果他不参加比赛，这个队肯定会输。

8.Indifferent: adj. 冷漠的不在乎的e.g. He is indifferent to fame. 他不在乎名声。

9.Exchange: n.&v. 交换汇兑e.g. We exchanged our opinions about the event at themeeting.在会上，我们就此事交换了意见。

Receipt: 发票，收据，收入，进款，收到Here is your receipt. 这是您的收据Keen：热心的；敏锐的；激烈的；锋利的He is not very keen on jazz. 他对爵士音乐不感兴趣Retailer：零售商The retailer can absorb some of the increase incosts, but he is certain to pass on a percentage tothe customers. 零售商可以吸取一部分涨价因素，但他一定会按一定的比例转嫁给顾客。

安瓶幻灯

美国·艾思黛尔
iStelle-术后极速修复系列
安
瓶
美国·艾思黛尔
目录
1. 美国iStelle(艾思黛尔)公司介绍
2. 中国总代理—万润时代公司介绍 3. 安瓶主要成分--干细胞信息素的来源及作用机理 4. 微脂囊包裹技术 5. 安瓶的主要成分、适用范围及使用方法。 6. 五年大样本临床观察及效果对比图。 7. iStelle(艾思黛尔)安瓶与竞品的比较 8. iStelle(艾思黛尔)系列介绍 9. 各类证书 10.小结
常见问题解答
iStelle(艾思黛尔)安瓶容量怎么才1.7ml，量太少了吧？
答： iStelle(艾思黛尔)安瓶的核心成份为高浓度的细胞信息素及玻尿酸，
具备高活性，同时应用了最先进的微脂囊技术，具有很强的透皮吸收功效，使用1—2瓶完全可使术后肌肤得到很好的修复，如需要抑制瘢痕形成。需要使用3个月左右。
术后第一天
40岁
女性
当日同时操作：水光针、5D
童颜术、自体血清填充三项. 术后第一天
美国·艾思黛尔
安瓶--同时做微整形三项效果
术后第三天
女士，40岁同时操作：水光针、5D童颜术、自体血清填充三项; 术后第三天。术后7天淡妆出镜，接受采访
美国·艾思黛尔
安瓶—对儿童皮肤挫伤的修复对比
小朋友， 4岁,意外摔伤，使用iStelle安瓶，每6小时涂抹创面一次 48h完全结痂，第5天结痂脱落,皮肤基本恢复第6天皮肤完全恢复，没有一点
疤克：只能使用在完全愈合的伤口上，起到淡化疤痕的作用；愈肤宁：主要为几聚糖(Chitosan),为含氨多糖，干燥后可形成透明保护薄膜。金扶宁：主要成分重组人粒细胞巨噬细胞刺激因子，主要为消炎的功效，没有促进伤口愈合及细胞再生的作用；

IDEA2009获奖作品

The Structural Economic Expansion in Detroit (SEED) mass transit system is an easily expandable, two-level, elevated mag-lev system meant to connect Detroit with the surrounding economies in Pontiac and Ann Arbor. The system was designed to revitalize the city of Detroit, reduce urban sprawl, and create tightly organized communities around the transit stops.
The Haptic Reader helps blind people to read non-Braille books. When you place it on the page of a book it scans the letters on the page. The letters are converted to Braille characters, which appear on the surface of the device. The text can also be converted to voice, which is played through the embedded speaker.
Energy Seed is a collection bin for batteries that uses leftover power to light the attached LED street lamps. The design's aesthetic takes its cue from a flowering plant. When people deposit their batteries, it is like planting a seed that later, when it's dark, turns into a flower. It also encourages people to discard their batteries in a responsiblethose with limited hand mobility to manipulate objects that they would otherwise be unable to use. This device is used by slipping the finger holds over the thumb and forefinger, and then snapping objects into place via the clip. At a slight angle, the clip directs objects downward, giving the user a natural range of motion.

美剧Boston Legal波士顿法律第4季第6集剧本(英语)

Boston LegalThe Object of My AffectionSeason 4, Episode 6Written by Corinne Brinkerhoff & David E. Kelley© 2007 David E. Kelley Productions. All Rights Reserved.Airdate: November 6, 2007Transcribed by ToxicAngel for .Transcribed from aired episode; this is not an official script. Images © 2007 ABCScene: Court CorridorAlan Shore and his client Patrice Kelley are getting off of the elevator. There is a swarm of reporters with cameras and microphones rushing at them with questions.Alan Shore: Excuse Us.Patrice Kelley: This might be a opportunity for a sound byte.Alan Shore: The time for sound bytes is past.Scene: Judge Byron Fudd’s CourtroomGretchen Winters is on the stand being questioned by ADA Stewart BettsGretchen Winters: It was a typical day, in a typical office place in America. But what would happen next was anything but typical.Judge Byron Fudd: Uh, Ms Winters, just tell us, try not to channel Stone Phillips.Gretchen Winters: Yes your honor. As I said, I saw that woman enter (pointing to Patrice Kelley) and I knew who she was.ADA Stewart Betts: Let the record reflect that the witness has indicated the defendant.Gretchen Winters: I followed Sean’s trial, the news had covered it extensively, her face was prominent being that she was the mother of the victim. Oh she was a cool woman on camera, with a soft gentility, the belide… Judge Byron Fudd: Uhm, Ms Winters.Gretchen Winters: Yes, as I said, she entered and she walked toward Sean who was in his office right beside my desk. While Gretchen is telling what happened, it flashes back to the scene of Patrice walking into the office. She didn’t seem to be upset. She seemed calm, cool. As she got to Sean’s office, Sean said, “What are you doing?” and she said, “I’vecome to kill you Sean. Is this a badtime?” Just like that. “Is this a badtime?” I saw it, there in her hand, agun. End of Flashback.Whitney Rome: Stop! Your Honor,this is hearsay, if the witness is tobelieved this wasn’t an exitedutterance from our client,…ADA Stewart Betts: It was adeclaration against interest,hearsay,…Whitney Rome: No, our clientalready admitted she shot him,…ADA Stewart Betts: And she’sclaiming insanity. Testimony of herdemeanor and state of mind arerelevant Your Honor.Judge Byron Fudd: Objection Overruled, you may continue Ms. Winters.Flashback to the office where Patrice shot Sean while Gretchen Winters tells the story.Gretchen Winters: Gladly, Anyway, it was the most horrible thing I’d ever experienced. There’s Sean, lying on the floor, blood gushing from his head.ADA Stewart Betts: Whoa whoa whoa whoa. You skipped ahead. Back up to before he was shot.Gretchen Winters: Oh, I’m terriblysorry, I get ahead of myself when I getexcited. Anyway, where was I…oh,yes. She walked in, said what shesaid, then raised the gun. And shepointed it. Calmly, her hand was notshaking. And she said, “you have fiveseconds to live. I’d give you ten but wereally can’t keep hell waiting.” Andthen… she just pulled the trigger. Thebullet his him right between the eyesand he dropped. End of flashback. Itwas a cold-blooded and viciousexecution. It was awful, just to thinkabout it… Shall I tell it again?Scene: Crane Poole and Schmidt – Denny Crane’s OfficeDenny Crane is sitting at his desk flipping through a file. Nancy Wilding approaches Denny’s office and knocks on the door.Denny Crane:Standing and motioning to the chair across from his desk. Oh, please come in.Nancy Wilding: Sure, I’m thrilled, actually and a little stunned. I’ve worked here for six years and I don’t believe I’ve actually been in your office.Denny Crane: Actually, I’m afraid the circumstances of this meeting are not pleasant.Nancy Wilding: Oh.Denny Crane: We’re letting you go.Nancy Wilding: What? Why?Denny Crane: It’s not that your performance hasn’t been good, I’m told you do fine fine work. But since partnership is not in your future… we prefer to let those associates go rather than mislead them, it’s only fair. Nancy Wilding: Would you mind telling me why partnership’s not in my future?Denny Crane: Not at all. You’re fat.Nancy Wilding: Excuse me.Denny Crane: We can’t have fat people working at Crane Poole and Schmidt. That’s all, and seriously, thank you for your past work, I mean that.Nancy Wilding: So, I’m being fired because I’m fat?Denny Crane: Yes, off you go now.Nancy Wilding:Standing to leave. So ifI was thin, I’d still have my job?Denny Crane: Hell, if you were thin, I’dprobably try and have sex with you.Nancy Wilding: You did try.Denny Crane: Really?Nancy Wilding: Last week.Denny Crane: Did we have it? It doesn’tmatter, look I can’t let my personalfeelings get in the way, I have to think ofthe firm. No tubsters at C.P. and S. Offyou go now.Nancy just stares back, incredulous.Denny Crane:(Into the speakerphone)Security please.Scene: Judge Fudd’s CourtroomWhitney Rome is questioning Dr. Marcini.Dr. Marcini: It was a kind of disassociative state that we call automatism.Dr. Marcini: Yes. Basically… Ms. Kelley went into a form of automatic pilot. We see it with battered wives. The abuse triggers this extreme, almost psychotic reaction in the brain… here, the abuse was obviously the murder of her child. Then seeing the killer set free.ADA Stewart Betts is up.ADA Stewart Betts: She’s fine now?Dr. Marcini: Seems so, yes.ADA Stewart Betts: And was she on automatic pilot during all the planning stages of this crime?Dr. Marcini: I can’t really know. I didn’t examine her.ADA Stewart Betts: When you did examine her after the shooting… was she on automatic pilot then?Dr. Marcini: No. She had regained control.ADA Stewart Betts: And you know she was on automatic pilot during the murder based on what information? Dr. Marcini: What she felt and experienced at the time of the shooting.ADA Stewart Betts: Who told you what she felt and experienced?Dr. Marcini: She did.Scene: Lobby of Crane Poole and SchmidtLeigh Swift is awkwardly walking throughthe lobby. She has her hands firmly gluedto her thighs. She approaches Carl Sack.Carl Sack: Hello.Leigh Swift: Hello, my name is Leigh Swift.L-E-I-G-H, I only point this out because it ismisspelled sixty-seven percent of the time,and I am her today in hopes of securing legalcounsel, preferably from-Carl Sack: Jerry Espenson.Leigh Swift: How did you know?Carl Sack: Shot in the dark?Jerry comes around the corner with hishands on his thighs.Carl Sack: Impeccable timing.Jerry Espenson: Hello.Leigh Swift: Hello.Carl Sack:Raising a hand. High fives all around. No? This is Leigh, Jerry. I’ll get you the correct spelling on that later, could you perhaps escort her out of the common area?Jerry Espenson: Let’s go to my office.Jerry and Leigh walk off toward his office, both of them with their hands on their thighs. Nancy Wilding walks up to Carl carrying a box.Nancy Wilding: Hello. Mr. Sack, I just wanted to come say goodbye.Carl Sack: “Goodbye”, who the hell are you?Nancy Wilding: My name is Nancy Wilding, I’m an associate, I was fired. Denny Crane fired me because I’m fat.Carl Sack: He did what?Nancy Wilding: Yes. So, it’s goodbye.Carl Sack: Wait. No, no. You’re not fired, I’ll talk to Denny.Nancy Wilding: Oh, if only it were that easy. See, I’ve been damaged. And, I’ve hit the lottery. We’ll see you all in court.Scene: Denny Crane’s OfficeDenny is drinking a glass of scotch. Carl is across the desk from him.Carl Sack: Are you out of your mind?Denny Crane: Why does everybody ask me that?Carl Sack: For God’s sakes Denny, you cannot fire somebody because their fat. Never mind the indecency of it, can’t you see that as a lawyer? And you know what, she’s poised to make noise over this. And youDenny Crane: No I won’t, let me tell you something Sack, it doesn’t matter what people are saying as long as they talk about you.Carl just looks at him like he can’t believe what he is hearing.Scene: Jerry Espenson’s OfficeJerry and Leigh enter the office.Leigh Swift: I’ve been to six other lawyers. None of them would take my case. But all of them asked if I was related to you.Jerry Espenson: Perhaps you could tell me why you’re here.Leigh Swift: I’ve lost my lover. His name was Gebrauchskasten, and he was forcibly taken, against his will, by force.Jerry Espenson: Have you filed a police report?Leigh Swift: Oh, the police have been dismissive. I suspect they’re discriminating against Gebrauchskasten based on his ethnicity.Jerry Espenson: I really doubt they’d ignore a kidnapping.Leigh Swift: Here he is. She hands Jerry a photograph of a utility box. Jerry looks confused. That’s Gebrauchskasten, his name is German for utility box.Jerry Espenson: This box…Leigh Swift: Is my lover.Scene: CourthouseAlan, Whitney and Patrice areentering an empty meeting room.Alan Shore: Nobody here believesyou are actually crazy. It wasrevenge, I know it, you know it, thejury knows it. Our insanity defense issimply a pretext to allow the jury to letyou go, but first they have to wantyou to go free. For that to happenthey have to like you, and for that tohappen, the jury has to feel what youfeel.Patrice Kelley: I don’t feel. After mydaughter was killed I stopped feeling.It’s how I survive.Whitney Rome: Well, it won’t behow you survive prison, which is where you’re headed if the jury doesn’t see a human being sitting in that chair. Patrice Kelley: I’ll discuss it with God.Alan Shore: Look at me. If this jury thinks for a moment that you’re pulling one over on them, you’re gone. You need to be uneffectively, emotionally forthright and sincere.Patrice Kelley: I honestly don’t know if I can do that.Scene: Judge Fudd’s CourtroomPatrice Kelley is on the stand.Patrice Kelley: After Hannah was killed, all I had to grab hold of was this quest to see her killer convicted and sentenced.Alan Shore: Do you remember what you felt when you heard the verdict of “Not Guilty” read?Patrice Kelley: I don’t think I do really. I went numb, at some point I lost myself, I started to pray because I often find consolation in my faith and one day I heard a voice.Alan Shore: A voice?Patrice Kelley: Yes, it wasn’t my own, and it said “You must kill Sean Harmon”.Alan Shore: You didn’t recognize this voice?Patrice Kelley: No, but for whatever reason, I became convinced that it was God.Patrice Kelley: I know how crazy it sounds, but at the time I was reading a lot of the Bible and so many of the verses I would hear in this voice, Leviticus – He that killeth a man, he shall be put to death. Exodus – He that smiteth a man so that he die, he surely shall be put to death. I kept hearing this over and over and I became convinced that my daughter’s sole (Now starting to cry) would rest only with vengeance. Harmon had to die, it was up to me to kill him. I would have to be the one to avenge my baby’s death.Alan Shore: What do you remember about the day you shot Sean Harmon.Patrice Kelley: I remember driving to his place of work, approaching him, I didn’t feel scared. I recall aiming the gun, shooting him, and I’m ashamed to admit it, but I remember I felt joyous.Alan Shore: Joyous?Patrice Kelley: Yes. Between his living a free man and his dying, it felt more moral for him to be dead, and I felt like I was somehow carrying out God’s word. It was joyous.Scene: Crane Poole and Schmidt, Jerry Espenson’s OfficeKatie Lloyd and Jerry Espenson are researching Leigh Swift’s case.Katie Lloyd: Objectophilia – A type of neo-sexuality indicative of a modern trend away from human to human intimacy. It sounds like a coping mechanism. A way to compensate for a lack of human affection, I supposed we can all relate to that.Jerry Espenson: So what do I do? She’s in love with a box.Katie Lloyd: Well, what do you want to do Jerry?Jerry Espenson: Well, she’s a very nice lady. I suppose I would like to help her.Katie Lloyd: Do that, then.Jerry Espenson: She has not legal case, it’s ridiculous even for this firm.Katie Lloyd: Maybe you could locate her lover.Scene: Crane Poole and Schmidt, Denny Crane’sOfficeDenny is sitting at his desk playing a computergame. Lorraine Weller knocks on his door.Lorraine Weller: Hello Denny, busy?Denny Crane: Can’t you tell, I’m in the middle ofkidnapping a hooker.Lorraine Weller: May I speak with you a second?Denny Crane: Actually, I was on my way out,care to ride the elevator with me?Lorraine Weller: You’re just dying to get me in anelevator aren’t you?Denny Crane: It crossed my mind.Lorraine Weller: Carl asked me to give you ahand with this Nancy Wilding matter.Denny Crane: Oh, that’s why you’re here, to giveme a hand.Lorraine Weller: You know what I would like todo Denny? I would like to get Nancy Wilding andher lawyer in, officially offer her her job back,coupled with a heart felt apology.Denny Crane: Why should you apologize? Youdidn’t do anything wrong.Lorraine Weller: I was thinking it would comefrom you.Denny Crane: No.Lorraine Weller: Denny. I don’t want to bebothered with this case any more than you do.Let’s you and I make it go away together. Can wedo that, Denny? You and I together.Denny is looking at her like she just proposed something much more interesting.Scene: Judge Fudd’s courtroomPatrice is being questioned byADA Stewart BettsADA Stewart Betts: Did you evermention to anyone before killingSean Harmon that you were gettingmessages from God?Patrice Kelley: No.ADA Stewart Betts: You claim tobe a religious person, did youdiscuss this with clergy?Patrice Kelley: No.ADA Stewart Betts: You’re gettingmessages from God. You don’t talkto your own priest, you just order agun?Patrice Kelley: Not the actions of asane person I admit.ADA Stewart Betts: You’re sanenow, right? In fact, when examinedby court appointed psychiatrists todetermine your competency to standtrial, they found you sane, this justthirty-six hours after her crime. Itseems like such a small convenientwindow of insanity.Alan Shore: Objection.Judge Byron Fudd: ObjectionSustained. The jury will disregardthat.ADA Stewart Betts: So, as Iunderstand it, you know now thatGod was not speaking to you?Patrice Kelley: Yes, I was probablyprojecting. I wanted Sean Harmondead, it was me, but I didn’t think Icould reconcile murder with my sense of morality so my subconscious somehow found a way to make it God’s word, so that I could maintain me moral esteem and still kill Sean Harmon.Scene: Crane Poole and Schmidt – Denny Crane’s officeDenny and Alan are visiting. Denny is pacing the floor, Alan is sitting on the sofa drinking scotch.Alan Shore: It is one of those answers that could either win the day or bury us.Denny Crane: She seems to know exactly what she’s doing, I’d give her the benefit of the doubt.Alan Shore: Let’s talk about you Denny. You certainly knew what you were doing when you fired Nancy Wilding for being fat. What’s going on? Were you retaliating because she rejected your sexual advances. Denny Crane: If I had a nickel for every girl that turned me down, actually I do.Alan Shore: What is it then? Is it another way to be the center of attention?Denny Crane: I should be on that case. I should be in that courtroom with you Ms Kelley not in my office kidnapping hookers (Alan gives him a look), on the tv.Alan Shore: Denny.Denny Crane: Don’t. Just don’t.Alan Shore: You need to let Lorraine make this case go away.Denny Crane: I’ll do what I want.Alan Shore: Fine.Scene: Crane Poole and Schmidt – Carl Sack’s officeJerry Espenson and Katie Lloyd are standing. Carl is pacing the floor behind them lecturing them. Carl Sack: You are representing a woman who is in love with a utility box. Is that right, Jerry?Jerry Espenson:mumblesCarl Sack: I’m sorry?Jerry Espenson: Yes, Mr. Sack. That’s right I’m representing a woman who’s in love with a utility box. Carl Sack:To Katie. Something tells meyou’re involved.Katie Lloyd: I’m not actually, except toencourage Jerry. I think it’s brilliant.Jerry Espenson:In a high pitched voice.Brilliant.Katie Lloyd: I think the law in it’s noblest isused to protect the weakest and mostvulnerable members of our society. Theclient here is an objectophile, a fragile one atthat. Every other law firm summarilyrejected her, how wonderful that this firmendeavors to prioritize compassion andhumanity over profit. It positively warms thecockles of my heart. Jerry is off to meet withthe developer perhaps you would care tojoin. I’m sure your own cockles could use ajolly.Scene: Judge Fudd’s CourtroomWhitney has Father Kevin Maher on the stand.Father Kevin Maher: Well, I can’t speak towhether God spoke to this woman, but… myview is He would certainly forgive her for heractions.Whitney Rome: For killing Sean Harmon?Father Kevin Maher: The Lord’s powers offorgiveness are without limit. And in thiscase there’s always the “an eye for an eye”principle.Whitney Rome: That justifies killingsomebody?Father Kevin Maher: The phrase is to befound in the Old Testament and I believe itspeaks for itself.Whitney Rome: What about the NewTestament, Jesus says turn the other cheek,does he not?Father Kevin Maher: Well, my reading ofthat is Jesus was voicing a very personal view of how a saintly individual should act. I don’t interpret that as condemning revenge.ADA Stewart Betts is now up.ADA Stewart Betts: So, you, a man of the cloth, don’t believe that all human life is holy?Father Kevin Maher: I do, I also believe “Whoever sheds the blood of man by man shall his blood be shed.” Genesis.Professor Jeffery Benoit is now on the stand.Professor Jeffery Benoit: I have studied Judeo-Christian teachings for thirty-three years, I consider myself both a Biblical and a Talmudic scholar, and I found Father Maher’s testimony to be strikingly without merit.ADA Stewart Betts: Because?Professor Jeffery Benoit: The “eye for and eye” verse in the Bible suggests a limitation on retribution. It is forbidden to take two eyes for one, or, for that matter, to inflict any punishment that would exceed the offense. ADA Stewart Betts: Yes, but the underlying offense of Sean Harmon was murder.Professor Jeffery Benoit: Even so, it was never meant to advocate revenge murder. I mean consider the words of Jesus, “If anyone strikes you on the left cheek, offer him the other as well.” Jesus never would have endorsed this revenge killing. He was against vengeance.Alan Shore is now up.Alan Shore: Well, except forwhen it came to believing in himright? Mark 16:16, He thatbelieveth and is baptized shallbe saved, but he that believethnot shall be damned. Anddamnation, if hell is everythingit’s cracked up to be, is a fateworse than the painful death thatproceeds it. So, according to thisguy Mark, Jesus was okay withvengeance wasn’t he professor?Professor Jeffery Benoit: If Iwas a Christian I suppose Iwould be very much offended bythat.Alan Shore: But you’re a Jew. Certainly Jews are okay with revenge?Professor Jeffery Benoit: You know something about Jewish law I don’t?Alan Shore: I know if you cross Irael’s borders without a proper invitation, the bombs they go a-bursting, I know when Israel kidnapped Eichmann and hanged him, Jewish people the world over cheered.Professor Jeffery Benoit: First of all, Eichmann was responsible for mass murder.Alan Shore: So, it’s not whether Judaism supports revenge, but when.Professor Jeffery Benoit: You’re offensive.Alan Shore: Really? I was just going to say the same about you. Judaism has never been preoccupied with forgiveness, justice, justice you shall pursue, that’s what the Torah commands. My client was pursuing justice when she avenged the death of her only daughter. What’s truly offensive is you sitting high on your scholarly horse and suggesting that God, anybody’s God would condemn her for it. Moreover…ADA Stewart Betts: Objection!Alan Shore: I suspect if your child was murdered and it was your child’s murderer who went free, you wouldn’t be pontificating about forgiveness.ADA Stewart Betts: Objection, Your Honor!Alan Shore: And when’s the last time one of your kids got bludgeoned too death?Judge Byron Fudd: Mr. Shore.Scene – Construction SiteSteve Hughes: This is really difficult for me to grasp.Jerry Espenson: It’s very simple. You relocated the box. We would simply like to get possession of it.Steve Hughes: No, that much I got. It was the part about her being in love with it.Jerry Espenson: Of course my client’s predilection must strike you as unconventional. But I would nevertheless ask you to respect – she has found a meaningful relationship that works for her.Steve Hughes: With the boxLeigh Swift: I’m an objectophile.Jerry Espenson: We were hoping that perhaps the person involved in the item’s removal can help track itJerry Espenson: When you say destroyed…Cut Jerry’s Office. The compressed box hasbeen delivered to Jerry and he is opening thebox containing it to show Leigh.Leigh Swift: That’s all of him?Jerry Espenson: I’m told he’s all there.Leigh Swift: It’s not the same.Jerry Espenson: Leigh, have you thought ofgetting counseling?Leigh Swift: You must think I’m a rather sickperson.Jerry Espenson: No, I don’t. There are manypeople who find inanimate objects desirable. I hada life size doll.Leigh Swift: At least your object had a face.Jerry Espenson: Oh, she had more than a face.I’d given her a personality, sense of humor, I would even debate politics with her on occasion. Most of it is about fear of intimacy and trust with a real person. I read one expert, he says we’ve become such a socially isolated society what with computers and so forth with so many socially isolated individuals, objectophilia is not all together surprising. Leigh has started staring at a clock radio on Jerry’s table. Are you listening?Leigh Swift: What? Oh, yes, sorry. It’s just that your clock radio reminded me of one of my exes for a sec. Jerry Espenson: I think you can achieve an intimate and trusting relationship with a real person. It’s very terrifying I know. But I think you should give real people a try.Leigh Swift:Nods and walks to the door to leave. Jerry, thank you for everything. For not laughing at me. For, well, you’re a very compassionate man.Jerry Espenson: If there’s anything I can do for you.Leigh Swift: You’ve been so kind. It might be very hard for me to be alone tonight.Jerry Espenson: Oh, uh, well… Leigh looks from Jerry to his radio and he realizes she is not referring to him. He grabs the radio and hands it to Leigh. Take it.Leigh Swift: Are you sure?Jerry Espenson: Please.Leigh Swift: I’ll bring it back, just something to hold.Scene: Crane Poole and Schmidt – Conference RoomLorraine Weller, Denny Crane, Nancy Wilder and herlawyer Emma Path are all sitting around theconference table.Lorraine Weller: We are officially offering Nancy her jobback.Emma Path: Rejected. She’s not coming back to a firm offat bigots.Lorraine Weller: We’ll offer $25,000 to cover her feelings.Emma Path: Also rejected.Denny Crane: Are you this hostile in bed, because I likethat.Lorraine Weller: Denny.Denny Crane: Look, I really am sorry for what I said. Butlet’s face it, we live in a very cosmetic world these days.And perception so often seems to count more thansubstance. Beauty begets beauty. What I was really tryingto say was you’re fat.Nancy Wilding: Keep talking Mr. Crane. All I hear isKa’ching Ka’ching Ka’ching.Denny Crane: A jury is not going to give you money,jury’s like winners, look around the room, (pointing toLorraine) winner, (pointing to himself) winner, (pointingLet’s review, winner, winner, loser, loser. Now I wouldappreciate it if you would leave my conference roombefore anyone sees you and confuses you withsomeone I would actually hire. Off you go now. Takethe man eater with you, bye bye.Scene – Crane Poole and Schmidt – Carl Sack’s OfficeGracie Jane on television. Carl is watching, Dennycomes in.Gracie Jane: The evidence is all in folks. It’s down toclosing arguments. We know what the prosecution isgoing to say. Let’s talk about the defense. There is onlyone argument to make here, we all know what it is, the victim here killed this poor woman’s daughter. Carl turns off the tv.Denny Crane: What do you want?Carl Sack: Could you please sit Denny? Denny sits. Do you know the reason I came to the Boston Office? Denny Crane: Shirley.Carl Sack: That would be one reason. The other was to, well, ring out some of the madness. And now we have you, firing an associate because she’s fat.Denny Crane: I’d like to stay and chat Carl, but I’ve got a trial coming up, the client can’t fire me because I’m the client. Denny goes to get up.Carl Sack: Please sit. May I sharesomething with you?Denny Crane: Shirley?Carl Sack: No, not Shirley. There’s areason your name comes first on thedoor. More than anything else, thisplace is you. If I’ve come to realize onething more than anything since arriving,is how the people that work at CranePoole and Schmidt so love doing so, inlarge part for you. What you do toyourself in theory is your own business,but it really isn’t.Denny doesn’t know what to say. Hegets up to leave, turns lookingthoughtful, and farts.Denny Crane: Denny Crane.Scene: Judge Fudd’s CourtroomADA Stewart Betts is giving his closing argument.ADA Stewart Betts: I don’t think I need to persuade you that the evidence clearing shows that Patrice Kelley was not insane. In truth, her defense never really argued that she was. To the contrary, they introduced all kinds of evidence, religious, moral and otherwise to convince you that what she did made total sense. Her daughter was murdered her killer was free. Of course, of course she was outraged. And many of you would have been tempted to take the law into your own hands just like she did. But you wouldn’t have. As much as you’d want to give in to anarchy, and lawlessness and vigilantism, you wouldn’t have because we have laws against it. We have consequences like prison to stop us from giving in to our violent primal, all be it, sometimes natural urges. Patrice Kelley is sitting here because she said, “Screw the law”, and now she is hoping that the twelve of you will do exactly the same thing, screw the law you took an oath to uphold. The role of the juror in this country is most noble. It is perhaps the highest form of public service, not because it’s easy, but because it’s often times difficult. Here you are being asked to convict a good woman. A woman you no doubt relate to. A woman your hearts quite appropriately go out to. It’s difficult, as the truth often is. The truth here is that this was an act of revenge. Patrice Kelley deliberately, methodically, and reflectively killed Sean Harmon.。

ENTRA 09春夏系列新装发布

少女之情怀，又要隐含精致女人的心脉；既显高雅，且不孤傲；既有品位，也不乏情趣。
全新帝舵男装运动时计Ａｒｎｕ系列ｅｏａｔ
全新帝舵男装运动时计Ａｒｎｕ系列，选用不锈钢或ｅｏａｔ
］ｃ．８ｔ黄金及钢精制，无论设计或功能方面，务求所有款式在佩戴上更为舒适。开关按钮、旋转式外圈、实心表带、符合人体工程学设计的表扣、防磨蓝水晶玻璃以及旋转入式表冠，每一个细节互相紧扣，确保腕表时刻展示超凡性能。此外，Ａｒｎｕ系列多功能时计的款式防水深达１０ｅｏａｔ５米，而海洋王子型款式更可防水深达２０。０米
资讯
ＩＮＦＯ
ＥＴＡ０春夏系列新装发布ＮＲ９
ＥＴ４０春夏发布会上，春的宝蓝、玫红、金ＮＲ９
色，夏的紫丁香色，水蓝……缤纷的色彩给人对春天
的到来寄予强烈的期待。。春夏系列采用韩国进口面９
料，通过立体剪裁和多种剪裁方式的结合，塑造出高贵女性的曲线魅力。设计风格表达了女性毫无所惧不受约束的创新姿态，设计理念满足了时尚 “ ｆｉｅｏｆｃ ” 女性的消费诉求：既要保持职场之严谨，又能缓弛职场之压力；既要融入团队，又要显露个性；既要洋溢
１４浙商２
ቤተ መጻሕፍቲ ባይዱ
Ｍｇｉ２９ａｚ０ａｅ０４ｎ

超精细液晶笔记本电脑

超精细液晶笔记本电脑
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【期刊名称】《《军民两用技术与产品》》
【年(卷),期】2002(000)012
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GENERALIZED INSTANTANEOUS REACTIVE POWER THEORY INPOLY-PHASE POWER SYSTEMSR. S. Herrera, P. Salmerón, J. R. Vázquez, S. P. Litrán, A. PérezESCUELA POLITÉCNICA SUPERIOR. UNIVERSITY OF HUELVADepartment of Electrical EngineeringCtra/ Palos de la Frontera s/n, Palos de la Frontera, Huelva, SpainTel.: +034– 959 21 75 85, Fax: +034 – 959 21 73 04E-Mail: reyes.sanchez@dfaie@uhu.es; patricio@uhu.es; vazquez@uhu.es; salvador@uhu.es;aperez@uhu.esURL: http://www.uhu.es/epsKeywords«Instantaneous Reactive Power Theory», «Active Power Filter», «Power Quality», «Multiphase systems».AbstractThe systematic use of Active Power Filters, APFs, to compensate nonlinear loads, has extended the use of the instantaneous reactive power theory. Originally, the p-q theory appeared; it obtained constant instantaneous power in the source side after compensation. Later, other formulations have been developed. They have allowed different compensation objectives to be obtained. Nevertheless, all of them can only be applied to three-phase systems, i.e. those formulations frameworks can not be used to establish control strategies in poly-phase systems. This paper presents a new approach, based on geometric algebra, which can be applied to multiphase systems. A new tensor product is introduced that allows the operative definition of the instantaneous reactive power tensor and its derived instantaneous reactive current component. In addition, in this paper a new concept of instantaneous power multivector is introduced which allows the instantaneous reactive power theory to be encoded in an analog way as single-phase systems analysis. The new expressions are applied to a practical multi-phase system. Power and current terms are calculated and the associated waveforms are presented. Results corroborate the correspondence with the traditional electric power theory.IntroductionAt the beginning of the eighties, the instantaneous reactive power theory was published. It had the objective of being applied in a systematic way to the active power filters (APF) control design to compensate nonlinear loads, [1,2]. Besides, it has been used as theoretical framework to establish the electric properties of energy transmission between source and load in the most general asymmetry and distortion conditions. A lot of approaches have been appeared since the publication of the Akagi et al. original work, [3-17]. They compose an important set of formulations that may be considered into the instantaneous reactive power theory framework. Thus, besides the original formulation, they stand out, among others, the modified p-q or cross product formulation, [3-6], the d-q formulation, [7], (or its alternative, the i d-i q, [8]) in the rotating frame, the p-q-r formulation, [9], and the vectorial formulation, [10-12]. All of them relate the power transfer in a three-phase system in function to the instantaneous power (instantaneous real power) p(t) and to the instantaneous imaginary (or reactive) power, q(t), depending on the formulation. This last quantity marks the difference between the instantaneous reactive power theory and the rest of other possible theories about the electric power. The instantaneous imaginary (or reactive) power, q(t), are formally defined, in most of the cases, as the voltage and current vectors cross product. In any case, instantaneous reactive power theory reclaim the fact that to relate the energytransfer between source and load in a three-phase system, p(t) is not enough, but a power quantity like q(t) is necessary. In fact, those power variables are the base of the current decomposition in its different components, and only in the case of single-phase systems, p(t) is enough .All the formulations proposed have been limited to three or four-wire, three-phase systems, and all of them have a difficult generalization to poly-phase systems. Up now there have been a few attempts in the regular papers. In [5], it is proposed the decomposition of an n-dimensional current vector in twoorthogonal components, p i G and q i G . The first one, the instantaneous power current ()p i t G, is obtained by means of the projection of the current vector, ()i t G, over the voltage vector, ()v t G. The second one, the instantaneous non-active (or reactive) current ()q i t G, is the ()p i t Gcomplement to obtain the current ()i t G, and from the length ()q i t G, the instantaneous reactive power q(t) is derived. However, in [5] it is not established an operative expression to obtain the current component ()q i t G, or the power q(t). An important advance in the generalization to multiphase systems is presented in [13-14]. In this paper an instantaneous n-phase power p(t) and an instantaneous n-phase reactive power tensor q are proposed, where the second one is a second-order asymmetrical tensor. They are defined by means of formal expressions.On the other hand, over the last 40 years geometric algebra has been developed. It constituted a mathematical framework based on Clifford and Grassman algebras. The geometric algebra integrates vectors and matrix and the operations traditionally applied to them into a unified and coherent language. In addition, its expressions can be expanded to any number of dimensions in a easy way, [18]. Into de geometric algebra framework, the geometric product is presented. It allows the instantaneous power multivector to be defined. Thus, the power analysis of n-phase systems is possible in an analog way as the single-phase systems.In this paper, the [13-14] line is followed and, into the geometric algebra framework, there are introduced the mathematical operations necessary to define, in an operative way, each of current components and each of power terms in polyphase systems. The development is not only the calculation of instantaneous reactive current as the difference between instantaneous current and instantaneous power current, but it evolves the introduction of an instantaneous reactive current defined in function to an instantaneous imaginary power.Instantaneous Reactive Power Theory for Polyphase SystemsMathematical FoundationsBased on Fig. 1, the voltage and current vectors are defined as follows:[]1212;......Tn T n i i i i u u u u ==⎡⎤⎣⎦==i u G G (1)From these voltage and current vectors within n-phase systems, the instantaneous real power, p(t), and theinstantaneous reactive power tensor, q(t), can be defined. The first one is obtained from the inner product, whose result is a scalar valor and the second one is obtained from the outer product, whose result is a hemi-symmetrical tensor, represented by a matrix. It is:()()()()()();u t i t p t u t i t t =⋅=×q G G G G(2)In fact, the outer product is defined by means of the tensor product in the next way:()()()()u t i t i u u i ×=⊗−⊗G G G G G G (3)which, in explicit way, has expressions derived from now on.Fig. 1: n-phase system where the voltage is defined with respect to an arbitrary referenceThe tensor product of current vector over voltage vector is:1112112122221212...........................n n n n n n n n i u i u i u i i u i u i u i i u u u u i u i u i u i ⎡⎤⎡⎤⎢⎥⎢⎥⎢⎥⎢⎥⎡⎤⎣⎦⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎣⎦⎣⎦⊗==G G (4)And the tensor product of voltage vector over current vector is:1112112122221212...........................n n n n n n n n u i u i u i u u i u i u i u u i i i i u i u i u i u ⎡⎤⎡⎤⎢⎥⎢⎥⎢⎥⎢⎥⎡⎤⎣⎦⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎣⎦⎣⎦⊗==G G (5)So, the instantaneous reactive power tensor gets the next form:12121112122211220...0..................0n n n n n n n n i u u i i u u i u i i u i u u i u i u i i u u i i u ⎡⎤⎢⎥⎢⎥⎢⎥⎢⎥⎣⎦−−−−=×=−−q G G (6)where all the terms above and below the main diagonal are the same and with opposed sign, and so it is a hemi-symmetrical tensor. Its norm determines the instantaneous reactive power q(t):()1/2()u u u q t ⋅==q q(7)Both power terms characterize the energy transfer between source and load in a multiphase system.Moreover, the definition of an only power term is possible, which encodes all the information about the power transfer in an n-phase system. Thus, the instantaneous power multivector is defined as the geometric product of voltage and current vectors:ui u i u i ==⋅+×s(t)G G GG G G(8)It is obtained from the combination of inner and outer products. From (2), s(t) can be expressed as:()p t =+s(t)q(t)(9)i.e., the instantaneous power multivector combines in an only mathematical entity the scalar valor which represents the instantaneous power and the tensor value which represents the instantaneous reactive power. This kind of representation is usual in the geometric algebra framework, whose elements belongs to this kind of entity are denominated multivectors.Into the geometric algebra framework the reverse of an element, for example q(t), is defined as the following expression:()()1/2†1k k −=−q q (10)where k is the vectors number which generate q , i.e., k=2. It allows the s(t) multivector norm to be defined as:()1/2=+s ss(11)wheremeans scalar value.From (10) and (11) the square value of s(t) multivector norm can be obtained:()()2220()p p p q s t +=++=+=s q q(12)Where s(t) is the instantaneous apparent power. The introduction of the instantaneous power multivector allows a power term for multiphase system to be obtained, according to the same approach used in sinusoidal steady state.Current vector decompositionConsidering any vector, as for example voltage vector u G, its inverse, into the geometric algebra framework, can be defined as follows:††12†u−==u u u u u (13)where u is the instantaneous norm of vector ()u t . Multiplying by the left side s(t) multivector the ()u t Ginverse, next expression is obtained:()11i t −−===u s(t)u ui i (14)Thus, from (9):()†2222p p uuuu==+=+u u u uq i s(t)q(15)where the fact that †≡u u has been considered. In this way, current vector is divided in two currentcomponents: instantaneous power current ()()p i t =p i t G,()2p t u=p u i(16)and instantaneous reactive current ()()q i t =q i t G,2u=q uq i (17)In (17), voltage vector u and tensor q operate by means of geometrical product, i.e.:=⋅+×=×uq u q u q q u (18)because u·q ≡0.Therefore, into the geometric algebra framework, a decomposition of current vector has been possible for multiphase systems. This decomposition is orthogonal. In fact:()()222p q p q pq i i i +++==++=+ii i i i i(19)On the other hand, according to (19) and (9), current vector norm has the following expression:222222222222222222222p p q q u p q q u p p p p q i u u u u u u u u u u u u ++++++⎛⎞⎛⎞⎛⎞⎛⎞+=+=+=+=+=⎜⎟⎜⎟⎜⎟⎜⎟⎜⎟⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠⎝⎠⎝⎠u u u u uq q u i i i i (20)And so,()222222222pq p q s t ui ui ui +===+(21)The similarity to single-phase circuits is complete. Thus, the next equation generalizes the instantaneous power theory to n-phase systems from n=1. I. e.:()()2t t uu i =s G G (22)Several compensation approaches can be achieved applying this new formulation: instantaneous compensation or average compensation. Into the second approach framework, several objectives can be considered: constant source current, unity power factor and balanced sinusoidal source current, [11], [14]-[16]. Besides, thanks to know the mathematical expression of instantaneous reactive power, there are other compensation objectives to impose.Compensation CurrentIn previous sections, general power terms have been derived within geometric algebra framework. In addition, those expressions have been used to decompose the current vector into two orthogonal components. Therefore, in this section, a control strategy is established and the compensation current is derived by means of the developed expressions. The considered system is shown in figure 2, which presents two elements supplied by an only source. One of those elements can be considered the load and the other the compensator.Fig. 2 General three-phase four-wire systemThus, according to the fact that the instantaneous power multivector is additive, it is:S L C =+s s s(23)where s S is the source instantaneous power multivector, s L the corresponding to the load and s C , the corresponding to the compensator. The instantaneous compensation strategy imposes that the compensator instantaneous power multivector is the same as the load instantaneous reactive power, that is:C L =−s q(24)In addition, within this strategy, the compensation instantaneous power multivector has the following expression:()C C Lq ==−s ui u i(25)and:C Lq =−i i(26)Thus, according to (22):()22L C C uu−==u q us i(27)On the other hand, the instantaneous current supplied by the source is the next:()2222L L L S L C L L Lp p i uuuu−=+=+=−=≡us uq u u i i i s q G(28)Therefore, applying a control strategy which compensates the load instantaneous reactive power tensor, the instantaneous current supplied by the source sets to the instantaneous power current incoming the load.Practical ApplicationIn this section, definitions presented in section II are applied to the system shown in figure 3. It is a 12 pulses rectifier. A three-phase source supplies a three-winding transformer YY, Y Δ. Secondary winding supplies two rectifiers connected in series and with an inductive load in the dc side. The voltage and source current presented in this section have been measured in the transformer secondary winding, which constitute a six-phase system, section M in figure 3. This system has been chosen to illustrate the definitions proposed in previous sections because it corresponds to a practical case where six-phase waveforms can be identified. Besides, in the system usual configuration, the six-phase voltage is composed of two three-phase voltage systems delayed 30º. Thus, the six-phase voltage system is unbalanced sinusoidal, as can be seen in table Ia). This is a poly-phase system with general configuration derived from a practical circuit frequently used in power electronics. The application of the approach developed along the paper to a system of this kind reveals that the approach allows the analysis of a practical and general case.Fig. 3 Twelve pulse rectifier, used as load in the power systemBesides, the phase 1 of the current components in M has been presented in table I. They have been calculated according to definitions presented in section II.Table Id) shows the phase 1 of the six-phase waveform corresponding to the current required by the load. It corresponds to a strongly non linear load. Table Ib) presents the phase 1 of instantaneous power current waveform obtained applying (16). The complete waveform corresponds to two balanced three-phase systems with an argument difference of 30º between both. This current includes the complete instantaneous real power, which can be seen in table Ie). This waveform is the corresponding to the inner product T ⋅u i and to the expression T ⋅p u i where i p has been calculated according to the equation (16).Table I: Simulation resultsThese two waveforms are superimposed. So, effectively, the instantaneous power current carries the whole instantaneous real power. Table Ic) presents the phase 1 of the six-phase waveform correspondingto the instantaneous reactive current. It transfers the whole instantaneous reactive power. To corroborate it, table If) presents two waveforms. One of them has been calculated as follows:()q t =(29)where s(t) is the instantaneous apparent power obtained according to the next expression:()()()s t u t i t =G G(30)Another graph has been calculated as the norm (according to (12)) of the second-order skew-symmetric tensor defined in (6).The waveforms presented in table I third column, second row are superimposed, too. So, the instantaneous reactive current transfers the whole instantaneous reactive power.ConclusionsIn this paper, a generalized instantaneous reactive power theory formulation has been presented. This new formulation proposes a way of calculating the instantaneous reactive power which can be applied not only to three-phase power systems, but to n-phase power systems. It has been developed into the geometric algebra framework. Thus, it is introduced a new tensor product which allows the determination of the instantaneous reactive power tensor and the instantaneous reactive current component. In addition, the instantaneous power multivector is introduced which allows the instantaneous reactive power theory to be encoded in an analog way as single-phase systems analysis. This new approach allows the definitions of different compensation strategies in n-phase systems. The power and current concepts presented in the paper are used to calculate the compensation current in a general m-phase system. Moreover, the new expressions are applied to a practical multi-phase system. Power and current terms are calculated and the associated waveforms are presented. Results corroborate the correspondence with the traditional electric power theory.References[1] H. Akagi, Y. Kanazawa, A. Nabae. “Generalized Theory of the Instantaneous Reactive Power in Three-PhaseCircuits”. Proceedings IPEC83, Tokio, 1983, pp. 1375-1386[2] Hirofumi Akagi, Yoshihira Kanazawa, Akira Nabae. “Instantaneous Reactive Power Compensators ComprisingSwitching Devices without Energy Storage Components”. IEEE Transactions on Industry Applications, Vol. IA-20, No. 3, May/June 1984, pp. 625-630.[3] A. Nabae and H. Nakano, S. Togasawa, An Instantaneous Distortion Current Compensator Without AnyCoordinate Transformation, Proc. 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