Duality of Type II 7-branes and 8-branes
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a rXiv:c ond-ma t/967161v123J ul1996Twist Boundary Conditions of Quantum Spin Chains near the Gaussian Fixed Points A.Kitazawa Department of Physics,Tokyo Institute of Technology,Oh-okayama,Meguro-ku,Tokyo 152,Japan February 1,2008Abstract Duality transformation,which relates a high-temperature phase to a low-temperature one,is used exactly to determine the critical point for several models (2D Ising,Potts,Ashkin-Teller,8-vertex),as the self dual condition.By changing boundary condition,numerically we can determine the self-dual(critical)point of the Ashkin-Teller(or Gaus-sian)model.This is the first explicit application of the duality to the numerical calculation,with the use of boundary conditions.In this short note,we propose a new method to determine the 2D Gaus-sian critical point of quantum spin chains.Although the finite-size scaling method is a powerful tool to determine the critical point,difficulty may occur for some cases.This difficulty comes from the structure of scaling operators.By changing the boundary condition,we have the other struc-ture of operators.Therefore,selecting boundary conditions,we can use the preferable structure to determine the critical point.The obtained resultsare summarized in eq.(20)and Fig.2.As an effective theory of the 1D quantum spin systems,the following sine-Gordon model (in Euclidean space-time)has been studiedS =12πα2 dτdx cos √We make the identificationφ≡φ+√2π.There exists the U(1)symmetry for thefieldθbut the second term of eq.(1)violates the U(1)symmetry forφ.For the freefield theory,the scaling dimensions of the vertex operators exp(±in√2φ)are n2/2K and Km2/2, where the integer variables n and m are electric and magnetic charges in the Coulomb gas picture.After the scaling transformation a→e dl a,we have the following renor-malization group equationsdK−18y2,dy2)y.These are the famous recursion relations of Kosterlitz.Up to thefirst orderof y,wefind that y is an irrelevantfield for K>4and relevant for K<4.There is a separatrix32K−1−8ln K−1−y2=0which separates the infrared unstable region from the infrared stable region,and on this separatrix,theBerezinskii-Kosterlitz-Thouless transition occurs.The2D Gaussianfixedline lies on y=0.For K<4and y=0,yflows to infinity.For y>0, φis renormalized toπ/√L x n+2πλC n1n2πz h1αin which h1and¯h1are the conformal weights of O1(x1=h1+¯h1).From eq.(4),we have the following RG equationdλ2cos√2are not allowed.)Thus the OPE coefficient in eq.(4)is zero.This indicates that we cannot expect the simple behavior of thefinite size scaling method.In addition,for the irrelevant scalingfield(x>2),the system is in the massless phase,so thefinite size scaling method does not work to determine thefixed points.If we put artificially half magnetic charges m=±1/2in the system,theOPE relations areO1(z,¯z)O e1/2(0,0)=√2 α¯zK/4O e1/2(0,0)+···,O1(z,¯z)O o1/2(0,0)=−√2 α¯zK/4O o1/2(0,0)+···,(6)whereO1=√2φ,O e1/2=√√O o 1/2=√√2π.(8)Hence when the twist angle Φis π,halfodd integer magnetic charges appear.Recently Fukui and Kawakami[3]studied this model analytically and their results are consistent with eq.(8).However,since their studies were based on the integrability,the off-critical behaviors were not treated.To see what happens when the boundary condition is changed in the Coulomb gas picture,we review the case of the following action[4]S =1√2L ,then we can eliminate the second term of eq.(9)with the additional constant term Φ2K/2πL ,but the boundarycondition is changed as θ(τ,L )=θ(τ,0)−Φ/√2πK ∞−∞dτ L0dx (∂µφ)2+i √2π ∞−∞dτ∂τφ(τ,0).(10)4This shows that there exist magnetic charges∓Φ/2πatτ=±∞.Thus we obtain the ground state energy as[2]2π2 Φ2π 2K.(12) We denote the state corresponding to the vertex operator V n,m=e i√2mφas|n,m .Since there exists a magnetic chargeΦ/2πatτ=−∞,wefind the change of this state as|n,m Φ=|n,m+Φ/2π Φ=0,(13) and because there exists a magnetic charge−Φ/2πatτ=∞,the conjugate state isΦ n,m|=0 n,m+Φ/2π|.(14) Hence we obtain[2]E n,m(Φ)−E0(0)=2π2K+K2π 2,(15)orE n,m(Φ)−E0(Φ)=2π2K+K2π .(16)From this equation,wefind that the state|n,0 Φcorresponds to|n,Φ/2π 0 which has the excitation energy E n,0(Φ)−E0(Φ)=E n,0(0)−E0(0),and the momentum nΦ/L.Note that Dotsenko and Fateev[5]considered the similar situationS=12 Φ′asΦ n,m|=0 n,m+Φ′/2π|(which is consistent to eq.(16)),but in(9) the conjugate relation does not change.This may be only the difference of picture.In the case ofΦ=π,we have half odd integer magnetic charges effec-tively.In this case,|0,−1 π(=|0,−1/2 0)and|0 π(=|0,1/2 0)are degen-erate for freefield theory.Introducing the perturbation term of eq.(1)and using thefirst order perturbation theory,we obtain the hybridized states|ψ1 π=12(|0,−1 π+|0 π)(18) whose parity is even,and|ψ2 π=12i(|0,−1 π−|0 π)(19)whose parity is odd.(Note that only whenΦ=0andπ,parity is a good quantum number.)Using the OPE(6),we obtain thefinite size dependence of energy up to thefirst order perturbation asE1(π)−E0(0)=2π8+2πλ√2 2πL K2LK/2−2+··· .(20)Thus wefind that the energy eigenvalues of these states cross linearly at λ=0.In this stage we consider the symmetry of the states(18),(19).In the Ashkin-Teller language,the half magnetic charge operator√2 (√2)corresponds to the operator˜P=σ1µ2(˜P∗=µ1σ2)[6].The sine-Gordon model(1)is invariant under the transformationφ→φ+π2,θ→θ,and y→−y,(21)and the operators√2and√2are transformed as√2→−√2,√2→√2,(22) thus at the point y=0the system has the self-duality[7].6To verify the above things numerically,we study the following S=1 quantum spin chain,H=Lj=1(1−δ(−1)j)(S x j S x j+1+S y j S y j+1+∆S z j S z j+1).(23)The effective action of this model is described as eq.(1).The whole phasediagram was shown in ref.[8].The transition between the dimer and theHaldane phases is of the2D Gaussian ing the Lanczos method,wecalculate energy eigenvalues offinite systems(L=8,10,12,14).Figure1shows the scaled gap behavior of L=10,12,14systems with the periodicboundary condition for∆=0.5.We can see a minimum of the scaledgap.In Fig.2,we show two low lying energies of the subspace S z= 0with the boundary condition S x L+1=−S x1,S y L+1=−S y1,S z L+1=S z1,which correspond to E1(π)and E2(π).We see the expected behavior(20)for this twisted boundary condition.The obtained Gaussianfixed pointsagree with those obtained by the other method[9].The conformal anomalynumber is calculated as c=0.998for the periodic boundary condition andc(π)=−3.185for theΦ=πtwisted boundary condition.In table1,weshow some extrapolated scaling dimensions.These numerical values areconsistent with eqs.(11),(12),(15),(20).With this method,we can alsodetermine the Gaussianfixed line in the massless XY phase[10]and applyto the S=1spin chains with the single ion anisotropy[11,12].Lastly we remark the case of the following sine-Gordon model,S=12πα2 dτdx cos√2φ(z1)√8φ(z2)e±i√√References[1]J.L.Cardy,Nucl.Phys.B270[FS16],186(1986).[2]F.C.Alcaraz,M.N.Barber,and M.T.Batchelor,Phys.Rev.Lett.58,771(1987),and Ann.Phys.(N.Y.)182,280(1988).[3]T.Fukui and N.Kawakami,preprint cond-mat/9606190[4]H.W.J.Bl¨o te,J.L.Cardy,and M.P.Nightingale,Phys.Rev.Lett.56,742(1986).[5]Vl.S.Dotsenko and V.A.Fateev,Nucl.Phys.B240[FS12],312(1984),B251[FS13],691(1985).[6]L.P.Kadanoffand A.C.Brown,Ann.Phys.(N.Y.)121,318(1979).[7]M.Kohmoto,M.den Nijs,and L.P.Kadanoff,Phys.Rev.B24,5229(1981).[8]A.Kitazawa,K.Nomura,and K.Okamoto,Phys.Rev.Lett.76,4038(1996).[9]K.Nomura and A.Kitazawa,preprint cond-mat/9606127[10]A.Kitazawa and K.Nomura,in preparation[11]J.S´o lyom and T.A.L.Ziman,Phys.Rev.B30,3980(1984).[12]H.J.Schulz and T.A.L.Ziman,Phys.Rev.B33,6545(1986).[13]K.Nomura and K.Okamoto,J.Phys.A:Math.Gen.27,5773(1994).[14]T.Giamarchi and H.J.Schulz,Phys.Rev.B39,4620(1989).x1,0=1/2K x0,1/2(=x0(π))0.17860.34972.7992.798Figure captionsFig.1:The scaled gap behavior of L=10(△),L=12(2)and L=14(3) systems with the periodic boundary condition for∆=0.5.Fig.2:The low lying energies of the L=14system with theΦ=πboundary condition for∆=0.5.Parity even state(E1(π))is denoted as solid line and parity odd state(E2(π))is denoted as dashed line.The crossing point is the critical point and its estimated value isδc=0.2524.9。
doi:10.3969/j.issn.1000484X.2021.01.013miRNA-7靶向SP1的3'UTR双荧光素酶报告基因载体构建及评价①刘文莉国东②刘加霏②王玉珊②张焕虎②宋文刚(北华大学医学技术学院,吉林132013)中图分类号R735.2文献标志码A文章编号1000-484X(2021)01-0072-06[摘要]目的:构建胃癌细胞核转录因子SP1的3'非翻译区(3忆UTR)双荧光素酶报告基因载体,验证microRNA-7 (miR-7)调控SP1的分子机制。
方法:应用相关生物信息学软件预测miR-7靶向作用于SP1基因的3'UTR区;PCR扩增人胃黏膜上皮细胞SP1的3'UTR,插入至psiCHECK2载体双荧光素酶基因下游,构建野生型(w-3'UTR)和突变型重组表达载体(m-3'UTR),鉴定正确后,分别与miR-7模拟物(mimics)/抑制物(inhibitor)/阴性对照物(NC)共转染胃癌细胞MKN45,检测荧光素酶活性及SP1表达情况。
结果:成功构建SP1的3'UTR野生型(psiCHECK2-SP1-w-3'UTR)和突变型(psiCHECK2-SP1-m-3'UTR)表达载体,双荧光素酶报告基因检测显示w-3'UTR/miR-7-mimics组的相对荧光素酶活性表达受抑制,与miR-7NC组比较降低75%,差异具有统计学意义(P<0.001),而m-3'UTR/miR-7-mimics组的活性表达没有受到影响(P>0.05)。
RT-PCR 和Western blot检测结果显示miR-7-mimics组SP1表达水平低于miR-7NC组(P<0.001),而miR-7-inhibitor组SP1表达水平高于miR-7NC组(P<0.001)o结论:成功构建SP1的3'UTR野生型双荧光素酶报告基因表达载体,miR-7能够显著降低其荧光素酶活性,提示miR-7能靶向负调控SP1的表达。
AMSCO ® V-PRO ® MAX LOW TEMPERATURESTERILIZATION SYSTEM (For Use Outside U.S.A. Only)Item ________________________Location(s)_______________________________________________The Selections Checked Below Apply To This EquipmentUNIT POWER SUPPLY ❑North America:200-208/230 Vac, 3 phase, 50/60 Hz, 16 Amp ❑Europe/Asia:400 Vac, 3 phase, 50 Hz, 10 Amp ❑Japan:200 Vac, 3 phase, 50/60 Hz, 16 AmpLABELS AND MANUALS ❑French ❑Finnish ❑ Danish ❑Italian ❑Russian ❑ Portuguese ❑German ❑Polish ❑ Hungarian❑Spanish ❑ JapaneseMOUNTING❑Single Door, Cabinet ❑Single Door, Recessed ❑Double Door, CabinetAPPLICATIONThe Amsco V-PRO maX Low Temperature Sterilization System is intended for use in the terminal sterilization of properly prepared (cleaned, rinsed and dried) reusable metal and nonmetal medical devices used in Healthcare Facilities. The STERIS developed low pressure and low temperature Sterilization Cycles are suitable for sterilizing medical devices sensitive to heat and moisture.The Amsco V-PRO maX Low Temperature Sterilization System performs three pre-programmed Sterilization Cycles: the Lumen Cycle (approximately 55 minutes to complete), the Non Lumen Cycle (approximately 28minutes to complete) and the Flexible Cycle (approximately 35 minutes to complete).This sterilization system using the Lumen Cycle can sterilize* the following:1.Lumened and non-lumened instruments with diffusion-restricted spaces such as the hinged portion of forceps and scissors.2.Medical devices (including single, dual and triplechanneled rigid and semi-rigid endoscopes) with the following configurations:1•Single channeled devices with a stainless lumen thatis ≥0.77mm (~1/32") internal diameter (D) and ≤500mm (19-11/16") in length•Dual channeled devices with stainless lumens thatare ≥0.77mm (~1/32") ID and ≤ 527 mm (20-3/4") in length•Triple channeled devices with stainless lumens thatare either:»≥ 1.2 mm (~3/64") ID and ≤ 275 mm (~10-55/64")in length»≥ 1.8 mm (~5/64") ID and ≤ 310 mm (~12-13/64")in length»≥ 2.8 mm (~7/64") ID and ≤ 317 mm (12-31/64") in length1Validation testing for all channel/lumen sizes was conducted using a ma ximum of 20 lumens per loa d. Hospita l loa ds should not exceed this validated number of lumens. Validation studies were performed using a va lida tion loa d consisting of two instrument trays and two pouches for a total weight of 8.91kg (19.65 lb).This sterilization system using the Non Lumen Cycle can sterilize 2 non-lumened instruments including non-lumened rigid, semi-rigid and flexible endoscopes and non-lumened instruments with stainless-steel diffusion-restricted areas such as the hinged portion of forceps or scissors.2Validation studies conducted using validation load of two instrument trays and two pouches for a total weight of 8.91kg (19.65 lb).This sterilization system using the Flexible Cycle can sterilize single or dual lumen surgical flexible endoscopes (such as those used in ENT, Urology and Surgical Care) and bronchoscopes in either of two configurations:1.Two flexible endoscopes with a light cord (if not integral to endoscope) and mat with no additional load.3 The flexible endoscopes may contain either:» A single lumen with an inside diameter of ≥ 1 mm (~3/64") and a length of ≤ 1050 mm (41")»Or two lumens with:•One lumen with an inside diameter of ≥ 1 mm (~3/64") and a length of ≤ 998 mm (39")•And the other lumen with an inside diameter of ≥ 1mm (~3/64") and a length of ≤ 850 mm (33")3The valida tion studies were conducted with two flexible endoscopes, ea ch pa cka ged into a tra y with silicone ma t a nd light cord (if not integra l to endoscope).(Typical - details may vary.)2.One flexible endoscope with a light cord (if not integral toendoscope) and mat and additional non-lumenedinstruments including instruments with diffusion-restricted areas such as the hinged portion of forcepsand scissors.4The flexible endoscope may containeither:» A single lumen with an inside diameter of ≥ 1 mm (~3/64") and a length of ≤ 1050 mm (41")»Or two lumens with:•One lumen with an inside diameter of ≥ 1 mm(~3/64") and a length of ≤ 998 mm (39")•And the other lumen with an inside diameter of≥ 1mm (~3/64") and a length of ≤ 850 mm (33")4The validation studies were conducted with a flexible endoscope in a tray with silicone mat and light cord (if not integral to endoscope). Also included in the load were an additional instrument tray and one pouch for a total weight of 11kg (24lb).DESCRIPTIONThe Amsco V-PRO maX Low Temperature Sterilization System is specifically designed to only process goods using vaporized hydrogen peroxide under vacuum conditions. The process is fully automated, is compatible with a broad range of materials and has rapid Sterilization Cycle times. There are no toxic by-products created by the Sterilization Cycle – only water vapor and oxygen are produced.The Amsco V-PRO maX Low Temperature Sterilization System is NOT intended to process liquids, linens, powders or cellulose materials.The system utilizes specially designed, disposable, multi-use Cartridges (available separately) containing VAPROX® HC Sterilant and is available in either a single door (freestanding or recessed) or double door configuration.Articles to be sterilized are placed on a racking system within the aluminum chamber. An automated control enables the cycle to be started and monitored by the operator. The touch screen is user friendly and easy to operate.System installation requires no plumbing, ventilation or air supply – only a dedicated electrical connection is needed. A power cord is supplied for this connection.STANDARDSThis Amsco V-PRO maX Low Temperature Sterilization System meets the applicable requirements of the following standards, as certified by INTERTEK Testing Services:•Underwriters Laboratories (UL) Standard UL 61010-1, Second Edition•Canadian Standards Association (CSA) CAN/CSA 22.2 No. 61010-1, Second EditionGoverning Directive for the affixing of the CE mark: •Medical Device Directive (MDD) 2007/47/ECStandards applied to demonstrate conformity to the directives:•EN 61010-1•EN 60601-1-2•EN 14937•IEC 61010-2-040Each sterilization system is designed, fabricated, assembled and tested in accordance with all applicable sections of UL and CSA.SIZE (W X H X L)Overall Dimensions:•838 x 1908 x 973 mm (33 x 75-1/8 x 38-5/16")Chamber Size:•432 x 381 x 826 mm (17 x 15 x 32-1/2")Chamber Volume:•136 L (4.8 cubic feet)FEATURESThe chamber and door assembly are aluminum equipped with a silicone rubber gasket for each door and a welded backhead on single door units.Insulation fitted on the chamber wall exterior, door and backhead is 25mm (1") thick (nominal). Insulation is held in place with hook-and-loop closures.Insulation is constructed of asbestos- and chloride-free, oil and water resistant (silicone impregnated) fiberglass.Automatic door locking mechanism keeps the sterilization system door locked during the entire Sterilization Cycle. After cycle completion, air pressure is used to unlock the door. The sterilizer door cannot be opened if either electrical power or air pressure is lost during sterilizer operation. When sterilization system is in Standby mode, there are no door opening restrictions. Chamber heating is achieved through electric strip heaters attached to the chamber sides, bottom wall, door and backhead. Operating temperature is approximately 50°C (122°F)Sterilant cartridge interface only accepts VAPROX HC Sterilant Cartridges (Cups). The system control automatically tracks the amount of VAPROX HC Sterilant used and the Sterilant expiration date. The control prompts the user on the control display when a new Cup is needed.The proprietary Cartridge is equipped with a data matrix code to ensure the correct Cup is used in the sterilization unit and that the Cup contents are not expired; no Cup code (or other information) needs to be entered by the user.Catalytic converter receives outflow from chamber during all cycle phases. Catalytic converter converts hydrogen peroxideinto water vapor and oxygen.CartridgeInterfaceHMI Display PrinterOther Components:The following are furnished to obtain a complete working unit, ready for (but not including) connection to the facility service lines:•Resistive Thermal Detectors (RTDs) are installed for sensing and displaying temperature control of vaporizer and chamber. Signals from all system RTDs, converted into electrical impulses, provide accurate control inputs and readouts throughout the entire cycle.•Pressure Transducers are installed for sensing and displaying chamber pressure control. Signals from allsystem pressure transducers, converted into electricalimpulses, provide accurate control inputs and readouts throughout the entire cycle.•Pneumatic and Solenoid Valves and Switches are used in the sterilization system design to simplify piping andincrease serviceability.•Air Supply and Vacuum Filters are supplied to ensure air entering chamber is HEPA (High Efficiency Particulate Air) filtered (prevent chamber recontamination) and airexhausted from vacuum pump is free of entrapped oil and odor.•Sterilization System Panels are constructed of plastic and stainless steel.•Sterilization System Frame and support system is constructed of welded carbon steel with protective paint.•High Power Vacuum Pump is supplied to produce cycle vacuum pulses that remove air and moisture from thechamber. The direct drive rotary vane pump is quiet(<60dB) with low vibration. A powerful 2.2 kW (3 HP)motor produces a displacement of 90 m3/hr (53 CFM) and helps alleviate moisture sensitivity in the sterilization unit.The Sterilizer operating pressure is from atmosphericpressure down to less than 1 Torr.CONTROL DESCRIPTIONThe Amsco V-PRO maX Low Temperature Sterilization System is equipped with an Allen-Bradley Compact Logix™ (Panel View Plus™ 6 1000 Display1) control system and an impact printer.•Control Display Panel is located on the front of the sterilization unit in the center while facing the unit. Thiscolor touch panel provides user information and allows user inputs. The display is a 640 x 480 pixel resolution,10.4" screen. Use of this panel and associated screens isnormally self-explanatory. The screens are color coded for operator convenience as follows:»Control Screens -»Condition Phase - Green»Sterilize Phase - Blue»Aeration Phase - Violet»Service Screens - Light Blue»Option Screens - Purple»Alarm Screens - RedNOTE: This Sterilization System permits no manual control of the Sterilization Cycles.The Ready, Status, Standby and Cup Empty screensinclude a cup level indicator (similar to a cell phone battery indicator) in the lower right corner (see Typical Operator Screens). For normal operation, each bar representsapproximately four cycles remaining (e.g., four bars means cup contains enough sterilant for 13-16 cycles).•Printer is located on the front of the sterilization unit on the right side while facing the unit. This alphanumeric impact printer provides an easy to read permanent record of the Sterilization Cycle. Printer provides a 5.7cm (2-1/4"), 24-character wide cycle tape and paper take-up.1CompactLogix™ and PanelView™ Plus 6 1000 are trademarks ofAllen-Bradley, a Rockwell Automation Company.p yTypical Operator ScreensCYCLE DESCRIPTIONThe Amsco V-PRO maX Low Temperature Sterilization System is equipped with three pre-programmed Sterilization Cycles: Lumen Cycle (approximately 55 minutes to complete),Non Lumen Cycle (approximately 28 minutes to complete) and Flexible Cycle (approximately 35 minutes to complete). Each Sterilization Cycle proceeds through three phases: CONDITION, STERILIZE and AERATION.•CONDITION – Lumen Cycle: This cycle phase is a set time vacuum pulse to remove air and moisture from thechamber. When setpoint is reached, load is tested foracceptable moisture content. If content is acceptable,cycle proceeds. If not, Condition pulse repeats.Non Lumen Cycle: This cycle phase is a vacuum pulse to remove air and moisture from the chamber. When setpoint is reached, load is tested for acceptable moisture content. If content is acceptable, cycle proceeds. If not, Condition pulse as identified for Lumen Cycle is initiated.Flexible Cycle: This cycle phase is a vacuum pulse toremove air and moisture from the chamber. When setpoint is reached, load is tested for acceptable moisture content. If content is acceptable, cycle proceeds. If not, Condition pulse as identified for Lumen Cycle is initiated.NOTE: If Condition phase fails the second moisture check, the cycle Aborts.•STERILIZE – This cycle phase is a series of four pulses.Each pulse consists of: vacuum pulled to setpoint;VAPROX HC Sterilant vapor drawn into chamber; hold for programmed time; filtered air is introduced to setpoint; hold for programmed time; deep vacuum pulled to setpoint.•AERATION – This cycle phase pulls a vacuum to setpoint and continues to evacuate for programmed time to reduce chamber vapor concentration. Once Aeration phase iscomplete, chamber pressure returns to atmospheric and chamber door is unlocked.PREVENTIVE MAINTENANCECustomers are encouraged to contact STERIS concerning annual maintenance programs. Preventive maintenance, adjustments and replacement of worn parts are provided on a scheduled basis to help ensure optimal equipment performance and help minimize untimely and costly interruptions. STERIS maintains a worldwide staff of well-equipped, factory-trained technicians to provide these services, as well as on-site installation, training, and expert repair services. Contact STERIS for details.CUSTOMER IS RESPONSIBLE FOR COMPLIANCE WITH APPLICABLE LOCAL AND NATIONAL CODES AND REGULATIONS.NOTES1.For general installation information, refer to STERIS GeneralNotes for Sterilizers (drawing 062941-091). This drawing should always accompany the equipment drawing.2.Refer to equipment drawing showing all utility and spacerequirements for actual installation specifications.Clearances shown are minimum required for servicingequipment. Floor surface must be hard and level.3.STERIS recommends maintaining and operatingsterilization system in area where temperature does not exceed 40°C (104°F) and has ventilation systemexchanging area air at least 10 times per hour.4.STERIS recommends a dedicated, grounded electricalcircuit be provided for each unit. Use of an extension cord is not recommended.5.Consult MSDS regarding storage and handling ofVAPROX HC Sterilant Cartridges (Cups).6.Unit weight: Single Door – 386 kg (850 lb) recessed and463kg (1020 lb) free-standing; Double Door – 562kg(1240lb) recessed one wall.7.Heat loss at 21°C (70°F) – Peak=1,046 BTU/hr;Avg.=942BTU/hr.8.Electrical Consumption, per cycle=2.2 kW-hr average;out of cycle=0.7 kW-hr average.9.STERIS assumes no responsibility for changes to theSterilization Unit made necessary through failure to observe the supplied necessary specifications (e.g., incorrect facility power supply). Specifications are subject to change without notice.EQUIPMENT DRAWINGS (REQUIRED FOR INSTALLATION)Equipment DrawingPart NumberEquipment Drawing Title129385-449Single Door, Recessed 129385-450Single Door, Cabinet 129385-451Double Door, CabinetSINGLE DOOR, CABINET MODEL SHOWNDimensions are in inches [mm]Not Fo rI n s t a l l at i o n SIDE VIEW PLAN VIEWFRONT VIEWDrawing is not to scale.Dimensions are typical.30 1/2[775]DOOR SWINGFor Further Information, contact:STERIS Corporation5960 Heisley RoadMentor, OH 44060-1834 • USA440-354-2600 • 800-548-4873This document is intended for the exclusive use of STERIS Customers, includingarchitects or designers. Reproduction in whole or in part by any party other than。
第30卷第2期 水下无人系统学报 Vol.30No.22022年4月JOURNAL OF UNMANNED UNDERSEA SYSTEMS Apr. 2022收稿日期: 2021-10-14; 修回日期: 2021-11-16.通信作者简介: 郭 君(1980-), 男, 博士, 高级工程师, 主要从事系统、结构、流体、振动、噪声等领域的设计、仿真及试验研究.[引用格式] 张宁, 郭君, 尹韶平, 等. 数字孪生技术发展现状及其在水下无人系统中的应用展望[J]. 水下无人系统学报, 2022,30(2): 137-146.数字孪生技术发展现状及其在水下无人系统中的应用展望张 宁, 郭 君*, 尹韶平, 高智勇(中国船舶集团有限公司 第705研究所, 陕西 西安, 710077)摘 要: 为填补数字孪生技术在水下无人系统行业应用的空白, 文章首先对数字孪生技术的发展历程以及国内外发展现状进行了介绍, 分析了数字孪生技术的特点; 其次讨论了水下无人系统数字孪生技术的内涵与关键技术, 从标准体系、设计、试验、制造加工以及运行维护等不同角度对水下无人系统行业的数字孪生技术发展应用进行了展望; 最后结合泵台试验给出了水下无人系统数字孪生技术的典型应用案例。
研究结果可为数字孪生技术在水下无人系统行业的进一步应用提供参考。
关键词: 水下无人系统; 数字孪生; 泵台中图分类号: TJ630.33; U662.9 文献标识码: R 文章编号: 2096-3920(2022)02-0137-10 DOI: 10.11993/j.issn.2096-3920.2020.04.001Development of Digital Twin Technology and Its Application Prospectin Unmanned Undersea SystemZHANG Ning , GUO Jun *, YIN Shao-ping , GAO Zhi-yong(The 705 Research Institute, China State Shipbuilding Corporation Limited, Xi’an 710077, China)Abstract: To fill the gap of digital twin technology in the unmanned undersea system industry, this paper introduces the development process and status of digital twin technology at home and abroad and summarizes the characteristics. Sub-sequently, the connotation and key technologies of applying digital twins in unmanned undersea systems are discussed. The development and application of digital twin in the unmanned undersea system industry are prospected from different perspectives, including standard systems, design, testing, manufacturing, and operations. Finally, a typical application case of digital twin technology in an unmanned undersea system is presented based on a pump bench test. The results can provide a reference for the further application of digital twin technology in the unmanned undersea system industry. Keywords: unmanned undersea system; digital twin; pump platform0 引言随着现代电子信息技术的蓬勃发展, 社会生产力和生产关系产生了巨大的变革, 人类社会经济结构也随之产生了质的飞跃。
DF-52431:B • 10/7/14 — Page 1 of 2ANN-RLYRelay ModuleAnnunciatorsDF-52431:B • B-200GeneralThe ANN-RL Y relay module provides 10 programmable Form-C relays when used with a compatible FACP (Fire Alarm Con-trol Panel). The ANN-RL Y module may be mounted inside the FACP main circuit board chassis or in the battery area of the enclosure using optional mounting bracket P/N: ANN-MBRL Y .Reference Installation Instructions document #53033.The ANN-RL Y and the FACP communicate over a two-wire serial interface employing the ANN-BUS communication for-mat. An additional two wires are used for 24-volt DC power. A single four-conductor unshielded cable may be used for both power and data communications.Up to eight ANN-BUS devices may be connected to the ANN-BUS of each FACP .Features•ANN-RL Y connects to the ANN-BUS terminal on the FACP and requires minimal programming.•Provides 10 programmable Form-C relays.•T en Form-C relays can be programmed for various func-tions; Alarm, T rouble, Supervisory, AC Loss, Waterflow Delay, Input Zones and Silenceable Alarm.•Compatible with the MS9600LS, MS-9600UDLS, MS-9200UDLS, MS-9050UD, MS-5UD-3, MPR-2001, MRP-2002and MS-10UD-7.•May be powered by 24 VDC from the host FACP or by remote power supply (requires 24 VDC).•Up to eight ANN-BUS devices may be connected to the ANN-BUS of each FACP .•Listed to UL Standard 864, 9th Edition.Specifications•Maximum ANN-BUS Voltage: 24 VDC •Maximum Current:–Alarm: 75 mA Standby: 15 mA•Ambient T emperature: 32ºF to 120ºF (0ºC to 49ºC)•Relative Humidity: 93% ± 2% RH (noncondensing) at 32ºC ± 2ºC (90ºF ± 3ºF)•For use indoors in a dry location•Connections to FACP are power-limited and supervised.•Relay Contact Ratings: 2 Amps @ 30VDC (Resistive) 0.5Amps @ 30VAC (Resistive)Agency Listings and ApprovalsThe listings and approvals below apply to the ANN-RL Y. In some cases, certain modules may not be listed by certain approval agencies, or listing may be in process. Consult fac-tory for latest listing status.•UL: S2424•FM Approved•Fire Dept. of New York: #COA 6177•CSFM: 7120-0075:0222The ANN-BUSPOWERING THE DEVICES ON THE ANN-BUS FROM AUXILIARY POWER SUPPLYANN-BUS devices can be powered by an auxiliary power sup-ply when available panel power is exceeded. See FACP man-ual for information.ANN-BUS DEVICE ADDRESSINGEach ANN-BUS device requires a unique address (ID Num-ber) in order to communicate with the FACP . A maximum of eight devices can be connected to the FACP ANN-BUS com-munication circuit. See the FACP manual for more information.WIRE REQUIREMENTSThe ANN-RL Y connects to the FACP ANN-BUS communica-tions circuit. T o determine the type of wire and the maximum wiring distance, calculate the total worst case current draw for all modules on a single 4-conductor bus. Use the table on the following page to determine the maximum distance the mod-ules can be located from the FACP . In general, the wire length is limited by resistance, but for heavier wire gauges, capaci-tance is the limiting factor. These cases are marked in the chart with an asterisk (*). Maximum length can never be more than 6,000 feet (1,800 m), regardless of gauge used. Refer to the appropriate FACP manual for wiring details.Ordering Information•ANN-RLY: Relay Module provides 10 programmable Form C relays.•ANN-MBRL Y: Optional mounting bracket.•ROME: Relay Option Module Enclosure, includes one ANN-RL Y Relay module and one ANN-MBRL Y bracket installed.52431c o v .j p gPage 2 of 2 — DF-52431:B • 10/7/14This document is not intended to be used for installation purposes. We try to keep our product information up-to-date and accurate. We cannot cover all specific applications or anticipate all requirements.All specifications are subject to change without notice.For more information, contact Fire•Lite Alarms. Phone: (800) 627-3473, FAX: (877) 699-4105.Fire•Lite® Alarms is a registered trademark of Honeywell International Inc. ©2014 by Honeywell International Inc. All rights reserved. Unauthorized useof this document is strictly prohibited.ANN-RLY Relay Module。
海上无人系统跨域协同运用与技术发展邱志明, 孟祥尧, 马 焱, 王 亮, 肖玉杰(海军研究院, 北京, 100442)摘 要: 海上无人系统跨域协同是未来海上无人系统的发展趋势和重要的应用方式。
随着各种海上无人系统的快速发展和在世界局部战争冲突中的应用, 如何更好地使用海上无人系统跨域完成作战任务成为研究的重点。
文中以不同空间域的海上无人系统为研究对象, 梳理总结了当前海上无人系统以及国外海上无人系统跨域运用的发展现状。
重点针对海上无人系统的跨域协同运用基本原理和方法进行了分析, 提出了海上无人系统跨域协同运用的关键问题, 并在此基础上梳理了技术发展中需要重点关注的关键技术。
最后提出了未来发展的几点启示, 以期为海上无人系统的跨域运用和技术发展提供参考和借鉴。
关键词: 海上无人系统; 跨域协同; 技术发展中图分类号: TJ6; U674 文献标识码: R 文章编号: 2096-3920(2024)02-0184-10DOI: 10.11993/j.issn.2096-3920.2024-0053Cross-domain Collaborative Application and Technology Development ofMaritime Unmanned SystemsQIU Zhiming, MENG Xiangyao, MA Yan, WANG Liang, XIAO Yujie(Naval Research Institute, Beijing 100442, China)Abstract: Cross-domain collaboration of maritime unmanned systems is the future development trend and important way of application of maritime unmanned systems. With the rapid development of various maritime unmanned systems and their application in local wars and conflicts in the world, how to better use maritime unmanned systems to complete cross-domain combat missions has become the focus of research. With maritime unmanned systems in different spatial domains as the research objects, the current maritime unmanned systems and the development status of cross-domain application of maritime unmanned systems in other countries were summarized. The basic principles and methods of cross-domain collaborative application of maritime unmanned systems were analyzed, and the key issues of cross-domain collaborative application of maritime unmanned systems were put forward. On this basis, the key technologies requiring attention in the development of technologies were sorted out. Finally, several enlightenments for future development were put forward, so as to provide a reference for the cross-domain application and technology development of maritime unmanned systems.Keywords: maritime unmanned system; cross-domain collaboration; technology development0 引言在新一轮科技革命和世界海军强国竞争的双重驱动下, 无人系统在海战中的地位日益突出。
Dual (multiple) certification of stainless steel productsIntroductionAlthough dual or multiple certification can mean the issue of two separate EN 10204 certificate types for the same inspected / tested or delivered batch of steel, the term normally infers the mention of more than one standard or grade (or both) on the same test certificate.Where more than one standard is ordered, the chemical (cast) composition and mechanical properties are checked against each of the standard's ranges, for each grade. Often this involves both standard and low carbon variants of the grade being certified togetherThis form of multiple certification is not recognised by the individual standards organizations. The practice is the result of commercial pressure from stockholders to minimise stock levels for each size range, so that the same piece of steel can be sold to as many standards and grade designations as is possible for the same basic steel composition. These requirements became widespread in the 1980's and is now considered in the stainless steel supply industry as acceptable.Multiple grade and standard certificationThe principle of multiple certification can be illustrated by considering a product that can conform to either 1.4301 or 1.4307.If the actual carbon content of the steel product is 0.020% it is likely to meet both the full chemical analysis and mechanical property requirements of both steel grade numbers ie 1.4301 and 1.4307 (1.4306 may not be met as the nickel ranges for 1.4301 and 1.4306 only overlap at the top end of the 1.4301 range).The steel designation (number) should conform to the standard, so where BSEN 10088 is involved the European steel number has to be used ie 1.4307 and 1.4301 in this case and not 304L and 304. These steel designations can only be used if the second certified standard uses these designations, as they for example in American ASTM standards. So '304/304L to BSEN 10088-2' for a batch of plates is incorrectAn illustration of this approach to multiple certification is to mention both standards and grade designations, in an appropriate format : -BSEN 10088-2 1.4301/1.4307, ASTM A240 304/ 304LIt is important that the steel products multi-certified in this way are not assumed to fully comply with all requirements of each standard mentioned, taken individually. For example it may not be possible for a product to comply with all dimensional tolerance requirements of all the cited (and related) standards. The format of the declared standards should however make this clear. The steel should comply with ALL the requirements of the first (primary) standard mentioned. For standards and grades mentioned after the primary standard only the cast chemical composition and mechanical properties of the products certified can be expected to meet these 'secondary' standards.There are no universally agreed rules for secondary standard conformance however so it is advisable to check with the manufacturing mill that issued the certificate to confirm the scope of the certified steel properties. This is especially important in a case where separate certificates might have been issued to different standards for the same batch of steel products. Taken individually both these certificates imply FULL compliance of the products with the standards certified.。
Key features• High-quality kinetic screening and affinity characterization • Microfluidics-free Dip and Read™ format reduces assay time and maintenance cost• Eight parallel, independent channels for maximum speed and flexibility• Versatility to detect anything from small molecules to mammalian cells• Non-destructive sampling allows full sample recovery• Up to 12 hours of unattended run time• Sample plate cooling for temperature sensitive proteins• Perfectly suited to operate in GxP-regulated environmentsThe Octet® RED96e system detects a diverse range of bio-molecules from small molecules to proteins to mammalian cells. The Octet platform offers an advanced fluidics-free approach with a wide variety of off-the-shelf Dip and Read biosensors for rapid binding kinetics and quantitation analysis. The system utilizes ForteBio’s Bio-Layer Interferometry (BLI) technology, enabling direct detection of specific proteins and other biomolecules — even in complex mixtures like cell cul-ture supernatants and lysates. The 8-channel Octet RED96e system performs quantitation of 96 samples in 32 minutes, and kinetic screening of 64 samples in 1.5 hours. Analysis can be done using a single channel or up to eight channels, enabling more flexibility in sample throughput when needschange. An optional microplate evaporation cover minimizes losses in sample volume, allowing full post-analysis sample recovery even after a 12 hour experiment.Figure 1: Human IgG Quantitation. Example data from human IgG analyte binding to Protein A biosensors. Binding was performed at 30°C, with a shake speed of 1000 rpm and a two-minute read per well. Human IgG solution was prepared at 0.025 μg/mL up to 300 μg/mL and the standard curve shown on a log-log scale was generated using the initial slope algorithm and fitted with the unweighted 5-parameter logistic (5PL)regression model.BindingRateConcentration (µg/mL)1010101010Quantitation assaysThe Octet RED96e system directly measures the presence of specific proteins and other molecules in solution with minimal interference from complex matrices. Accurate and reproducible concentrations can be determined in as little as two minutes per sample or 32 minutes for a whole plate using a simple, one-step assay (Figure 1). High sensitivity in quantitation can be achieved to sub-ng/ml levels with 2-step and 3-step assay formats, allow-ing automated measurement of contaminants such as host cell proteins and residual protein A faster and more precisely than ELISA. Process economics can be improved further by regener-ating and re-using the biosensors.Octet RED96e SystemUnmatched versatility for discovery, development and quality controlKinetic assaysThe Octet RED96e system monitors binding events in real time to calculate on rates (k a ), off rates (k d ), and affinity con-stants (K D ). The superior sensitivity of the system enables measurement of small organic molecules (Figure 2) and kinetic constants over a broad range. The temperature of one 96-well sample plate can be controlled from 15–40°C, which enables reliable kinetic determinations from low up to physiological temperatures for temperature sensitive proteins (Figure 3). Additional advantages afforded by sample cooling include the ability to rapidly determine binding rate constants at multiple temperatures to extrapolate thermodynamic mea-surements. The Octet RED96e system’s eight channels can be used independently to measure samples for screening pur-poses or in tandem, pairing the sample read with a dedicated reference for high-quality kinetic characterization.B i n d i n g (n m )20040060080010001200Time (sec)00.050.100.150.200.25A4.88E-092.85E+041.39E-04Time (sec)B i n d i n g (n m )200400600800100012000.050.150.250.350.45Bk d (1/s)5.64E-094.59E+042.59E-04Time (sec)B i n d i n g (n m )2004006008001000120000.050.150.250.350.450.55CK D (M)k a (1/Ms)k d (1/s)6.73E-095.30E+043.57E-04B i n d i n g (n m )Time (sec)K D k a k d 2.00E-61.53E53.06E-1Octet Data Analysis HT softwarePre-defined templates in Octet Data Acquisition softwarestreamlines setup prior to running an assay and minimizes train-ing needs. Octet Data Analysis High Throughput (HT) software can overlay data from multiple plates over an extensive range of parameters and metrics to analyze acquired data from an entire project, thereby reducing analysis time from hours to minutes. Data Analysis HT Analysis settings in Octet DataAnalysis HT software can be saved and re-loaded for new simi-lar datasets to speed up routine assays. The software can also generate customized reports of the experiments, combining various data elements such as graphs, text boxes, data tables, images and experimental details (Figure 4). These reports are ready to be uploaded to an electronic notebook or stored in the company database.Figure 2: Small molecule kinetics. Example data from benzenesulfonamide(MW 157 Da) binding to biotin-carbonic anhydrase loaded on Super Streptavidin biosensors. Binding was performed at 25°C, with a shake speed of 1000 rpm. A 100 μM benzensulfonamide solution was prepared and serially diluted 1:4.Figure 3: Large molecule characterization. Example data from human Prostate Specific Antigen (PSA, MW 30 kDa) binding to a biotinylated anti-human PSA mouse monoclonal antibody loaded onto Streptavidin biosensors. Binding was performed at 15°C (A), 25°C (B) and 30°C (C), with a shake speed of 1000 rpm. A 200 nM PSA solution was prepared and serial diluted 1:2 to obtain the 5 concentrations run.Figure 4: Octet Data Analysis HT software enables making customized reports that can be uploaded into electronic notebooks and added to the database. In addition to customized report, Data Analysis HT enables analysis of multiple plates and experiments together to maximize workflow efficiency.Operate in GxP regulated environmentsThe Octet RED96e system has been developed to operate reli-ably in a regulated environment. ForteBio offers 21 CFR Part 11 software and a full line of GxP products and services as part of the Octet RED96e GxP Package. These include:• Octet CFR software and ForteBio FB Server features such as:•Controlled access with multiple user privileges — adminis-trator, developer, supervisor, lab user•Primary data integrity — digitally signed acquired data thatis rendered invalid after data tampering•Electronic signatures — enable data to be locked afteranalysis is complete•Enhanced audit trail — all actions are recorded and time-stamped with details of old vs. new values•Full control of routine assays that speed up analysis— method files and analysis settings can be saved forroutine assays•Customized reports — created by combining various dataelements such as graphs, text, data tables and imagesready to be uploaded to your ELN• Installation and Operational Qualification (IQ/OQ) and Per-formance Qualification (PQ) packages ensure your systemis qualified and operate as intended and that performance meets specifications• Performance Certification (PC) services maintain your system in a calibrated state and in peak condition• Customer-run Software Validation Package and support to trim validation time down to just three days• Biosensor Validation Support Services for multiple biosensor lot sampling and selection• Excellent Global T echnical Support assistance Octet RED96e system specifications*DetectiontechnologyBio-Layer Interferometry (BLI)Biosensor type Disposable, single-use fiber optic biosensorswith optional reuse by regeneration and/orre-racking in the sensor tray Informationprovided• Yes/No binding• Kinetic and affinity analysis (k obs, k a, k d, K D)• Specific and selective detection ofmolecules, even in crude samples• Relative and absolute quantitation ofspecific proteins in crude matrices orpurified samplesData presentation• Plots displaying real-time kinetic bindingsensorgrams, fitted result plots, andresiduals of fits• Concentration data analysis includingcalibration curves and output of tabulatedconcentration data• Tabulated kinetic data• Epitope binning and cross-blockingmatrices and trace overlaysSample types Proteins, antibodies, peptides, DNA, RNA,liposomes, bacterial cells, viruses, mamma-lian cells, small molecules in various mediaincluding serum, buffers containing DMSO,periplasmic fractions, untreated cell culturesupernatants, and crude cell lysates Number ofspectrometers8Maximumsimultaneous reads8Data collection rate2, 5, or 10 HzSample positionand format1 standard 96-well, black, flat bottommicroplateSample volume 180–220 μL/well, non-destructive testing Orbital flowcapacityStatic or 100–1500 rpmAnalysistemperature range15–40°C, 1°C increments* A ll specifications are subject to change without notice.ForteBio47661 Fremont Boulevard Fremont, CA 94538888.OCTET-75 or 650.322.1360************************ForteBio Analytics (Shanghai) Co., Ltd. No. 88 Shang Ke Road Zhangjiang Hi-tech Park Shanghai, China 201210*************************Molecular Devices (UK) Ltd. 660-665 Eskdale Winnersh Triangle Wokingham, Berkshire RG41 5TS, United Kingdom +44 118 944 8000*************Molecular Devices (Germany) GmbH Bismarckring 3988400 Biberach an der Riss Germany+ 00800 665 32860©2019 Molecular Devices, LLC. All trademarks used herein are the property of Molecular Devices, LLC. Specifications subject to change without notice. Patents: /product patents. FOR RESEARCH USE ONL Y. NOT FOR USE IN DIAGNOSTIC PROCEDURES.DS-41-0257 Rev CSafety standardsCE, NemkoOrdering informationPart No. UOM DescriptionOCTET RED96ESystemIncludes Octet RED96e instru-ment, Octet software, desktop computer, LCD monitor, acces-sory kit and one-year warranty OCTET RED96E-GxP SystemIncluded Octet RED96e instru-ment, Octet CFR software, desktop computer, LC monitor, accessory kit, IQ/OQ kit, PQ Kits and one-year warranty 18-5132PackSingle-use evaporation covers to extend the experiment up to 12 hours. 3 covers per packFor more information about ForteBio’s Octet platform for label-free, real-time detection of biomolecular interactions, applications, and services, visit or contact us directly.Workflow Up to 8 assays in parallel; up to 96 assays per 96-well plateAnalysis time per sampleHuman IgG quantitation in 2 minutes for 8 samples, ≤ 32 minutes for 96 samples Direct quantitation range for human IgG with Protein A Biosensor0.05–2000 μg/mL。
※Photo may vary from actual product.Product NumberAFP7MC16EC Part NumberAFP7MC16EC ProductFP7 Motion Control Unit DetailsEtherCAT type Product name FP7 Motion control unit AFP7MC16EC | FP7 Motion control unitSpec DetailAs of March 27, 2023Specifications and design of the products are subject to change without notice for the product improvement.ItemSpecificationsProduct NumberAFP7MC16EC Part Number AFP7MC16EC Connected slave Panasonic AC servo motor MINAS A6B / A5B series EtherCAT-compatible S-LINK V gateway controller SL-VGU1-EC (Note1) A6B and SL-VGU1-EC are compatible with the FP7 motion control unit Ver.1.2 or later.(Note2) One unit or more A6B or A5B must exist on the network. Also,A6B and A5B can both be used on the network.(Note3) The hub for EtherCAT / Ethernet cannot be used.Number of control axes Real axis : 16 axesVirtual axis : 8 axesCommunication cycle 0.5ms / 1ms / 2ms / 4msInterpolation control 2-axis linear interpolation, 2-axis circular interpolation,3-axis linear interpolation and 3-axis spiral interpolationNumber of occupied I/O points Input : 16 points, Output : 16 pointsAutomatic operation : Positioning control (CSP) : Position specification method Absolute (specified absolute position), Increment (specified relativeposition)Automatic operation : Positioning control (CSP) : Position specified unit pulseμm (select a minimum instruction unit of 0.1 μm or 1 μm)inch (select a minimum instruction unit of 0.00001 inch or 0.0001 inch)degree (select a minimum instruction unit of 0.1 degree or 1 degree)Automatic operation : Positioning control (CSP) : Position reference range pulse : -2,147,483,648 to 2,147,483,647pulseμm (0.1μm) : -214,748,364.8 to 214,748,364.7μmμm (1μm) : -2,147,483,648 to 2,147,483,647μminch (0.00001inch) : -21,474.83648 to 21,474.83647inchinch (0.0001inch) : -214,748.3648 to 214,748.3647inchdegree (0.1degree) : -214,748,364.8 to 214,748,364.7degreedegree (1degree) : -2,147,483,648 to 2,147,483,647degreeAutomatic operation : Positioning control (CSP) : Speed reference rangepulse : 1〜2,147,483,647ppsμm : 1〜2,147,483,647μm/sinch : 0.001〜2,147,483.647inch/sdegree : 0.001〜2,147,483.647rev/s Automatic operation : Positioningcontrol (CSP) : Acceleration /deceleration typeLinear acceleration/deceleration,S-shaped acceleration/deceleration Automatic operation : Positioningcontrol (CSP) : Acceleration /deceleration time0 to 10,000ms(adjustable in 1 ms increments)Automatic operation : Positioningcontrol (CSP) : Number of positioningtables Each axis : 1,000 pointsAutomatic operation : Positioning control (CSP) : Control method : Independent PTP control (E point control, C point control), CP control (P point control), Speed control (J point control)Automatic operation : Positioning control (CSP) : Control method : 2-axis interpolation : Linear interpolation E point, P point and C point controls : Specify synthesis speed or major axis speedAutomatic operation : Positioningcontrol (CSP) : Control method : 2-axis interpolation : CircularinterpolationE point, P point and C point controls : Center point or passing pointAutomatic operation : Positioning control (CSP) : Control method : 3-axis interpolation : Linear interpolation E point, P point and C point controls : Specify synthesis speed or major axis speedAutomatic operation : Positioningcontrol (CSP) : Control method : 3-axis interpolation : Spiral interpolationE point, P point and C point controls : Center point or passing pointAutomatic operation : Positioningcontrol (CSP) : Other function : Dwelltime0 to 32,767ms (adjustable in 1 ms increments)Manual operation : JOG/inching operation : Speed reference range pulse : 1〜2,147,483,647ppsμm : 1〜2,147,483,647μm/sinch : 0.001〜2,147,483.647inch/s degree : 0.001〜2,147,483.647rev/sManual operation : JOG/inching operation : Acceleration / deceleration type Linear acceleration/deceleration,S-shaped acceleration/decelerationManual operation : JOG/inchingoperation : Acceleration / decelerationtime0 to 10,000ms (adjustable in 1 ms increments)Manual operation : Home return : Speed reference range pulse : 1〜2,147,483,647ppsμm : 1〜2,147,483,647μm/sinch : 0.001〜2,147,483.647inch/s degree : 0.001〜2,147,483.647rev/sManual operation : Home return : Acceleration / deceleration type Linear acceleration/deceleration,S-shaped acceleration/decelerationManual operation : Home return :Acceleration / deceleration time0 to 10,000ms (adjustable in 1 ms increments)Manual operation : Home return : Return methods DOG method (4 types), Limit method (2 types), Data set method, Z phase method, Stop-on-contact method (2 types)Stop function : Deceleration stop :Deceleration timeAxis operation mode startup time of activated axisStop function : Emergency stop :Deceleration time0 to 10,000 ms (adjustable in 1 ms increments)Stop function : Limit stop :Deceleration time0 to 10,000 ms (adjustable in 1 ms increments)Stop function : Error stop :Deceleration time0 to 10,000 ms (adjustable in 1 ms increments)Stop function : System stop :Deceleration timeImmediate stop (1 ms), all axes stopSynchronous operation function :Synchronous basic setting : MasteraxisSelection possible of real axis and virtual axisSynchronous operation function :Synchronous basic setting : SlaveaxisMax. 8 axes/masterSynchronous operation function :Electronic gear function : OperationsettingGear ratio settingSynchronous operation function :Electronic gear function : OperationmethodDirect method, Acceleration/deceleration methodSynchronous operation function :Electronic clutch function : Clutch ONtriggerContact inputProductNumberAFPSMTEN Part Number AFPSMTENProduct name Control MotionIntegratorProductNumberAFPSMTKEYPart Number AFPSMTKEYProductnameControl MotionIntegratorSynchronous operation function :Electronic clutch function : ClutchmethodDirect method, Linear slide methodSynchronous operation function : Electronic cam function : Cam curve Select from 20 typesMultiple curves can be specified within a phase (0 to 100 %).Synchronous operation function :Electronic cam function : Resolution1024, 2048, 4096, 8192, 16384, 32768Synchronous operation function : Electronic cam function : Number of cam patterns 16 to 64(Depends on resolution)Other specifications : Software limit function : Set range pulse : -2,147,483,648 to 2,147,483,647pulseμm (0.1μm) : -214,748,364.8 to 214,748,364.7μmμm (1μm) : -2,147,483,648 to 2,147,483,647μminch (0.00001inch) : -21,474.83648 to 21,474.83647inch inch (0.0001inch) : -214,748.3648 to 214,748.3647inch degree (0.1degree) : -214,748,364.8 to 214,748,364.7degree degree (1degree) : -2,147,483,648 to 2,147,483,647degreeOther specifications : Monitor judgment : Torque judgment Torque judgmentSelection possible of active/non-active and error/warning 0.0 to ±500.0 %Other specifications : Monitor judgment : Actual speed judgment Actual speed judgmentSelection possible of active/non-active and error/warning 0.0 to ±5,000 rpmOther specifications : Backup Parameters and positioning data are saved to flash memory (battery free)Other specifications ・Limit input CWL, CCWL monitor and proximity (DOG) monitor・General-purpose input : 5 points, General-purpose output : 1 point (I/O from AMP)・Auxiliary output contact and auxiliary output cord[[COMMON GENERALSPECIFICATIONS]]Ambienttemperature0 to +55 ℃+32 to +131 ℉, Storage: -40 to +70 ℃-40 to +158 ℉[[COMMON GENERAL SPECIFICATIONS]]Ambient humidity 10 to 95 % RH (at +25 ℃+77 ℉, no condensation), Storage: 10 to 95 % RH (at +25 ℃+77 ℉, no condensation)[[COMMON GENERAL SPECIFICATIONS]]Vibration resistance 5 to 8.4 Hz, single amplitude of 3.5 mm 0.138 in, 1 sweep/min. (IEC 61131-2) ; 8.4 to 150 Hz, constant acceleration of 9.8 m/s2, 1 sweep/min. (IEC 61131-2), 10 times each in X, Y, and Z directions[[COMMON GENERALSPECIFICATIONS]]Shock resistance147 m/s2 or more ,3 times each in X, Y, and Z directions (IEC61131-2)[[COMMON GENERALSPECIFICATIONS]]Noise immunity1,000 V [p-p] with pulse width 50 ns and 1 μs (using a noise simulator)[[COMMON GENERALSPECIFICATIONS]]OperatingconditionFree from corrosive gasses and excessive dust[[INDIVIDUAL GENERALSPECIFICATIONS]]Rated voltagerange-[[INDIVIDUAL GENERALSPECIFICATIONS]]Currentconsumption180 mA approx.[[INDIVIDUAL GENERALSPECIFICATIONS]]Net weight150 g approx.Accessories© Panasonic Industry Co., Ltd.。
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a rXiv:h ep-th/96115v36M a y1996R/95/55hep-th/9601150UG-15/95January 1996/revised March 1996Duality of Type II 7-branes and 8-branes ⋆E.Bergshoeff and M.de Roo Institute for Theoretical Physics,University of Groningen,Nijenborgh 4,9747AG Groningen,The Netherlands and M.B.Green,G.Papadopoulos and P.K.Townsend DAMTP,University of Cambridge,Silver St.,Cambridge CB39EW,U.K.ABSTRACTWe present a version of ten-dimensional IIA supergravity containing a9-form potential for which thefield equations are equivalent to those of the standard, massless,IIA theory for vanishing10-formfield strength,F10,and to those of the ‘massive’IIA theory for non-vanishing F10.We present a multi8-brane solution of these equations that generalizes the8-brane of Polchinski and Witten.We show that this solution is T-dual to a new multi7-brane solution of S1compactified IIB supergravity,and that the latter is T-dual to the IIA6-brane.When combined with the Sl(2;Z)U-duality of the type IIB superstring,the T-duality between type II7-branes and8-branes implies a quantization of the cosmological constant of type IIA superstring theory.These results are made possible by the construction of a new massive N=2D=9supergravity theory.We also discuss the11-dimensional interpretation of these type II p-branes.21.IntroductionRecent advances in our understanding of non-perturbative superstring theory have led to the establishment of many connections between hitherto unrelated superstring theories.Many of these connections involve p-brane solutions of the respective supergravity theories that couple to the(p+1)-form potentials in the Ramond-Ramond(RR)sector.Most of these RR p-branes,and all of the IIA ones,are singular as solutions of ten-dimensional(D=10)supergravity,so their status in superstring theory was unclear until recently(see[1]for a recent review). It now appears[2]that the RR p-branes of type II supergravity theories have their place in type II superstring theory as‘Dirichlet-branes’,or‘D-branes’[3].These include the p-branes for p=0,2,4,6in the type IIA case and the p-branes for p=1,3,5in the type IIB case.However,they also include a type IIB7-brane,and a type IIA8-brane and it is possible to view the D=10spacetime as a type IIB 9-brane[2].Note that since the dual of a p-brane in D=10is a(6−p)-brane,only p-branes with p≤6have duals with p≥0for which a standard(Minkowski space) interpretation is available⋆,so the p-branes with p≥7have implications that are qualitatively different from those with p≤6.This difference is also apparent in the p-brane solutions of the effective IIA or IIB supergravityfield equations. These solutions generally involve a function that is harmonic on the(9−p)-space ‘transverse’to the(p+1)-dimensional worldvolume of the p-brane.For p≤6the transverse space has dimension3or greater so there exist harmonic functions that are constant at infinity,but for p≥7the transverse space has dimension2or less and the asymptotic properties are therefore qualitatively different.Partly for this reason little attention has been given so far to the p≥7branes.Since p-branes couple naturally to(p+1)-form potentials,one expects tofind a stable p-brane solution of a supergravity theory only if it includes a(p+1)-form potential.From this perspective the IIB D=107-brane is the most straightforwardof the p≥7cases because the pseudo-scalarfield of IIB supergravity can be exchanged for its8-form dual.Indeed,a type IIB7-brane solution has recently been described[4];it can be viewed as a dimensional‘oxidation’of the‘stringy cosmic string’solution of[5].However,this class of7-brane solutions is specific to the uncompactified IIB supergravity and is therefore not expected to be related by T-duality to other type II p-branes.Here we shall present a new class of multi7-brane solutions of the S1-compactified IIB supergravity.In the decompactification limit the new solutions reduce to the trivial D=10Minkowski spacetime solution. Nevertheless,as we shall see,these solutions are T-dual to both the6-brane and the IIA8-brane solutions of the IIA theory.The existence of an8-brane solution of IIA supergravity is obscured by the ab-sence of a9-form potential,A9,in the standard IIA supergravity theory.However, there is one in type IIA superstring theory[2]and this suggests that it should be possible to introduce one into the IIA supergravity theory.The9-form potential would have a10-formfield-strength F10.Assuming a standard kinetic term of the form F210,the inclusion of thisfield does not lead to any additional degrees of freedom(per spacetime point)and so is not immediately ruled out by supersym-metry considerations,but it allows the introduction of a cosmological constant, as explained many years ago in the context of a four-formfield strength in four-dimensionalfield theories[6,7].As it happens,a version of type IIA supergravity theory with a cosmological constant was constructed(up to quartic fermion terms) some time ago by Romans[8],who called it the‘massive’IIA supergravity theory; the complete construction via superspace methods was found subsequently[9].It has been argued that the existence of the massive IIA supergravity is related to the existence of the9-form potential of type IIA superstring theory[2].Here we shall confirm this suggestion by reformulating the massive IIA supergravity through the introduction of a9-form potential†.The new theory has the advantage that its solutions include those of both the massless and the massive IIA theory.We pro-pose this new IIA supergravity theory as the effectivefield theory of the type IIA superstring,allowing for the9-form potential.It has been suggested[2,10]that the expectation value of the dual of this10-formfield strength should be interpreted as the cosmological constant of the massive IIA supergravity theory.One result of this paper is the determination of the precise relation between these quantities; they are conjugate variables in a sense discussed previously in the D=4context [11].The massive IIA supergravity theory has the peculiarity that D=10Minkowski spacetime is not a solution of thefield equations(and neither is the product of D=4Minkowski spacetime with a Calabi-Yau space).Various Kaluza-Klein(KK) type solutions were found by Romans but none of them were supersymmetric, i.e.his solutions break all the supersymmetries.A supersymmetric multi8-brane configuration was recently proposed as a solution of the Killing spinor condition in an appropriate bosonic background[12].We verify that this is a solution of the field equations of the new IIA supergravity theory and we present a generalization of it.The solutions are all singular at the‘centres’of the metric,i.e.the8-brane positions,but this is a general feature of RR p-branes.It is known that after compactification on S1the perturbative type IIA and type IIB superstrings are equivalent[3,13],being related by a Z2T-duality trans-formation that takes the radius R of the S1of one superstring theory into a radius 1/R,in appropriate units,of the other superstring theory.It follows that the same effective N=2D=9field theory should be obtained by dimensional reduction of either the IIA or IIB theory in D=10,and this is in fact the case[14].If this Z2 T-duality is valid non-perturbatively too,then p-brane solutions of the IIA theory must correspond to p-brane solutions of the IIB theory and vice-versa,in the sense that there are solutions of either the IIA or the IIB theory that reduce to the same solution of the S1-compactified theory.In particular the double-dimensional reduction to D=9of a given IIA8-brane should be equivalent to the direct reduc-tion to D=9of some IIB7-brane.There is a potential difficulty in verifying this because the relevant D=9theory must be a massive N=2supergravity theory.It5is not too difficult to see how to obtain a massive N=2D=9supergravity from the massive D=10IIA theory but it is not so obvious how the resulting theory may also be obtained from the(necessarily massless)D=10IIB theory,although it must be possible if T-duality is to be valid non-perturbatively.As we shall show, it is possible by an application of a mechanism for obtaining a massive theory in a lower dimension from a massless one in a higher dimension.This mechanism is essentially that of Scherk and Schwarz[15]but in our case supersymmetry is preserved by the reduction.This result allows us to map8-brane solutions of the D=10IIA theory into7-brane solutions of the IIB theory,and vice-versa.These IIB7-brane and IIA8-brane solutions may be seen as the effective field theory realization of the associated D-branes of the corresponding type II superstring theory.In this context,the Sl(2;R)symmetry of the IIB supergravity is expected to be replaced by an Sl(2;Z)U-duality[16],which amounts to an identification of points in the space Sl(2,R)/U(1)of IIB vacua that differ by the action of Sl(2,Z).One interesting consequence of this IIB duality,when combined with the T-duality of the7-brane and8-brane,is a quantization of the cosmological constant of the S1-compactified IIA superstring theory⋆.The organisation of this article is as follows.In section2,we begin with a review of the massive IIA supergravity,introducing some simplifications.In section3,we construct the new formulation of the bosonic sector of this theory,incorporating the 9-form gaugefield A9,in which the cosmological constant emerges as an integration constant.In section4,we construct supersymmetric multi8-brane solutions of the massive IIA supergravity theory,some of which are asymptoticallyflat.In section5,we show how both the massive IIA supergravity and the(massless) IIB supergravity theories may be dimensionally reduced to yield a new D=9N=2 massive supergravity theory.We then use this to establish the massive Type II T duality rules.In section6,we construct the most general seven brane solutions of the IIB theory that are both compatible with the KK ansatz and preserve half thesupersymmetry.We then show that the massless T duality transformations take this solution to the IIA 6-brane while the massive T -duality transformations take it to the IIA 8-brane solution.In section 7we further comment on the relation to type IIA superstring theory and the quantization of the cosmological constant,and on the connection to D=11‘M-theory’.Finally,in Appendix A we give a simplified formulation of the supersymmetry transformations of IIB supergravity.2.The massive D=10IIA supergravityThe bosonic field content of the massive IIA D=10supergravity theory com-prises (in our notation)the (Einstein)metric,g (E ),the dilaton,σ,a massive 2-form tensor field B ′and a three-form potential C ′.One introduces the field-strengthsG =4dC ′+6m (B ′)2H =3dB ′(2.1)where m is a mass parameter.The Lagrangian for these fields is [8]L =2|∂σ|2−112e12σ|B ′|2−12σ +120m 2(B ′)5 .(2.2)The notation for forms being used here is that a q -form Q has components Q M 1...M q given byQ =Q M 1...M q dx M 1∧...∧dx M q .(2.3)Thus,the (1/9)εdC ′dC ′B ′term in (2.2)is shorthand for1Instead,one first makes the field redefinitionsB ′=B +2mAdA .(2.5)This redefinition introduces the gauge invarianceδA =−m ΛδB =2d Λδ˜C =12Ad Λ(2.6)for which the gauge-invariant field strengths areF =2dA +mBH =3dBG =4d ˜C +24BdA +6mB 2.(2.7)The bosonic Lagrangian of the massive IIA theory is nowL = 2|∂σ|2−112e 12σ|F |2−12σ+12mB 4dA +9and the gauge-invariantfield strengths,F,H,and G are now given byF=2dA+mBH=3dBG=4dC+24AdB+6mB2.(2.11)At the same time,to make contact with string theory,it is convenient to introduce the string metricg MN=e−1−g e−2σ R+4|∂σ|2−112|G|2−19ε dCdCB+mdCB3+9−g e−2σ R+4|∂σ|2−112|G|2−1 9 M11G2H,(2.14)where M11is an11-manifold with boundary M10.Apart from the cosmological constant,the m-dependent terms in the action can be simply understood as arising from the replacement of the usual m-independentfield strengths of the massless type IIA theory by their m-dependent generalizations(2.11).Furthermore,the m-dependence of thesefield strengths is completelyfixed by the‘Stueckelberg’gauge transformationδA=−mΛof A,as are the remainingΛ-transformations.The relation of the constant m appearing in this transformation with the cosmological constant cannot be understood purely within the context of the bosonic Lagrangian but is,of course,fixed by supersymmetry.9Observe that the cosmological constant term in(2.14)is now(in the string metric)independent of the dilaton.This is typical of the RR sector and is consistent with the idea that m can be interpreted as the expectation value of the dual of a RR10-formfield strength.This interpretation would have the additional virtue of restoring the invariance under the discrete symmetry in which all RRfields change sign,a symmetry that is broken by the terms linear in m in(2.13).We shall now show how to reformulate the massive IIA theory along these lines.As we shall see the cosmological constant is simply related to,but not equal to,the expectation value of the ten-formfield strength.3.D=10IIA supergravity with9-form potentialWe shall start with the bosonic Lagrangian of(2.13).Expanding in powers of m,the associated action I(m)isI(m)=I(0)+ d10x 2m√9εdCB3 −1−g 1+2|B|2+6|B2|2 +m2M.This additional equation isδI(M)−gM,as a matter of principle(although it may equal it in special backgrounds),but is rather the value of the variable canonically conjugate to it.Note that the gauge and supersymmetry transformations of the action I(M) no longer vanish.However,the variations of I(M)are proportional to dM and can therefore be cancelled by a variation of the new9-form gauge potential A9.This determines the gauge and supersymmetry transformations of A9.The supersym-metry variation will not be needed for our purposes so we omit it.TheΛ-gauge transformation of A9found in this way isδ(εA9)=2−g Λ·F+(ΛB)·G −1−gM=K−1(B) ε(F10+1−g[(dC+6AdB)·B2−2dA·B] ,(3.6) whereK(B)=1+2|B2|+6|B2|2−1−gεB5.(3.7)Using this relation in(3.5)we arrive at the Lagrangian L new=L0+ √9dCB3)+2√supersymmetry,so we shall begin by considering the variation of the gravitino one-form ψand the dilatino λin the presence of configurations of the above form.The full variations of the massive IIA theory can be found in [8]in the Einstein–frame.They depend on the constant m .In the new theory,this constant is replaced by the function M given in (3.6).Here,however,we shall need the fermion variations in the string-frame .For M =0these are implicit in the superspace results of [17].For the backgrounds considered here,for which all fermions vanish and√8Me σΓǫδǫλ=−12 ΓM ∂M σ+58Me σ¯Γy ǫ0= g −1f ′¯Γy +14Me σ¯Γy ǫ,(4.3)where the prime indicates differentiation with respect to y and ¯Γare the constant ,orthonormal frame basis,gamma–matrices.To find non-zero solutions for ǫwe are now forced to suppose that ǫhas a definite ‘chirality’in the sense that¯Γy ǫ=±ǫ.(4.4)We then find thatg −1f ′=∓1and thatg−1 e−σ ′=±5σ.(4.7)5We are also free to choose g(y)to be any function that is non-singular where f(y)is non-singular⋆.For example,the choice g=f leads to a manifestly confor-mallyflat form of the8-brane metric.A solution in this form was given in[12]. We postpone a discussion of this solution until we have the general solution,to be given below.The choice of g that we shall make here is g=f−1.In this case,use of the A9field equation M′=0in(4.6)yields∂2y e−4σ=H(y).(4.9)5This leads to the8-brane configurationds2=H−12dy2(4.10)e−4σ=H5M=±H′.where the prime indicates differentiation with respect to y.We have verified that this configuration is a solution of the full set offield equations.The Killing spinorǫis given byǫ=H−1†Presumably,this is acceptable because the metric is also singular at y=y0;in any case,we shall see below that this feature is not generic for the general8-brane solution of the new IIA supergravity theory.8-brane solution.It can be interpreted as a domain wall separating regions with different values of M.The regions y→±∞are at infinite affine distance.The solution therefore has two asymptotic regions relative to which an8-brane charge, Q±,may be defined as the value of M as y→±∞.For the above solution,Q+=c Q−=a.(4.15)The constant b determines the value ofσ,and hence the value of the string coupling constant eσat the8-brane core.In particular,if b=0the string coupling constant goes to infinity at the core.Note that the solution(4.13)of the masive IIA theory is the special case for which a=c and b=0.The multi8-brane generalization of(4.14)with the same charges is found by allowing kink singularities of H at n+1ordered points y=y0<y1<y2<...<y n. The function H isH= −a(y−y0)+ n i=1µi(y i−y0)+b y<y0(c− n i=1µi)|y−y0|+ n i=1µi|y−y i|+b y>y0(4.16) whereµi are positive constants and a,b,c are non-negative constants.The asymptotically left-flat or right-flat solutions are those for which Q−=0 or Q+=0,respectively.The asymptoticallyflat solutions are those which are both asymptotically left-flat and right-flat.An example of an asymptoticallyflat three 8-brane solution is given by H=µ2 |y−y0|−|y−y1| +γ2,whereµandγare arbitrary constants.If we now introduce a new variable w(y)such thatdw2,(4.17) then the above8-brane solution becomesds2=Z−1(4.18)6(w),where Z(w)is a harmonic function of w,related to H(y)byZ(w)=H35.Massive D=9N=2supergravityThe standard dimensional reduction to D=9of either the massless IIA su-pergravity theory or the IIB supergravity theory yields the massless N=2D=9 supergravity theory[14](see also[18]).Here we shall construct a massive N=2 D=9supergravity theory.We shall do this in two ways.Thefirst involves the massive IIA supergravity theory.Atfirst sight it might seem that this theory cannot be dimensionally reduced to D=9because the product of D=9Minkowski space with S1is not a solution of thefield equations.However,all we need is a solution with an abelian isometry and the massive IIA8-brane is such a solution. This allows us to reduce the massive D=10IIA theory to D=9⋆.We shall then show that exactly the same theory can be found by a Scherk-Schwarz dimensional reduction of the IIB supergravity theory.We begin by dimensionally reducing the massive IIA supergravity theory.Since we ultimately wish to make contact with the IIB theory via T-duality,it is conve-nient to use the conventions of[14],where the massless T-duality rules are given. Thus,thefirst step is to rewrite the results of section2in the notation of[14].The field content in D=10is given byˆgˆµˆν,ˆCˆµˆνˆρ,ˆB(1)ˆµˆν,ˆA(1)ˆµ,ˆφ (5.1) where thefieldsˆC andˆA(1)are the R-R sectorfields.We refer to[14]for details of the notation,but we remark here that in this section only the metric signature is‘mostly minus’and that the hats indicate D=10variables;the D=9variables resulting from the dimensional reduction will be without hats.Our starting point is the following(string-frame)action,obtained by translating(2.14)into the con-ventions of[14]:I IIA=1−ˆg e−2ˆφ −ˆR+4|dˆφ|2−34|ˆF(1)m|2+32m2 +12ˆη(1)δˆC=−mˆη(1)ˆB(1).(5.3)The m-dependence of the corresponding R-R curvatures is given byˆF(1) m=ˆF(1)m=0+mˆB(1)ˆGm=ˆGm=0+mbyI=1g e−2φ −R+4|dφ|2−34k2|F(2)|2+12m2k−14k|F(1)m|2+34k−1|H(2)m|2−12η(1)−mΛA(2)δB(1)=dη(1)−A(2)dΛδB(2)=A(1)dΛ+mΛB(1)+m2m(B(1))2−mB(1)A(2)BH(2)m=H(2)m=0−ℓH(1)m=0−mBB(1).(5.8)The expressions for the m=0curvatures may again be found in[14].We now turn to the(massless)D=10Type IIB theory.Itsfield content isgiven byˆjˆµˆν,ˆB(i)ˆµˆν,ˆℓ,ˆϕ,ˆD(+)ˆµˆνˆρˆσ ,i=1,2.(5.9) The R-R sectorfields areˆB(2),ˆD(+)andˆℓ.The action is given by⋆I IIB=1−j e−2ˆϕ −ˆR+4|dˆϕ|2−32|dˆℓ|2−36|ˆF(D)|2 −1-component of the D=10Stueckelberg symmetry.From the IIB point of view it should come from a general coordinate transformation in the x=Λfor m=0[14].In order to reproduce the Stueckelberg Λ-transformations we should therefore introduce an extra x⋆Strictly speaking,there is no action for the D=10Type IIB theory.However,when properly used,the given action leads to a well-defined action in D=9.For more details about this point,see e.g.[19].can be given the correct Λtransformation provided we introduce the following additional dependence linear in xˆB(2)µν=B (2)µν−B [µA (1)ν]+mx µ=−A (1)µ+mx ,all the xˆB (1)ˆµˆν,m =0.(5.12)Finally,we still have to reproduce the correct η(1)Stueckelberg symmetries.For m =0this symmetry is related to the following Type IIB gauge symmetry:δˆB (i )=d ˆΣ(i )δˆD =34d ˆΣ(1)ˆB (2),(5.13)with ˆΣ(i )=η(i )µ.It turns out that the following x η(1)µ.(5.14)This equation also follows from the requirement that the ansatz for ˆB(2)µνbe consis-tent with the m =0rule δB (1)=dη(1).We have therefore recovered by non-trivial dimensional reduction of IIB su-pergravity the massive N=2D=9supergravity found earlier from reduction of the massive IIA theory.It is of interest to see how this mechanism is related to the Scherk-Schwarz(SS)mechanism[15].The essential ingredient in their method was a global U(1)symmetry in the higher dimension.Let Q be the anti-hermitian generator of this U(1)symmetry and let∂denote differentiation with respect to the KK coordinate.Then the SS mechanism can be summarised by the equation ∂=mQ.In our case the relevant U(1)group acts onˆℓ(which is periodically identified)by a shift,so we should require∂ˆℓ=m.The solution isˆℓ=ℓ+mxthat is consistent with the xWe give here only the rules that receive an m-dependent correction.These are the following:ˆℓ=ˆA(1)xˆB(2)µν=3−2ˆA(1)[µˆB(1)ν]x[µˆB(1)ν]xˆA(1)x+mx[µˆB(1)ν]xˆB(2)xˆg x+mxµ/ˆg xx=χ+κ(r),(6.2) where the functionκis such thatdκω=.We may choose theidentification such thatx+1.(6.4) The metric now readsds2=f2(r)d˜x·d˜x+a2(r) dx,ˆϕ=ˆϕ(r)(6.6) where˜m is piecewise constant,and we set the rest of thefields equal to zero.Next,we substitute this ansatz into the(string frame)Killing spinor equationsδǫψ≡Dǫ+14 ΓM∂Mˆϕ+ieˆϕΓM∂Mˆℓ ǫ=0,(6.7)and assume thatǫ=ǫ(r)where¯Γx8eˆϕ˜mǫ=0(6.9) andf′±14˜meˆϕ=0,ˆϕ′±eˆϕ˜m=0,(6.10) where the prime indicates differentiation with respect to r.Using the last two equations in(6.10),we have that∂2r e−ˆϕ =0.(6.11) Thus we can sete−ˆϕ=H(r),(6.12) where H is a harmonic function of r,of the type described in section4.The last of equations(6.10)now yields˜m=±H′,(6.13) while the remainder of equations(6.10)yields the full7-brane solution in terms of H and three constants of integration,which can be removed by rescaling the coordinates and shiftingˆℓ.This solution isds2=H−12(r) dx(6.14).The Killing spinor corresponding to this solution is given byǫ=H−1ǫ0=±i¯Γrǫ0.(6.15)We suggest that this7-brane solution of IIB supergravity is thefield theory realization of the Dirichlet7-brane of type IIB superstring theory.As a check on this interpretation we shall now verify that it is T-dual to the IIA6-brane solution of[20].To this end we take{˜x}=(v m,u),where v m are coordinates for 7-dimensional Minkowski spacetime(the6-brane worldvolume),and also take the ignorable coordinate u to be an angular coordinate.We can then apply(massless)T-duality rules of[14],in the u direction.This leads to the following solution of IIA supergravity:ds2=H−12(r) du2+dx4(r)ˆA(1)=±H′(r)x,r).Thus,this is the form of the6-brane compatible with a KK reduction to D=8.This is an encouraging sign that the7-brane will also be T-dual to a IIA8-brane solution,since one expects the6-brane and8-brane to be equivalent on reduction to D=8.In order to show that this is indeed the case we need to establish the T-duality of the7-brane to the8-brane.We shall now show that the massive T–duality rules that we have given in section5relate the IIA eight–brane of section4to the IIB seven–brane given in(6.14).Although the general massive Type II T duality rules are complicated they become very simple for the special solutions considered here. Sinceˆg x=1/ˆg xxˆϕ=ˆφ−1).(6.18)To show that under the massive T duality rules the IIA eight brane solution of section4is T dual to the IIB seven brane solution,(6.14),wefirst make thechange of notation{xµ}=(˜x,x.The8-brane solution is then as follows:ds2=H−12(r)dx2(r)dr2,(6.19)e−4σ=H5(r)M=±H′(r),It is now straightforward to show that the T–duality rules,(6.18),applied to the x12d2s p+1+HSo far,the context of our discussion has been that of supergravity rather than superstring theory.A new feature of the IIB superstring theory is its conjectured Sl(2;Z)U-duality which requires,in particular,that the pseudoscalarˆℓbe period-ically identified,i.e.that it take values in S1.Without loss of generality we can suppose that the identification is such thatˆℓ∼ˆℓ+1(7.2)Returning now to the ansatz(6.6),we note that since x+1,the consistency of this ansatz requires˜m to be an integer.Of course,since˜m is not dimensionless, this result holds only for a particular choice of units.Such a choice is implicit in the choice of periodicity of x(7.3)R Bfor integer n.Recall now that the equivalence of the7-brane with the8-brane under T-duality requires that m=˜m.This means,assuming IIB U-duality,that the IIA8-brane solution can be mapped to a IIB7-brane solution by T-duality only if the cosmological constant m of the massive IIA theory is quantized as above,i.e. each time one passes through a IIA8-brane the cosmological constant must jump by an integer multiple of basic unit1/R B.The single8-brane solution should be related to the Dirichlet8-brane of[2]. This is a string background in which open string states arise withfixed(Dirichlet) boundary conditions that are imposed in one space-like dimension at one or bothα′)in which the IIA mass parameter is expressed entirely in IIA terms.ends of the string.These conditions restrict at least one of the end-points of open strings to lie in the nine-dimensional worldvolume of an8-brane.The8-brane couples to a9-form gaugefield with a ten-formfield strength F10.If the new IIA supergravity constructed here is indeed the effectivefield theory of the IIA superstring in the presence of this10-formfield strength then it should be possible to recover the Lagrangian(3.8)by string theory considerations.Neglecting terms of order B2,which in any case follow from gauge invariance,the only term in(3.8) that is linear in F10is proportional to(εF10)dA·B.(7.4)This is the crucial term that has to be reproduced in string theory.There is a ver-tex operator in the RR sector of the type IIA theory that couples a ten-formfield strength to the worldsheet.This vertex operator has the form F10¯SS,where S is the spacetime spinor worldsheetfield of the spacetime supersymmetric worldsheet action.There are non-trivial tree diagrams that mix F10withfields from the RR and NSNS sectors,producing a term of the form(7.4),as required.The require-ments of gauge invariance suggest that a more systematic consideration of string theory in the presence of D-branes would produce the full effective Lagrangian (3.8).Since all the p-brane solutions of D=10IIA supergravity for p<8can be viewed as arising from some11-dimensional supermembrane theory,or‘M-theory’, [23,21,24,25,26]it would be surprising if the8-brane did not also have an11-dimensional interpretation.The obvious possibility is that the D=108-brane is the double-dimensional reduction of a D=11supersymmetric9-brane.Such an object would be expected(see[1])to carry a9-form‘charge’appearing in the D=11supertranslation algebra as a central charge.This is possible because the 2-form charge normally associated with the D=11supermembrane is algebraically equivalent to a9-form.It is not easy to see how to implement this idea,however, since there is no‘massive’D=11supergravity theory.One possibility is suggested。